Index: src/sas/calculator/media/density_calculator_help.rst
===================================================================
--- src/sas/calculator/media/density_calculator_help.rst	(revision 0d66541cf69270c2b833e4f21df2f2d3fed2cd9c)
+++ src/sas/calculator/media/density_calculator_help.rst	(revision 0d66541cf69270c2b833e4f21df2f2d3fed2cd9c)
@@ -0,0 +1,3 @@
+..density_calculator_help.rst
+
+Placeholder for density calculator help
Index: src/sas/calculator/media/kiessig_calculator_help.rst
===================================================================
--- src/sas/calculator/media/kiessig_calculator_help.rst	(revision 0d66541cf69270c2b833e4f21df2f2d3fed2cd9c)
+++ src/sas/calculator/media/kiessig_calculator_help.rst	(revision 0d66541cf69270c2b833e4f21df2f2d3fed2cd9c)
@@ -0,0 +1,3 @@
+..kiessig_calculator_help.rst
+
+Placeholder for Kiessig calculator help
Index: src/sas/calculator/media/resolution_calculator_help.rst
===================================================================
--- src/sas/calculator/media/resolution_calculator_help.rst	(revision 0d66541cf69270c2b833e4f21df2f2d3fed2cd9c)
+++ src/sas/calculator/media/resolution_calculator_help.rst	(revision 0d66541cf69270c2b833e4f21df2f2d3fed2cd9c)
@@ -0,0 +1,3 @@
+..resolution_calculator_help.rst
+
+Placeholder for resolution calculator help
Index: src/sas/calculator/media/sas_calculator_help.rst
===================================================================
--- src/sas/calculator/media/sas_calculator_help.rst	(revision 0d66541cf69270c2b833e4f21df2f2d3fed2cd9c)
+++ src/sas/calculator/media/sas_calculator_help.rst	(revision 0d66541cf69270c2b833e4f21df2f2d3fed2cd9c)
@@ -0,0 +1,3 @@
+..sas_calculator_help.rst
+
+Placeholder for generic SAS calculator help
Index: src/sas/calculator/media/sld_calculator.rst
===================================================================
--- src/sas/calculator/media/sld_calculator.rst	(revision 0d66541cf69270c2b833e4f21df2f2d3fed2cd9c)
+++ src/sas/calculator/media/sld_calculator.rst	(revision 0d66541cf69270c2b833e4f21df2f2d3fed2cd9c)
@@ -0,0 +1,3 @@
+..sld_calculator.rst
+
+Placeholder for SLD calculator help
Index: src/sas/calculator/media/slit_calculator_help.rst
===================================================================
--- src/sas/calculator/media/slit_calculator_help.rst	(revision 0d66541cf69270c2b833e4f21df2f2d3fed2cd9c)
+++ src/sas/calculator/media/slit_calculator_help.rst	(revision 0d66541cf69270c2b833e4f21df2f2d3fed2cd9c)
@@ -0,0 +1,3 @@
+..slit_calculator_help.rst
+
+Placeholder for slit calculator help
Index: src/sas/data_util/media/data_operator_help.rst
===================================================================
--- src/sas/data_util/media/data_operator_help.rst	(revision 0d66541cf69270c2b833e4f21df2f2d3fed2cd9c)
+++ src/sas/data_util/media/data_operator_help.rst	(revision 0d66541cf69270c2b833e4f21df2f2d3fed2cd9c)
@@ -0,0 +1,3 @@
+..data_operator_help.rst
+
+Placeholder for data operator help
Index: src/sas/fit/media/fitting_help.rst
===================================================================
--- src/sas/fit/media/fitting_help.rst	(revision 0d66541cf69270c2b833e4f21df2f2d3fed2cd9c)
+++ src/sas/fit/media/fitting_help.rst	(revision 0d66541cf69270c2b833e4f21df2f2d3fed2cd9c)
@@ -0,0 +1,3 @@
+..fitting_help.rst
+
+Placeholder for fitting help
Index: src/sas/guiframe/gui_manager.py
===================================================================
--- src/sas/guiframe/gui_manager.py	(revision b9a5f0eb8e8cbff8f8d934bbfa4ea18168141e13)
+++ src/sas/guiframe/gui_manager.py	(revision ad8872e858cccb6a879912fc45aa48bc8e7128ab)
@@ -24,4 +24,6 @@
 import logging
 import httplib
+import webbrowser
+
 
 from sas.guiframe.events import EVT_CATEGORY
@@ -1325,5 +1327,6 @@
     def _add_help_menu(self):
         """
-        add help menu
+        add help menu to menu bar.  Includes welcome page, about page,
+        tutorial PDF and documentation pages. 
         """
         # Help menu
@@ -1336,22 +1339,10 @@
                 id = wx.NewId()
                 self._help_menu.Append(id, '&Welcome', '')
-                self._help_menu.AppendSeparator()
                 wx.EVT_MENU(self, id, self.show_welcome_panel)
 
-        # Look for help item in plug-ins 
-        for item in self.plugins:
-            if hasattr(item, "help"):
-                id = wx.NewId()
-                self._help_menu.Append(id,'&%s Help' % item.sub_menu, '')
-                wx.EVT_MENU(self, id, item.help)
-
-        # Only show new Sphinx docs link if version of wx supports displaying
-        # it correctly.
-        show_sphinx_docs = float(wx.__version__[:3]) >= 2.9
-        if show_sphinx_docs:
-            self._help_menu.AppendSeparator()
-            id = wx.NewId()
-            self._help_menu.Append(id, '&Sphinx Documentation', '')
-            wx.EVT_MENU(self, id, self._onSphinxDocs)
+        self._help_menu.AppendSeparator()
+        id = wx.NewId()
+        self._help_menu.Append(id, '& Documentation', '')
+        wx.EVT_MENU(self, id, self._onSphinxDocs)
 
         if config._do_tutorial and (IS_WIN or sys.platform =='darwin'):
@@ -2162,5 +2153,8 @@
     def _onSphinxDocs(self, evt):
         """
-        Pop up a Sphinx Documentation dialog.
+        Bring up Sphinx Documentation.  If Wx 2.9 or higher is installed 
+        with proper HTML support then Pop up a Sphinx Documentation dialog
+        locally.  If not pop up a new tab in the default system browser 
+        calling the documentation website.
         
         :param evt: menu event
@@ -2168,17 +2162,24 @@
         # Running SasView "in-place" using run.py means the docs will be in a
         # different place than they would otherwise.
-        SPHINX_DOC_ENV = "SASVIEW_DOC_PATH"
-        if SPHINX_DOC_ENV in os.environ:
-            docs_path = os.path.join(os.environ[SPHINX_DOC_ENV], "index.html")
+
+        show_sphinx_docs = float(wx.__version__[:3]) >= 2.9
+        if show_sphinx_docs:
+            SPHINX_DOC_ENV = "SASVIEW_DOC_PATH"
+            if SPHINX_DOC_ENV in os.environ:
+                docs_path = os.path.join(os.environ[SPHINX_DOC_ENV], "index.html")
+            else:
+                docs_path = os.path.join(PATH_APP, "..", "..", "doc", "index.html")
+
+            if os.path.exists(docs_path):
+                from documentation_window import DocumentationWindow
+
+                sphinx_doc_viewer = DocumentationWindow(None, -1, docs_path)
+                sphinx_doc_viewer.Show()
+            else:
+                logging.error("Could not find Sphinx documentation at '%' -- has it been built?" % docs_path)
         else:
-            docs_path = os.path.join(PATH_APP, "..", "..", "doc", "index.html")
-
-        if os.path.exists(docs_path):
-            from documentation_window import DocumentationWindow
-
-            sphinx_doc_viewer = DocumentationWindow(None, -1, docs_path)
-            sphinx_doc_viewer.Show()
-        else:
-            logging.error("Could not find Sphinx documentation at '%' -- has it been built?" % docs_path)
+            #For red hat and maybe others who do not have Wx 3.0
+            #just send to webpage of documentation
+            webbrowser.open_new_tab('http://www.sasview.org/sasview')
 
     def set_manager(self, manager):
Index: src/sas/guiframe/media/data_explorer_help.rst
===================================================================
--- src/sas/guiframe/media/data_explorer_help.rst	(revision 0d66541cf69270c2b833e4f21df2f2d3fed2cd9c)
+++ src/sas/guiframe/media/data_explorer_help.rst	(revision 0d66541cf69270c2b833e4f21df2f2d3fed2cd9c)
@@ -0,0 +1,3 @@
+..data_explorer_help.rst
+
+Placeholder for data explorer help
Index: src/sas/guiframe/media/graph_help.rst
===================================================================
--- src/sas/guiframe/media/graph_help.rst	(revision 0d66541cf69270c2b833e4f21df2f2d3fed2cd9c)
+++ src/sas/guiframe/media/graph_help.rst	(revision 0d66541cf69270c2b833e4f21df2f2d3fed2cd9c)
@@ -0,0 +1,3 @@
+..graph_help.rst
+
+Placeholder for graph help
Index: src/sas/invariant/media/invariant_help.rst
===================================================================
--- src/sas/invariant/media/invariant_help.rst	(revision 0d66541cf69270c2b833e4f21df2f2d3fed2cd9c)
+++ src/sas/invariant/media/invariant_help.rst	(revision 0d66541cf69270c2b833e4f21df2f2d3fed2cd9c)
@@ -0,0 +1,3 @@
+..invariant_help.rst
+
+Placeholder for invariant help
Index: src/sas/invariant/media/pr_help.rst
===================================================================
--- src/sas/invariant/media/pr_help.rst	(revision 0d66541cf69270c2b833e4f21df2f2d3fed2cd9c)
+++ src/sas/invariant/media/pr_help.rst	(revision 0d66541cf69270c2b833e4f21df2f2d3fed2cd9c)
@@ -0,0 +1,3 @@
+..pr_help.rst
+
+Placeholder for P(r) help
Index: src/sas/models/c_extension/c_models/librefl.c
===================================================================
--- src/sas/models/c_extension/c_models/librefl.c	(revision 794922220f2fb3b23dd08c648aabf87b4850596c)
+++ src/sas/models/c_extension/c_models/librefl.c	(revision a6d2e3bad0df8c61e5449e577b9e32949fe723ed)
@@ -8,5 +8,5 @@
 #include <stdlib.h>
 #if defined(_MSC_VER)
-#include "winFuncs.h"
+#include "../libigor/winFuncs.h"
 #endif
 
Index: src/sas/models/media/model_functions.html
===================================================================
--- src/sas/models/media/model_functions.html	(revision 794922220f2fb3b23dd08c648aabf87b4850596c)
+++ 	(revision )
@@ -1,8144 +1,0 @@
-<head>
-<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
-<meta name="modelfunctions" content="Model Functions">
-</head>
-<body lang="EN-US">
-<p><b><span style="font-size: 16pt;">Model Functions</span></b></p>
-<ul style="margin-top: 0in;" type="disc">
-<li><a href="#Introduction"><b>Introduction</b></a></li>
-<li><a href="#Shapes"><b>Shapes</b></a>: 
-    <ul>
-    <li>Sphere based:<br/>
-    <a href="#SphereModel">SphereModel (Magnetic 2D Model)</a>, 
-    <a href="#BinaryHSModel">BinaryHSModel</a>, 
-    <a href="#FuzzySphereModel">FuzzySphereModel</a>, 
-    <a href="#RaspBerryModel">RaspBerryModel</a>, 
-    <a href="#CoreShellModel">CoreShellModel (Magnetic 2D Model)</a>,
-    <a href="#Core2ndMomentModel">Core2ndMomentModel</a>, 
-    <a href="#CoreMultiShellModel">CoreMultiShellModel (Magnetic 2D Model)</a>, 
-    <a href="#VesicleModel">VesicleModel</a>, 
-    <a href="#MultiShellModel">MultiShellModel</a>, 
-    <a href="#OnionExpShellModel">OnionExpShellModel</a>, 
-    <a href="#SphericalSLDModel">SphericalSLDModel</a>, 
-    <a href="#LinearPearlsModel">LinearPearlsModel</a>, 
-    <a href="#PearlNecklaceModel">PearlNecklaceModel</a>
-    </li>
-    <li>Cylinder based:<br/>
-    <a href="#CylinderModel">CylinderModel (Magnetic 2D Model)</a>, 
-    <a href="#CoreShellCylinderModel">CoreShellCylinderModel</a>, 
-    <a href="#CoreShellBicelleModel">CoreShellBicelleModel</a>,
-    <a href="#HollowCylinderModel">HollowCylinderModel</a>,
-    <a href="#FlexibleCylinderModel">FlexibleCylinderModel</a>,
-    <a href="#FlexibleCylinderModel">FlexCylEllipXModel</a>,
-    <a href="#StackedDisksModel">StackedDisksModel</a>,
-    <a href="#EllipticalCylinderModel">EllipticalCylinderModel</a>, 
-    <a href="#BarBellModel">BarBellModel</a>, 
-    <a href="#CappedCylinderModel">CappedCylinderModel</a>,
-    <a href="#PringleModel">PringleModel</a> 
-    </li>
-    <li>Parallelpipeds:<br/>
-    <a href="#ParallelepipedModel">ParallelepipedModel (Magnetic 2D Model)</a>,
-    <a href="#CSParallelepipedModel">CSParallelepipedModel</a>,
-    <a href="#RectangularHollowPrismInfThinWallsModel">RectangularHollowPrismInfThinWallsModel</a>,
-    <a href="#RectangularPrismModel">RectangularPrismModel</a>,
-    <a href="#RectangularHollowPrismModel">RectangularHollowPrismModel</a>
-    </li>
-    <li>Ellipsoids:<br/>
-    <a href="#EllipsoidModel">EllipsoidModel</a>, 
-    <a href="#CoreShellEllipsoidModel">CoreShellEllipsoidModel</a>, 
-    <a href="#CoreShellEllipsoidXTModel">CoreShellEllipsoidXTModel</a>, 
-    <a href="#TriaxialEllipsoidModel">TriaxialEllipsoidModel</a>
-    </li>
-    <li>Lamellar:<br/> 
-    <a href="#LamellarModel">LamellarModel</a>, 
-    <a href="#LamellarFFHGModel">LamellarFFHGModel</a>, 
-    <a href="#LamellarPSModel">LamellarPSModel</a>, 
-    <a href="#LamellarPSHGModel">LamellarPSHGModel</a>
-    </li>
-    <li>Paracrystals:<br/>
-    <a href="#LamellarPCrystalModel">LamellarPCrystalModel</a>, 
-    <a href="#SCCrystalModel">SCCrystalModel</a>, 
-    <a href="#FCCrystalModel">FCCrystalModel</a>, 
-    <a href="#BCCrystalModel">BCCrystalModel</a>
-    </li>
-    </ul>
-<li><a href="#Shape-Independent"><b>Shape-Independent</b></a>: 
-    <a href="#Absolute%20Power_Law">AbsolutePower_Law</a>, 
-    <a href="#BEPolyelectrolyte">BEPolyelectrolyte</a>, 
-    <a href="#BroadPeakModel">BroadPeakModel</a>,
-    <a href="#CorrLength">CorrLength</a>, 
-    <a href="#DABModel">DABModel</a>, 
-    <a href="#Debye">Debye</a>, 
-    <a href="#Number_Density_Fractal">FractalModel</a>, 
-    <a href="#FractalCoreShell">FractalCoreShell</a>, 
-    <a href="#GaussLorentzGel">GaussLorentzGel</a>, 
-    <a href="#Guinier">Guinier</a>, 
-    <a href="#GuinierPorod">GuinierPorod</a>, 
-    <a href="#Lorentz">Lorentz</a>, 
-    <a href="#Mass_Fractal">MassFractalModel</a>, 
-    <a href="#MassSurface_Fractal">MassSurfaceFractal</a>, 
-    <a href="#Peak%20Gauss%20Model">PeakGaussModel</a>, 
-    <a href="#Peak%20Lorentz%20Model">PeakLorentzModel</a>, 
-    <a href="#Poly_GaussCoil">Poly_GaussCoil</a>, 
-    <a href="#PolymerExclVolume">PolyExclVolume</a>, 
-    <a href="#PorodModel">PorodModel</a>, 
-    <a href="#RPA10Model">RPA10Model</a>, 
-    <a href="#StarPolymer">StarPolymer</a>, 
-    <a href="#Surface_Fractal">SurfaceFractalModel</a>, 
-    <a href="#TeubnerStreyModel">Teubner Strey</a>, 
-    <a href="#TwoLorentzian">TwoLorentzian</a>, 
-    <a href="#TwoPowerLaw">TwoPowerLaw</a>, 
-    <a href="#UnifiedPowerRg">UnifiedPowerRg</a>, 
-    <a href="#LineModel">LineModel</a>, 
-    <a href="#ReflectivityModel">ReflectivityModel</a>, 
-    <a href="#ReflectivityIIModel">ReflectivityIIModel</a>, 
-    <a href="#GelFitModel">GelFitModel</a>.</li>
-    
-<li><a href="#Model"><b>Customized Models</b></a>: 
-    <a href="#testmodel">testmodel</a>, 
-    <a href="#testmodel_2">testmodel_2</a>, 
-    <a href="#sum_p1_p2">sum_p1_p2</a>, 
-    <a href="#sum_Ap1_1_Ap2">sum_Ap1_1_Ap2</a>, 
-    <a href="#polynomial5">polynomial5</a>, 
-    <a href="#sph_bessel_jn">sph_bessel_jn</a>.</li>
-    
-<li><a href="#Structure_Factors"><b>Structure Factors</b></a>: 
-    <a href="#HardsphereStructure">HardSphereStructure</a>, 
-    <a href="#SquareWellStructure">SquareWellStructure</a>, 
-    <a href="#HayterMSAStructure">HayterMSAStructure</a>, 
-    <a href="#StickyHSStructure">StickyHSStructure</a>.</li>
-    
-<li><a href="#References"><b>References</b></a></li>
-</ul>
-<p style="margin-left: 0.25in; text-indent: -0.25in;"><b><span style="font-size: 16pt;">1.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp; </span></b><a name="Introduction"></a><b><span style="font-size: 16pt;">Introduction </span></b></p>
-
-<p>&nbsp;Many of our models use the form factor calculations implemented in a c-library provided by the NIST Center for Neutron Research and thus some content and figures in this document are originated from or shared with the NIST Igor analysis package.</p>
-<p style="margin-left: 0.25in; text-indent: -0.25in;"><b><span style="font-size: 16pt;">2.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp; </span></b><a name="Shapes"></a><b><span style="font-size: 16pt;">Shapes (Scattering Intensity Models)</span></b></p>
-<p>This software provides form factors for various particle shapes. After giving a mathematical definition of each model, we draw the list of parameters available to the user. Validation plots for each model are also presented. Instructions on how to use the software is available with the source code.</p>
-
-<p>To easily compare to the scattering intensity measured in experiments, we normalize the form factors by the volume of the particle:</p>
-<p style="text-align: center;" align="center"><span style="position: relative; top: 12pt;"><img src="img/image001.PNG" alt="" /></span>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</p>
-<p>with</p>
-<p style="text-align: center;" align="center"><span style="position: relative; top: 8pt;"><img src="img/image002.PNG" alt="" /></span>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</p>
-<p>where <em>P</em>0<em>(<b>q</b>)</em> is the un-normalized form factor, <em>&rho;(<b>r</b>)</em> is the scattering length density at a given point in space and the integration is done over the volume <em>V</em> of the scatterer.</p>
-<p>For systems without inter-particle interference, the form factors we provide can be related to the scattering intensity by the particle volume fraction:<span style="position: relative; top: 5pt;"> <img src="img/image003.PNG" alt="" /></span>.</p>
-<p>Our so-called 1D scattering intensity functions provide <em>P(q) </em>for the case where the scatterer is randomly oriented. In that case, the scattering intensity only depends on the length of q. The intensity measured on the plane of the SANS detector will have an azimuthal symmetry around <em>q</em>=0.</p>
-<p>Our so-called 2D scattering intensity functions provide <em>P(q, </em><em><span style="font-family: 'Arial','sans-serif';">&phi;</span>)</em> for an oriented system as a function of a q-vector in the plane of the detector. We define the angle <span style="font-family: 'Arial','sans-serif';">&phi;</span> as the angle between the q vector and the horizontal (x) axis of the plane of the detector.</p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.1.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="SphereModel"></a><b><span style="font-size: 14pt;">Sphere Model (Magnetic 2D Model)</span></b></p>
-<p>This model provides the form factor, P(q), for a monodisperse spherical particle with uniform scattering length density. The form factor is normalized by the particle volume as described below.</p>
-For magnetic scattering, please see the '<a href="polar_mag_help.html">Polarization/Magnetic Scattering</a>' in Fitting Help.
-<p style="margin-left: 0.85in; text-indent: -0.35in;"><b>1.1.</b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp; </span>Definition</b></p>
-<p>The 1D scattering intensity is calculated in the following way (Guinier, 1955):</p>
-<p style="text-align: center;" align="center"><span style="position: relative; top: 16pt;"><img src="img/image004.PNG" alt="" /></span></p>
-<p>where scale is a volume fraction, V is the volume of the scatterer, r is the radius of the sphere, bkg is the background level and sldXXX is the scattering length density (SLD) of the scatterer or the solvent.<\p>
-<p>Note that if your data is in absolute scale, the 'scale' should represent the volume fraction (unitless) if you have a good fit.  If not, it should represent the volume fraction * a factor (by which your data might need to be rescaled).</p>
-<p>The 2D scattering intensity is the same as above, regardless of the orientation of the q vector.</p>
-<p>The returned value is scaled to units of [cm-1] and the parameters of the sphere model are the following:</p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 13.5pt;">
-<td style="border: 1pt solid width: 101pt; height: 13.5pt;" valign="top" width="135">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 101pt; height: 13.5pt;" valign="top" width="135">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 101pt; height: 13.5pt;" valign="top" width="135">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 12.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 101pt; height: 12.8pt;" valign="top" width="135">
-<p>scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 101pt; height: 12.8pt;" valign="top" width="135">
-<p>None</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 101pt; height: 12.8pt;" valign="top" width="135">
-<p>1</p>
-</td>
-</tr>
-<tr style="height: 12.8pt;">
-<td style="border-width: medium 1pt 1pt; vertical-align: top; width: 101pt; height: 12.8pt;">
-<p>radius</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 101pt; height: 12.8pt;" valign="top" width="135">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 101pt; height: 12.8pt;" valign="top" width="135">
-<p>60</p>
-</td>
-</tr>
-<tr style="height: 12.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 101pt; height: 12.8pt;" valign="top" width="135">
-<p>sldSph</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 101pt; height: 12.8pt;" valign="top" width="135">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 101pt; height: 12.8pt;" valign="top" width="135">
-<p>2.0e-6</p>
-</td>
-</tr>
-<tr style="height: 12.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 101pt; height: 12.8pt;" valign="top" width="135">
-<p>sldSolv</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 101pt; height: 12.8pt;" valign="top" width="135">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 101pt; height: 12.8pt;" valign="top" width="135">
-<p>1.0e-6</p>
-</td>
-</tr>
-<tr style="height: 12.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 101pt; height: 12.8pt;" valign="top" width="135">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 101pt; height: 12.8pt;" valign="top" width="135">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 101pt; height: 12.8pt;" valign="top" width="135">
-<p>0</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p>Our model uses the form factor calculations implemented in a c-library provided by the NIST Center for Neutron Research (Kline, 2006).</p>
-<p style="margin-left: 0.85in; text-indent: -0.35in;"><b>2.1.</b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp; </span>Validation of the sphere model</b></p>
-<p>Validation of our code was done by comparing the output of the 1D model to the output of the software provided by the NIST (Kline, 2006). Figure 1 shows a comparison of the output of our model and the output of the NIST software.</p>
-<p style="text-align: center; page-break-after: avoid;" align="center"><img src="img/image005.jpg" alt="sphere_1D_validation" width="573" height="315" /></p>
-<p style="text-align: center; page-break-after: avoid;" align="center">&nbsp;</p>
-<p>Figure 1: Comparison of the DANSE scattering intensity for a sphere with the output of the NIST SANS analysis software. The parameters were set to: Scale=1.0, Radius=60 &Aring;, Contrast=1e-6 &Aring; -2, and Background=0.01 cm -1.</p>
-<p style="margin-left: 0.25in;"><i>2013/09/09 and 2014/01/06 - Description reviewed by King, S. and Parker, P.</i></p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.2.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="BinaryHSModel"></a><b><span style="font-size: 14pt;">BinaryHSModel</span></b></p>
-<p>This model (binary hard sphere model) provides the scattering intensity, for binary mixture of spheres including hard sphere interaction between those particles. Using Percus-Yevick closure, the calculation is an exact multi-component solution:</p>
-<p style="text-align: center;" align="center"><span style="position: relative; top: 5pt;"><img src="img/image006.PNG" alt="" /></span></p>
-<p>where Sij are the partial structure factors and fi are the scattering amplitudes of the particles. And the subscript 1 is for the smaller particle and 2 is for the larger. The number fraction of the larger particle, (<em>x</em> = &nbsp;n2/(n1+n2), n = the number density) is internally calculated based on:</p>
-<p style="text-align: center;" align="center"><span style="position: relative; top: 24pt;"><img src="img/image007.PNG" alt="" /></span>.</p>
-<p>The 2D scattering intensity is the same as 1D, regardless of the orientation of the <em>q</em> vector which is defined as<span style="font-size: 14pt; position: relative; top: 8pt;"><img src="img/image008.PNG" alt="" /></span><span style="font-size: 14pt;">.</span></p>
-<p>The parameters of the binary hard sphere are the following (in the names, l (or ls) stands for larger spheres while s (or ss) for the smaller spheres):</p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 18.8pt;">
-<td style="border: 1pt solid width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>0.001</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>l_radius</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>100.0</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>ss_sld</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>0.0</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; vertical-align: top; width: 107pt; height: 18.8pt;">
-<p>ls_sld</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>3e-6</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>solvent_sld</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>6e-6</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>s_radius</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>25.0</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>vol_frac_ls</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>0.1</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>vol_frac_ss</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>0.2</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="text-align: center;" align="center"><img id="Picture 197" src="img/image009.jpg" alt="" width="484" height="361" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot using the default values above (w/200 data point).</b></p>
-<p>Our model uses the form factor calculations implemented in a c-library provided by the NIST Center for Neutron Research (Kline, 2006).</p>
-<p>See the reference for details.</p>
-<p>REFERENCE</p>
-<p>N. W. Ashcroft and D. C. Langreth, Physical Review, v. 156 (1967) 685-692.</p>
-<p>[Errata found in Phys. Rev. 166 (1968) 934.]</p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.3.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="FuzzySphereModel"></a><b><span style="font-size: 14pt;">FuzzySphereModel</span></b></p>
-<p><b>&nbsp;</b>This model is to calculate the scattering from spherical particles with a "fuzzy" interface.</p>
-<p style="margin-left: 0.85in; text-indent: -0.35in;"><b>1.1.</b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp; </span>Definition</b></p>
-<p>The 1D scattering intensity is calculated in the following way (Guinier, 1955):</p>
-<p>The returned value is scaled to units of [cm-1 sr-1], absolute scale.</p>
-<p>The scattering intensity I(q) is calculated as:</p>
-<p style="text-align: center;" align="center"><span style="position: relative; top: 12pt;"><img src="img/image010.PNG" alt="" /></span></p>
-<p>where the amplitude A(q) is given as the typical sphere scattering convoluted with a Gaussian to get a gradual drop-off in the scattering length density:</p>
-<p style="text-align: center;" align="center"><span style="position: relative; top: 18pt;"><img src="img/image011.PNG" alt="" /></span></p>
-<p>Here A2(q) is the form factor, P(q). The &lsquo;scale&rsquo; is equivalent to the volume fraction of spheres, each of volume, V. Contrast (<em><span style="font-family: 'Arial','sans-serif';">&Delta;</span>&rho;</em> ) is the difference of scattering length densities of the sphere and the surrounding solvent.</p>
-<p>The poly-dispersion in radius and in fuzziness is provided.</p>
-<p>(direct from the reference)</p>
-<p>The "fuzziness" of the interface is defined by the parameter (sigma)fuzzy. The particle radius R represents the radius of the particle where the scattering length density profile decreased to 1/2 of the core density. The (sigma)fuzzy&nbsp; is the width of the smeared particle surface: i.e., the standard deviation from the average height of the fuzzy interface. The inner regions of the microgel that display a higher density are described by the radial box profile extending to a radius of approximately Rbox ~ R - 2(sigma). the profile approaches zero as Rsans ~ R + 2(sigma).</p>
-<p>For 2D data: The 2D scattering intensity is calculated in the same way as 1D, where the <em>q</em> vector is defined as<span style="font-size: 14pt; position: relative; top: 8pt;"><img src="img/image008.PNG" alt="" /></span><span style="font-size: 14pt;">.</span></p>
-<p>REFERENCE</p>
-<p>M. Stieger, J. S. Pedersen, P. Lindner, W. Richtering, Langmuir 20 (2004) 7283-7292.</p>
-<p>TEST DATASET</p>
-<p>This example dataset is produced by running the FuzzySphereModel, using 200 data points, qmin = 0.001 &Aring;-1,&nbsp; qmax = 0.7 A-1 and the default values:</p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 18.8pt;">
-<td style="border: 1pt solid width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; vertical-align: top; width: 107pt; height: 18.8pt;">
-<p>None</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>1.0</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>radius</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>60</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>fuzziness</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>10</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sldSolv</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>3e-6</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sldSph</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>1e-6</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>0.001</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="text-align: center;" align="center"><img src="img/image012.jpg" alt="" width="442" height="275" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot using the default values (w/200 data point).</b></p>
-<p>&nbsp;</p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.4.</span></b> <a name="RaspBerryModel"></a><b><span style="font-size: 14pt;">RaspBerryModel</span></b></p>
-<p>&nbsp;</p>
-<p>Calculates the form factor, P(q), for a "Raspberry-like" structure where there are smaller spheres at the surface of a larger sphere, such as the structure of a Pickering emulsion.&nbsp;</p>
-<p style="margin-left: 0.85in; text-indent: -0.35in;"><b>1.1.</b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp; </span>Definition</b></p>
-<p>The structure is:<br /> <img src="img/raspberry_pic.jpg" alt="" /></p>
-<p><br /> Ro = the radius of the&nbsp;large sphere<br /> Rp = the radius of the smaller sphere on the surface<br /> delta = the fractional penetration depth<br /> surface coverage = fractional coverage of the large sphere surface (0.9 max)<br /> <br /> <br /> The large and small spheres have their own SLD, as well as the solvent. The surface coverage term is a fractional coverage (maximum of approximately 0.9 for hexagonally packed spheres on a surface). Since not all of the small spheres are necessarily attached to the surface, the excess free (small) spheres scattering is also included in the calculation. The function calculated follows equations (8)-(12) of the reference below, and the equations are not reproduced here.<br /> <br /> The returned value is scaled to units of [cm-1]. No interparticle scattering is included in this model.</p>
-<p>For 2D data: The 2D scattering intensity is calculated in the same way as 1D, where the <em>q</em> vector is defined as<span style="font-size: 14pt; position: relative; top: 8pt;"><img src="img/image008.PNG" alt="" /></span><span style="font-size: 14pt;">.</span></p>
-<p>&nbsp;&nbsp; REFERENCE<br /> Kjersta Larson-Smith, Andrew Jackson, and Danilo C Pozzo, "Small angle scattering model for Pickering emulsions and raspberry particles." Journal of Colloid and Interface Science (2010) vol. 343 (1) pp. 36-41.</p>
-<p>TEST DATASET</p>
-<p>This example dataset is produced by running the RaspBerryModel, using 2000 data points, qmin = 0.0001 &Aring;-1,&nbsp; qmax = 0.2 A-1 and the default values, where Ssph/Lsph stands for Smaller/Large sphere and&nbsp;surfrac_Ssph for the surface fraction of the smaller spheres.</p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 18.8pt;">
-<td style="border: 1pt solid width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr>
-<td>&nbsp; delta_Ssph</td>
-<td>&nbsp;</td>
-<td>&nbsp; 0</td>
-</tr>
-<tr>
-<td>&nbsp; radius_Lsph</td>
-<td>&nbsp; &Aring;</td>
-<td>&nbsp; 5000</td>
-</tr>
-<tr>
-<td>&nbsp; radius_Ssph</td>
-<td>&nbsp; &Aring;</td>
-<td>&nbsp; 100</td>
-</tr>
-<tr>
-<td>&nbsp; sld_Lsph</td>
-<td>&nbsp;&nbsp;&Aring; -2</td>
-<td>&nbsp; -4e-07</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sld_Ssph</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; vertical-align: top; width: 107pt; height: 18.8pt;">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>3.5e-6</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sld_solv</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>6.3e-6</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>surfrac_Ssph</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&nbsp;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>0.4</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>volf_Lsph</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>0.05</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>volf_Lsph</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&nbsp;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>0.005</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>0</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="text-align: center;" align="center"><img src="img/raspberry_plot.jpg" alt="" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot using the values of /2000 data points.</b></p>
-<p style="text-align: center;" align="center">&nbsp;</p>
-<p>&nbsp;</p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.5.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="CoreShellModel"></a><b><span style="font-size: 14pt;">Core Shell (Sphere) Model (Magnetic 2D Model)</span></b></p>
-<p>This model provides the form factor, P(<em>q</em>), for a spherical particle with a core-shell structure. The form factor is normalized by the particle volume.</p>
-For magnetic scattering, please see the '<a href="polar_mag_help.html">Polarization/Magnetic Scattering</a>' in Fitting Help.
-<p style="margin-left: 0.85in; text-indent: -0.35in;"><b>1.1.</b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp; </span>Definition</b></p>
-<p>The 1D scattering intensity is calculated in the following way (Guinier, 1955):</p>
-<p style="text-align: center;" align="center"><span style="position: relative; top: 16pt;"><img src="img/image013.PNG" alt="" /></span>&nbsp;</p>
-<p style="text-align: right;" align="right">&nbsp;</p>
-<p>where <em>scale</em> is a scale factor, <em>Vs</em> is the volume of the outer shell, <em>Vc</em> is the volume of the core, <em>rs</em> is the radius of the shell, <em>rc</em> is the radius of the core, <em>&rho;c</em> is the scattering length density of the core, <em>&rho;s</em> is the scattering length density of the shell, &rho;solv is the scattering length density of the solvent, and <em>bkg</em> is the background level.</p>
-<p>The 2D scattering intensity is the same as P(q) above, regardless of the orientation of the q vector.</p>
-<p>For P*S: The outer most radius (= radius + thickness) is used as the effective radius toward S(Q) when P(Q)*S(Q) is applied.</p>
-<p>The returned value is scaled to units of [cm-1] and the parameters of the core-shell sphere model are the following:</p>
-<p>Here, radius = the radius of the core and thickness = the thickness of the shell.</p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 18.8pt;">
-<td style="border: 1pt solid vertical-align: top; width: 107pt; height: 18.8pt;">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>None</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>1.0</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>(core) radius</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>60</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>thickness</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>10</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>core_sld</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>1e-6</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>shell_sld</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>2e-6</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>solvent_sld</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>3e-6</p>
-</td>
-</tr>
-<tr style="height: 19.5pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.5pt;" valign="top" width="143">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.5pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.5pt;" valign="top" width="143">
-<p>0.001</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p>Our model uses the form factor calculations implemented in a c-library provided by the NIST Center for Neutron Research (Kline, 2006).</p>
-<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</p>
-<p>REFERENCE</p>
-<p>Guinier, A. and G. Fournet, "Small-Angle Scattering of X-Rays", John Wiley and Sons, New York, (1955).</p>
-<p style="margin-left: 0.85in; text-indent: -0.35in;"><b>2.1.</b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp; </span>Validation of the core-shell sphere model</b></p>
-<p>Validation of our code was done by comparing the output of the 1D model to the output of the software provided by the NIST (Kline, 2006). Figure 1 shows a comparison of the output of our model and the output of the NIST software.</p>
-<p style="text-align: center; page-break-after: avoid;" align="center"><img src="img/image014.jpg" alt="core_shell_sphere_1D_validation" width="573" height="315" /></p>
-<p>Figure 7: Comparison of the DANSE scattering intensity for a core-shell sphere with the output of the NIST SANS analysis software. The parameters were set to: Scale=1.0, Radius=60 &Aring;, Contrast=1e-6 &Aring; -2, and Background=0.001 cm -1.</p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.6.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="Core2ndMomentModel"></a><b><span style="font-size: 14pt;">Core2ndMomentModel</span></b></p>
-<p>This model describes the scattering from a layer of surfactant or polymer adsorbed on spherical particles under the conditions that (i) the&nbsp;<span style="font-weight: bold;">particles (cores) are contrast-matched to the dispersion medium,</span> (ii) <span style="font-weight: bold;">S(Q)~1 </span>(ie, the particle volume fraction is dilute), (iii)<span style="font-weight: bold;"> the particle radius is &gt;&gt; layer thickness</span> (ie, the interface is locally flat), and (iv) scattering from excess unadsorbed adsorbate in the bulk medium is absent or has been corrected for.</p>
-<p>Unlike a core-shell model, this model does not assume any form for the density distribution of the adsorbed species normal to the interface (cf, a core-shell model which assumes the density distribution to be a homogeneous step-function). For comparison, if the thickness of a (core-shell like) step function distribution is t, the second moment, sigma = sqrt((t^2)/12). The&nbsp;sigma is the second moment about the mean of the density distribution (ie, the distance of the centre-of-mass of the distribution from the interface).</p>
-<p style="margin-left: 0.85in; text-indent: -0.35in;"><b>1.1.</b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp; </span>Definition</b></p>
-<p>The I0 is calculated in the following way (King, 2002):</p>
-<p style="text-align: center;" align="center"><span style="position: relative; top: 16pt;"><img style="width: 542px; height: 55px;" src="img/secondmeq1.jpg" alt="" /></span>&nbsp;</p>
-<p style="text-align: right;" align="right">&nbsp;</p>
-<p>where <em>scale</em> is a scale factor,&nbsp;<em>&rho;poly</em> is the sld of the polymer (or surfactant) layer,&nbsp;&rho;solv is the sld of the solvent/medium and cores, phi_cores is the volume fraction of the core paraticles, and Gamma and delta are&nbsp;the adsorbed amount and the bulk density of the polymers respectively. The sigma is the second moment of the thickness distribution.&nbsp;</p>
-<p>&nbsp;</p>
-<p>Note that all parameters except the 'sigma' are correlated for fitting so that fitting&nbsp;those with more than one parameters will be generally failed. &nbsp;And note that unlike other shape models, no volume normalization was applied to this model.</p>
-<p>The returned value is scaled to units of [cm-1] and the parameters are the following:</p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 18.8pt;">
-<td style="border: 1pt solid width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>None</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>1.0</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>density_poly</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>g/cm2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>0.7</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>radius_core</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>500</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>ads_amount</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>mg/m&nbsp;2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>1.9</p>
-</td>
-</tr>
-<tr>
-<td>&nbsp; second_moment</td>
-<td>&nbsp; &Aring;</td>
-<td>&nbsp; 23.0</td>
-</tr>
-<tr>
-<td>&nbsp; volf_cores</td>
-<td>&nbsp; None</td>
-<td>&nbsp; 0.14</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sld_poly</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>1.5e-6</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sld_solv</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>6.3e-6</p>
-</td>
-</tr>
-<tr style="height: 19.5pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.5pt;" valign="top" width="143">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.5pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.5pt;" valign="top" width="143">
-<p>0.0</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</p>
-<p>REFERENCE</p>
-<p>S. King, P. Griffiths, J. Hone, and T. Cosgrove, "SANS from Adsorbed Polymer Lyaers", Macromol. Symp. <span style="font-weight: bold;">190</span>, 33-42&nbsp; (2002).</p>
-<p>&nbsp;</p>
-<p style="text-align: center; page-break-after: avoid;" align="center"><img style="width: 526px; height: 333px;" src="img/secongm_fig1.jpg" alt="core_scondmoment_1D_validation" /></p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.7.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="CoreMultiShellModel"></a><b><span style="font-size: 14pt;">CoreMultiShell(Sphere)Model (Magnetic 2D Model)</span></b></p>
-<p>This model provides the scattering from spherical core with from 1 up to 4 shell structures. It&nbsp;has a core of a specified radius, with four shells. The SLDs of the core and each shell are individually specified.&nbsp;</p>
-For magnetic scattering, please see the '<a href="polar_mag_help.html">Polarization/Magnetic Scattering</a>' in Fitting Help.
-<p style="margin-left: 0.85in; text-indent: -0.35in;"><b>1.1.</b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp; </span>Definition</b></p>
-<p>The returned value is scaled to units of [cm-1sr-1], absolute scale.</p>
-<p>This model is a trivial extension of the CoreShell function to a larger number of shells. See the CoreShell function for a diagram and documentation.</p>
-<p>Be careful that the SLDs and scale can be highly correlated. Hold as many of these fixed as possible.</p>
-<p>The 2D scattering intensity is the same as P(q) of 1D, regardless of the orientation of the q vector.</p>
-<p>For P*S: The outer most radius (= radius + 4 thicknesses) is used as the effective radius toward S(Q) if P(Q)*S(Q) is applied.</p>
-<p>The returned value is scaled to units of [cm-1] and the parameters of the CoreFourshell sphere model are the following:</p>
-<p>Here, rad_core = the radius of the core, &nbsp;thick_shelli = the thickness of the shell i and sld_shelli = the SLD of the shell i.</p>
-<p>And the sld_core and the sld_solv are the SLD of the core and the solvent, respectively.</p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 18.8pt;">
-<td style="border: 1pt solid vertical-align: top; width: 107pt; height: 18.8pt;">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>None</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>1.0</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>rad_core</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>60</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sld_core</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>6.4e-6</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sld_shell1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>1e-6</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sld_shell2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>2e-6</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sld_shell3</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>3e-6</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sld_shell4</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>4e-6</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sld_solv</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>6.4e-6</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>thick_shell1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>10</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>thick_shell2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>10</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>thick_shell3</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>10</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>thick_shell4</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>10</p>
-</td>
-</tr>
-<tr style="height: 19.5pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.5pt;" valign="top" width="143">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.5pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.5pt;" valign="top" width="143">
-<p>0.001</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p>Our model uses the form factor calculations implemented in a c-library provided by the NIST Center for Neutron Research (Kline, 2006).</p>
-<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</p>
-<p>REFERENCE</p>
-<p>See the CoreShell documentation.&nbsp;</p>
-<p>TEST DATASET</p>
-<p>This example dataset is produced by running the CoreMultiShellModel using 200 data points, qmin = 0.001 &Aring;-1,&nbsp; qmax = 0.7 &Aring;-1 and the above default values.</p>
-<p style="text-align: center;" align="center"><img id="Picture 131" src="img/image015.jpg" alt="" width="540" height="390" /></p>
-<p style="text-align: center;" align="center"><b>Figure: 1D plot using the default values (w/200 data point).</b></p>
-<p>&nbsp;The scattering length density profile for the default sld values (w/ 4 shells).</p>
-<p style="text-align: center;" align="center"><img src="img/image016.jpg" alt="" width="504" height="351" /></p>
-<p style="text-align: center;" align="center"><b>Figure: SLD profile against the radius of the sphere for default SLDs.</b></p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.8.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="VesicleModel"></a><b><span style="font-size: 14pt;">VesicleModel</span></b></p>
-<p>This model provides the form factor, P(<em>q</em>), for an unilamellar vesicle. The form factor is normalized by the volume of the shell.</p>
-<p>The 1D scattering intensity is calculated in the following way (Guinier, 1955):</p>
-<p style="text-align: center;" align="center"><span style="position: relative; top: 16pt;"><img src="img/image017.PNG" alt="" /></span>&nbsp;</p>
-<p style="text-align: right;" align="right">&nbsp;</p>
-<p>where <em>scale</em> is a scale factor, <em>Vshell</em> is the volume of the shell, <em>V1</em> is the volume of the core, <em>V2</em> is the total volume, <em>R1</em> is the radius of the core, <em>r2</em> is the outer radius of the shell, <em>&rho;1</em> is the scattering length density of the core and the solvent, <em>&rho;2</em> is the scattering length density of the shell, and <em>bkg</em> is the background level. And <em>J1</em> = (sin<em>x </em>- <em>x</em>cos<em>x</em>)/<em>x</em>2. The functional form is identical to a "typical" core-shell structure, except that the scattering is normalized by the volume that is contributing to the scattering, namely the volume of the shell alone. Also, the vesicle is best defined in terms of a core radius (= R1) and a shell thickness, t. &nbsp;</p>
-<p style="text-align: center;" align="center"><img id="Picture 31" src="img/image018.jpg" alt="" width="284" height="272" /></p>
-<p>The 2D scattering intensity is the same as <em>P</em>(<em>q</em>) above, regardless of the orientation of the <em>q</em> vector&nbsp; which is defined as<span style="font-size: 14pt; position: relative; top: 8pt;"><img src="img/image008.PNG" alt="" /></span><span style="font-size: 14pt;">.</span></p>
-<p>For P*S: The outer most radius (= radius + thickness) is used as the effective radius toward S(Q) when P(Q)*S(Q) is applied.</p>
-<p>The returned value is scaled to units of [cm-1] and the parameters of the vesicle model are the following:</p>
-<p>In the parameters, the &lsquo;radius&rsquo; represents the core radius (R1) and the &lsquo;thickness&rsquo; (R2 &ndash; R1) is the shell thickness.</p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 18.8pt;">
-<td style="border: 1pt solid vertical-align: top; width: 107pt; height: 18.8pt;">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>None</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>1.0</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>radius</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>100</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>thickness</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>30</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>core_sld</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>6.3e-6</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>shell_sld</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>0</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>0.0</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="text-align: center;" align="center"><img id="Picture 158" src="img/image019.jpg" alt="" width="454" height="356" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot using the default values (w/200 data point).</b></p>
-<p>Our model uses the form factor calculations implemented in a c-library provided by the NIST Center for Neutron Research (Kline, 2006).</p>
-<p>REFERENCE</p>
-<p>Guinier, A. and G. Fournet, "Small-Angle Scattering of X-Rays", John Wiley and Sons, New York, (1955).</p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.9.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="MultiShellModel"></a><b><span style="font-size: 14pt;">MultiShellModel</span></b></p>
-<p>This model provides the form factor, P(<em>q</em>), for a multi-lamellar vesicle with N shells where the core is filled with solvent and the shells are interleaved with layers of solvent. For N = 1, this return to the vesicle model (above).</p>
-<p style="text-align: center;" align="center"><img id="Picture 32" src="img/image020.jpg" alt="" width="423" height="371" /></p>
-<p>The 2D scattering intensity is the same as 1D, regardless of the orientation of the <em>q</em> vector which is defined as<span style="font-size: 14pt; position: relative; top: 8pt;"><img src="img/image008.PNG" alt="" /></span><span style="font-size: 14pt;">.</span></p>
-<p>For P*S: The outer most radius (= core_radius + n_pairs&nbsp; * s_thickness&nbsp; + (n_pairs -1) * w_thickness) is used as the effective radius toward S(Q) when P(Q)*S(Q) is applied.</p>
-<p>The returned value is scaled to units of [cm-1] and the parameters of the multi-shell model are the following:</p>
-<p>In the parameters, the &lsquo;s_thickness&rsquo; is the shell thickness while the &lsquo;w_thickness&rsquo; is the solvent thickness, and the n_pair is the number of shells.</p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 18.8pt;">
-<td style="border: 1pt solid vertical-align: top; width: 107pt; height: 18.8pt;">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>None</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>1.0</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>core_radius</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>60.0</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>n_pairs</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>None</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>2.0</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>core_sld</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>6.3e-6</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>shell_sld</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>0.0</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>0.0</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>s_thickness</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>10</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>w_thickness</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>10</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="text-align: center;" align="center"><img id="Picture 173" src="img/image021.jpg" alt="" width="484" height="368" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot using the default values (w/200 data point).</b></p>
-<p>Our model uses the form factor calculations implemented in a c-library provided by the NIST Center for Neutron Research (Kline, 2006).</p>
-<p>REFERENCE</p>
-<p>Cabane, B., Small Angle Scattering Methods, Surfactant Solutions: New Methods of Investigation, Ch.2, Surfactant Science Series Vol. 22, Ed. R. Zana, M. Dekker, New York, 1987.</p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.10.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="OnionExpShellModel"></a><b><span style="font-size: 14pt;">OnionExpShellModel</span></b></p>
-<p>&nbsp;&nbsp;</p>
-<p>This model provides the form factor, <em>P</em>(<em>q</em>), for a multi-shell sphere where the scattering length density (SLD) of the each shell is described by an exponential (linear, or flat-top) function. The form factor is normalized by the volume of the sphere where the SLD is not identical to the SLD of the solvent. We currently provide up to 9 shells with this model.</p>
-<p>The 1D scattering intensity is calculated in the following way:</p>
-<p><span style="font-size: 12pt; font-family: 'Times New Roman','serif';"><img src="img/image022.gif" alt="" width="143" height="21" /></span></p>
-<p><span style="font-size: 12pt; font-family: 'Times New Roman','serif';"><img src="img/image023.gif" alt="" width="230" height="54" /></span></p>
-<p>where, for a spherically symmetric particle with a particle density <em><span style="font-family: Symbol;">r</span></em><span style="font-family: Symbol;">(</span><em>r</em><span style="font-family: Symbol;">)</span> [L.A.Feigin and D.I.Svergun, &lsquo;Structure Analysis by Small-Angle X-Ray and Neutron Scattering&rsquo;, Plenum Press, New York, 1987],</p>
-<p><span style="font-size: 12pt; font-family: 'Times New Roman','serif';"><img src="img/image024.gif" alt="" width="200" height="41" /></span></p>
-<p>so that</p>
-<p style="text-align: center;" align="center"><span style="font-size: 12pt; font-family: 'Times New Roman','serif';"><img src="img/image025.gif" alt="" width="519" height="87" /></span><br /> &nbsp;</p>
-<p style="text-align: center;" align="center"><span style="font-size: 12pt; font-family: 'Times New Roman','serif';"><img src="img/image026.gif" alt="" width="338" height="44" /></span></p>
-<p><span style="font-size: 12pt; font-family: 'Times New Roman','serif';"><img src="img/image027.gif" alt="" width="466" height="89" /></span></p>
-<p>Here we assumed that the SLDs of the core and solvent are constant against <em>r</em>. Now let&rsquo;s consider the SLD of a shell, <em><span style="font-family: Symbol;">r</span>shelli</em>, defineded by</p>
-<p><span style="font-size: 12pt; font-family: 'Times New Roman','serif';"><img src="img/image028.gif" alt="" width="373" height="68" /></span></p>
-<p>An example of a possible SLD profile is shown below where sld_in_shelli (<em><span style="font-family: Symbol;">r</span>in</em> ) and thick_shelli (<em><span style="font-family: Symbol;">D</span>tshelli</em> ) stand for the SLD of the inner side of the i&rsquo;th shell and the thickness of the i&rsquo;th shell in the equation above, respectively.</p>
-<p>For |A|&gt;0,</p>
-<p style="text-align: center;" align="center"><span style="font-size: 12pt; font-family: 'Times New Roman','serif';"><img src="img/image029.gif" alt="" width="481" height="327" /></span></p>
-<p>For A <b>~ </b>0 (eg., A = - 0.0001), this function converges to that of the linear SLD profile (ie, <em><span style="font-family: Symbol;">r</span>shelli</em>(<em>r</em>) = <em>A<b>&rsquo;</b></em>(<em>r</em> - <em>rshelli-1</em>) /<em><span style="font-family: Symbol;">D</span>tshelli</em>) + <em>B<b>&rsquo;</b></em>), so this case it is equivalent to</p>
-<p><span style="font-size: 12pt; font-family: 'Times New Roman','serif';"><img src="img/image030.gif" alt="" width="531" height="45" /></span></p>
-<p><span style="font-size: 12pt; font-family: 'Times New Roman','serif';"><img src="img/image031.gif" alt="" width="483" height="45" /></span></p>
-<p><span style="font-size: 12pt; font-family: 'Times New Roman','serif';"><img src="img/image032.gif" alt="" width="303" height="43" /></span></p>
-<p><span style="font-size: 12pt; font-family: 'Times New Roman','serif';"><img src="img/image033.gif" alt="" width="287" height="43" /></span></p>
-<p>For A = 0, the exponential function has no dependence on the radius (so that &lsquo;sld_out_shell#&rsquo; (<em><span style="font-family: Symbol;">r</span>out</em>) is ignored this case) and becomes flat. We set the constant to <em><span style="font-family: Symbol;">r</span>in</em> for convenience, and thus the form factor contributed by the shells is</p>
-<p><span style="font-size: 12pt; font-family: 'Times New Roman','serif';"><img src="img/image034.gif" alt="" width="342" height="43" /></span></p>
-<p><span style="font-size: 12pt; font-family: 'Times New Roman','serif';"><img src="img/image035.gif" alt="" width="315" height="43" /></span></p>
-<p>In the equation,</p>
-<p><span style="font-size: 12pt; font-family: 'Times New Roman','serif';"><img src="img/image036.gif" alt="" width="347" height="95" /></span></p>
-<p>Finally, the form factor can be calculated by</p>
-<p><span style="font-size: 12pt; font-family: 'Times New Roman','serif';"><img src="img/image037.gif" alt="" width="143" height="21" /></span></p>
-<p>where</p>
-<p><span style="font-size: 12pt; font-family: 'Times New Roman','serif';"><img src="img/image038.gif" alt="" width="144" height="21" /></span></p>
-<p><span style="font-family: Symbol;">&nbsp;</span></p>
-<p><span style="font-family: Symbol;">&nbsp;</span></p>
-<p style="text-align: center;" align="center"><span style="font-family: Symbol;"><img id="Object 1" src="img/image039.gif" alt="" width="658" height="487" /></span></p>
-<p style="text-align: center;" align="center"><span style="font-family: Symbol;">&nbsp;</span></p>
-<p>The 2D scattering intensity is the same as <em>P</em>(<em>q</em>) above, regardless of the orientation of the <em>q</em> vector&nbsp; which is defined as<span style="font-size: 12pt; font-family: 'Times New Roman','serif'; position: relative; top: 4.5pt;"><img src="img/image040.gif" alt="" width="111" height="23" /></span><span style="font-size: 14pt;">.</span></p>
-<p>For P*S: The outer most radius is used as the effective radius toward S(Q) when P(Q)*S(Q) is applied.</p>
-<p>The returned value is scaled to units of [cm-1] and the parameters of this model are the following:</p>
-<p>In the parameters, the &lsquo;rad_core&rsquo; represents the core radius (R1) and the &lsquo;thick_shell1&rsquo; (R2 &ndash; R1) is the thickness of the shell1, etc.</p>
-<p>Note: Only No. of shells&nbsp; = 1 is given below.</p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 18.8pt;">
-<td style="border: 1pt solid width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; vertical-align: top; width: 107pt; height: 18.8pt;">
-<p>A_shell1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>None</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>1</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>None</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>1.0</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>rad_core</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>200</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>thick_shell1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>50</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sld_core</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>1.0e-06</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sld_in_shell1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>1.7e-06</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sld_out_shell1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>2.0e-06</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sld_solv</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>6.4e-06</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>0.0</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="text-align: center;" align="center"><img src="img/image041.jpg" alt="" width="493" height="334" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot using the default values (w/400 point).</b></p>
-<p style="text-align: center;" align="center">&nbsp;<img src="img/image042.jpg" alt="" width="497" height="372" /></p>
-<p style="text-align: center;" align="center">&nbsp;<b>Figure. SLD profile from the default values.</b></p>
-<p>REFERENCE</p>
-<p>L.A.Feigin and D.I.Svergun, &lsquo;Structure Analysis by Small-Angle X-Ray and Neutron Scattering&rsquo;, Plenum Press, New York, 1987</p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.11.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="SphericalSLDModel"></a><b><span style="font-size: 14pt;">SphericalSLDModel</span></b></p>
-<p>&nbsp;&nbsp;</p>
-<p>Similarly to the OnionExpShellModel, this model provides the form factor, <em>P</em>(<em>q</em>), for a multi-shell sphere, where the interface between the each neighboring shells can be described by one of the functions including error, power-law, and exponential functions. This model is to calculate the scattering intensity by building a continuous custom SLD profile against the radius of the particle. The SLD profile is composed of a flat core, a flat solvent, a number (up to 9 shells) of flat shells, and the interfacial layers between the adjacent flat shells (or core, and solvent) (See below). Unlike OnionExpShellModel (using an analytical integration), the interfacial layers are sub-divided and numerically integrated assuming each sub-layers are described by a line function. The number of the sub-layer can be given by users by setting the integer values of &lsquo;npts_inter#&rsquo; in GUI. The form factor is normalized by the total volume of the sphere.</p>
-<p>The 1D scattering intensity is calculated in the following way:</p>
-<p><span style="font-size: 12pt; font-family: 'Times New Roman','serif';"><img src="img/image022.gif" alt="" width="143" height="21" /></span></p>
-<p><span style="font-size: 12pt; font-family: 'Times New Roman','serif';"><img src="img/image043.gif" alt="" width="344" height="56" /></span></p>
-<p>where, for a spherically symmetric particle with a particle density <em><span style="font-family: Symbol;">r</span></em><span style="font-family: Symbol;">(</span><em>r</em><span style="font-family: Symbol;">)</span> [L.A.Feigin and D.I.Svergun, &lsquo;Structure Analysis by Small-Angle X-Ray and Neutron Scattering&rsquo;, Plenum Press, New York, 1987],</p>
-<p><span style="font-size: 12pt; font-family: 'Times New Roman','serif';"><img src="img/image024.gif" alt="" width="200" height="41" /></span></p>
-<p>so that</p>
-<p style="text-align: center;" align="center"><span style="font-size: 12pt; font-family: 'Times New Roman','serif';"><img src="img/image044.gif" alt="" /></span></p>
-<p style="text-align: center;" align="center"><span style="font-size: 12pt; font-family: 'Times New Roman','serif';"><img src="img/image045.gif" alt="" /></span></p>
-<p style="text-align: center;" align="center"><span style="font-size: 12pt; font-family: 'Times New Roman','serif';"><img src="img/image046.gif" alt="" /></span></p>
-<p style="text-align: center;" align="center"><span style="font-size: 12pt; font-family: 'Times New Roman','serif';"><img src="img/image047.gif" alt="" /></span></p>
-<p style="text-align: center;" align="center"><span style="font-size: 12pt; font-family: 'Times New Roman','serif';"><img src="img/image048.gif" alt="" /></span></p>
-<p><span style="font-size: 12pt; font-family: 'Times New Roman','serif';"><img src="img/image027.gif" alt="" /></span></p>
-<p>Here we assumed that the SLDs of the core and solvent are constant against <em>r</em>. The SLD at the interface between shells, <em><span style="font-family: Symbol;">r</span>inter_i</em>, is calculated with a function chosen by an user, where the functions are:</p>
-<p style="text-indent: -0.25in;">1)<span style="font-family: 'Times New Roman'; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>Exp;&nbsp;&nbsp;&nbsp;</p>
-<p><span style="font-size: 12pt; font-family: 'Times New Roman','serif';"><img src="img/image049.gif" alt="" /></span></p>
-<p style="text-indent: -0.25in;">2)<span style="font-family: 'Times New Roman'; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>Power-Law;</p>
-<p>&nbsp;</p>
-<p><span style="font-size: 12pt; font-family: 'Times New Roman','serif';"><img src="img/image050.gif" alt="" /></span></p>
-<p style="text-indent: -0.25in;">3)<span style="font-family: 'Times New Roman'; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>Erf;</p>
-<p><span style="font-size: 12pt; font-family: 'Times New Roman','serif';"><img src="img/image051.gif" alt="" /></span></p>
-<p>&nbsp;</p>
-<p>&nbsp;</p>
-<p>Then the functions are normalized so that it varies between 0 and 1 and they are constrained such that the SLD is continuous at the boundaries of the interface as well as each sub-layers and thus the B and C are determined.</p>
-<p>Once the <em><span style="font-family: Symbol;">r</span>inter_i</em> is found at the boundary of the sub-layer of the interface, we can find its contribution to the form factor P(q);</p>
-<p style="text-align: center;" align="center"><span style="font-size: 12pt; font-family: 'Times New Roman','serif';"><img src="img/image052.gif" alt="" width="306" height="55" /></span></p>
-<p style="text-align: center;" align="center"><span style="font-size: 12pt; font-family: 'Times New Roman','serif';"><img src="img/image053.gif" alt="" width="304" height="58" /></span></p>
-<p style="text-align: center;" align="center"><span style="font-size: 12pt; font-family: 'Times New Roman','serif';"><img src="img/image054.gif" alt="" width="701" height="186" /></span></p>
-<p>where we assume that rho_inter_i (r) can be approximately linear within a sub-layer j.</p>
-<p>In the equation,</p>
-<p><span style="font-size: 12pt; font-family: 'Times New Roman','serif';"><img src="img/image055.gif" alt="" /></span></p>
-<p>Finally, the form factor can be calculated by</p>
-<p><span style="font-size: 12pt; font-family: 'Times New Roman','serif';"><img src="img/image037.gif" alt="" /></span></p>
-<p>where</p>
-<p><span style="font-size: 12pt; font-family: 'Times New Roman','serif';"><img src="img/image038.gif" alt="" /></span></p>
-<p><span style="font-family: Symbol;">&nbsp;</span></p>
-<p><span style="font-family: Symbol;">&nbsp;</span></p>
-<p style="text-align: center;" align="center"><span style="font-family: Symbol;"><img id="Object 20" src="img/image056.gif" alt="" /></span></p>
-<p style="text-align: center;" align="center"><span style="font-family: Symbol;">&nbsp;</span></p>
-<p>The 2D scattering intensity is the same as <em>P</em>(<em>q</em>) above, regardless of the orientation of the <em>q</em> vector&nbsp; which is defined as<span style="font-size: 12pt; font-family: 'Times New Roman','serif'; position: relative; top: 4.5pt;"><img src="img/image040.gif" alt="" /></span><span style="font-size: 14pt;">.</span></p>
-<p>For P*S: The outer most radius is used as the effective radius toward S(Q) when P(Q)*S(Q) is applied.</p>
-<p>The returned value is scaled to units of [cm-1] and the parameters of this model are the following:</p>
-<p>In the parameters, the &lsquo;rad_core0&rsquo; represents the core radius (R1).</p>
-<p>Note: Only No. of shells&nbsp; = 1 is given below.</p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 18.8pt;">
-<td style="border: 1pt solid width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; vertical-align: top; width: 107pt; height: 18.8pt;">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>0.0</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>npts_inter</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>35</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>1</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sld_solv</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>1e-006</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>func_inter1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Erf</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>nu_inter</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>2.5</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>thick_inter1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>50</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sld_flat1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>4e-006</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>thick_flat1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>100</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>func_inter0</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Erf</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>nu_inter0</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>2.5</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>rad_core0</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>50</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sld_ core0</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>2.07e-06</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>thick_ core0</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>50</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="text-align: center;" align="center"><img src="img/image057.jpg" alt="" width="481" height="332" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot using the default values (w/400 point).</b></p>
-<p style="text-align: center;" align="center">&nbsp;<img src="img/image058.jpg" alt="" width="536" height="344" /></p>
-<p style="text-align: center;" align="center">&nbsp;<b>Figure. SLD profile from the default values.</b></p>
-<p>REFERENCE</p>
-<p>L.A.Feigin and D.I.Svergun, &lsquo;Structure Analysis by Small-Angle X-Ray and Neutron Scattering&rsquo;, Plenum Press, New York, 1987</p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.12.</span></b> <b><a name="LinearPearlsModel"></a><span style="font-size: 14pt;">LinearPearlsModel</span></b></p>
-<p><a name="LinearPearlsModel"></a>This model provides the form factor for pearls linearly joined by short strings: N pearls (homogeneous spheres), the radius R and the string segment length (or edge separation) l (= A- 2R)). The A is the center to center pearl separation distance. The thickness of each string is assumed to be negligable.</p>
-<p>&nbsp;</p>
-<p><a name="LinearPearlsModel"></a><img src="img/linearpearls.jpg" alt="" /></p>
-<p style="margin-left: 0.85in; text-indent: -0.35in;"><a name="LinearPearlsModel"></a><b>1.1.</b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp; </span>Definition</b></p>
-<p><a name="LinearPearlsModel"></a>&nbsp;</p>
-<p><a name="LinearPearlsModel"></a>The output of the scattering intensity function for the linearpearls model is given by (Dobrynin, 1996):</p>
-<p style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><a name="LinearPearlsModel"></a><img src="img/linearpearl_eq1.gif" alt="" /></span><a name="LinearPearlsModel"></a>&nbsp;</p>
-<p><a name="LinearPearlsModel"></a>where the mass mp &nbsp;is (sld(of a pearl) &ndash; sld(of solvent)) * (volume of the N pearls), V is the total volume.</p>
-<p><a name="LinearPearlsModel"></a>The 2D scattering intensity is the same as P(q) above, regardless of the orientation of the q vector.</p>
-<p><a name="LinearPearlsModel"></a>The returned value is scaled to units of [cm-1] and the parameters are the following:</p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 19.25pt;">
-<td style="border: 1pt solid width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; vertical-align: top; width: 107pt; height: 19.25pt;">
-<p>scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>None</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>1.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>radius</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>80.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>edge_separation</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>350.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>num_pearls</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>(integer)</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>3</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>sld_pearl</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>1e-6</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>sld_solv</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>6.3e-6</p>
-</td>
-</tr>
-<tr style="height: 20pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 20pt;" valign="top" width="143">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 20pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 20pt;" valign="top" width="143">
-<p>0.0</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="text-align: center;" align="center"><a name="LinearPearlsModel"></a>&nbsp;</p>
-<p style="text-align: center;" align="center"><a name="LinearPearlsModel"></a><img src="img/linearpearl_plot.jpg" alt="" /></p>
-<p><a name="LinearPearlsModel"></a>REFERENCE</p>
-<p><a name="LinearPearlsModel"></a>A. V. Dobrynin, M. Rubinstein and S. P. Obukhov, Macromol. 29, 2974-2979, 1996.</p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><a name="LinearPearlsModel"></a><b><span style="font-size: 14pt;">2.13.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b><a name="PearlNecklaceModel"></a><span style="font-size: 14pt;">PearlNecklaceModel</span></b></p>
-<p><a name="PearlNecklaceModel"></a>This model provides the form factor for a pearl necklace composed of two elements: N pearls (homogeneous spheres) freely jointed by M rods (like strings) (with a total mass Mw = M *mr + N * ms, the radius R and the string segment length (or edge separation) l (= A- 2R)). The A is the center to center pearl separation distance.</p>
-<p>&nbsp;</p>
-<p><a name="PearlNecklaceModel"></a><img src="img/pearl_fig.jpg" alt="" /></p>
-<p style="margin-left: 0.85in; text-indent: -0.35in;"><a name="PearlNecklaceModel"></a><b>1.1.</b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp; </span>Definition</b></p>
-<p><a name="PearlNecklaceModel"></a>The output of the scattering intensity function for the pearlnecklace model is given by (Schweins, 2004):</p>
-<p style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><a name="PearlNecklaceModel"></a><img src="img/pearl_eq1.gif" alt="" /></span><a name="PearlNecklaceModel"></a>&nbsp;</p>
-<p><a name="PearlNecklaceModel"></a>where</p>
-<p style="text-align: center;" align="center"><span style="position: relative; top: 16pt;"><a name="PearlNecklaceModel"></a><img src="img/pearl_eq2.gif" alt="" /></span><span style="position: relative; top: 14pt;"><a name="PearlNecklaceModel"></a>,</span><a name="PearlNecklaceModel"></a>&nbsp;&nbsp;</p>
-<p style="text-align: center;" align="center"><span style="position: relative; top: 17pt;"><a name="PearlNecklaceModel"></a><img src="img/pearl_eq3.gif" alt="" /></span><span style="position: relative; top: 14pt;"><a name="PearlNecklaceModel"></a>,</span></p>
-<p style="text-align: center;" align="center"><span style="position: relative; top: 16pt;"><a name="PearlNecklaceModel"></a><img src="img/pearl_eq4.gif" alt="" /></span><span style="position: relative; top: 14pt;"><a name="PearlNecklaceModel"></a>,</span></p>
-<p style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><a name="PearlNecklaceModel"></a><img src="img/pearl_eq5.gif" alt="" /></span><a name="PearlNecklaceModel"></a>&nbsp;,</p>
-<p style="text-align: center;" align="center"><span style="position: relative; top: 14pt;"><a name="PearlNecklaceModel"></a><img src="img/pearl_eq6.gif" alt="" />,</span></p>
-<p><span style="position: relative; top: 14pt;"><a name="PearlNecklaceModel"></a>and</span></p>
-<p style="text-align: center;" align="center"><span style="position: relative; top: 14pt;"><a name="PearlNecklaceModel"></a><img src="img/pearl_eq7.gif" alt="" />.</span></p>
-<p>&nbsp;</p>
-<p><a name="PearlNecklaceModel"></a>where the mass mi &nbsp;is (sld(of i) &ndash; sld(of solvent)) * (volume of the N pearls/rods), V is the total volume of the necklace.</p>
-<p><a name="PearlNecklaceModel"></a>The 2D scattering intensity is the same as P(q) above, regardless of the orientation of the q vector.</p>
-<p><a name="PearlNecklaceModel"></a>The returned value is scaled to units of [cm-1] and the parameters are the following:</p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 19.25pt;">
-<td style="border: 1pt solid width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; vertical-align: top; width: 107pt; height: 19.25pt;">
-<p>scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>None</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>1.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>radius</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>80.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>edge_separation</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>350.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>num_pearls</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>(integer)</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>3</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>sld_pearl</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>1e-6</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>sld_solv</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>6.3e-6</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>sld_string</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>1e-6</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>thick_string</p>
-<p>(=rod diameter)</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>2.5</p>
-</td>
-</tr>
-<tr style="height: 20pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 20pt;" valign="top" width="143">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 20pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 20pt;" valign="top" width="143">
-<p>0.0</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="text-align: center;" align="center"><a name="PearlNecklaceModel"></a>&nbsp;</p>
-<p style="text-align: center;" align="center"><a name="PearlNecklaceModel"></a><img src="img/pearl_plot.jpg" alt="" /></p>
-<p><a name="PearlNecklaceModel"></a>REFERENCE</p>
-<p><a name="PearlNecklaceModel"></a>R. Schweins and K. Huber, &lsquo;Particle Scattering Factor of Pearl Necklace Chains&rsquo;, Macromol. Symp., 211, 25-42, 2004.</p>
-<p><a name="PearlNecklaceModel"></a>&nbsp;</p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><a name="PearlNecklaceModel"></a><b><span style="font-size: 14pt;">2.14.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="CylinderModel"></a><b><span style="font-size: 14pt;">Cylinder Model (Magnetic 2D Model)</span></b></p>
-<p>This model provides the form factor for a right circular cylinder with uniform scattering length density. The form factor is normalized by the particle volume.</p>
-For magnetic scattering, please see the '<a href="polar_mag_help.html">Polarization/Magnetic Scattering</a>' in Fitting Help.
-<p style="margin-left: 0.85in; text-indent: -0.35in;"><b>1.1.</b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp; </span>Definition</b></p>
-<p>The output of the 2D scattering intensity function for oriented cylinders is given by (Guinier, 1955):</p>
-<p style="text-align: center;" align="center"><span style="position: relative; top: 12pt;"><img src="img/image059.PNG" alt="" /></span>&nbsp;</p>
-<p style="text-align: center;" align="center"><span style="position: relative; top: 14pt;"><img src="img/image060.PNG" alt="" /></span>&nbsp;&nbsp;</p>
-<p>where <span style="font-family: 'Arial','sans-serif';">&alpha;</span> is the angle between the axis of the cylinder and the q-vector, V is the volume of the cylinder, L is the length of the cylinder, r is the radius of the cylinder, and <em><span style="font-family: 'Arial','sans-serif';">&Delta;</span>&rho;</em> (contrast) is the scattering length density difference between the scatterer and the solvent. J1 is the first order Bessel function.</p>
-<p>To provide easy access to the orientation of the cylinder, we define the axis of the cylinder using two angles theta and phi. Those angles are defined on Figure 2.</p>
-<p style="text-align: center; page-break-after: avoid;" align="center"><img src="img/image061.jpg" /></p>
-<p style="text-align: center;" align="center"><a name="_Ref173213915"></a><a name="_Ref173306040"></a>Figure 2. Definition of the angles for oriented cylinders.</p>
-
-<p style="text-align: center;" align="center"><img src="img/image062.jpg" alt="" width="379" height="256" /></p>
-<p style="text-align: center;" align="center">Figure. Examples of the angles for oriented pp against the detector plane.</p>
-
-
-<p>For P*S: The 2nd virial coefficient of the cylinder is calculate based on the radius and length values, and used as the effective radius toward S(Q) when P(Q)*S(Q) is applied.</p>
-<p>The returned value is scaled to units of [cm-1] and the parameters of the cylinder model are the following:</p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 19.85pt;">
-<td style="border: 1pt solid vertical-align: top; width: 107pt; height: 19.85pt;">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.85pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.85pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 19.85pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.85pt;" valign="top" width="143">
-<p>scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.85pt;" valign="top" width="143">
-<p>None</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.85pt;" valign="top" width="143">
-<p>1.0</p>
-</td>
-</tr>
-<tr style="height: 19.85pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.85pt;" valign="top" width="143">
-<p>radius</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.85pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.85pt;" valign="top" width="143">
-<p>20.0</p>
-</td>
-</tr>
-<tr style="height: 19.85pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.85pt;" valign="top" width="143">
-<p>length</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.85pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.85pt;" valign="top" width="143">
-<p>400.0</p>
-</td>
-</tr>
-<tr style="height: 19.85pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.85pt;" valign="top" width="143">
-<p>contrast</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.85pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.85pt;" valign="top" width="143">
-<p>3.0e-6</p>
-</td>
-</tr>
-<tr style="height: 19.85pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.85pt;" valign="top" width="143">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.85pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.85pt;" valign="top" width="143">
-<p>0.0</p>
-</td>
-</tr>
-<tr style="height: 19.85pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.85pt;" valign="top" width="143">
-<p>cyl_theta</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.85pt;" valign="top" width="143">
-<p>degree</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.85pt;" valign="top" width="143">
-<p>60</p>
-</td>
-</tr>
-<tr style="height: 20.6pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 20.6pt;" valign="top" width="143">
-<p>cyl_phi</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 20.6pt;" valign="top" width="143">
-<p>degree</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 20.6pt;" valign="top" width="143">
-<p>60</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p>The output of the 1D scattering intensity function for randomly oriented cylinders is then given by:</p>
-<p style="text-align: center;" align="center"><a name="_Ref173306528"></a><a name="_Ref173306479"></a><span style="position: relative; top: 16pt;"><img src="img/image063.PNG" alt="" /></span>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</p>
-<p>The <em>cyl_theta</em> and <em>cyl_phi</em> parameter are not used for the 1D output. Our implementation of the scattering kernel and the 1D scattering intensity use the c-library from NIST.</p>
-<p style="margin-left: 0.85in; text-indent: -0.35in;"><b>2.1.</b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp; </span>Validation of the cylinder model</b></p>
-<p>Validation of our code was done by comparing the output of the 1D model to the output of the software provided by the NIST (Kline, 2006). Figure 3 shows a comparison of the 1D output of our model and the output of the NIST software.</p>
-<p>In general, averaging over a distribution of orientations is done by evaluating the following:</p>
-<p style="text-align: center;" align="center"><span style="position: relative; top: 16pt;"><img src="img/image064.PNG" alt="" /></span>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</p>
-<p>where <em>p(&theta;,</em><em><span style="font-family: 'Arial','sans-serif';">&phi;</span>)</em> is the probability distribution for the orientation and <em>P0(q,</em><em><span style="font-family: 'Arial','sans-serif';">&alpha;</span>)</em> is the scattering intensity for the fully oriented system. Since we have no other software to compare the implementation of the intensity for fully oriented cylinders, we can compare the result of averaging our 2D output using a uniform distribution <em>p(&theta;,</em><em><span style="font-family: 'Arial','sans-serif';">&phi;</span>)</em> = 1.0.&nbsp; Figure 4 shows the result of such a cross-check.</p>
-<p style="text-align: center; page-break-after: avoid;" align="center"><img src="img/image065.jpg" alt="cylinder_1D_validation" width="573" height="315" /></p>
-<p style="text-align: center; page-break-after: avoid;" align="center">&nbsp;</p>
-<p><a name="_Ref173211066"></a><a name="_Ref173211049"></a>Figure 3: Comparison of the DANSE scattering intensity for a cylinder with the output of the NIST SANS analysis software. The parameters were set to: Scale=1.0, Radius=20 &Aring;, Length=400 &Aring;, Contrast=3e-6 &Aring; -2, and Background=0.01 cm -1.</p>
-<p>&nbsp;</p>
-<p style="text-align: center; page-break-after: avoid;" align="center"><img src="img/image066.jpg" alt="cylinder_2D_average" width="573" height="315" /></p>
-<p style="text-align: center; page-break-after: avoid;" align="center">&nbsp;</p>
-<p><a name="_Ref173213305"></a>Figure 4: Comparison of the intensity for uniformly distributed cylinders calculated from our 2D model and the intensity from the NIST SANS analysis software. The parameters used were: Scale=1.0, Radius=20 &Aring;, Length=400 &Aring;, Contrast=3e-6 &Aring; -2, and Background=0.0 cm -1.</p>
-<p>&nbsp;</p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.15.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="CoreShellCylinderModel"></a><b><span style="font-size: 14pt;">Core-Shell Cylinder Model</span></b></p>
-<p>This model provides the form factor for a circular cylinder with a core-shell scattering length density profile. The form factor is normalized by the particle volume.</p>
-<p style="margin-left: 0.85in; text-indent: -0.35in;"><b>1.1.</b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp; </span>Definition</b></p>
-<p>The output of the 2D scattering intensity function for oriented core-shell cylinders is given by (Kline, 2006):</p>
-<p style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="img/image067.PNG" alt="" /></span>&nbsp;</p>
-<p style="text-align: center;" align="center"><span style="position: relative; top: 32pt;"><img src="img/image068.PNG" alt="" /></span>&nbsp;</p>
-<p style="text-align: center;" align="center"><span style="position: relative; top: 32pt;"><img src="img/image239.PNG" alt="" /></span>&nbsp;</p>
-<p>where <span style="font-family: 'Arial','sans-serif';">&alpha;</span> is the angle between the axis of the cylinder and the q-vector, <em>Vs</em> is the volume of the outer shell (i.e. the total volume, including the shell), <em>Vc</em> is the volume of the core, <em>L</em> is the length of the core, <em>r</em> is the radius of the core, <em>t</em> is the thickness of the shell, <em>&rho;c</em> is the scattering length density of the core, <em>&rho;s</em> is the scattering length density of the shell, &rho;solv is the scattering length density of the solvent, and <em>bkg</em> is the background level. The outer radius of the shell is given by <em>r+t</em> and the total length of the outer shell is given by <em>L+2t</em>. J1 is the first order Bessel function.</p>
-<p style="text-align: center;" align="center"><img src="img/image069.jpg" alt="" width="449" height="230" /></p>
-<p>To provide easy access to the orientation of the core-shell cylinder, we define the axis of the cylinder using two angles &theta; and <span style="font-family: 'Arial','sans-serif';">&phi;</span>. Similarly to the case of the cylinder, those angles are defined on Figure 2 in Cylinder Model.</p>
-<p>For P*S: The 2nd virial coefficient of the solid cylinder is calculate based on the (radius+thickness) and 2(length +thickness) values, and used as the effective radius toward S(Q) when P(Q)*S(Q) is applied.</p>
-<p>The returned value is scaled to units of [cm-1] and the parameters of the core-shell cylinder model are the following:</p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 19.25pt;">
-<td style="border: 1pt solid width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>None</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>1.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>radius</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>20.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>thickness</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>10.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>length</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>400.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; vertical-align: top; width: 107pt; height: 19.25pt;">
-<p>core_sld</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>1e-6</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>shell_sld</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>4e-6</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>solvent_sld</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>1e-6</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>axis_theta</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>degree</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>90</p>
-</td>
-</tr>
-<tr style="height: 20pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 20pt;" valign="top" width="143">
-<p>axis_phi</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 20pt;" valign="top" width="143">
-<p>degree</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 20pt;" valign="top" width="143">
-<p>0.0</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p>The output of the 1D scattering intensity function for randomly oriented cylinders is then given by the equation above.</p>
-<p>The <em>axis_theta</em> and axis<em>_phi</em> parameters are not used for the 1D output. Our implementation of the scattering kernel and the 1D scattering intensity use the c-library from NIST.</p>
-<p style="margin-left: 0.85in; text-indent: -0.35in;"><b>2.1.</b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp; </span>Validation of the core-shell cylinder model</b></p>
-<p>Validation of our code was done by comparing the output of the 1D model to the output of the software provided by the NIST (Kline, 2006). Figure 8 shows a comparison of the 1D output of our model and the output of the NIST software.</p>
-<p>Averaging over a distribution of orientation is done by evaluating the equation above. Since we have no other software to compare the implementation of the intensity for fully oriented core-shell cylinders, we can compare the result of averaging our 2D output using a uniform distribution <em>p(&theta;,</em><em><span style="font-family: 'Arial','sans-serif';">&phi;</span>)</em> = 1.0.&nbsp; Figure 9 shows the result of such a cross-check.</p>
-<p style="text-align: center; page-break-after: avoid;" align="center"><img src="img/image070.jpg" alt="core_shell_cylinder_1D_validation" width="573" height="315" /></p>
-<p style="text-align: center; page-break-after: avoid;" align="center">&nbsp;</p>
-<p><a name="_Ref173307149"></a>Figure 8: Comparison of the DANSE scattering intensity for a core-shell cylinder with the output of the NIST SANS analysis software. The parameters were set to: Scale=1.0, Radius=20 &Aring;, Thickness=10 &Aring;, Length=400 &Aring;, Core_sld=1e-6 &Aring; -2, Shell_sld=4e-6 &Aring; -2, Solvent_sld=1e-6 &Aring; -2, and Background=0.01 cm -1.</p>
-<p>&nbsp;</p>
-<p style="text-align: center; page-break-after: avoid;" align="center"><img id="Picture 23" src="img/image071.jpg" alt="core_shell_cylinder_2D_average" width="573" height="315" /></p>
-<p style="text-align: center; page-break-after: avoid;" align="center">&nbsp;</p>
-<p><a name="_Ref173307204"></a>Figure 9: Comparison of the intensity for uniformly distributed core-shell cylinders calculated from our 2D model and the intensity from the NIST SANS analysis software. The parameters used were: Scale=1.0, Radius=20 &Aring;, Thickness=10 &Aring;, Length=400 &Aring;, Core_sld=1e-6 &Aring; -2, Shell_sld=4e-6 &Aring; -2, Solvent_sld=1e-6 &Aring; -2, and Background=0.0 cm -1.</p>
-
-<p style="text-align: center; page-break-after: avoid;" align="center"><img src="img/image061.jpg" /></p>
-<p style="text-align: center;" align="center"><a name="_Ref173213915"></a><a name="_Ref173306040"></a>Figure. Definition of the angles for oriented core-shell cylinders.</p>
-<p style="text-align: center;" align="center"><img src="img/image062.jpg" alt="" width="379" height="256" /></p>
-<p style="text-align: center;" align="center">Figure. Examples of the angles for oriented pp against the detector plane.</p>
-
-
-<p style="margin-left: 0.25in;"><i>2013/11/26 - Description reviewed by Heenan, R.</i></p>
-
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.16.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="CoreShellBicelleModel"></a><b><span style="font-size: 14pt;">Core-Shell (Cylinder) Bicelle Model</span></b></p>
-<p>This model provides the form factor for a circular cylinder with a core-shell scattering length density profile. The form factor is normalized by the particle volume. This model is a more general case of <a href="#CoreShellCylinderModel">core-shell cylinder model </a> (see&nbsp;above and reference below) in that the parameters of the shell are separated into a face-shell and a rim-shell so that users can set different values of the thicknesses and slds.&nbsp;</p>
-<p>&nbsp;</p>
-<p>The returned value is scaled to units of [cm-1] and the parameters of the core-shell cylinder model are the following:</p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 19.25pt;">
-<td style="border: 1pt solid width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>None</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>1.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>radius</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>20.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>rim_thick</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>10.0</p>
-</td>
-</tr>
-<tr>
-<td>face_thick</td>
-<td>&Aring;</td>
-<td>10.0</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>length</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>400.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; vertical-align: top; width: 107pt; height: 19.25pt;">
-<p>core_sld</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>1e-6</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>rim_sld</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>4e-6</p>
-</td>
-</tr>
-<tr>
-<td>face_sld</td>
-<td>&Aring; -2</td>
-<td>4e-6</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>solvent_sld</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>1e-6</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>axis_theta</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>degree</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>90</p>
-</td>
-</tr>
-<tr style="height: 20pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 20pt;" valign="top" width="143">
-<p>axis_phi</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 20pt;" valign="top" width="143">
-<p>degree</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 20pt;" valign="top" width="143">
-<p>0.0</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p>The output of the 1D scattering intensity function for randomly oriented cylinders is then given by the equation above.</p>
-<p>The <em>axis_theta</em> and axis<em>_phi</em> parameters are not used for the 1D output. Our implementation of the scattering kernel and the 1D scattering intensity use the c-library from NIST.</p>
-<p>&nbsp;</p>
-<p style="text-align: center;" align="center"><img id="cscylbicelle" style="width: 512px; height: 377px;" src="img/cscylbicelle_pic.jpg" alt="" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot using the default values (w/200 data point).</b></p>
-
-
-<p style="text-align: center; page-break-after: avoid;" align="center"><img src="img/image061.jpg" /></p>
-<p style="text-align: center;" align="center"><a name="_Ref173213915"></a><a name="_Ref173306040"></a>Figure. Definition of the angles for the 
-oriented Core-Shell Cylinder Bicelle Model.</p>
-<p style="text-align: center;" align="center"><img src="img/image062.jpg" alt="" width="379" height="256" /></p>
-<p style="text-align: center;" align="center">Figure. Examples of the angles for oriented pp against the detector plane.</p>
-
-
-<p>&nbsp;REFERENCE<br /> Feigin, L. A, and D. I. Svergun, "Structure Analysis by Small-Angle X-Ray and Neutron Scattering", Plenum Press, New York, (1987).</p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.17.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="HollowCylinderModel"></a><b><span style="font-size: 14pt;">HollowCylinderModel</span></b></p>
-<p>This model provides the form factor, P(<em>q</em>), for a monodisperse hollow right angle circular cylinder (tube) where the form factor is normalized by the volume of the tube:</p>
-<p>P(q) = scale*&lt;f^2&gt;/Vshell+background where the averaging &lt; &gt; id applied only for the 1D calculation. &nbsp;The inside and outside of the hollow cylinder have the same SLD.</p>
-<p>The 1D scattering intensity is calculated in the following way (Guinier, 1955):</p>
-<p style="text-align: center;" align="center"><img src="img/image072.PNG" alt="" /></p>
-<p>&nbsp;</p>
-<p>where <em>scale</em> is a scale factor, <em>J1</em> is the 1st order Bessel function, <em>J1</em> (x)= (sin<em>x </em>- <em>x</em>cos<em>x</em>)/<em>x</em>2.</p>
-<p style="text-align: center;" align="center"><img src="img/image073.jpg" alt="" width="468" height="259" /></p>
-<p>To provide easy access to the orientation of the core-shell cylinder, we define the axis of the cylinder using two angles &theta; and <span style="font-family: 'Arial','sans-serif';">&phi;</span>. Similarly to the case of the cylinder, those angles are defined on Figure 2 in Cylinder Model.</p>
-<p>For P*S: The 2nd virial coefficient of the solid cylinder is calculate based on the (radius) and 2(length) values, and used as the effective radius toward S(Q) when P(Q)*S(Q) is applied.</p>
-<p>In the parameters, the &lsquo;contrast&rsquo; represents SLD (shell) - SLD (solvent) and the radius = Rhell while core_radius = Rcore.</p>
-<p>&nbsp;</p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 18.8pt;">
-<td style="border: 1pt solid vertical-align: top; width: 107pt; height: 18.8pt;">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>None</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>1.0</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>radius</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>30</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>length</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>400</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>core_radius</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>20</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sldCyl</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>6.3e-6</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sldSolv</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>5e-06</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>0.01</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="text-align: center;" align="center"><img id="Picture 220" src="img/image074.jpg" alt="" width="468" height="344" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot using the default values (w/1000 data point).</b></p>
-<p>Our model uses the form factor calculations implemented in a c-library provided by the NIST Center for Neutron Research (Kline, 2006).</p>
-
-<p style="text-align: center; page-break-after: avoid;" align="center"><img src="img/image061.jpg" /></p>
-<p style="text-align: center;" align="center"><a name="_Ref173213915"></a><a name="_Ref173306040"></a>Figure. Definition of the angles for the 
-oriented HollowCylinderModel.</p>
-<p style="text-align: center;" align="center"><img src="img/image062.jpg" alt="" width="379" height="256" /></p>
-<p style="text-align: center;" align="center">Figure. Examples of the angles for oriented pp against the detector plane.</p>
-
-<p>REFERENCE</p>
-<p>Feigin, L. A, and D. I. Svergun, "Structure Analysis by Small-Angle X-Ray and Neutron Scattering", Plenum Press, New York, (1987).</p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.18.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="FlexibleCylinderModel"></a><b><span style="font-size: 14pt;">FlexibleCylinderModel</span></b></p>
-<p>This model provides the form factor, P(<em>q</em>), for a flexible cylinder where the form factor is normalized by the volume of the cylinder: Inter-cylinder interactions are NOT included. P(q) = scale*&lt;f^2&gt;/V+background where the averaging &lt; &gt;&nbsp; is applied over all orientation for 1D. &nbsp;The 2D scattering intensity is the same as 1D, regardless of the orientation of the <em>q</em> vector which is defined as<span style="font-size: 12pt; font-family: 'Times New Roman','serif'; position: relative; top: 4.5pt;"><img src="img/image040.gif" alt="" width="111" height="23" /></span><span style="font-size: 14pt;">. </span></p>
-<p style="text-align: center;" align="center"><img id="Picture 35" src="img/image075.jpg" alt="" width="411" height="187" /></p>
-<p>The chain of contour length, L, (the total length) can be described a chain of some number of locally stiff segments of length lp. The persistence length,lp, is the length along the cylinder over which the flexible cylinder can be considered a rigid rod. The Kuhn length (b = 2*lp) is also used to describe the stiffness of a chain. The returned value is in units of [cm-1], on absolute scale. In the parameters, the sldCyl and sldSolv&nbsp; represent SLD (chain/cylinder) &nbsp;and SLD (solvent) respectively.</p>
-<p>&nbsp;</p>
-<p>&nbsp;</p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 18.8pt;">
-<td style="border: 1pt solid vertical-align: top; width: 107pt; height: 18.8pt;">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>None</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>1.0</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>radius</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>20</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>length</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>1000</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sldCyl</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>1e-06</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sldSolv</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>6.3e-06</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>0.01</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>kuhn_length</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>100</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="text-align: center;" align="center"><img id="Picture 228" src="img/image076.jpg" alt="" width="465" height="345" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot using the default values (w/1000 data point).</b></p>
-
-<p>Our model uses the form factor calculations implemented in a c-library provided by the NIST Center for Neutron Research (Kline, 2006):</p>
-<p>From the reference, "Method 3 With Excluded Volume" is used. The model is a parametrization of simulations of a discrete representation of the worm-like chain model of Kratky and Porod applied in the pseudocontinuous limit.&nbsp; See equations (13,26-27) in the original reference for the details.</p>
-<p>REFERENCE</p>
-<p>Pedersen, J. S. and P. Schurtenberger (1996). &ldquo;Scattering functions of semiflexible polymers with and without excluded volume effects.&rdquo; Macromolecules 29: 7602-7612.</p>
-<p>Correction of the formula can be found in:</p>
-<p>Wei-Ren Chen, Paul D. Butler, and Linda J. Magid, "Incorporating Intermicellar Interactions in the Fitting of SANS Data from Cationic Wormlike Micelles" Langmuir, August 2006.</p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.19.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b><span style="font-size: 14pt;">FlexCylEllipXMo<a name="FlexCylEllipXModel"></a>del</span></b></p>
-<p><b>Flexible Cylinder with Elliptical Cross-Section: &nbsp;</b>Calculates the form factor for a flexible cylinder with an elliptical cross section and a uniform scattering length density. The non-negligible diameter of the cylinder is included by accounting for excluded volume interactions within the walk of a single cylinder. The form factor is normalized by the particle volume such that P(q) = scale*&lt;f^2&gt;/Vol + bkg, where &lt; &gt; is an average over all possible orientations of the flexible cylinder.</p>
-<p style="margin-left: 0.85in; text-indent: -0.35in;"><b>1.1.</b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp; </span>Definition</b></p>
-<p>The function calculated is from the reference given below. From that paper, "Method 3 With Excluded Volume" is used. The model is a parameterization of simulations of a discrete representation of the worm-like chain model of Kratky and Porod applied in the pseudo-continuous limit.&nbsp; See equations (13, 26-27) in the original reference for the details.</p>
-<p>NOTE: there are several typos in the original reference that have been corrected by WRC. Details of the corrections are in the reference below.</p>
-<p>&nbsp;- Equation (13): the term (1-w(QR)) should swap position with w(QR)</p>
-<p>&nbsp;- Equations (23) and (24) are incorrect. WRC has entered these into Mathematica and solved analytically. The results were converted to code.</p>
-<p>&nbsp;- Equation (27) should be q0 = max(a3/sqrt(RgSquare),3) instead of max(a3*b/sqrt(RgSquare),3)</p>
-<p>&nbsp;- The scattering function is negative for a range of parameter values and q-values that are experimentally accessible. A correction function has been added to give the proper behavior.</p>
-<p style="text-align: center;" align="center"><img src="img/image077.jpg" alt="" width="484" height="209" /></p>
-<p>The chain of contour length, L, (the total length) can be described a chain of some number of locally stiff segments of length lp. The persistence length, lp, is the length along the cylinder over which the flexible cylinder can be considered a rigid rod. The Kuhn length (b) used in the model is also used to describe the stiffness of a chain, and is simply b = 2*lp.</p>
-<p>The cross section of the cylinder is elliptical, with minor radius a. The major radius is larger, so of course, the axis ratio (parameter 4) must be greater than one. Simple constraints should be applied during curve fitting to maintain this inequality.</p>
-<p>The returned value is in units of [cm-1], on absolute scale.</p>
-<p>The sldCyl&nbsp; = SLD (chain), sldSolv = SLD (solvent). The &lsquo;scale&rsquo;, and the contrast are both multiplicative factors in the model and are perfectly correlated. One or both of these parameters must be held fixed during model fitting.</p>
-<p>If the &lsquo;scale&rsquo; is set equal to the particle volume fraction, <span style="font-family: Symbol;">f</span>, the returned value is the scattered intensity per unit volume, I(q) = <span style="font-family: Symbol;">f</span>*P(q). However, no inter-particle interference effects are included in this calculation.</p>
-<p>For 2D data: The 2D scattering intensity is calculated in the same way as 1D, where the <em>q</em> vector is defined as<span style="font-size: 14pt; position: relative; top: 8pt;"><img src="img/image008.PNG" alt="" /></span><span style="font-size: 14pt;">.</span></p>
-<p>REFERENCE</p>
-<p>Pedersen, J. S. and P. Schurtenberger (1996). &ldquo;Scattering functions of semiflexible polymers with and without excluded volume effects.&rdquo; Macromolecules 29: 7602-7612.</p>
-<p>Corrections are in:</p>
-<p>Wei-Ren Chen, Paul D. Butler, and Linda J. Magid, "Incorporating Intermicellar Interactions in the Fitting of SANS Data from Cationic Wormlike Micelles" Langmuir, August 2006.</p>
-<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</p>
-<p>TEST DATASET</p>
-<p>This example dataset is produced by running the Macro FlexCylEllipXModel, using 200 data points, qmin = 0.001 &Aring;-1,&nbsp; qmax = 0.7 &Aring;-1 and the default values below.</p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 18.8pt;">
-<td style="border: 1pt solid width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>axis_ratio</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>1.5</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; vertical-align: top; width: 107pt; height: 18.8pt;">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>0.0001</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Kuhn_length</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>100</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>(Contour) length</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>1e+3</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>radius</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>20.0</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>1.0</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sldCyl</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>1e-6</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sldSolv</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>6.3e-6</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="text-align: center;" align="center"><img src="img/image078.jpg" alt="" width="440" height="300" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot using the default values (w/200 data points).</b></p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.20.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="StackedDisksModel"></a><b><span style="font-size: 14pt;">StackedDisksModel </span></b></p>
-<p>This model provides the form factor, P(<em>q</em>), for stacked discs (tactoids) with a core/layer structure where the form factor is normalized by the volume of the cylinder. &nbsp;Assuming the next neighbor distance (d-spacing) in a stack of parallel discs obeys a Gaussian distribution, a structure factor S(q) proposed by Kratky and Porod in 1949 is used in this function. Note that the resolution smearing calculation uses 76 Gauss quadrature points to properly smear the model since the function is HIGHLY oscillatory, especially around the q-values that correspond to the repeat distance of the layers.</p>
-<p>The 2D scattering intensity is the same as 1D, regardless of the orientation of the <em>q</em> vector which is defined as<span style="font-size: 14pt; position: relative; top: 8pt;"><img src="img/image008.PNG" alt="" /></span><span style="font-size: 14pt;">.</span></p>
-<p><span style="font-size: 14pt;">&nbsp;</span></p>
-<p style="text-align: center;" align="center">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<img id="Picture 36" src="img/image079.gif" alt="" width="214" height="93" /></p>
-<p style="text-align: center;" align="center"><img id="Picture 37" src="img/image080.gif" alt="" width="173" height="136" /></p>
-<p>The returned value is in units of [cm-1 sr-1], on absolute scale.</p>
-<p>The scattering intensity I(q) is:</p>
-<p style="text-align: center;" align="center"><span style="position: relative; top: 9pt;"><img src="img/image081.PNG" alt="" /></span></p>
-<p>where the contrast,</p>
-<p style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="img/image082.PNG" alt="" /></span></p>
-<p>N is the number of discs per unit volume, <span style="font-family: Symbol;">a</span>&nbsp;is the angle between the axis of the disc and q, and Vt and Vc are the total volume and the core volume of a single disc, respectively.</p>
-<p style="text-align: center;" align="center"><img src="img/image083.PNG" alt="" /></p>
-<p>&nbsp;</p>
-<p>&nbsp;</p>
-<p>where d = thickness of the layer (layer_thick), 2h= core thickness (core_thick),&nbsp; and R = radius of the disc (radius).</p>
-<p style="text-align: center;" align="center"><span style="position: relative; top: 14pt;"><img src="img/image084.PNG" alt="" /></span></p>
-<p>where n = the total number of the disc stacked (n_stacking), D=the next neighbor center to cent distance (d-spacing), and <span style="font-family: Symbol;">s</span>D&nbsp;= the Gaussian standard deviation of the d-spacing (sigma_d).</p>
-<p>To provide easy access to the orientation of the stackeddisks, we define the axis of the cylinder using two angles &theta; and <span style="font-family: 'Arial','sans-serif';">&phi;</span>. Similarly to the case of the cylinder, those angles are defined on Figure 2 of CylinderModel.</p>
-<p>&nbsp;For P*S: The 2nd virial coefficient of the solid cylinder is calculate based on the (radius) and length = n_stacking*(core_thick +2*layer_thick) values, and used as the effective radius toward S(Q) when P(Q)*S(Q) is applied.</p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 18.8pt;">
-<td style="border: 1pt solid width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>0.001</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>core_sld</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>4e-006</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>core_thick</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>10</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>layer_sld</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>0</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>layer_thick</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>15</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>n_stacking</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>1</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; vertical-align: top; width: 107pt; height: 18.8pt;">
-<p>radius</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>3e+003</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>0.01</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sigma_d</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>0</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>solvent_sld</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>5e-006</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="text-align: center;" align="center"><img src="img/image085.jpg" alt="" width="451" height="334" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot using the default values (w/1000 data point).</b></p>
-<p style="text-align: center;" align="center"><img id="Picture 101" src="img/image086.jpg"  /></p>
-<p style="text-align: center;" align="center">Figure. Examples of the angles for oriented stackeddisks against the detector plane.</p>
-
-<p style="text-align: center;" align="center"><img src="img/image062.jpg" alt="" width="379" height="256" /></p>
-<p style="text-align: center;" align="center">Figure. Examples of the angles for oriented pp against the detector plane.</p>
-
-
-<p>Our model uses the form factor calculations implemented in a c-library provided by the NIST Center for Neutron Research (Kline, 2006):</p>
-<p>REFERENCE</p>
-<p>Guinier, A. and Fournet, G., "Small-Angle Scattering of X-Rays", John Wiley and Sons, New York, 1955.</p>
-<p>Kratky, O. and Porod, G., J. Colloid Science, 4, 35, 1949.</p>
-<p>Higgins, J.S. and Benoit, H.C., "Polymers and Neutron Scattering", Clarendon, Oxford, 1994.</p>
-
-
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.21.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="EllipticalCylinderModel"></a><b><span style="font-size: 14pt;">Elliptical Cylinder Model</span></b></p>
-<p>This function calculates the scattering from an oriented elliptical cylinder.</p>
-<p><b>For 2D (orientated system):</b></p>
-<p>The angles theta and phi define the orientation of the axis of the cylinder. The angle psi is defined as the orientation of the major axis of the ellipse with respect to the vector Q. A gaussian poydispersity can be added to any of the orientation angles, and also for the minor radius and the ratio of the ellipse radii.</p>
-<p style="text-align: center;" align="center"><img id="Picture 40" src="img/image098.gif" alt="" width="352" height="172" /></p>
-<p style="text-align: center;" align="center"><b>Figure. a= r_minor and </b><b><span style="font-family: Symbol;">n</span>= r_ratio (i.e., r_major/r_minor).</b></p>
-<p>The function calculated is:</p>
-<p style="text-align: center;" align="center"><span style="position: relative; top: 16pt;"><img src="img/image099.PNG" alt="" /></span>&nbsp;</p>
-<p>with the functions:</p>
-<p>&nbsp;</p>
-<p style="text-align: center;" align="center"><img src="img/image100.PNG" alt="" /></p>
-<p>&nbsp;</p>
-<p>and the angle psi is defined as the orientation of the major axis of the ellipse with respect to the vector Q.</p>
-<p><b>For 1D (no preferred orientation):</b></p>
-<p>The form factor is averaged over all possible orientation before normalized by the particle volume: P(q) = scale*&lt;f^2&gt;/V .</p>
-<p>The returned value is scaled to units of [cm-1].</p>
-<p>To provide easy access to the orientation of the elliptical, we define the axis of the cylinder using two angles &theta; , <span style="font-family: 'Arial','sans-serif';">&phi; </span>and<span style="font-family: Symbol;">Y</span>. Similarly to the case of the cylinder, those angles, &theta; &nbsp;and <span style="font-family: 'Arial','sans-serif';">&phi;,</span> are defined on Figure 2 of CylinderModel. The angle <span style="font-family: Symbol;">Y </span>is the rotational angle around its own long_c axis against the q plane. For example, <span style="font-family: Symbol;">Y </span>= 0 when the r_minor axis is parallel to the x-axis of the detector.</p>
-<p>All angle parameters are valid and given only for 2D calculation (Oriented system).</p>
-<p style="text-align: center;" align="center"><img id="Picture 105" src="img/image101.jpg" /></p>
-<p style="text-align: center;" align="center"><b>Figure. Definition of angels for 2D</b>.</p>
-<p style="text-align: center;" align="center"><img id="Picture 114" src="img/image062.jpg" alt="" width="379" height="256" /></p>
-<p style="text-align: center;" align="center"><span style="font-size: 12pt;">Figure. Examples of the angles for oriented elliptical cylinders </span></p>
-<p style="text-align: center;" align="center"><span style="font-size: 12pt;">against the detector plane.</span></p>
-<p><b>For P*S</b>: The 2nd virial coefficient of the solid cylinder is calculate based on the averaged radius (=sqrt(r_minor^2*r_ratio))&nbsp; and length values, and used as the effective radius toward S(Q) when P(Q)*S(Q) is applied.</p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 19.25pt;">
-<td style="border: 1pt solid width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>None</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>1.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; vertical-align: top; width: 107pt; height: 19.25pt;">
-<p>r_minor</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>20.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>r_ratio</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>1.5</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>length</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>400.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>sldCyl</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>4e-6</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>sldSolv</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>1e-006</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="text-align: center;" align="center"><img id="Picture 503" src="img/image102.jpg" alt="" width="443" height="328" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot using the default values (w/1000 data point).</b></p>
-<p style="margin-left: 1.35in; text-indent: -0.25in;"><span style="font-family: Symbol;">&middot;</span><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><b>Validation of the elliptical cylinder 2D model</b></p>
-<p>Validation of our code was done by comparing the output of the 1D calculation to the angular average of the output of 2 D calculation over all possible angles. The Figure below shows the comparison where the solid dot refers to averaged 2D while the line represents the result of 1D calculation (for 2D averaging, 76, 180, 76 points are taken for the angles of theta, phi, and psi respectively).</p>
-<p style="text-align: center;" align="center"><img id="Picture 106" src="img/image103.gif" alt="" width="448" height="278" /></p>
-<p style="text-align: center;" align="center"><b>Figure. Comparison between 1D and averaged 2D.</b></p>
-<p><b>&nbsp;</b></p>
-<p>In the 2D average, more binning in the angle phi is necessary to get the proper result. The following figure shows the results of the averaging by varying the number of bin over angles.</p>
-<p style="text-align: center;" align="center"><img id="Picture 107" src="img/image104.gif" alt="" width="409" height="303" /></p>
-<p style="text-align: center;" align="center"><b>Figure. The intensities averaged from 2D over different number </b></p>
-<p style="text-align: center;" align="center"><b>of points of binning of angles.</b></p>
-<p>REFERENCE</p>
-<p style="text-indent: 0.25in;">L. A. Feigin and D. I. Svergun &ldquo;Structure Analysis by Small-Angle X-Ray and Neutron Scattering&rdquo;, Plenum, New York, (1987).</p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.22.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="BarBellModel"></a><b><span style="font-size: 14pt;">BarBell(/DumBell)Model</span></b></p>
-<p>Calculates the scattering from a barbell-shaped cylinder (This model simply becomes the DumBellModel when the length of the cylinder, L, is set to zero). That is, a sphereocylinder with spherical end caps that have a radius larger than that of the cylinder and the center of the end cap radius lies outside of the cylinder All dimensions of the barbell are considered to be monodisperse. See the diagram for the details of the geometry and restrictions on parameter values.&nbsp;</p>
-<p style="margin-left: 0.85in; text-indent: -0.35in;"><b>1.1.</b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp; </span>Definition</b></p>
-<p>The returned value is scaled to units of [cm-1sr-1], absolute scale.</p>
-<p>The barbell geometry is defined as:</p>
-<p style="text-align: center;" align="center"><img src="img/image105.jpg" alt="" width="519" height="181" /></p>
-<p>r is the radius of the cylinder. All other parameters are as defined in the diagram. Since the end cap radius R &gt;= r and by definition for this geometry h &gt; 0,&nbsp; h is then defined by r and R as:</p>
-<p>h = sqrt(R^2 - r^2).</p>
-<p>The scattering intensity I(q) is calculated as:</p>
-<p style="text-align: center;" align="center"><span style="position: relative; top: 12pt;"><img src="img/image106.PNG" alt="" /></span></p>
-<p>where the amplitude A(q) is given as:</p>
-<p>&nbsp;</p>
-<p style="text-align: center;" align="center"><img src="img/image107.PNG" alt="" /></p>
-<p>&nbsp;</p>
-<p>The &lt; &gt; brackets denote an average of the structure over all orientations. &lt;A^2(q)&gt; is then the form factor, P(q). The scale factor is equivalent to the volume fraction of cylinders, each of volume, V. Contrast is the difference of scattering length densities of the cylinder and the surrounding solvent.</p>
-<p>The volume of the barbell is:</p>
-<p style="text-align: center;" align="center"><img src="img/image108.jpg" alt="" width="227" height="46" /></p>
-<p>and its radius of gyration:</p>
-<p style="text-align: center;" align="center"><img src="img/image109.jpg" alt="" width="368" height="103" /></p>
-<p>The necessary conditions of R &gt;= r is not enforced in the model. It is up to you to restrict this during analysis.</p>
-<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; REFERENCES</p>
-<p>H. Kaya, J. Appl. Cryst. (2004) 37, 223-230.</p>
-<p>H. Kaya and N-R deSouza, J. Appl. Cryst. (2004) 37, 508-509. (addenda and errata)</p>
-<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; TEST DATASET</p>
-<p>This example dataset is produced by running the Macro PlotBarbell(), using 200 data points, qmin = 0.001 &Aring;-1,&nbsp; qmax = 0.7 &Aring;-1 and the above default values.</p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 19.25pt;">
-<td style="border: 1pt solid width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; vertical-align: top; width: 107pt; height: 19.25pt;">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>None</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>1.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>len_bar</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>400.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>rad_bar</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>20.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>rad_bell</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>40.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>sld_barbell</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>1.0e-006</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>sld_solv</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>6.3e-006</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="text-align: center;" align="center"><img id="Picture 59" src="img/image110.jpg" alt="" width="480" height="356" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot using the default values (w/256 data point).</b></p>
-<p>For 2D data: The 2D scattering intensity is calculated similar to the 2D cylinder model. At the theta = 45 deg and phi =0 deg with default values for other parameters,</p>
-<p style="text-align: center;" align="center"><img id="Picture 66" src="img/image111.jpg" alt="" width="425" height="346" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 2D plot (w/(256X265) data points).</b></p>
-
-<p style="text-align: center; page-break-after: avoid;" align="center"><img src="img/image061.jpg" /></p>
-<p style="text-align: center;" align="center"><img src="img/image062.jpg" alt="" width="379" height="256" /></p>
-<p style="text-align: center;" align="center">Figure. Examples of the angles for oriented pp against the detector plane.</p>
-
-
-<p style="text-align: center;" align="center"><a name="_Ref173213915"></a><a name="_Ref173306040"></a>Figure. Definition of the angles for oriented 2D barbells.</p>
-
-
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.23.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="CappedCylinderModel"></a><b><span style="font-size: 14pt;">CappedCylinder(/ConvexLens)Model</span></b></p>
-<p>Calculates the scattering from a cylinder with spherical section end-caps(This model simply becomes the ConvexLensModel when the length of the cylinder L = 0. &nbsp;That is, a sphereocylinder with end caps that have a radius larger than that of the cylinder and the center of the end cap radius lies within the cylinder. See the diagram for the details of the geometry and restrictions on parameter values.</p>
-<p style="margin-left: 0.85in; text-indent: -0.35in;">&nbsp;</p>
-<p style="margin-left: 0.85in; text-indent: -0.35in;"><b>1.1.</b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp; </span>Definition</b></p>
-<p>The returned value is scaled to units of [cm-1sr-1], absolute scale.</p>
-<p>The Capped Cylinder geometry is defined as:</p>
-<p style="text-align: center;" align="center"><img src="img/image112.jpg" alt="" width="416" height="223" /></p>
-<p>r is the radius of the cylinder. All other parameters are as defined in the diagram. Since the end cap radius R &gt;= r and by definition for this geometry h &lt; 0,&nbsp; h is then defined by r and R as:</p>
-<p>h = -1*sqrt(R^2 - r^2).</p>
-<p>The scattering intensity I(q) is calculated as:</p>
-<p style="text-align: center;" align="center"><img src="img/image113.jpg" alt="" width="288" height="45" /></p>
-<p>where the amplitude A(q) is given as:</p>
-<p style="text-align: center;" align="center"><img src="img/image114.jpg" alt="" width="384" height="159" /></p>
-<p>The &lt; &gt; brackets denote an average of the structure over all orientations. &lt;A^2(q)&gt; is then the form factor, P(q). The scale factor is equivalent to the volume fraction of cylinders, each of volume, V. Contrast is the difference of scattering length densities of the cylinder and the surrounding solvent.</p>
-<p>The volume of the Capped Cylinder is:</p>
-<p>(with h as a positive value here)</p>
-<p style="text-align: center;" align="center"><img src="img/image115.jpg" alt="" width="257" height="47" /></p>
-<p>and its radius of gyration:</p>
-<p style="text-align: center;" align="center"><img src="img/image116.jpg" alt="" width="406" height="114" /></p>
-<p>The necessary conditions of R &gt;= r is not enforced in the model. It is up to you to restrict this during analysis.</p>
-<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; REFERENCES</p>
-<p>H. Kaya, J. Appl. Cryst. (2004) 37, 223-230.</p>
-<p>H. Kaya and N-R deSouza, J. Appl. Cryst. (2004) 37, 508-509. (addenda and errata)</p>
-<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; TEST DATASET</p>
-<p>This example dataset is produced by running the Macro CappedCylinder(), using 200 data points, qmin = 0.001 &Aring;-1,&nbsp; qmax = 0.7 &Aring;-1 and the above default values.</p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 19.25pt;">
-<td style="border: 1pt solid width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>None</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>1.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; vertical-align: top; width: 107pt; height: 19.25pt;">
-<p>len_cyl</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>400.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>rad_cap</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>40.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>rad_cyl</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>20.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>sld_capcyl</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>1.0e-006</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>sld_solv</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>6.3e-006</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="text-align: center;" align="center"><img id="Picture 72" src="img/image117.jpg" alt="" width="533" height="381" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot using the default values (w/256 data point).</b></p>
-<p>For 2D data: The 2D scattering intensity is calculated similar to the 2D cylinder model. At the theta = 45 deg and phi =0 deg with default values for other parameters,</p>
-<p style="text-align: center;" align="center"><img id="Picture 71" src="img/image118.jpg" alt="" width="402" height="334" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 2D plot (w/(256X265) data points).</b></p>
-<p style="text-align: center; page-break-after: avoid;" align="center"><img src="img/image061.jpg" /></p>
-<p style="text-align: center;" align="center"><a name="_Ref173213915"></a><a name="_Ref173306040"></a>Figure. Definition of the angles for oriented 2D cylinders.</p>
-<p style="text-align: center;" align="center"><img src="img/image062.jpg" alt="" width="379" height="256" /></p>
-<p style="text-align: center;" align="center">Figure. Examples of the angles for oriented pp against the detector plane.</p>
-
-<!-- Pringle form factor AJJ 2014-02-17 -->
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.24.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="PringleModel"></a><b><span style="font-size: 14pt;">PringleModel</span></b></p>
-<p>This model provides the form factor, P(<em>q</em>), for a 'pringle' or 'saddle-shaped' object (a hyperbolic paraboloid).</p>
-<p style="text-align: center;" align="center">&nbsp;&nbsp;</p>
-<p>The returned value is in units of [cm-1], on absolute scale.</p>
-<p>The form factor calculated is:</p>
-<p style="text-align: center;" align="center"><img src="img/pringle_eqn_1.jpg" alt="" height='60px'/></p>
-<p>where</p>
-<p style="text-align: center;" align="center"><img src="img/pringle_eqn_2.jpg" alt="" height='120px'/></p>
-<p>&nbsp;</p>
-<p>The parameters of the model and a plot comparing the pringle model with the equivalent cylinder are shown below.</p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 18.8pt;">
-<td style="border: 1pt solid width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; vertical-align: top; width: 107pt; height: 18.8pt;">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>0.0</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>alpha</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p></p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>0.001</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>beta</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p></p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>0.02</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>radius</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>60</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">&nbsp;</td>
-<p></p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>1</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sld_pringle</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>1e-006</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sld_solvent</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>6.3e-006</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>thickness</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>10</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="text-align: center;" align="center"><img id="Picture 492" src="img/pringle-vs-cylinder.png" alt="" width="455" height="351" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot using the default values (w/150 data point).</b></p>
-<p>REFERENCE</p>
-<p>S. Alexandru Rautu, Private Communication.</p>
-
-
-
-
-
-
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.25.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="ParallelepipedModel"></a><b><span style="font-size: 14pt;">ParallelepipedModel (Magnetic 2D Model) </span></b></p>
-<p>This model provides the form factor, P(<em>q</em>), for a rectangular cylinder (below) where the form factor is normalized by the volume of the cylinder. P(q) = scale*&lt;f^2&gt;/V+background where the volume V= ABC and the averaging &lt; &gt;&nbsp; is applied over all orientation for 1D. &nbsp;</p>
-For magnetic scattering, please see the '<a href="polar_mag_help.html">Polarization/Magnetic Scattering</a>' in Fitting Help.
-<p><span style="font-size: 14pt;">&nbsp;</span></p>
-<p style="text-align: center;" align="center"><img src="img/image087.jpg" alt="" width="326" height="247" /></p>
-<p>The side of the solid must be satisfied the condition of A&lt;B</p>
-<p>By this definition, assuming</p>
-<p>a = A/B&lt;1; b=B/B=1; c=C/B&gt;1, the form factor,</p>
-<p style="text-align: center;" align="center"><span style="position: relative; top: 48pt;"><img src="img/image088.PNG" alt="" /></span></p>
-<p>The contrast is defined as</p>
-<p style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="img/image089.PNG" alt="" /></span></p>
-<p>The scattering intensity per unit volume is returned in the unit of [cm-1]; &nbsp;I(q) = <span style="font-family: Symbol;">f</span>P(q).</p>
-<p>For P*S: The 2nd virial coefficient of the solid cylinder is calculate based on the averaged effective radius (= sqrt(short_a*short_b/pi)) and length( = long_c) values, and used as the effective radius toward S(Q) when P(Q)*S(Q) is applied.</p>
-<p>To provide easy access to the orientation of the parallelepiped, we define the axis of the cylinder using two angles &theta; , <span style="font-family: 'Arial','sans-serif';">&phi; </span>and<span style="font-family: Symbol;">Y</span>. Similarly to the case of the cylinder, those angles, &theta; &nbsp;and <span style="font-family: 'Arial','sans-serif';">&phi;,</span> are defined on Figure 2 of CylinderModel. The angle <span style="font-family: Symbol;">Y </span>is the rotational angle around its own long_c axis against the q plane. For example, <span style="font-family: Symbol;">Y </span>= 0 when the short_b axis is parallel to the x-axis of the detector.</p>
-<p style="text-align: center;" align="center"><img src="img/image090.jpg"/></p>
-<p style="text-align: center;" align="center"><b>Figure. Definition of angles for 2D</b>.</p>
-<p style="text-align: center;" align="center"><img src="img/image091.jpg" alt="" width="379" height="256" /></p>
-<p style="text-align: center;" align="center">Figure. Examples of the angles for oriented pp against the detector plane.</p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 18.8pt;">
-<td style="border: 1pt solid width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>0.0</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; vertical-align: top; width: 107pt; height: 18.8pt;">
-<p>contrast</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>5e-006</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>long_c</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>400</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>short_a</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>35</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>short_b</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>75</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>1</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="text-align: center;" align="center"><img id="Picture 492" src="img/image092.jpg" alt="" width="455" height="351" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot using the default values (w/1000 data point).</b></p>
-<p style="margin-left: 1.35in; text-indent: -0.25in;"><span style="font-family: Symbol;">&middot;</span><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><b>Validation of the parallelepiped 2D model</b></p>
-<p>Validation of our code was done by comparing the output of the 1D calculation to the angular average of the output of 2 D calculation over all possible angles. The Figure below shows the comparison where the solid dot refers to averaged 2D while the line represents the result of 1D calculation (for the averaging, 76, 180, 76 points are taken over the angles of theta, phi, and psi respectively).</p>
-<p style="text-align: center;" align="center"><img id="Picture 104" src="img/image093.gif" alt="" width="481" height="299" /></p>
-<p style="text-align: center;" align="center"><b>Figure. Comparison between 1D and averaged 2D.</b></p>
-<p>Our model uses the form factor calculations implemented in a c-library provided by the NIST Center for Neutron Research (Kline, 2006):</p>
-<p>REFERENCE</p>
-<p>Mittelbach and Porod, Acta Physica Austriaca 14 (1961) 185-211.</p>
-<p>Equations (1), (13-14). (in German)</p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.26.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b><span style="font-size: 14pt;"><a name="CSParallelepipedModel"></a>CSParallelepipedModel</span></b></p>
-<p>Calculates the form factor for a rectangular solid with a core-shell structure. The thickness and the scattering length density of the shell or "rim" can be different on all three (pairs) of faces.&nbsp; The form factor is normalized by the particle volume such that P(q) = scale*&lt;f^2&gt;/Vol + bkg, where &lt; &gt; is an average over all possible orientations of the rectangular solid. An instrument resolution smeared version is also provided.</p>
-<p>The function calculated is the form factor of the rectangular solid below. The core of the solid is defined by the dimensions ABC such that A &lt; B &lt; C.&nbsp;</p>
-<p style="text-align: center;" align="center"><img id="Picture 38" src="img/image087.jpg" alt="" width="326" height="247" />&nbsp;</p>
-<p>There are rectangular "slabs" of thickness tA that add to the A dimension (on the BC faces). There are similar slabs on the AC (=tB) and AB (=tC) faces. The projection in the AB plane is then:</p>
-<p style="text-align: center;" align="center"><img src="img/image094.jpg" alt="" width="334" height="277" /></p>
-<p>The volume of the solid is:</p>
-<p><span style="position: relative; top: 5pt;"><img src="img/image095.PNG" alt="" /></span></p>
-<p>meaning that there are "gaps" at the corners of the solid.</p>
-<p>The intensity calculated follows the parallelepiped model, with the core-shell intensity being calculated as the square of the sum of the amplitudes of the core and shell, in the same manner as a core-shell sphere.</p>
-<p>For the calculation of the form factor to be valid, the sides of the solid MUST be chosen such that A &lt; B &lt; C. If this inequality in not satisfied, the model will not report an error, and the calculation will not be correct.</p>
-<p>FITTING NOTES:</p>
-<p>If the scale is set equal to the particle volume fraction, f, the returned value is the scattered intensity per unit volume, I(q) = f*P(q). However, no interparticle interference effects are included in this calculation.</p>
-<p>There are many parameters in this model. Hold as many fixed as possible with known values, or you will certainly end up at a solution that is unphysical.</p>
-<p>Constraints must be applied during fitting to ensure that the inequality A &lt; B &lt; C&nbsp; is not violated. The calculation will not report an error, but the results will not be correct.</p>
-<p>The returned value is in units of [cm-1], on absolute scale.</p>
-<p>For P*S: The 2nd virial coefficient of this CSPP is calculate based on the averaged effective radius (= sqrt((short_a+2*rim_a)*(short_b+2*rim_b)/pi)) and length( = long_c+2*rim_c) values, and used as the effective radius toward S(Q) when P(Q)*S(Q) is applied.</p>
-<p>To provide easy access to the orientation of the CSparallelepiped, we define the axis of the cylinder using two angles &theta; , <span style="font-family: 'Arial','sans-serif';">&phi; </span>and<span style="font-family: Symbol;">Y</span>. Similarly to the case of the cylinder, those angles, &theta; &nbsp;and <span style="font-family: 'Arial','sans-serif';">&phi;,</span> are defined on Figure 2 of CylinderModel. The angle <span style="font-family: Symbol;">Y </span>is the rotational angle around its own long_c axis against the q plane. For example, <span style="font-family: Symbol;">Y </span>= 0 when the short_b axis is parallel to the x-axis of the detector.</p>
-<p style="text-align: center;" align="center"><img id="Picture 102" src="img/image090.jpg" /></p>
-<p style="text-align: center;" align="center"><b>Figure. Definition of angles for 2D</b>.</p>
-<p style="text-align: center;" align="center"><img id="Picture 103" src="img/image091.jpg" alt="" width="379" height="256" /></p>
-<p style="text-align: center;" align="center">Figure. Examples of the angles for oriented cspp against the detector plane.</p>
-<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; TEST DATASET</p>
-<p>This example dataset is produced by running the Macro Plot_CSParallelepiped(), using 100 data points, qmin = 0.001 &Aring;-1,&nbsp; qmax = 0.7 &Aring;-1 and the below default values.&nbsp;</p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 18.8pt;">
-<td style="border: 1pt solid width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; vertical-align: top; width: 107pt; height: 18.8pt;">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>0.06</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sld_pcore</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>1e-006</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sld_rimA</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>2e-006</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sld_rimB</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>4e-006</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sld_rimC</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>2e-006</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sld_solv</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>6e-006</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>rimA</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>10</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>rimB</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>10</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>rimC</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>10</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>longC</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>400</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>shortA</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>35</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>midB</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>75</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>1</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="text-align: center;" align="center"><img id="Picture 33" src="img/image096.jpg" alt="" width="450" height="338" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot using the default values (w/256 data points).</b></p>
-<p style="text-align: center;" align="center"><b>&nbsp;</b></p>
-<p style="text-align: center;" align="center"><img id="Picture 34" src="img/image097.jpg" alt="" width="451" height="339" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 2D plot using the default values (w/(256X265) data points).</b></p>
-
-<p>Our model uses the form factor calculations implemented in a c-library provided by the NIST Center for Neutron Research (Kline, 2006):</p>
-<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; REFERENCE</p>
-<p>see: Mittelbach and Porod, Acta Physica Austriaca 14 (1961) 185-211.</p>
-<p>Equations (1), (13-14). (yes, it's in German)&nbsp;</p>
-
-
-
-
-
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.27.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b><span style="font-size: 14pt;"><a name="RectangularHollowPrismInfThinWallsModel"></a>RectangularHollowPrismInfThinWallsModel</span></b></p>
-
-<p>This model provides the form factor, P( <em>q</em>), for a hollow rectangular prism
-with infinitely thin walls.</p>
-<p><em>Definition</em></p>
-<p>The 1D scattering intensity for this model is calculated according to the equations given by
-Nayuk and Huber (Nayuk, 2012).</p>
-<p>Assuming a hollow parallelepiped with infinitely thin walls, edge lengths A &le; B &le; C
-	<span class="formula"><i>A</i>â
-â€â
-<i>B</i>â
-â€â
-<i>C</i></span>
-
-and presenting an orientation with respect to the scattering vector given by &theta; and &phi;,
-where &theta; is the angle between the <em>z</em> axis and the longest axis of the parallelepiped <em>C</em>, and &phi;
-is the angle between the scattering vector (lying in the <em>xy</em> plane) and the <em>y</em> axis,
-the form factor is given by:</p>
-
-<p style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="img/RectangularHollowPrismInfThinWalls_1.png" alt="" /></span></p>
-
-<p>where</p>
-
-<p style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="img/RectangularHollowPrismInfThinWalls_2.png" alt="" /></span></p>
-
-<p style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="img/RectangularHollowPrismInfThinWalls_3.png" alt="" /></span></p>
-
-<p style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="img/RectangularHollowPrismInfThinWalls_4.png" alt="" /></span></p>
-
-<p>and</p>
-
-<p style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="img/RectangularHollowPrismInfThinWalls_5.png" alt="" /></span></p>
-
-<p>The 1D scattering intensity is calculated as:</p>
-
-<p style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="img/RectangularHollowPrismInfThinWalls_6.png" alt="" /></span></p>
-
-<p>where <em>V</em> is the volume of the rectangular prism, <span class="formula"><i>&rho;</i><sub><span class="mbox">pipe</span></sub></span>
- is the scattering length of the
-parallelepiped, <span class="formula"><i>&rho;</i><sub><span class="mbox">solvent</span></sub></span>
- is the scattering length of the solvent, and
-(if the data are in absolute scale) scale represents the volume fraction (which is unitless) .</p>
-<p>The 2D scattering intensity is not computed by this model.</p>
-<p>The returned value is scaled to units of cm<sup>-1</sup> and the parameters of the RectangularHollowPrismInfThinWallModel
-are the following:</p>
-<table border="1" class="docutils">
-<colgroup>
-<col width="40%" />
-<col width="23%" />
-<col width="37%" />
-</colgroup>
-<thead valign="bottom">
-<tr><th class="head">Parameter name</th>
-<th class="head">Units</th>
-<th class="head">Default value</th>
-</tr>
-</thead>
-<tbody valign="top">
-<tr><td>scale</td>
-<td>None</td>
-<td>1</td>
-</tr>
-<tr><td>short_side</td>
-<td>&Aring;</td>
-<td>35</td>
-</tr>
-<tr><td>b2a_ratio</td>
-<td>None</td>
-<td>1</td>
-</tr>
-<tr><td>c2a_ratio</td>
-<td>None</td>
-<td>1</td>
-</tr>
-<tr><td>sldPipe</td>
-<td>&Aring;<sup>-2</sup></td>
-<td>6.3e-6</td>
-</tr>
-<tr><td>sldSolv</td>
-<td>&Aring;<sup>-2</sup></td>
-<td>1.0e-6</td>
-</tr>
-<tr><td>background</td>
-<td>cm<sup>-1</sup></td>
-<td>0</td>
-</tr>
-</tbody>
-</table>
-<p>REFERENCES</p>
-<ol class="upperalpha simple" start="18">
-<li>Nayuk and K. Huber, <em>Z. Phys. Chem.</em> 226 (2012) 837-854.</li>
-</ol>
-<p><em>Validation of the RectangularHollowPrismInfThinWallsModel</em></p>
-<p>Validation of the code was done qualitatively by comparing the output of the 1D model to the curves
-shown in (Nayuk, 2012).</p>
-
-
-
-
-
-
-
-
-
-
-
-
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.28.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b><span style="font-size: 14pt;"><a name="RectangularPrismModel"></a>RectangularPrismModel</span></b></p>
-<p>This model provides the form factor, P( <em>q</em>), for a rectangular prism.</p>
-<p>Note that this model is almost totally equivalent to the existing
-ParallelepipedModel. The only difference is that the way the
-relevant parameters are defined here (<em>a</em>, <em>b/a</em>, <em>c/a</em> instead of <em>a</em>, <em>b</em>, <em>c</em>)
-allows to use polydispersity with this model while keeping the shape
-of the prism (e.g. setting <em>b/a</em> = 1 and <em>c/a</em> = 1 and applying polydispersity
-to <em>a</em> will generate a distribution of cubes of different sizes).</p>
-<p><em>Definition</em></p>
-<p>The 1D scattering intensity for this model was calculated by Mittelbach and Porod (Mittelbach, 1961),
-but the implementation here is closer to the equations given by Nayuk and Huber (Nayuk, 2012).</p>
-<p>The scattering from a massive parallelepiped with an orientation with respect to the scattering vector
-given by &theta; and &phi; is given by:</p>
-
-<p style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="img/RectangularPrism_1.png" alt="" /></span></p>
-
-<p>where <em>A</em>, <em>B</em> and <em>C</em> are the sides of the parallelepiped and must fulfill <span class="formula"><i>A</i>â
-&le;â
-<i>B</i>â
-&le;â
-<i>C</i></span>
-,
-&theta; is the angle between the <em>z</em> axis and the longest axis of the parallelepiped <em>C</em>, and &phi;
-is the angle between the scattering vector (lying in the <em>xy</em> plane) and the <em>y</em> axis.</p>
-<p>The normalized form factor in 1D is obtained averaging over all possible orientations:</p>
-
-<p style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="img/RectangularPrism_2.png" alt="" /></span></p>
-
-<p>The 1D scattering intensity is calculated as:</p>
-
-<p style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="img/RectangularPrism_3.png" alt="" /></span></p>
-
-<p>where <em>V</em> is the volume of the rectangular prism, <span class="formula"><i>&rho;</i><sub><span class="mbox">pipe</span></sub></span>
- is the scattering length of the
-parallelepiped, <span class="formula"><i>&rho;</i><sub><span class="mbox">solvent</span></sub></span>
- is the scattering length of the solvent, and
-(if the data are in absolute scale) scale represents the volume fraction (which is unitless) .</p>
-<p>The 2D scattering intensity is not computed by this model.</p>
-<p>The returned value is scaled to units of cm<sup>-1</sup> and the parameters of the RectangularPrismModel are the following:</p>
-<table border="1" class="docutils">
-<colgroup>
-<col width="40%" />
-<col width="23%" />
-<col width="37%" />
-</colgroup>
-<thead valign="bottom">
-<tr><th class="head">Parameter name</th>
-<th class="head">Units</th>
-<th class="head">Default value</th>
-</tr>
-</thead>
-<tbody valign="top">
-<tr><td>scale</td>
-<td>None</td>
-<td>1</td>
-</tr>
-<tr><td>short_side</td>
-<td>&Aring;</td>
-<td>35</td>
-</tr>
-<tr><td>b2a_ratio</td>
-<td>None</td>
-<td>1</td>
-</tr>
-<tr><td>c2a_ratio</td>
-<td>None</td>
-<td>1</td>
-</tr>
-<tr><td>sldPipe</td>
-<td>&Aring;<sup>-2</sup></td>
-<td>6.3e-6</td>
-</tr>
-<tr><td>sldSolv</td>
-<td>&Aring;<sup>-2</sup></td>
-<td>1.0e-6</td>
-</tr>
-<tr><td>background</td>
-<td>cm<sup>-1</sup></td>
-<td>0</td>
-</tr>
-</tbody>
-</table>
-<p>REFERENCES</p>
-<ol class="upperalpha simple" start="16">
-<li>Mittelbach and G. Porod, <em>Acta Physica Austriaca</em> 14 (1961) 185-211.</li>
-</ol>
-<ol class="upperalpha simple" start="18">
-<li>Nayuk and K. Huber, <em>Z. Phys. Chem.</em> 226 (2012) 837-854.</li>
-</ol>
-<p><em>Validation of the RectangularPrismModel</em></p>
-<p>Validation of the code was done by comparing the output of the 1D model to the output of the existing
-parallelepiped model.</p>
-
-
-
-
-
-
-
-
-
-
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.29.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b><span style="font-size: 14pt;"><a name="RectangularHollowPrismModel"></a>RectangularHollowPrismModel</span></b></p>
-<p>This model provides the form factor, P( <em>q</em>), for a hollow rectangular parallelepiped
-with a wall thickness Î.</p>
-<p><em>Definition</em></p>
-<p>The 1D scattering intensity for this model is calculated by forming the difference of the
-amplitudes of two massive parallelepipeds differing in their outermost dimensions in
-each direction by the same length increment 2 &Delta; (Nayuk, 2012).</p>
-<p>As in the case of the massive parallelepiped, the scattering amplitude is computed for a particular
-orientation of the parallelepiped with respect to the scattering vector and then averaged over all
-possible orientations, giving:</p>
-
-<p style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="img/RectangularHollowPrism_1.png" alt="" /></span></p>
-
-<p>where &theta; is the angle between the <em>z</em> axis and the longest axis of the parallelepiped, &phi;
-is the angle between the scattering vector (lying in the <em>xy</em> plane) and the <em>y</em> axis, and:</p>
-
-<p style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="img/RectangularHollowPrism_2.png" alt="" /></span></p>
-
-<p>where <em>A</em>, <em>B</em> and <em>C</em> are the external sides of the parallelepiped fulfilling <span class="formula"><i>A</i>â
-&le;â
-<i>B</i>â
-&le;â
-<i>C</i></span>
-,
-and the volume <em>V</em> of the parallelepiped is:</p>
-
-<p style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="img/RectangularHollowPrism_3.png" alt="" /></span></p>
-
-<p>The 1D scattering intensity is calculated as:</p>
-
-<p style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="img/RectangularHollowPrism_4.png" alt="" /></span></p>
-
-<p>where <span class="formula"><i>&rho;</i><sub><span class="mbox">pipe</span></sub></span>
- is the scattering length of the
-parallelepiped, <span class="formula"><i>&rho;</i><sub><span class="mbox">solvent</span></sub></span>
- is the scattering length of the solvent, and
-(if the data are in absolute scale) scale represents the volume fraction (which is unitless) .</p>
-<p>The 2D scattering intensity is not computed by this model.</p>
-<p>The returned value is scaled to units of cm<sup>-1</sup> and the parameters of the RectangularHollowPrismModel
-are the following:</p>
-<table border="1" class="docutils">
-<colgroup>
-<col width="40%" />
-<col width="23%" />
-<col width="37%" />
-</colgroup>
-<thead valign="bottom">
-<tr><th class="head">Parameter name</th>
-<th class="head">Units</th>
-<th class="head">Default value</th>
-</tr>
-</thead>
-<tbody valign="top">
-<tr><td>scale</td>
-<td>None</td>
-<td>1</td>
-</tr>
-<tr><td>short_side</td>
-<td>&Aring;</td>
-<td>35</td>
-</tr>
-<tr><td>b2a_ratio</td>
-<td>None</td>
-<td>1</td>
-</tr>
-<tr><td>c2a_ratio</td>
-<td>None</td>
-<td>1</td>
-</tr>
-<tr><td>thickness</td>
-<td>&Aring;</td>
-<td>1</td>
-</tr>
-<tr><td>sldPipe</td>
-<td>&Aring;<sup>-2</sup></td>
-<td>6.3e-6</td>
-</tr>
-<tr><td>sldSolv</td>
-<td>&Aring;<sup>-2</sup></td>
-<td>1.0e-6</td>
-</tr>
-<tr><td>background</td>
-<td>cm<sup>-1</sup></td>
-<td>0</td>
-</tr>
-</tbody>
-</table>
-<p>REFERENCES</p>
-<ol class="upperalpha simple" start="18">
-<li>Nayuk and K. Huber, <em>Z. Phys. Chem.</em> 226 (2012) 837-854.</li>
-</ol>
-<p><em>Validation of the RectangularHollowPrismModel</em></p>
-<p>Validation of the code was done qualitatively by comparing the output of the 1D model to the curves
-shown in (Nayuk, 2012).</p>
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.30.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="EllipsoidModel"></a><b><span style="font-size: 14pt;">Ellipsoid Model</span></b></p>
-<p>This model provides the form factor for an ellipsoid (ellipsoid of revolution) with uniform scattering length density. The form factor is normalized by the particle volume.</p>
-<p style="margin-left: 0.85in; text-indent: -0.35in;"><b>1.1.</b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp; </span>Definition</b></p>
-<p>The output of the 2D scattering intensity function for oriented ellipsoids is given by (Feigin, 1987):</p>
-<p style="text-align: center;" align="center"><span style="position: relative; top: 12pt;"><img src="img/image059.PNG" alt="" /></span>&nbsp;&nbsp;</p>
-<p style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="img/image119.PNG" alt="" /></span>&nbsp;&nbsp;&nbsp;</p>
-<p style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="img/image120.PNG" alt="" /></span>&nbsp;&nbsp;&nbsp;&nbsp;</p>
-<p>where <span style="font-family: 'Arial','sans-serif';">&alpha;</span> is the angle between the axis of the ellipsoid and the q-vector, V is the volume of the ellipsoid, Ra is the radius along the rotation axis of the ellipsoid, Rb is the radius perpendicular to the rotation axis of the ellipsoid and <em><span style="font-family: 'Arial','sans-serif';">&Delta;</span>&rho;</em> (contrast) is the scattering length density difference between the scatterer and the solvent.</p>
-<p>To provide easy access to the orientation of the ellipsoid, we define the rotation axis of the ellipsoid using two angles &theta; and <span style="font-family: 'Arial','sans-serif';">&phi;</span>. Similarly to the case of the cylinder, those angles are defined on Figure 2. For the ellipsoid, &theta; is the angle between the rotation axis and the z-axis.</p>
-<p>For P*S: The 2nd virial coefficient of the solid ellipsoid is calculate based on the radius_a and radius_b values, and used as the effective radius toward S(Q) when P(Q)*S(Q) is applied.</p>
-<p>The returned value is scaled to units of [cm-1] and the parameters of the ellipsoid model are the following:</p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 19.85pt;">
-<td style="border: 1pt solid width: 135.1pt; height: 19.85pt;" valign="top" width="180">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 78.9pt; height: 19.85pt;" valign="top" width="105">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.85pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 19.85pt;">
-<td style="border-width: medium 1pt 1pt; width: 135.1pt; height: 19.85pt;" valign="top" width="180">
-<p>scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 78.9pt; height: 19.85pt;" valign="top" width="105">
-<p>None</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.85pt;" valign="top" width="143">
-<p>1.0</p>
-</td>
-</tr>
-<tr style="height: 19.85pt;">
-<td style="border-width: medium 1pt 1pt; vertical-align: top; width: 135.1pt; height: 19.85pt;">
-<p>radius_a (polar)</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 78.9pt; height: 19.85pt;" valign="top" width="105">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.85pt;" valign="top" width="143">
-<p>20.0</p>
-</td>
-</tr>
-<tr style="height: 19.85pt;">
-<td style="border-width: medium 1pt 1pt; width: 135.1pt; height: 19.85pt;" valign="top" width="180">
-<p>radius_b (equatorial)</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 78.9pt; height: 19.85pt;" valign="top" width="105">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.85pt;" valign="top" width="143">
-<p>400.0</p>
-</td>
-</tr>
-<tr style="height: 19.85pt;">
-<td style="border-width: medium 1pt 1pt; width: 135.1pt; height: 19.85pt;" valign="top" width="180">
-<p>sldEll</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 78.9pt; height: 19.85pt;" valign="top" width="105">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.85pt;" valign="top" width="143">
-<p>4.0e-6</p>
-</td>
-</tr>
-<tr style="height: 19.85pt;">
-<td style="border-width: medium 1pt 1pt; width: 135.1pt; height: 19.85pt;" valign="top" width="180">
-<p>sldSolv</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 78.9pt; height: 19.85pt;" valign="top" width="105">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.85pt;" valign="top" width="143">
-<p>1.0e-6</p>
-</td>
-</tr>
-<tr style="height: 19.85pt;">
-<td style="border-width: medium 1pt 1pt; width: 135.1pt; height: 19.85pt;" valign="top" width="180">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 78.9pt; height: 19.85pt;" valign="top" width="105">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.85pt;" valign="top" width="143">
-<p>0.0</p>
-</td>
-</tr>
-<tr style="height: 19.85pt;">
-<td style="border-width: medium 1pt 1pt; width: 135.1pt; height: 19.85pt;" valign="top" width="180">
-<p>axis_theta</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 78.9pt; height: 19.85pt;" valign="top" width="105">
-<p>degree</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.85pt;" valign="top" width="143">
-<p>90</p>
-</td>
-</tr>
-<tr style="height: 20.6pt;">
-<td style="border-width: medium 1pt 1pt; width: 135.1pt; height: 20.6pt;" valign="top" width="180">
-<p>axis_phi</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 78.9pt; height: 20.6pt;" valign="top" width="105">
-<p>degree</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 20.6pt;" valign="top" width="143">
-<p>0.0</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="text-align: center;" align="center"><img id="Picture 129" src="img/image121.jpg" alt="" width="483" height="332" /></p>
-<p>The output of the 1D scattering intensity function for randomly oriented ellipsoids is then given by the equation above.</p>
-<p>The <em>axis_theta</em> and axis<em>_phi</em> parameters are not used for the 1D output. Our implementation of the scattering kernel and the 1D scattering intensity use the c-library from NIST.</p>
-<p style="text-align: center;" align="center"><img src="img/image122.jpg" alt="" width="379" height="256"/></p>
-<p style="text-align: center;" align="center"><span style="font-size: 12pt;">Figure. The angles for oriented ellipsoid </span></p>
-
-<p style="margin-left: 0.85in; text-indent: -0.35in;"><b>2.1.</b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp; </span>Validation of the ellipsoid model</b></p>
-<p>Validation of our code was done by comparing the output of the 1D model to the output of the software provided by the NIST (Kline, 2006). Figure 5 shows a comparison of the 1D output of our model and the output of the NIST software.</p>
-<p>Averaging over a distribution of orientation is done by evaluating the equation above. Since we have no other software to compare the implementation of the intensity for fully oriented ellipsoids, we can compare the result of averaging our 2D output using a uniform distribution <em>p(&theta;,</em><em><span style="font-family: 'Arial','sans-serif';">&phi;</span>)</em> = 1.0.&nbsp; Figure 6 shows the result of such a cross-check.</p>
-<p style="text-align: center;" align="center"><b><em><span style="color: #3366ff;">&nbsp;</span></em></b></p>
-<p>The discrepancy above q=0.3 &Aring; -1 is due to the way the form factors are calculated in the c-library provided by NIST. A numerical integration has to be performed to obtain P(q) for randomly oriented particles. The NIST software performs that integration with a 76-point Gaussian quadrature rule, which will become imprecise at high q where the amplitude varies quickly as a function of q. The DANSE result shown has been obtained by summing over 501 equidistant points in <span style="font-family: 'Arial','sans-serif';">&alpha;</span>. Our result was found to be stable over the range of q shown for a number of points higher than 500.</p>
-<p style="text-align: center; page-break-after: avoid;" align="center"><b><img id="Picture 16" src="img/image123.jpg" alt="ellipsoid_1D_validation" width="573" height="315" /></b></p>
-<p><a name="_Ref173222904"></a>Figure 5: Comparison of the DANSE scattering intensity for an ellipsoid with the output of the NIST SANS analysis software. The parameters were set to: Scale=1.0, Radius_a=20 &Aring;, Radius_b=400 &Aring;,</p>
-<p>Contrast=3e-6 &Aring; -2, and Background=0.01 cm -1.</p>
-<p style="text-align: center; page-break-after: avoid;" align="center"><img src="img/image124.jpg" alt="ellipsoid_2D_average" width="573" height="315" /></p>
-<p style="text-align: center; page-break-after: avoid;" align="center">&nbsp;</p>
-<p><a name="_Ref173223004"></a>Figure 6: Comparison of the intensity for uniformly distributed ellipsoids calculated from our 2D model and the intensity from the NIST SANS analysis software. The parameters used were: Scale=1.0, Radius_a=20 &Aring;, Radius_b=400 &Aring;, Contrast=3e-6 &Aring; -2, and Background=0.0 cm -1.</p>
-<p>&nbsp;</p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.31.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="CoreShellEllipsoidModel"></a><b><span style="font-size: 14pt;">CoreShellEllipsoidModel </span></b></p>
-<p>This model provides the form factor, P(<em>q</em>), for a core shell ellipsoid (below) where the form factor is normalized by the volume of the cylinder. P(q) = scale*&lt;f^2&gt;/V+background where the volume V= 4pi/3*rmaj*rmin2 and the averaging &lt; &gt;&nbsp; is applied over all orientation for 1D. &nbsp;</p>
-<p style="text-align: center;" align="center">&nbsp;&nbsp;<img id="Picture 41" src="img/image125.gif" alt="" width="335" height="179" /></p>
-<p>The returned value is in units of [cm-1], on absolute scale.</p>
-<p>The form factor calculated is:</p>
-<p>&nbsp;</p>
-<p style="text-align: center;" align="center"><img src="img/image126.PNG" alt="" /></p>
-<p>&nbsp;</p>
-<p>To provide easy access to the orientation of the coreshell ellipsoid, we define the axis of the solid ellipsoid using two angles &theta; , <span style="font-family: 'Arial','sans-serif';">&phi;</span>. Similarly to the case of the cylinder, those angles, &theta; &nbsp;and <span style="font-family: 'Arial','sans-serif';">&phi;,</span> are defined on Figure 2 of CylinderModel.</p>
-<p>The contrast is defined as SLD(core) &ndash; SLD(shell) or SLD(shell &ndash; solvent). In the parameters, equat_core = equatorial core radius, polar_core = polar core radius, equat_shell = rmin (or equatorial outer radius), and polar_shell = = rmaj (or polar outer radius).</p>
-<p>For P*S: The 2nd virial coefficient of the solid ellipsoid is calculate based on the radius_a (= polar_shell) and radius_b (= equat_shell) values, and used as the effective radius toward S(Q) when P(Q)*S(Q) is applied.</p>
-<p>&nbsp;</p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 18.8pt;">
-<td style="border: 1pt solid width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>0.001</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>equat_core</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>200</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; vertical-align: top; width: 107pt; height: 18.8pt;">
-<p>equat_shell</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>250</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sld_solvent</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>6e-006</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>ploar_shell</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>30</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>ploar_core</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>20</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>1</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-style: none solid; border-width: medium 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sld_core</p>
-</td>
-<td style="border-style: none solid none none; border-width: medium 1pt medium medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-style: none solid none none; border-width: medium 1pt medium medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>2e-006</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sld_shell</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>1e-006</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="text-align: center;" align="center"><img id="Picture 526" src="img/image127.jpg" alt="" width="426" height="333" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot using the default values (w/1000 data point).</b></p>
-<p style="text-align: center;" align="center"><b>&nbsp;</b></p>
-<p style="text-align: center;" align="center"><img src="img/image122.jpg" alt="" width="379" height="256"/></p>
-<p style="text-align: center;" align="center">Figure. The angles for oriented coreshellellipsoid .</p>
-<p>Our model uses the form factor calculations implemented in a c-library provided by the NIST Center for Neutron Research (Kline, 2006):</p>
-<p>REFERENCE</p>
-<p>Kotlarchyk, M.; Chen, S.-H. J. Chem. Phys., 1983, 79, 2461.</p>
-<p>Berr, S.&nbsp; J. Phys. Chem., 1987, 91, 4760.</p>
-
-
-
-
-
-
-
-
-
-
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.32.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="CoreShellEllipsoidXTModel"></a><b><span style="font-size: 14pt;">CoreShellEllipsoidXTModel </span></b></p>
-
-<p>An alternative version of P( *q*) for the core plus shell ellipsoid (see 
-CoreShellEllipsoidModel), having as 
-parameters the core axial ratio X and a shell thickness, which are more often 
-what we would like to determine and behave better when polydispersity is 
-applied than the four independent radii in the original model.</p>
-
-<p>The geometric parameters are: equat_core = equatorial core radius = Rminor_core, 
-X_core = polar_core/equat_core = Rmajor_core/Rminor_core
-T_shell = equat_outer - equat_core = Rminor_outer - Rminor_core,
-XpolarShell = Tpolar_shell/T_shell = (Rmajor_outer - Rmajor_core)/(Rminor_outer - Rminor_core)</p>
-
-<p>In terms of the original radii:
-polar_core = equat_core * X_core,  equat_shell = equat_core + T_shell
-polar_shell = equat_core * X_core  + T_shell*XpolarShell
-(where we note that "shell" perhaps confusingly, relates to the outer radius).</p>
-
-<p>When X_core &lt; 1 the core is oblate, when X_core &gt; 1  it is prolate, 
-X_core =1 is a spherical core. For a fixed shell thickness XpolarShell = 1, to scale the 
-shell thickness pro-rata with the radius XpolarShell = X_core.</p>
-
-<p>When including and S(Q), the radius in S(Q) is calculated to be that of a
- sphere with the same 2nd virial coefficient of the outr surface of the ellipsoid. 
- This may have some undesirable effects if the aspect ratio of the ellipsoid is 
- large ( X&lt;&lt;1 or X&gt;&gt;1), when the S(Q) which assumes spheres wil not in any case be valid.</p>
- 
-<p>If SANS data are in absolute units, and sld's are correct, then "scale" should be the total 
-volume fraction of the "outer particle". When S(Q) is introduced this moves to the S(Q) 
-volume fraction, and "scale" should then be 1.0, or contain some ther units conversion factor 
-if you have say Xray data.</p>
-
-
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 18.8pt;">
-<td style="border: 1pt solid width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>0.001</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>equat_core</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>20</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; vertical-align: top; width: 107pt; height: 18.8pt;">
-<p>scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p></p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>0.05</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sld_core</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>2.0e-6</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sld_shell</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>1.0e-6</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sld_solv</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>6.3e-6</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>T_shell</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>30</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>X_core</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p></p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>3.0</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>XpolarShell</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143"></td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>1.0</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-
-
-
-
-
-
-
-
-
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.33.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="TriaxialEllipsoidModel"></a><b><span style="font-size: 14pt;">TriaxialEllipsoidModel</span></b></p>
-<p>This model provides the form factor, P(<em>q</em>), for an ellipsoid (below) where all three axes are of different lengths, i.e.,&nbsp; Ra =&lt; Rb =&lt; Rc (Note that users should maintains this inequality for the all calculations).&nbsp; P(q) = scale*&lt;f^2&gt;/V+background where the volume V= 4pi/3*Ra*Rb*Rc, and the averaging &lt; &gt;&nbsp; is applied over all orientation for 1D. &nbsp;</p>
-<p style="text-align: center;" align="center">&nbsp;&nbsp;<img id="Picture 42" src="img/image128.jpg" alt="" width="376" height="226" /></p>
-<p style="text-align: center;" align="center">&nbsp;&nbsp;</p>
-<p>The returned value is in units of [cm-1], on absolute scale.</p>
-<p>The form factor calculated is:</p>
-<p style="text-align: center;" align="center"><span style="position: relative; top: 33pt;"><img src="img/image129.PNG" alt="" /></span></p>
-<p>To provide easy access to the orientation of the triaxial ellipsoid, we define the axis of the cylinder using the angles &theta; , <span style="font-family: 'Arial','sans-serif';">&phi; </span>and<span style="font-family: Symbol;">Y</span>. Similarly to the case of the cylinder, those angles, &theta; &nbsp;and <span style="font-family: 'Arial','sans-serif';">&phi;,</span> are defined on Figure 2 of CylinderModel. The angle <span style="font-family: Symbol;">Y </span>is the rotational angle around its own semi_axisC axis against the q plane. For example, <span style="font-family: Symbol;">Y </span>= 0 when the semi_axisA axis is parallel to the x-axis of the detector.</p>
-<p>The radius of gyration for this system is Rg2 = (Ra2*Rb2*Rc2)/5.&nbsp; The contrast is defined as SLD(ellipsoid) &ndash; SLD(solvent). In the parameters, semi_axisA = Ra (or minor equatorial radius), semi_axisB = Rb (or major equatorial radius), and semi_axisC = Rc (or polar radius of the ellipsoid).</p>
-<p>For P*S: The 2nd virial coefficient of the solid ellipsoid is calculate based on the radius_a (=semi_axisC) and radius_b (=sqrt(semi_axisA* semi_axisB)) &nbsp;values, and used as the effective radius toward S(Q) when P(Q)*S(Q) is applied.</p>
-<p>&nbsp;</p>
-<p>&nbsp;</p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 18.8pt;">
-<td style="border: 1pt solid width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; vertical-align: top; width: 107pt; height: 18.8pt;">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>0.0</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>semi_axisA</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>35</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>semi_axisB</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>100</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>semi_axisC</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>400</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>1</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-style: none solid; border-width: medium 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sldEll</p>
-</td>
-<td style="border-style: none solid none none; border-width: medium 1pt medium medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-style: none solid none none; border-width: medium 1pt medium medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>1.0e-006</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sldSolv</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>6.3e-006</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="text-align: center;" align="center"><img id="Picture 545" src="img/image130.jpg" alt="" width="439" height="341" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot using the default values (w/1000 data point).</b></p>
-<p style="margin-left: 1.35in; text-indent: -0.25in;"><span style="font-family: Symbol;">&middot;</span><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><b>Validation of the triaxialellipsoid 2D model</b></p>
-<p>Validation of our code was done by comparing the output of the 1D calculation to the angular average of the output of 2 D calculation over all possible angles. The Figure below shows the comparison where the solid dot refers to averaged 2D while the line represents the result of 1D calculation (for 2D averaging, 76, 180, 76 points are taken for the angles of theta, phi, and psi respectively).</p>
-<p style="text-align: center;" align="center"><img src="img/image131.gif" alt="" width="438" height="272" /></p>
-<p style="text-align: center;" align="center"><b>Figure. Comparison between 1D and averaged 2D.</b></p>
-<p style="text-align: center;" align="center"><img src="img/image132.jpg" alt="" width="379" height="256" /></p>
-<p style="text-align: center;" align="center">Figure. The angles for oriented ellipsoid.</p>
-<p>Our model uses the form factor calculations implemented in a c-library provided by the NIST Center for Neutron Research (Kline, 2006):</p>
-<p>REFERENCE</p>
-<p>L. A. Feigin and D. I. Svergun &ldquo;Structure Analysis by Small-Angle X-Ray and Neutron Scattering&rdquo;, Plenum, New York, 1987.</p>
-
-
-
-
-
-
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.34.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="LamellarModel"></a><b><span style="font-size: 14pt;">LamellarModel</span></b></p>
-<p>This model provides the scattering intensity, I(<em>q</em>), for a lyotropic lamellar phase where a uniform SLD and random distribution in solution are assumed. &nbsp;The ploydispersion in the bilayer thickness can be applied from the GUI.</p>
-<p>The scattering intensity I(q) is:</p>
-<p style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="img/image133.PNG" alt="" /></span></p>
-<p>The form factor is,</p>
-<p style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="img/image134.PNG" alt="" /></span></p>
-<p>where <span style="font-family: Symbol;">d</span> = bilayer thickness.</p>
-<p>The 2D scattering intensity is calculated in the same way as 1D, where the <em>q</em> vector is defined as<span style="font-size: 12pt; font-family: 'Times New Roman','serif'; position: relative; top: 4.5pt;"><img src="img/image040.gif" alt="" width="111" height="23" /></span><span style="font-size: 14pt;">.</span></p>
-<p><span style="font-size: 14pt;">&nbsp;</span></p>
-<p>The returned value is in units of [cm-1], on absolute scale. In the parameters, sld_bi = SLD of the bilayer, sld_sol = SLD of the solvent, and bi_thick = the thickness of the bilayer.</p>
-<p>&nbsp;</p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 18.8pt;">
-<td style="border: 1pt solid vertical-align: top; width: 107pt; height: 18.8pt;">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>0.0</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sld_bi</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>1e-006</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>bi_thick</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>50</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sld_sol</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>6e-006</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>1</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="text-align: center;" align="center"><img id="Picture 571" src="img/image135.jpg" alt="" width="476" height="351" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot using the default values (w/1000 data point).</b></p>
-<p>Our model uses the form factor calculations implemented in a c-library provided by the NIST Center for Neutron Research (Kline, 2006):</p>
-<p>REFERENCE</p>
-<p>Nallet, Laversanne, and Roux, J. Phys. II France, 3, (1993) 487-502.</p>
-<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; also in J. Phys. Chem. B, 105, (2001) 11081-11088.</p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.35.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="LamellarFFHGModel"></a><b><span style="font-size: 14pt;">LamellarFFHGModel</span></b></p>
-<p>This model calculates the form factor from a lyotropic lamellar phase. The intensity calculated is for lamellae of two-layer scattering length density that are randomly distributed in solution (a powder average). The scattering length density of the tail region, headgroup region, and solvent are taken to be different.
-No inter-lamellar structure factor is calculated. Other models are available where S(q) is calculated.</p>
-<p>The returned value is scale*I(q) + background, and is in units of [cm<sup>-1</sup>]:</p>
-<p style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="img/image136.PNG" alt="" /></span></p>
-<p>where the form factor is given by:</p>
-<p style="text-align: center;" align="center"><img src="img/image137.jpg" alt="" width="432" height="46" /></p>
-<p>where &delta;<sub>T</sub> = tail length (or t_length), &delta;<sub>H</sub> = head thickness (or h_thickness), &Delta;&rho;<sub>H</sub> = SLD (headgroup) - SLD(solvent), and &Delta;&rho;<sub>T</sub> = SLD (tail) - SLD(solvent).
-<br>(sld_tail = SLD of the tail group, and sld_head = SLD of the head group)</p>
-<p>The 2D scattering intensity is calculated in the same way as 1D, where the q vector is defined as:</p>
-<p><img src="img/image040.gif" alt="" width="111" /></p>
-<p>NOTE: The total bilayer thickness = 2(&delta;<sub>H</sub> + &delta;<sub>T</sub>)</p>
-<p>The meaning of the multiplicative scale factor is not well-defined, but should be on the order of the volume fraction of solution occupied by the lamellar crystallites. Please see the original references for clarification.</p>
-<p>&nbsp;</p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 18.8pt;">
-<td style="border: 1pt solid width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>0.0</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sld_head</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>3e-006</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>1</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sld_solvent</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>6e-006</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; vertical-align: top; width: 107pt; height: 18.8pt;">
-<p>h_thickness</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>10</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>t_length</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>15</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sld_tail</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>0</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="text-align: center;" align="center"><img id="Picture 61" src="img/image138.jpg" alt="" width="505" height="344" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot using the default values (w/1000 data point).</b></p>
-<p>Our model uses the form factor calculations implemented in a c-library provided by the NIST Center for Neutron Research (Kline, 2006):</p>
-<p>REFERENCE</p>
-<p>Nallet, Laversanne, and Roux, J. Phys. II France, 3, (1993) 487-502.</p>
-<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; also in J. Phys. Chem. B, 105, (2001) 11081-11088.</p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.36.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="LamellarPSModel"></a><b><span style="font-size: 14pt;">LamellarPSModel</span></b></p>
-<p>This model provides the scattering intensity (<b>form factor</b> <b>*</b> <b>structure factor</b>), I(<em>q</em>), for a lyotropic lamellar phase where a random distribution in solution are assumed.</p>
-<p>The scattering intensity I(q) is:</p>
-<p style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="img/image139.PNG" alt="" /></span></p>
-<p>The form factor is</p>
-<p style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="img/image134.PNG" alt="" /></span></p>
-<p>and the structure is</p>
-<p style="text-align: center;" align="center"><span style="position: relative; top: 16pt;"><img src="img/image140.PNG" alt="" /></span></p>
-<p>where</p>
-<p>&nbsp;</p>
-<p style="text-align: center;" align="center"><img src="img/image141.PNG" alt="" /></p>
-<p>&nbsp;</p>
-<p>Here d= (repeat) spacing, <span style="font-family: Symbol;">d</span> = bilayer thickness, the contrast <span style="font-family: Symbol;">Dr</span> = SLD (headgroup) - SLD(solvent), K=smectic bending elasticity, B=compression modulus, and N = number of lamellar plates (n_plates).</p>
-<p>Note: When the Caille parameter is greater than approximately 0.8 to 1.0, the assumptions of the model are incorrect. And due to the complication of the model function, users are responsible to make sure that all the assumptions are handled accurately: see the original reference (below) for more details.</p>
-<p>The 2D scattering intensity is calculated in the same way as 1D, where the <em>q</em> vector is defined as<span style="font-size: 12pt; font-family: 'Times New Roman','serif'; position: relative; top: 4.5pt;"><img src="img/image040.gif" alt="" width="111" height="23" /></span><span style="font-size: 14pt;">.</span></p>
-<p>The returned value is in units of [cm-1], on absolute scale.</p>
-<p>&nbsp;</p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 18.8pt;">
-<td style="border: 1pt solid width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; vertical-align: top; width: 107pt; height: 18.8pt;">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>0.0</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>contrast</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>5e-006</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>1</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>delta</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>30</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>n_plates</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>20</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>spacing</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>400</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>caille</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>0.1</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="text-align: center;" align="center"><img id="Picture 659" src="img/image142.jpg" alt="" width="439" height="348" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot using the default values (w/6000 data point).</b></p>
-<p>Our model uses the form factor calculations implemented in a c-library provided by the NIST Center for Neutron Research (Kline, 2006):</p>
-<p>REFERENCE</p>
-<p>Nallet, Laversanne, and Roux, J. Phys. II France, 3, (1993) 487-502.</p>
-<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; also in J. Phys. Chem. B, 105, (2001) 11081-11088.</p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.37.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="LamellarPSHGModel"></a><b><span style="font-size: 14pt;">LamellarPSHGModel</span></b></p>
-<p>This model provides the scattering intensity (<b>form factor</b> <b>*</b> <b>structure factor</b>), I(<em>q</em>), for a lyotropic lamellar phase where a random distribution in solution are assumed. &nbsp;The SLD of the head region is taken to be different from the SLD of the tail region.</p>
-<p>The scattering intensity I(q) is:</p>
-<p style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="img/image139.PNG" alt="" /></span></p>
-<p>The form factor is,</p>
-<p style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="img/image143.PNG" alt="" /></span></p>
-<p>The structure factor is</p>
-<p style="text-align: center;" align="center"><span style="position: relative; top: 16pt;"><img src="img/image140.PNG" alt="" /></span></p>
-<p>where</p>
-<p>&nbsp;</p>
-<p style="text-align: center;" align="center"><img src="img/image141.PNG" alt="" /></p>
-<p>&nbsp;</p>
-<p>where <span style="font-family: Symbol;">dT</span> = tail length (or t_length), <span style="font-family: Symbol;">dH</span> = heasd thickness (or h_thickness) , <span style="font-family: Symbol;">Dr</span>H = SLD (headgroup) - SLD(solvent), and <span style="font-family: Symbol;">Dr</span>T = SLD (tail) - SLD(headgroup). Here d= (repeat) spacing, K=smectic bending elasticity, B=compression modulus, and N = number of lamellar plates (n_plates).</p>
-<p>Note: When the Caille parameter is greater than approximately 0.8 to 1.0, the assumptions of the model are incorrect. And due to the complication of the model function, users are responsible to make sure that all the assumptions are handled accurately: see the original reference (below) for more details.</p>
-<p>The 2D scattering intensity is calculated in the same way as 1D, where the <em>q</em> vector is defined as<span style="font-size: 12pt; font-family: 'Times New Roman','serif'; position: relative; top: 4.5pt;"><img src="img/image040.gif" alt="" width="111" height="23" /></span><span style="font-size: 14pt;">.</span></p>
-<p><span style="font-size: 14pt;">&nbsp;</span></p>
-<p>The returned value is in units of [cm-1], on absolute scale. In the parameters, sld_tail = SLD of the tail group, sld_head = SLD of the head group, and sld_solvent = SLD of the solvent.</p>
-<p>&nbsp;</p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 18.8pt;">
-<td style="border: 1pt solid width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; vertical-align: top; width: 107pt; height: 18.8pt;">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>0.001</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sld_head</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>2e-006</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>1</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sld_solvent</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>6e-006</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>deltaH</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>2</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>deltaT</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>10</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sld_tail</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>0</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>n_plates</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>30</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>spacing</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>40</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>caille</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>0.001</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="text-align: center;" align="center"><img id="Picture 687" src="img/image144.jpg" alt="" width="463" height="360" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot using the default values (w/6000 data point).</b></p>
-<p>Our model uses the form factor calculations implemented in a c-library provided by the NIST Center for Neutron Research (Kline, 2006):</p>
-<p>REFERENCE</p>
-<p>Nallet, Laversanne, and Roux, J. Phys. II France, 3, (1993) 487-502.</p>
-<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; also in J. Phys. Chem. B, 105, (2001) 11081-11088.</p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.38.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="LamellarPCrystalModel"></a><b><span style="font-size: 14pt;">LamellarPCrystalModel</span></b></p>
-<p>Lamella ParaCrystal Model: Calculates the scattering from a stack of repeating lamellar structures. The stacks of lamellae (infinite in lateral dimension) are treated as a paracrystal to account for the repeating spacing. The repeat distance is further characterized by a Gaussian polydispersity. This model can be used for large multilamellar vesicles.</p>
-<p>The scattering intensity I(q) is calculated as:</p>
-<p style="text-align: center;" align="center"><img src="img/image145.jpg" alt="" width="280" height="48" /></p>
-<p>The form factor of the bilayer is approximated as the cross section of an infinite, planar bilayer of thickness t.</p>
-<p style="text-align: center;" align="center"><img src="img/image146.jpg" alt="" width="177" height="54" /></p>
-<p>Here, the scale factor is used instead of the mass per area of the bilayer (G). The scale factor is the volume fraction of the material in the bilayer, not the total excluded volume of the paracrystal. ZN(q) describes the interference effects for aggregates consisting of more than one bilayer. The equations used are (3-5) from the Bergstrom reference below.</p>
-<p>Non-integer numbers of stacks are calculated as a linear combination of the lower and higher values:</p>
-<p style="text-align: center;" align="center"><img src="img/image147.jpg" alt="" width="268" height="32" /></p>
-<p>The 2D scattering intensity is the same as 1D, regardless of the orientation of the <em>q</em> vector which is defined as<span style="font-size: 12pt; font-family: 'Times New Roman','serif'; position: relative; top: 4.5pt;"><img src="img/image040.gif" alt="" width="111" height="23" /></span><span style="font-size: 14pt;">.</span></p>
-<p>The parameters of the model are the following (Nlayers= no. of layers, pd_spacing= polydispersity of spacing&hellip;):</p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 18.8pt;">
-<td style="border: 1pt solid width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>0</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; vertical-align: top; width: 107pt; height: 18.8pt;">
-<p>scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>1</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Nlayers</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>20</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>pd_spacing</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>0.2</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sld_layer</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>1e-6</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sld_solvent</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>6.34e-6</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>spacing</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>250</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>thickness</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>33</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="text-align: center;" align="center"><img src="img/image148.jpg" alt="" width="501" height="332" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot using the default values above (w/20000 data point).</b></p>
-<p>Our model uses the form factor calculations implemented in a c-library provided by the NIST Center for Neutron Research (Kline, 2006).</p>
-<p>See the reference for details.</p>
-<p>REFERENCE</p>
-<p>M. Bergstrom, J. S. Pedersen, P. Schurtenberger, S. U. Egelhaaf, J. Phys. Chem. B, 103 (1999) 9888-9897.</p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.39.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="SCCrystalModel"></a><b><span style="font-size: 14pt;">SC(Simple Cubic Para-)CrystalModel</span></b></p>
-<p>Calculates the scattering from a simple cubic lattice with paracrystalline distortion. Thermal vibrations are considered to be negligible, and the size of the paracrystal is infinitely large. Paracrystalline distortion is assumed to be isotropic and characterized by a Gaussian distribution.</p>
-<p>The returned value is scaled to units of [cm-1sr-1], absolute scale.</p>
-<p>The scattering intensity I(q) is calculated as:</p>
-<p style="text-align: center;" align="center"><img id="Picture 17" src="img/image149.jpg" alt="" width="215" height="50" /></p>
-<p>where scale is the volume fraction of spheres, Vp is the volume of the primary particle, V(lattice) is a volume correction for the crystal structure, P(q) is the form factor of the sphere (normalized) and Z(q) is the paracrystalline structure factor for a simple cubic structure. Equation (16) of the 1987 reference is used to calculate Z(q), using equations (13)-(15) from the 1987 paper for Z1, Z2, and Z3.</p>
-<p>The lattice correction (the occupied volume of the lattice) for a simple cubic structure of particles of radius R and nearest neighbor separation D is:</p>
-<p style="text-align: center;" align="center"><img id="Picture 18" src="img/image150.jpg" alt="" width="119" height="48" /></p>
-<p>The distortion factor (one standard deviation) of the paracrystal is included in the calculation of Z(q):</p>
-<p style="text-align: center;" align="center"><img id="Picture 19" src="img/image151.jpg" alt="" width="68" height="21" /></p>
-<p>where g is a fractional distortion based on the nearest neighbor distance.</p>
-<p>The simple cubic lattice is:</p>
-<p style="text-align: center;" align="center"><img id="Picture 20" src="img/image152.jpg" alt="" width="220" height="235" /></p>
-<p>For a crystal, diffraction peaks appear at reduced q-values givn by:</p>
-<p style="text-align: center;" align="center"><img id="Picture 21" src="img/image153.jpg" alt="" width="128" height="41" /></p>
-<p>where for a simple cubic lattice any h, k, l are allowed and none are forbidden. Thus the peak positions correspond to (just the first 5):</p>
-<p style="text-align: center;" align="center"><img id="Picture 22" src="img/image154.jpg" alt="" width="279" height="52" /></p>
-<p>NOTE: The calculation of Z(q) is a double numerical integral that must be carried out with a high density of points to properly capture the sharp peaks of the paracrystalline scattering. So be warned that the calculation is SLOW. Go get some coffee. Fitting of any experimental data must be resolution smeared for any meaningful fit. This makes a triple integral. Very, very slow. Go get lunch.</p>
-<p>REFERENCES</p>
-<p>Hideki Matsuoka et. al. Physical Review B,&nbsp; 36 (1987) 1754-1765.&nbsp; (Original Paper)</p>
-<p>Hideki Matsuoka et. al. Physical Review B,&nbsp; 41 (1990) 3854 -3856.&nbsp; (Corrections to FCC and BCC lattice structure calculation)</p>
-<p>&nbsp;</p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 18.8pt;">
-<td style="border: 1pt solid vertical-align: top; width: 107pt; height: 18.8pt;">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>0</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>dnn</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>220</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>1</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sldSolv</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>6.3e-006</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>radius</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>40</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sld_Sph</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>3e-006</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>d_factor</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>0.06</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; TEST DATASET</p>
-<p>This example dataset is produced using 200 data points, qmin = 0.01 &Aring;-1,&nbsp; qmax = 0.1 &Aring;-1 and the above default values.</p>
-<p style="text-align: center;" align="center"><img id="Picture 73" src="img/image155.jpg" alt="" width="515" height="403" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot in the linear scale using the default values (w/200 data point).</b></p>
-<p>&nbsp;The 2D (Anisotropic model) is based on the reference (above) which I(q) &nbsp;is approximated for 1d scattering. Thus the scattering pattern for 2D may not be accurate. Note that we are not responsible for any incorrectness of the 2D model computation.</p>
-<p style="text-align: center;" align="center"><img id="Object 23" src="img/image156.jpg" /></p>
-<p style="text-align: center;" align="center">&nbsp;</p>
-<p>&nbsp;</p>
-<p>&nbsp;</p>
-<p>&nbsp;</p>
-<p style="text-align: center;" align="center"><b><img src="img/image157.jpg" alt="" width="447" height="322" /></b></p>
-<p style="text-align: center;" align="center"><b>Figure. 2D plot using the default values (w/200X200 pixels).</b></p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.40.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="FCCrystalModel"></a><b><span style="font-size: 14pt;">FC(Face Centered Cubic Para-)CrystalModel</span></b></p>
-<p>Calculates the scattering from a face-centered cubic lattice with paracrystalline distortion. Thermal vibrations are considered to be negligible, and the size of the paracrystal is infinitely large. Paracrystalline distortion is assumed to be isotropic and characterized by a Gaussian distribution.&nbsp;</p>
-<p>The returned value is scaled to units of [cm-1sr-1], absolute scale.</p>
-<p>The scattering intensity I(q) is calculated as:</p>
-<p style="text-align: center;" align="center"><img src="img/image158.jpg" alt="" width="183" height="42" /></p>
-<p>where scale is the volume fraction of spheres, Vp is the volume of the primary particle, V(lattice) is a volume correction for the crystal structure, P(q) is the form factor of the sphere (normalized) and Z(q) is the paracrystalline structure factor for a face-centered cubic structure. Equation (1) of the 1990 reference is used to calculate Z(q), using equations (23)-(25) from the 1987 paper for Z1, Z2, and Z3.</p>
-<p>The lattice correction (the occupied volume of the lattice) for a face-centered cubic structure of particles of radius R and nearest neighbor separation D is:</p>
-<p style="text-align: center;" align="center"><img src="img/image159.jpg" alt="" width="125" height="54" /></p>
-<p>The distortion factor (one standard deviation) of the paracrystal is included in the calculation of Z(q):</p>
-<p style="text-align: center;" align="center"><img src="img/image160.jpg" alt="" width="60" height="19" /></p>
-<p>where g is a fractional distortion based on the nearest neighbor distance.</p>
-<p>The face-centered cubic lattice is:</p>
-<p style="text-align: center;" align="center"><img id="Picture 28" src="img/image161.jpg" alt="" width="243" height="260" /></p>
-<p>For a crystal, diffraction peaks appear at reduced q-values givn by:</p>
-<p style="text-align: center;" align="center"><img src="img/image162.jpg" alt="" width="136" height="45" /></p>
-<p>where for a face-centered cubic lattice&nbsp; h, k, l all odd or all even are allowed and reflections where h, k, l are mixed odd/even are forbidden. Thus the peak positions correspond to (just the first 5):</p>
-<p style="text-align: center;" align="center"><img id="Picture 30" src="img/image163.jpg" alt="" width="312" height="53" /></p>
-<p>NOTE: The calculation of Z(q) is a double numerical integral that must be carried out with a high density of points to properly capture the sharp peaks of the paracrystalline scattering. So be warned that the calculation is SLOW. Go get some coffee. Fitting of any experimental data must be resolution smeared for any meaningful fit. This makes a triple integral. Very, very slow. Go get lunch.</p>
-<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; REFERENCES</p>
-<p>Hideki Matsuoka et. al. Physical Review B,&nbsp; 36 (1987) 1754-1765.&nbsp; (Original Paper)</p>
-<p>Hideki Matsuoka et. al. Physical Review B,&nbsp; 41 (1990) 3854 -3856.&nbsp; (Corrections to FCC and BCC lattice structure calculation)</p>
-<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</p>
-<p>&nbsp;</p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 18.8pt;">
-<td style="border: 1pt solid vertical-align: top; width: 107pt; height: 18.8pt;">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>0</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>dnn</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>220</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>1</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sldSolv</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>6.3e-006</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>radius</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>40</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sld_Sph</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>3e-006</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>d_factor</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>0.06</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p>TEST DATASET</p>
-<p>This example dataset is produced using 200 data points, qmin = 0.01 &Aring;-1,&nbsp; qmax = 0.1 &Aring;-1 and the above default values.</p>
-<p style="text-align: center;" align="center"><img src="img/image164.jpg" alt="" width="539" height="394" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot in the linear scale using the default values (w/200 data point).</b></p>
-<p>&nbsp;The 2D (Anisotropic model) is based on the reference (above) in which I(q)&nbsp; is approximated for 1d scattering. Thus the scattering pattern for 2D may not be accurate. Note that we are not responsible for any incorrectness of the 2D model computation.</p>
-<p style="text-align: center;" align="center"><img src="img/image165.gif" /></p>
-<p style="text-align: center;" align="center">&nbsp;</p>
-<p>&nbsp;</p>
-<p>&nbsp;</p>
-<p>&nbsp;</p>
-<p style="text-align: center;" align="center"><img src="img/image166.jpg" alt="" width="473" height="352" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 2D plot using the default values (w/200X200 pixels).</b></p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.41.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="BCCrystalModel"></a><b><span style="font-size: 14pt;">BC(Body Centered Cubic Para-)CrystalModel</span></b></p>
-<p>Calculates the scattering from a body-centered cubic lattice with paracrystalline distortion. Thermal vibrations are considered to be negligible, and the size of the paracrystal is infinitely large. Paracrystalline distortion is assumed to be isotropic and characterized by a Gaussian distribution.The returned value is scaled to units of [cm-1sr-1], absolute scale.</p>
-<p>The scattering intensity I(q) is calculated as:</p>
-<p style="text-align: center;" align="center"><img id="Picture 25" src="img/image167.jpg" alt="" width="183" height="42" /></p>
-<p>where scale is the volume fraction of spheres, Vp is the volume of the primary particle, V(lattice) is a volume correction for the crystal structure, P(q) is the form factor of the sphere (normalized) and Z(q) is the paracrystalline structure factor for a body-centered cubic structure. Equation (1) of the 1990 reference is used to calculate Z(q), using equations (29)-(31) from the 1987 paper for Z1, Z2, and Z3.</p>
-<p>The lattice correction (the occupied volume of the lattice) for a body-centered cubic structure of particles of radius R and nearest neighbor separation D is:</p>
-<p style="text-align: center;" align="center"><img id="Picture 26" src="img/image159.jpg" alt="" width="125" height="54" /></p>
-<p>The distortion factor (one standard deviation) of the paracrystal is included in the calculation of Z(q):</p>
-<p style="text-align: center;" align="center"><img id="Picture 27" src="img/image160.jpg" alt="" width="60" height="19" /></p>
-<p>where g is a fractional distortion based on the nearest neighbor distance.</p>
-<p>The body-centered cubic lattice is:</p>
-<p style="text-align: center;" align="center"><img id="Picture 231" src="img/image168.jpg" alt="" width="269" height="256" /></p>
-<p>For a crystal, diffraction peaks appear at reduced q-values givn by:</p>
-<p style="text-align: center;" align="center"><img id="Picture 29" src="img/image162.jpg" alt="" width="136" height="45" /></p>
-<p>where for a body-centered cubic lattice, only reflections where (h+k+l) = even are allowed and reflections where (h+k+l) = odd are forbidden. Thus the peak positions correspond to (just the first 5):</p>
-<p style="text-align: center;" align="center"><img id="Picture 232" src="img/image169.jpg" alt="" width="320" height="53" /></p>
-<p>NOTE: The calculation of Z(q) is a double numerical integral that must be carried out with a high density of points to properly capture the sharp peaks of the paracrystalline scattering. So be warned that the calculation is SLOW. Go get some coffee. Fitting of any experimental data must be resolution smeared for any meaningful fit. This makes a triple integral. Very, very slow. Go get lunch.</p>
-<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; REFERENCES</p>
-<p>Hideki Matsuoka et. al. Physical Review B,&nbsp; 36 (1987) 1754-1765.&nbsp; (Original Paper)</p>
-<p>Hideki Matsuoka et. al. Physical Review B,&nbsp; 41 (1990) 3854 -3856.&nbsp; (Corrections to FCC and BCC lattice structure calculation)</p>
-<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</p>
-<p>&nbsp;</p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 18.8pt;">
-<td style="border: 1pt solid vertical-align: top; width: 107pt; height: 18.8pt;">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>0</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>dnn</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>220</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>1</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sldSolv</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>6.3e-006</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>radius</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>40</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>sld_Sph</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>&Aring; -2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>3e-006</p>
-</td>
-</tr>
-<tr style="height: 18.8pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>d_factor</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143">
-<p>0.06</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p>TEST DATASET</p>
-<p>This example dataset is produced using 200 data points, qmin = 0.001 &Aring;-1,&nbsp; qmax = 0.1 &Aring;-1 and the above default values.</p>
-<p style="text-align: center;" align="center"><img src="img/image170.jpg" alt="" width="474" height="339" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot in the linear scale using the default values (w/200 data point).</b></p>
-<p>&nbsp;The 2D (Anisotropic model) is based on the reference (1987) in which I(q) &nbsp;is approximated for 1d scattering. Thus the scattering pattern for 2D may not be accurate. Note that we are not responsible for any incorrectness of the 2D model computation.</p>
-<p style="text-align: center;" align="center"><img id="Object 31" src="img/image165.gif" /></p>
-<p style="text-align: center;" align="center">&nbsp;</p>
-<p>&nbsp;</p>
-<p>&nbsp;</p>
-<p>&nbsp;</p>
-<p style="text-align: center;" align="center"><img src="img/image171.jpg" alt="" width="477" height="344" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 2D plot using the default values (w/200X200 pixels).</b></p>
-<p style="margin-left: 0.25in; text-indent: -0.25in;"><b><span style="font-size: 16pt;">3.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp; </span></b><a name="Shape-Independent"></a><b><span style="font-size: 16pt;">Shape-Independent Models </span></b></p>
-<p>The following are models used for shape-independent SANS analysis.</p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.1.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b><span style="font-size: 14pt;">&nbsp;<a name="Debye"></a>Debye (Model)</span></b></p>
-<p style="margin-left: 0.25in;">The Debye model is a form factor for a linear polymer chain. In addition to the radius of gyration, Rg, a scale factor "scale", and a constant background term are included in the calculation.</p>
-<p style="text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 27pt;"><img src="img/image172.PNG" alt="" /></span></p>
-<p style="text-align: center;" align="center"><span style="font-size: 14pt;">&nbsp;</span></p>
-<p style="text-align: center;" align="center"><span style="font-size: 14pt;">&nbsp;</span></p>
-<p style="margin-left: 0.25in;">For 2D plot, the wave transfer is defined as<span style="font-size: 12pt; font-family: 'Times New Roman','serif'; position: relative; top: 4.5pt;"><img src="img/image040.gif" alt="" /></span><span style="font-size: 14pt;">.</span></p>
-<p><span style="font-size: 14pt;">&nbsp;</span></p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 19.25pt;">
-<td style="border: 1pt solid vertical-align: top; width: 107pt; height: 19.25pt;">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>None</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>1.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>rg</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>50.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0.0</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><img id="Picture 74" src="img/image173.jpg" alt="" width="423" height="273" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot using the default values (w/200 data point).</b></p>
-<p style="margin-left: 0.25in; text-align: center;" align="center">&nbsp;</p>
-<p style="margin-left: 0.25in;">Reference: Roe, R.-J., "Methods of X-Ray and Neutron Scattering in Polymer Science", Oxford University Press, New York (2000).</p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.2.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b><span style="font-size: 14pt;">&nbsp;<a name="BroadPeakModel"></a>BroadPeak Model</span></b></p>
-<p style="margin-left: 0.25in;">Calculate an empirical functional form for SANS data characterized by a broad scattering peak. Many SANS spectra are characterized by a broad peak even though they are from amorphous soft materials. The d-spacing corresponding to the broad peak is a characteristic distance between the scattering inhomogeneities (such as in lamellar, cylindrical, or spherical morphologies or for bicontinuous structures).</p>
-<p style="margin-left: 0.25in;">The returned value is scaled to units of [cm-1sr-1], absolute scale.</p>
-<p style="margin-left: 0.25in;">The scattering intensity I(q) is calculated by:&nbsp;</p>
-<p style="text-align: center;" align="center"><img id="Picture 233" src="img/image174.jpg" alt="" width="223" height="43" /></p>
-<p>Here the peak position is related to the d-spacing as Q0 = 2pi/d0. Soft systems that show a SANS peak include copolymers, polyelectrolytes, multiphase systems, layered structures, etc.</p>
-<p style="text-align: center;" align="center"><span style="font-size: 14pt;">&nbsp;</span></p>
-<p style="text-align: center;" align="center"><span style="font-size: 14pt;">&nbsp;</span></p>
-<p style="margin-left: 0.25in;">For 2D plot, the wave transfer is defined as<span style="font-size: 12pt; font-family: 'Times New Roman','serif'; position: relative; top: 4.5pt;"><img src="img/image040.gif" alt="" /></span><span style="font-size: 14pt;">.</span></p>
-<p><span style="font-size: 14pt;">&nbsp;</span></p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 19.25pt;">
-<td style="border: 1pt solid width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>scale_l (= C)</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>10</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>scale_p (=A)</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>1e-05</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>length_l (=<span style="font-family: Symbol;">x</span>)</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>50</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; vertical-align: top; width: 107pt; height: 19.25pt;">
-<p>q_peak (= Q0)</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0.1</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>exponent_p (=n)</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>2</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>exponent_l (=m)</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>3</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Background (=B)</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0.1</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><img src="img/image175.jpg" alt="" width="488" height="334" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot using the default values (w/200 data point).</b></p>
-<p style="margin-left: 0.25in; text-align: center;" align="center">&nbsp;</p>
-<p style="margin-left: 0.25in;">Reference: None.</p>
-<p style="margin-left: 0.25in;"><i>2013/09/09 - Description reviewed by King, S. and Parker, P.</i></p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.3.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b><span style="font-size: 14pt;">&nbsp;<a name="CorrLength"></a>CorrLength (CorrelationLengthModel)</span></b></p>
-<p style="margin-left: 0.25in;">Calculate an empirical functional form for SANS data characterized by a low-Q signal and a high-Q signal</p>
-<p>The returned value is scaled to units of [cm-1sr-1], absolute scale.</p>
-<p>The scattering intensity I(q) is calculated by:<span style="font-size: 14pt;">&nbsp;</span></p>
-<p style="text-align: center;" align="center"><img id="Picture 234" src="img/image176.jpg" alt="" width="186" height="46" /></p>
-<p style="text-align: center;" align="center">The first term describes Porod scattering from clusters (exponent = n) and the second term is a Lorentzian function describing scattering from polymer chains (exponent = m). This second term characterizes the polymer/solvent interactions and therefore the thermodynamics. The two multiplicative factors A and C, the incoherent background B and the two exponents n and m are used as fitting parameters. The final parameter (xi) is a correlation length for the polymer chains. Note that when m = 2, this functional form becomes the familiar Lorentzian function.<span style="font-size: 14pt;">&nbsp;</span></p>
-<p style="text-align: center;" align="center"><span style="font-size: 14pt;">&nbsp;</span></p>
-<p style="margin-left: 0.25in;">For 2D plot, the wave transfer is defined as<span style="font-size: 12pt; font-family: 'Times New Roman','serif'; position: relative; top: 4.5pt;"><img src="img/image040.gif" alt="" /></span><span style="font-size: 14pt;">.</span></p>
-<p><span style="font-size: 14pt;">&nbsp;</span></p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 19.25pt;">
-<td style="border: 1pt solid width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>scale_l (= C)</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>10</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>scale_p (=A)</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>1e-06</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>length_l (=<span style="font-family: Symbol;">x</span>)</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>50</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; vertical-align: top; width: 107pt; height: 19.25pt;">
-<p>exponent_p (=n)</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>2</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>exponent_l (=m)</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>3</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Background (=B)</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0.1</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><img id="Picture 80" src="img/image177.jpg" alt="" width="489" height="338" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot using the default values (w/500 data points).</b></p>
-<p style="margin-left: 0.25in; text-align: center;" align="center">&nbsp;</p>
-<p style="margin-left: 0.25in;">REFERENCE</p>
-<p style="margin-left: 0.25in;">B. Hammouda, D.L. Ho and S.R. Kline, &ldquo;Insight into Clustering in Poly(ethylene oxide) Solutions&rdquo;, Macromolecules 37, 6932-6937 (2004).</p>
-<p style="margin-left: 0.25in;"><i>2013/09/09 - Description reviewed by King, S. and Parker, P.</i></p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.4.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b><span style="font-size: 14pt;">&nbsp;<a name="Lorentz"></a>(Ornstein-Zernicke) Lorentz (Model)</span></b></p>
-<p style="text-indent: 0.25in;">The Ornstein-Zernicke model is defined by:</p>
-<p><span style="font-size: 14pt;">&nbsp;</span></p>
-<p style="text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 5pt;"><img src="img/image178.PNG" alt="" /></span></p>
-<p><span style="font-size: 14pt;">&nbsp;</span></p>
-<p style="text-indent: 0.25in;">The parameter L is referred to as the screening length.</p>
-<p style="text-indent: 0.25in;">&nbsp;</p>
-<p style="margin-left: 0.25in;">For 2D plot, the wave transfer is defined as<span style="font-size: 12pt; font-family: 'Times New Roman','serif'; position: relative; top: 4.5pt;"><img src="img/image040.gif" alt="" /></span><span style="font-size: 14pt;">.</span></p>
-<p style="text-indent: 0.25in;">&nbsp;</p>
-<p><span style="font-size: 14pt;">&nbsp;</span></p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 19.25pt;">
-<td style="border: 1pt solid width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; vertical-align: top; width: 107pt; height: 19.25pt;">
-<p>scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>None</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>1.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>length</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>50.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0.0</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="text-align: center;" align="center"><b><span style="font-size: 14pt;"><img id="Picture 75" src="img/image179.jpg" alt="" /></span></b></p>
-<p style="text-align: center;" align="center"><b><span style="font-size: 14pt;">&nbsp;</span>Figure. 1D plot using the default values (w/200 data point).</b></p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.5.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b><span style="font-size: 14pt;">&nbsp;<a name="DABModel"></a>DAB (Debye-Anderson-Brumberger)_Model</span></b></p>
-<p style="margin-left: 0.55in;"><b><span style="font-size: 14pt;">&nbsp;</span></b></p>
-<p style="margin-left: 0.25in;">Calculates the scattering from a randomly distributed, two-phase system based on the Debye-Anderson-Brumberger (DAB) model for such systems. The two-phase system is characterized by a single length scale, the correlation length, which is a measure of the average spacing between regions of phase 1 and phase 2. The model also assumes smooth interfaces between the phases and hence exhibits Porod behavior (I ~ Q-4) at large Q (Q*correlation length &gt;&gt; 1).</p>
-<p style="text-indent: 0.25in;">&nbsp;</p>
-<p style="text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 5pt;"><img src="img/image180.PNG" alt="" /></span></p>
-<p style="text-align: center;" align="center"><span style="font-size: 14pt;">&nbsp;&nbsp;</span></p>
-<p style="margin-left: 0.25in;">The parameter L is referred to as the correlation length.</p>
-<p style="margin-left: 0.25in;">For 2D plot, the wave transfer is defined as<span style="font-size: 12pt; font-family: 'Times New Roman','serif'; position: relative; top: 4.5pt;"><img src="img/image040.gif" alt="" /></span><span style="font-size: 14pt;">.</span></p>
-<p style="text-indent: 0.25in;">Note: If I(Q) is in absolute units (cm-1) scale must divided by 10^8 to convert it to &Aring;-1.</p>
-<p style="text-align: center;" align="center"><span style="font-size: 14pt;">&nbsp;</span></p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 19.25pt;">
-<td style="border: 1pt solid width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; vertical-align: top; width: 107pt; height: 19.25pt;">
-<p>scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;-4 </p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>1.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>length</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>50.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0.0</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="text-align: center;" align="center"><b><span style="font-size: 14pt;"><img id="Picture 76" src="img/image181.jpg" alt="" /></span></b></p>
-<p style="text-align: center;" align="center"><b><span style="font-size: 14pt;">&nbsp;</span>Figure. 1D plot using the default values (w/200 data point).</b></p>
-<p style="margin-left: 0.25in;">References:</p>
-<p style="margin-left: 0.5in;">Debye, Anderson, Brumberger, "Scattering by an Inhomogeneous Solid. II. The Correlation Function and its Application", J. Appl. Phys. 28 (6), 679 (1957).</p>
-<p style="margin-left: 0.5in;">&nbsp;</p>
-<p style="margin-left: 0.5in;">Debye, Bueche, "Scattering by an Inhomogeneous Solid", J. Appl. Phys. 20, 518 (1949).</p>
-<p style="margin-left: 0.25in;"><i>2013/09/09, 2014/04/22 - Description reviewed by King, S. and Parker, P.</i></p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.6.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b><span style="font-size: 14pt;">&nbsp; <a name="Absolute Power_Law"></a>Absolute Power_Law </span></b></p>
-<p style="margin-left: 0.25in;">This model describes a power law with background.</p>
-<p style="text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 5pt;"><img src="img/image182.PNG" alt="" /></span></p>
-<p style="text-align: center;" align="center"><span style="font-size: 14pt;">&nbsp;&nbsp;</span></p>
-<p style="margin-left: 0.25in;">Note the minus sign in front of the exponent.</p>
-<p style="text-align: center;" align="center"><span style="font-size: 14pt;">&nbsp;</span></p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 19.25pt;">
-<td style="border: 1pt solid vertical-align: top; width: 107pt; height: 19.25pt;">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>None</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>1.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>m</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>None</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>4</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0.0</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="text-align: center;" align="center"><img id="Picture 77" src="img/image183.jpg" alt="" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot using the default values (w/200 data point).</b></p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.7.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b><span style="font-size: 14pt;">&nbsp;<a name="TeubnerStreyModel"></a>Teubner Strey (Model)</span></b></p>
-<p style="margin-left: 0.25in;">This function calculates the scattered intensity of a two-component system using the Teubner-Strey model.</p>
-<p style="margin-left: 0.25in;"><b><span style="font-size: 14pt;">&nbsp;</span></b></p>
-<p style="text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 15pt;"><img src="img/image184.PNG" alt="" /></span></p>
-<p style="text-align: center;" align="center"><span style="font-size: 14pt;">&nbsp;</span></p>
-<p style="text-align: center;" align="center"><span style="font-size: 14pt;">&nbsp;</span></p>
-<p style="margin-left: 0.25in;">For 2D plot, the wave transfer is defined as<span style="font-size: 12pt; font-family: 'Times New Roman','serif'; position: relative; top: 4.5pt;"><img src="img/image040.gif" alt="" /></span><span style="font-size: 14pt;">.</span></p>
-<p><span style="font-size: 14pt;">&nbsp;</span></p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 19.25pt;">
-<td style="border: 1pt solid vertical-align: top; width: 107pt; height: 19.25pt;">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>None</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0.1</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>c1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>None</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>-30.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>c2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>None</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>5000.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0.0</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="text-align: center;" align="center"><img id="Picture 78" src="img/image185.jpg" alt="" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot using the default values (w/200 data point).</b></p>
-<p style="margin-left: 0.25in;">References:</p>
-<p style="margin-left: 0.5in;">Teubner, M; Strey, R. J. Chem. Phys., 87, 3195 (1987).</p>
-<p style="margin-left: 0.5in;">&nbsp;</p>
-<p style="margin-left: 0.5in;">Schubert, K-V., Strey, R., Kline, S. R. and E. W. Kaler, J. Chem. Phys., 101, 5343 (1994).</p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.8.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b><span style="font-size: 14pt;">&nbsp;<a name="Number_Density_Fractal"></a> <a name="FractalModel"></a>FractalModel</span></b></p>
-<p style="margin-left: 0.25in;">Calculates the scattering from fractal-like aggregates built from spherical building blocks following the Texiera reference. The value returned is in cm-1.</p>
-<p>&nbsp;</p>
-<p style="text-align: center;" align="center"><img src="img/image186.PNG" alt="" /></p>
-<p>&nbsp;</p>
-<p style="margin-left: 0.25in;">The scale parameter is the volume fraction of the building blocks, R0 is the radius of the building block, Df is the fractal dimension, &xi; is the correlation length, <em>&rho;solvent</em> is the scattering length density of the solvent, and <em>&rho;block</em> is the scattering length density of the building blocks.</p>
-<p style="margin-left: 0.25in;"><b>The polydispersion in radius is provided.</b></p>
-<p style="margin-left: 0.25in;">For 2D plot, the wave transfer is defined as<span style="font-size: 12pt; font-family: 'Times New Roman','serif'; position: relative; top: 4.5pt;"><img src="img/image040.gif" alt="" /></span><span style="font-size: 14pt;">.</span></p>
-<p style="text-align: center;" align="center"><span style="font-size: 14pt;">&nbsp;</span></p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 19.25pt;">
-<td style="border: 1pt solid width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; vertical-align: top; width: 107pt; height: 19.25pt;">
-<p>scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>None</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0.05</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>radius</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>5.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>fractal_dim</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>None</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>2</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>corr_length</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>100.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>block_sld</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;-2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>2e-6</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>solvent_sld</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;-2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>6e-6</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0.0</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><img id="Picture 79" src="img/image187.jpg" alt="" width="445" height="280" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot using the default values (w/200 data point).</b></p>
-<p style="margin-left: 0.25in; text-align: center;" align="center">&nbsp;</p>
-<p style="margin-left: 0.25in; text-align: center;" align="center">&nbsp;</p>
-<p style="margin-left: 0.25in;">References:</p>
-<p style="margin-left: 0.25in; text-indent: 0.25in;">J. Teixeira, (1988) J. Appl. Cryst., vol. 21, p781-785</p>
-<p><b><span style="font-size: 14pt;">&nbsp;</span></b></p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.9.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b><span style="font-size: 14pt;"><a name="Mass_Fractal"></a><a name="MassFractalModel"></a>MassFractalModel</span></b></p>
-<p style="margin-left: 0.25in;">Calculates the scattering from fractal-like aggregates based on the Mildner reference (below).&nbsp;</p>
-<p style="text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 85pt;"><br /> </span></p>
-<p style="text-align: center;" align="center"><span style="font-size: 12pt; font-family: 'Times New Roman','serif'; position: relative; top: 4.5pt;"><img src="img/mass_fractal_eq1.jpg" alt="" /></span><span style="font-size: 14pt;">&nbsp;</span></p>
-<p style="margin-left: 0.25in;">&nbsp;</p>
-<p style="margin-left: 0.25in;">&nbsp;</p>
-<p style="margin-left: 0.25in;">The R is the radius of the building block, Dm is the mass fractal dimension, &xi; is the correlation (or cutt-off)&nbsp; length, <em>&rho;solvent</em> is the scattering length density of the solvent, and <em>&rho;particle</em> is the scattering length density of particles.</p>
-<p style="margin-left: 0.25in;">Note: &nbsp;The mass fractal dimension is valid for 1&lt;mass_dim&lt;6.</p>
-<p style="text-align: center;" align="center"><span style="font-size: 14pt;">&nbsp;</span></p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 19.25pt;">
-<td style="border: 1pt solid width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; vertical-align: top; width: 107pt; height: 19.25pt;">
-<p>scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>None</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>1</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>radius</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>10.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>mass_dim</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>None</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>1.9</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>co_length</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>100.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&nbsp;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0.0</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><img id="Picture 79" style="width: 495px; height: 368px;" src="img/mass_fractal_fig1.jpg" alt="" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot</b></p>
-<p style="margin-left: 0.25in; text-align: center;" align="center">&nbsp;</p>
-<p style="margin-left: 0.25in; text-align: center;" align="center">&nbsp;</p>
-<p style="margin-left: 0.25in;">References:</p>
-<p style="margin-left: 0.25in; text-indent: 0.25in;">D. Mildner, and P. Hall,&nbsp; J. Phys. D.: Appl. Phys.,&nbsp; 19, 1535-1545&nbsp; (1986), Equation(9).</p>
-<p style="margin-left: 0.25in;"><i>2013/09/09 - Description reviewed by King, S. and Parker, P.</i></p>
-<p>&nbsp;</p>
-<p>&nbsp;</p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.10.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b> <b><span style="font-size: 14pt;"> <a name="Surface_Fractal"></a><a name="SurfaceFractalModel"></a>SurfaceFractalModel</span></b></p>
-<p style="margin-left: 0.25in;">Calculates the scattering&nbsp; based on the Mildner reference (below).&nbsp;</p>
-<p style="text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 85pt;"><br /> </span></p>
-<p style="text-align: center;" align="center"><span style="font-size: 12pt; font-family: 'Times New Roman','serif'; position: relative; top: 4.5pt;"><img src="img/surface_fractal_eq1.gif" alt="" /></span><span style="font-size: 14pt;">&nbsp;</span></p>
-<p style="margin-left: 0.25in;">&nbsp;</p>
-<p style="margin-left: 0.25in;">&nbsp;</p>
-<p style="margin-left: 0.25in;">The R is the radius of the building block, Ds is the surface fractal dimension, &xi; is the correlation (or cutt-off)&nbsp; length, <em>&rho;solvent</em> is the scattering length density of the solvent, and <em>&rho;particle</em> is the scattering length density of particles.</p>
-<p style="margin-left: 0.25in;">&nbsp;Note: &nbsp;The surface fractal dimension is valid for 1&lt;surface_dim&lt;3. &nbsp;Also it is valid in a limited q range (see the reference for details).</p>
-<p style="text-align: center;" align="center"><span style="font-size: 14pt;">&nbsp;</span></p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 19.25pt;">
-<td style="border: 1pt solid width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; vertical-align: top; width: 107pt; height: 19.25pt;">
-<p>scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>None</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>1</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>radius</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>10.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>surface_dim</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>None</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>2.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>co_length</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>500.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&nbsp;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0.0</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><img id="Picture 79" style="width: 507px; height: 375px;" src="img/surface_fractal_fig1.jpg" alt="" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot</b></p>
-<p style="margin-left: 0.25in; text-align: center;" align="center">&nbsp;</p>
-<p style="margin-left: 0.25in; text-align: center;" align="center">&nbsp;</p>
-<p style="margin-left: 0.25in;">References:</p>
-<p style="margin-left: 0.25in; text-indent: 0.25in;">D. Mildner, and P. Hall,&nbsp; J. Phys. D.: Appl. Phys.,&nbsp; 19, 1535-1545&nbsp; (1986), Equation(13).</p>
-<p>&nbsp;</p>
-<p>&nbsp;</p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.11.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b><span style="font-size: 14pt;"><a name="MassSurface_Fractal"></a><a name="MassSurfaceFractal"></a>MassSurfaceFractal</span></b></p>
-<p>&nbsp;&nbsp;&nbsp; A number of natural and commercial processes form high-surface area materials as a result of the vapour-phase aggregation of primary particles. Examples of such materials include soots, aerosols, and &lsquo;fume&rsquo; or pyrogenic silicas. These are all characterised by cluster mass distributions (sometimes also cluster size distributions) and internal surfaces that are fractal in nature. &nbsp; The scattering from such materials displays two distinct breaks in log-log representation, corresponding to the radius-of-gyration of the primary particles, rg, and the radius-of-gyration of the clusters (aggregates), Rg. Between these boundaries the scattering follows a power law related to the mass fractal dimension, Dm, whilst above the high-Q boundary the scattering follows a power law related to the surface fractal dimension of the primary particles, Ds.</p>
-<p style="margin-left: 0.55in;">The scattered intensity I(Q) is then calculated using a modified Ornstein-Zernicke equation:</p>
-<p style="text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 85pt;"><br /> </span></p>
-<p style="text-align: center;" align="center"><span style="font-size: 12pt; font-family: 'Times New Roman','serif'; position: relative; top: 4.5pt;"><img src="img/masssurface_fractal_eq1.jpg" alt="" /></span><span style="font-size: 14pt;">&nbsp;</span></p>
-<p style="margin-left: 0.25in;">&nbsp;</p>
-<p style="margin-left: 0.25in;">&nbsp;</p>
-<p style="margin-left: 0.25in;">The Rg is for the cluster, rg is for the primary, Ds is the surface fractal dimension, Dm is the mass fractal dimension, <em>&rho;solvent</em> is the scattering length density of the solvent, and <em>&rho;p</em> is the scattering length density of particles.</p>
-<p style="margin-left: 0.25in;">&nbsp;Note: &nbsp;The surface and mass fractal dimensions are valid for 0&lt;surface_dim&lt;6, 0&lt;mass_dim&lt;6, and (surface_mass+mass_dim)&lt;6.&nbsp;</p>
-<p style="text-align: center;" align="center"><span style="font-size: 14pt;">&nbsp;</span></p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 19.25pt;">
-<td style="border: 1pt solid width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; vertical-align: top; width: 107pt; height: 19.25pt;">
-<p>scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>None</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>1</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>primary_rg</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>4000.0</p>
-</td>
-</tr>
-<tr>
-<td>&nbsp; cluster_rg</td>
-<td>&nbsp; &Aring;</td>
-<td>&nbsp;86.7</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>surface_dim</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>None</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>2.3</p>
-</td>
-</tr>
-<tr>
-<td>&nbsp; mass_dim</td>
-<td>&nbsp;None</td>
-<td>&nbsp;1.8</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&nbsp;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0.0</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><img id="Picture 79" style="width: 507px; height: 370px;" src="img/masssurface_fractal_fig1.jpg" alt="" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot</b></p>
-<p style="margin-left: 0.25in; text-align: center;" align="center">&nbsp;</p>
-<p style="margin-left: 0.25in; text-align: center;" align="center">&nbsp;</p>
-<p style="margin-left: 0.25in;">References:</p>
-<p style="margin-left: 0.25in; text-indent: 0.25in;">P. Schmidt, J Appl. Cryst., 24, 414-435&nbsp; (1991), Equation(19).</p>
-<p style="margin-left: 0.25in; text-indent: 0.25in;">Hurd, Schaefer, Martin, Phys. Rev. A, 35, 2361-2364 (1987), Equation(2).</p>
-<p>&nbsp;</p>
-<p>&nbsp;</p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.12.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b><span style="font-size: 14pt;">&nbsp; <a name="FractalCoreShell"></a>FractalCoreShell(Model)</span></b></p>
-<p style="margin-left: 0.25in;">Calculates the scattering from a fractal structure with a primary building block of core-shell spheres.</p>
-<p><img src="img/fractcore_eq1.gif"/></p>
-<br>
-<br>
-The formfactor P(q) is <a href="#CoreShellModel">CoreShellModel</a> with bkg = 0, 
-<p><img src="img/image013.PNG"/>,</p>
-<br>
-while the fractal structure factor S(q);
-<p><img src="img/fractcore_eq3.gif"/></p>
-<br>
-<br>
-where Df = frac_dim, &#958; = cor_length, rc = (core) radius, and scale = volfraction.
-<p> The fractal structure is as documented in the fractal model. This model could find use for aggregates of coated particles, or aggregates of vesicles.&nbsp;The polydispersity computation of radius and thickness is provided.</p>
-<p style="margin-left: 0.25in;">The returned value is scaled to units of [cm-1sr-1], absolute scale.</p>
-<p style="margin-left: 0.25in;">See each of these individual models for full documentation.&nbsp;</p>
-<p style="margin-left: 0.25in;">For 2D plot, the wave transfer is defined as<span style="font-size: 12pt; font-family: 'Times New Roman','serif'; position: relative; top: 4.5pt;"><img src="img/image040.gif" alt="" /></span><span style="font-size: 14pt;">.</span></p>
-<p style="text-align: center;" align="center"><span style="font-size: 14pt;">&nbsp;</span></p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 19.25pt;">
-<td style="border: 1pt solid width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>volfraction</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0.05</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>frac_dim</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>2</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>thickness</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>5.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>raidus</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">&nbsp;&Aring;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>20.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>cor_length</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>100.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>core_sld</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;-2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>3.5e-6</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>shell_sld</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;-2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>1e-6</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>solvent_sld</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;-2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>6.35e-6</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0.0</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><img id="Picture 81" src="img/image188.jpg" alt="" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot using the default values (w/500 data points).</b></p>
-<p style="margin-left: 0.25in; text-align: center;" align="center">&nbsp;</p>
-<p style="margin-left: 0.25in; text-align: center;" align="center">&nbsp;</p>
-<p style="margin-left: 0.25in;">References:</p>
-<p style="text-indent: 0.25in;">See the PolyCore and Fractal documentation.<b><span style="font-size: 14pt;">&nbsp; </span></b></p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.13.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b><span style="font-size: 14pt;">&nbsp; <a name="GaussLorentzGel"></a>GaussLorentzGel(Model)</span></b></p>
-<p style="margin-left: 0.25in;">Calculates the scattering from a gel structure, typically a physical network. It is modeled as a sum of a low-q exponential decay plus a lorentzian at higher q-values. It is generally applicable to gel structures.</p>
-<p style="margin-left: 0.25in;">The returned value is scaled to units of [cm-1sr-1], absolute scale.</p>
-<p style="margin-left: 0.25in;">The scattering intensity I(q) is calculated as (eqn 5 from the reference):</p>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><img id="Picture 235" src="img/image189.jpg" alt="" /></p>
-<p style="margin-left: 0.25in; text-align: center;" align="center">&nbsp;</p>
-<p style="margin-left: 0.25in;">Uppercase Zeta is the static correlations in the gel, which can be attributed to the "frozen-in" crosslinks of some gels. Lowercase zeta is the dynamic correlation length, which can be attributed to the fluctuating polymer chain between crosslinks. IG(0) and IL(0) are the scaling factors for each of these structures. Your physical system may be different, so think about the interpretation of these parameters.</p>
-<p style="margin-left: 0.25in;">Note that the peaked structure at higher q values (from Figure 2 of the reference below) is not reproduced by the model. Peaks can be introduced into the model by summing this model with the PeakGauss Model function.</p>
-<p style="margin-left: 0.25in;">For 2D plot, the wave transfer is defined as<span style="font-size: 12pt; font-family: 'Times New Roman','serif'; position: relative; top: 4.5pt;"><img src="img/image040.gif" alt="" /></span><span style="font-size: 14pt;">.</span></p>
-<p style="text-align: center;" align="center"><span style="font-size: 14pt;">&nbsp;</span></p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 19.25pt;">
-<td style="border: 1pt solid width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; vertical-align: top; width: 107pt; height: 19.25pt;">
-<p>dyn_colength(=Dynamic correlation length)</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>20.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>scale_g(=Gauss scale factor)</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>100</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>scale_l(=Lorentzian scale factor)</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>50</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>stat_colength(=Static correlation Z)</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>100.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0.0</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><img id="Picture 82" src="img/image190.jpg" alt="" width="471" height="320" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot using the default values (w/500 data points).</b></p>
-<p style="margin-left: 0.25in; text-align: center;" align="center">&nbsp;</p>
-<p style="margin-left: 0.25in; text-align: center;" align="center">&nbsp;</p>
-<p style="text-indent: 0.5in;">REFERENCE:</p>
-<p style="text-indent: 0.5in;">G. Evmenenko, E. Theunissen, K. Mortensen, H. Reynaers, Polymer 42 (2001) 2907-2913.</p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.14.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b><span style="font-size: 14pt;">&nbsp;<a name="BEPolyelectrolyte"></a> BEPolyelectrolyte Model</span></b></p>
-<p style="margin-left: 0.25in;">Calculates the structure factor of a polyelectrolyte solution with the RPA expression derived by Borue and Erukhimovich. The value returned is in cm-1.</p>
-<p>&nbsp;</p>
-<p style="text-align: center;" align="center"><img src="img/image191.PNG" alt="" /></p>
-<p>&nbsp;</p>
-<p style="margin-left: 0.25in;">K is a contrast factor of the polymer, Lb is the Bjerrum length, h is the virial parameter, b is the monomer length, Cs is the concentration of monovalent salt, &alpha; is the ionization degree, Ca is the polymer molar concentration, and background is the incoherent background.</p>
-<p style="margin-left: 0.25in;">For 2D plot, the wave transfer is defined as<span style="font-size: 12pt; font-family: 'Times New Roman','serif'; position: relative; top: 4.5pt;"><img src="img/image040.gif" alt="" /></span><span style="font-size: 14pt;">.</span></p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 19.25pt;">
-<td style="border: 1pt solid width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>K</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Barns = 10-24 cm2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>10</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Lb</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>7.1</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>h</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;-3</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>12</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; vertical-align: top; width: 107pt; height: 19.25pt;">
-<p>b</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>10</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Cs</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Mol/L</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>alpha</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>None</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0.05</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Ca</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Mol/L</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0.7</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0.0</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="margin-left: 0.25in;">References:</p>
-<p style="margin-left: 0.5in;">Borue, V. Y., Erukhimovich, I. Y. Macromolecules 21, 3240 (1988).</p>
-<p style="margin-left: 0.5in;"><span lang="FR">Joanny, J.-F., Leibler, L. Journal de Physique 51, 545 (1990).</span></p>
-<p style="margin-left: 0.5in;"><span lang="FR">Moussaid, A., Schosseler, F., Munch, J.-P., Candau, S. J. Journal de Physique II France </span></p>
-<p style="margin-left: 0.5in;">3, 573 (1993).</p>
-<p style="margin-left: 0.5in;">Rapha&euml;l, E., Joanny, J.-F., Europhysics Letters 11, 179 (1990).</p>
-<p style="margin-left: 0.25in;"><b><span style="font-size: 14pt;">&nbsp;</span></b></p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.15.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b><span style="font-size: 14pt;">&nbsp;<a name="Guinier"></a>Guinier (Model)</span></b></p>
-<p style="margin-left: 0.25in;">A Guinier analysis is done by linearizing the data at low q by plotting it as log(I) versus Q2. The Guinier radius Rg can be obtained by fitting the following model:</p>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 7pt;"><img src="img/image192.PNG" alt="" /></span></p>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><span style="font-size: 14pt;">&nbsp;</span></p>
-<p style="margin-left: 0.25in;">For 2D plot, the wave transfer is defined as<span style="font-size: 12pt; font-family: 'Times New Roman','serif'; position: relative; top: 4.5pt;"><img src="img/image040.gif" alt="" /></span><span style="font-size: 14pt;">.</span></p>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><b><span style="font-size: 14pt;">&nbsp;</span></b></p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 19.25pt;">
-<td style="border: 1pt solid width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; vertical-align: top; width: 107pt; height: 19.25pt;">
-<p>scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>1.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Rg</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0.1</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="margin-left: 0.25in;"><b><span style="font-size: 14pt;">&nbsp;</span></b></p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.16.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b><span style="font-size: 14pt;">&nbsp;<a name="GuinierPorod"></a>GuinierPorod (Model)</span></b></p>
-<p style="margin-left: 0.25in;">Calculates the scattering for a generalized Guinier/power law object. This is an empirical model that can be used to determine the size and dimensionality of scattering objects.</p>
-<p style="margin-left: 0.25in;">The returned value is P(Q) as written in equation (1), plus the incoherent background term. The result is in the units of [cm-1sr-1], absolute scale.</p>
-<p style="margin-left: 0.25in;">A Guinier-Porod empirical model can be used to fit SAS data from asymmetric objects such as rods or platelets. It also applies to intermediate shapes between spheres and rod or between rods and platelets. The following functional form is used:&nbsp;</p>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><img id="Picture 1" src="img/image193.jpg" alt="" />&nbsp;&nbsp; (1)</p>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><span style="font-size: 14pt;">&nbsp;</span></p>
-<p style="margin-left: 0.25in;">This is based on the generalized Guinier law for such elongated objects [2]. For 3D globular objects (such as spheres), s = 0 and one recovers the standard Guinier formula. For 2D symmetry (such as for rods) s = 1 and for 1D symmetry (such as for lamellae or platelets) s = 2. A dimensionality parameter 3-s is defined, and is 3 for spherical objects, 2 for rods, and 1 for plates.</p>
-<p style="margin-left: 0.25in;">Enforcing the continuity of the Guinier and Porod functions and their derivatives yields:&nbsp;</p>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><img id="Picture 2" src="img/image194.jpg" alt="" /></p>
-<p style="margin-left: 0.25in;">and</p>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><img id="Picture 3" src="img/image195.jpg" alt="" /></p>
-<p style="margin-left: 0.25in; text-align: center;" align="center">&nbsp;</p>
-<p style="margin-left: 0.25in;">Note that the radius of gyration for a sphere of radius R is given by Rg = R sqrt(3/5) ,</p>
-<p style="margin-left: 0.25in;">&nbsp;that for the cross section of an randomly oriented cylinder of radius R is given by&nbsp; Rg = R / sqrt(2).</p>
-<p style="margin-left: 0.25in;">The cross section of a randomly oriented lamella of thickness T is given by Rg = T / sqrt(12).</p>
-<p style="margin-left: 0.25in;">The intensity given by Eq. 1 is the calculated result, and is plotted below for the default parameter values.</p>
-<p style="margin-left: 0.25in;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; REFERENCE</p>
-<p style="margin-left: 0.25in;">[1] Guinier, A.; Fournet, G. "Small-Angle Scattering of X-Rays", John Wiley and Sons, New York, (1955).</p>
-<p style="margin-left: 0.25in;">[2] Glatter, O.; Kratky, O., &ldquo;Small-Angle X-Ray Scattering&rdquo;, Academic Press (1982). Check out Chapter 4 on Data Treatment, pages 155-156.&nbsp;</p>
-<p style="margin-left: 0.25in;">For 2D plot, the wave transfer is defined as<span style="font-size: 14pt; position: relative; top: 8pt;"><img src="img/image008.PNG" alt="" /></span><span style="font-size: 14pt;">.</span></p>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><b><span style="font-size: 14pt;">&nbsp;</span></b></p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 19.25pt;">
-<td style="border: 1pt solid width: 123pt; height: 19.25pt;" valign="top" width="164">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 91pt; height: 19.25pt;" valign="top" width="121">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; vertical-align: top; width: 123pt; height: 19.25pt;">
-<p>Scale(=Guinier scale, G)</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 91pt; height: 19.25pt;" valign="top" width="121">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>1.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-style: none solid; border-width: medium 1pt; width: 123pt; height: 19.25pt;" valign="top" width="164">
-<p>rg</p>
-</td>
-<td style="border-style: none solid none none; border-width: medium 1pt medium medium; width: 91pt; height: 19.25pt;" valign="top" width="121">
-<p>&Aring;</p>
-</td>
-<td style="border-style: none solid none none; border-width: medium 1pt medium medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>100</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-style: none solid; border-width: medium 1pt; width: 123pt; height: 19.25pt;" valign="top" width="164">
-<p>dim(=Dimensional Variable, s)</p>
-</td>
-<td style="border-style: none solid none none; border-width: medium 1pt medium medium; width: 91pt; height: 19.25pt;" valign="top" width="121">&nbsp;</td>
-<td style="border-style: none solid none none; border-width: medium 1pt medium medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>1</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-style: none solid; border-width: medium 1pt; width: 123pt; height: 19.25pt;" valign="top" width="164">
-<p>m(=Porod exponent)</p>
-</td>
-<td style="border-style: none solid none none; border-width: medium 1pt medium medium; width: 91pt; height: 19.25pt;" valign="top" width="121">&nbsp;</td>
-<td style="border-style: none solid none none; border-width: medium 1pt medium medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>3</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 123pt; height: 19.25pt;" valign="top" width="164">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 91pt; height: 19.25pt;" valign="top" width="121">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0.1</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="margin-left: 0.25in;"><b><span style="font-size: 14pt;">&nbsp;</span></b></p>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><b><span style="font-size: 14pt;"><img id="Picture 4" src="img/image196.jpg" alt="" /></span></b></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot using the default values (w/500 data points).</b></p>
-<p style="text-align: center;" align="center"><b>&nbsp;</b></p>
-<p style="margin-left: 0.25in;"><b><span style="font-size: 14pt;">&nbsp;</span></b></p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.17.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b><span style="font-size: 14pt;">&nbsp;<a name="PorodModel"></a>PorodModel</span></b></p>
-<p style="margin-left: 0.25in;">A Porod analysis is done by linearizing the data at high q by plotting it as log(I) versus log(Q). In the high q region we can fit the following model:</p>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 6pt;"><img src="img/image197.PNG" alt="" /></span></p>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><span style="font-size: 14pt;">&nbsp;</span></p>
-<p style="margin-left: 0.25in;">C is the scale factor and &nbsp;Sv is the specific surface area of the sample and <span style="font-family: 'Arial','sans-serif';">&Delta;</span>&rho; is the contrast factor.</p>
-<p style="margin-left: 0.25in;">The background term is added for data analysis.</p>
-<p style="margin-left: 0.25in;">For 2D plot, the wave transfer is defined as<span style="font-size: 12pt; font-family: 'Times New Roman','serif'; position: relative; top: 4.5pt;"><img src="img/image040.gif" alt="" /></span><span style="font-size: 14pt;">.</span></p>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><b><span style="font-size: 14pt;">&nbsp;</span></b></p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 19.25pt;">
-<td style="border: 1pt solid vertical-align: top; width: 107pt; height: 19.25pt;">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;-4</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0.1</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.18.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b><span style="font-size: 14pt;">&nbsp;<a name="Peak Gauss Model"></a>PeakGaussModel</span></b></p>
-<p style="margin-left: 0.25in;">Model describes a Gaussian shaped peak including a flat background,</p>
-<p style="margin-left: 0.25in; text-align: center;" align="center">&nbsp;</p>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 6pt;"><img src="img/image198.PNG" alt="" /></span></p>
-<p style="margin-left: 0.25in; text-align: center;" align="center">&nbsp;</p>
-<p style="margin-left: 0.25in;">with the peak having height of I0 centered at qpk having standard deviation of B.&nbsp; The fwhm is 2.354*B.&nbsp;&nbsp;</p>
-<p style="margin-left: 0.25in;">Parameters I0, B, qpk, and BGD can all be adjusted during fitting.</p>
-<p style="margin-left: 0.25in;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; REFERENCE: None</p>
-<p style="margin-left: 0.25in;">For 2D plot, the wave transfer is defined as<span style="font-size: 12pt; font-family: 'Times New Roman','serif'; position: relative; top: 4.5pt;"><img src="img/image040.gif" alt="" /></span><span style="font-size: 14pt;">.</span></p>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><b><span style="font-size: 14pt;">&nbsp;</span></b></p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 19.25pt;">
-<td style="border: 1pt solid width: 123pt; height: 19.25pt;" valign="top" width="164">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 91pt; height: 19.25pt;" valign="top" width="121">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; vertical-align: top; width: 123pt; height: 19.25pt;">
-<p>scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 91pt; height: 19.25pt;" valign="top" width="121">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>100</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-style: none solid; border-width: medium 1pt; width: 123pt; height: 19.25pt;" valign="top" width="164">
-<p>q0</p>
-</td>
-<td style="border-style: none solid none none; border-width: medium 1pt medium medium; width: 91pt; height: 19.25pt;" valign="top" width="121">
-<p>&Aring;</p>
-</td>
-<td style="border-style: none solid none none; border-width: medium 1pt medium medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0.05</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-style: none solid; border-width: medium 1pt; width: 123pt; height: 19.25pt;" valign="top" width="164">
-<p>B</p>
-</td>
-<td style="border-style: none solid none none; border-width: medium 1pt medium medium; width: 91pt; height: 19.25pt;" valign="top" width="121">&nbsp;</td>
-<td style="border-style: none solid none none; border-width: medium 1pt medium medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0.005</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 123pt; height: 19.25pt;" valign="top" width="164">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 91pt; height: 19.25pt;" valign="top" width="121">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>1</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="margin-left: 0.25in;"><b><span style="font-size: 14pt;">&nbsp;</span></b></p>
-<p style="margin-left: 0.25in;"><b><span style="font-size: 14pt;">&nbsp;</span></b></p>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><b><span style="font-size: 14pt;"><img src="img/image199.jpg" alt="" /></span></b></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot using the default values (w/500 data points).</b></p>
-<p style="text-align: center;" align="center"><b>&nbsp;</b></p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.19.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b><span style="font-size: 14pt;">&nbsp;<a name="Peak Lorentz Model"></a>PeakLorentzModel</span></b></p>
-<p style="margin-left: 0.25in;">Model describes a Lorentzian shaped peak including a flat background,</p>
-<p>&nbsp;</p>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><img src="img/image200.PNG" alt="" /></p>
-<p>&nbsp;</p>
-<p style="margin-left: 0.25in;">with the peak having height of I0 centered at qpk having a hwhm (half-width-half-maximum) of B.&nbsp;</p>
-<p style="margin-left: 0.25in;">The parameters I0, B, qpk, and BGD can all be adjusted during fitting.</p>
-<p style="margin-left: 0.25in;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; REFERENCE: None</p>
-<p style="margin-left: 0.25in;">For 2D plot, the wave transfer is defined as<span style="font-size: 12pt; font-family: 'Times New Roman','serif'; position: relative; top: 4.5pt;"><img src="img/image040.gif" alt="" /></span><span style="font-size: 14pt;">.</span></p>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><b><span style="font-size: 14pt;">&nbsp;</span></b></p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 19.25pt;">
-<td style="border: 1pt solid width: 123pt; height: 19.25pt;" valign="top" width="164">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 91pt; height: 19.25pt;" valign="top" width="121">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 123pt; height: 19.25pt;" valign="top" width="164">
-<p>scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 91pt; height: 19.25pt;" valign="top" width="121">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>100</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-style: none solid; border-width: medium 1pt; vertical-align: top; width: 123pt; height: 19.25pt;">
-<p>q0</p>
-</td>
-<td style="border-style: none solid none none; border-width: medium 1pt medium medium; width: 91pt; height: 19.25pt;" valign="top" width="121">
-<p>&Aring;</p>
-</td>
-<td style="border-style: none solid none none; border-width: medium 1pt medium medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0.05</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-style: none solid; border-width: medium 1pt; width: 123pt; height: 19.25pt;" valign="top" width="164">
-<p>B</p>
-</td>
-<td style="border-style: none solid none none; border-width: medium 1pt medium medium; width: 91pt; height: 19.25pt;" valign="top" width="121">&nbsp;</td>
-<td style="border-style: none solid none none; border-width: medium 1pt medium medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0.005</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 123pt; height: 19.25pt;" valign="top" width="164">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 91pt; height: 19.25pt;" valign="top" width="121">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>1</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="margin-left: 0.25in;"><b><span style="font-size: 14pt;">&nbsp;</span></b></p>
-<p style="margin-left: 0.25in;"><b><span style="font-size: 14pt;">&nbsp;</span></b></p>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><b><span style="font-size: 14pt;"><img src="img/image201.jpg" alt="" /></span></b></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot using the default values (w/500 data points).</b></p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.20.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <a name="Poly_GaussCoil"></a>Poly_GaussCoil (Model)</span></b></p>
-<p style="margin-left: 0.25in;">Polydisperse Gaussian Coil: Calculate an empirical functional form for scattering from a polydisperse polymer chain ina good solvent. The polymer is polydisperse with a Schulz-Zimm polydispersity of the molecular weight distribution.&nbsp;</p>
-<p style="margin-left: 0.25in;">The returned value is scaled to units of [cm-1sr-1], absolute scale.</p>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="img/image202.PNG" alt="" /></span></p>
-<p style="margin-left: 0.25in;">where the dimensionless chain dimension is:</p>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><span style="position: relative; top: 12pt;"><img src="img/image203.PNG" alt="" /></span></p>
-<p style="margin-left: 0.25in;">and the polydispersion is</p>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="img/image204.PNG" alt="" /></span>.</p>
-<p style="margin-left: 0.25in;">The scattering intensity I(q) is calculated as:</p>
-<p style="margin-left: 0.25in;">The polydispersion in &lsquo;rg&rsquo; is provided.</p>
-<p><span style="font-size: 14pt;">&nbsp;</span></p>
-<p style="margin-left: 0.25in;">For 2D plot, the wave transfer is defined as<span style="font-size: 12pt; font-family: 'Times New Roman','serif'; position: relative; top: 4.5pt;"><img src="img/image040.gif" alt="" /></span><span style="font-size: 14pt;">.</span></p>
-<p style="margin-left: 0.25in;">TEST DATASET</p>
-<p style="margin-left: 0.25in;">&nbsp;This example dataset is produced by running the Poly_GaussCoil, using 200 data points, qmin = 0.001 &Aring;-1,&nbsp; qmax = 0.7 &Aring;-1&nbsp;&nbsp; and the default values below.</p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 19.25pt;">
-<td style="border: 1pt solid width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; vertical-align: top; width: 107pt; height: 19.25pt;">
-<p>Scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>None</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>1.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>rg</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>60.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>poly_m</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Mw/Mn</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>2</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0.001</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="margin-left: 0.25in; text-align: center;" align="center">&nbsp;</p>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><img id="Picture 69" src="img/image205.jpg" alt="" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot using the default values (w/200 data point).</b></p>
-<p style="margin-left: 0.25in; text-align: center;" align="center">&nbsp;</p>
-<p style="margin-left: 0.25in;">Reference:</p>
-<p style="margin-left: 0.25in;">Glatter &amp; Kratky - pg.404.</p>
-<p style="margin-left: 0.25in;">J.S. Higgins, and H.C. Benoit, &ldquo;Polymers and Neutron Scattering&rdquo;, Oxford Science</p>
-<p style="margin-left: 0.25in;">Publications (1996).</p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.21.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <a name="PolymerExclVolume"></a>PolymerExclVolume (Model)</span></b></p>
-<p style="margin-left: 0.25in;">Calculates the scattering from polymers with excluded volume effects.</p>
-<p style="margin-left: 0.25in;">The returned value is scaled to units of [cm-1sr-1], absolute scale.</p>
-<p style="margin-left: 0.25in;">The returned value is P(Q) as written in equation (2), plus the incoherent background term. The result is in the units of [cm-1sr-1], absolute scale.</p>
-<p style="margin-left: 0.25in;">A model describing polymer chain conformations with excluded volume was introduced to describe the conformation of polymer chains, and has been used as a template for describing mass fractals. The form factor for that model (Benoit, 1957) was originally presented in the following integral form:</p>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><img id="Picture 5" src="img/image206.jpg" alt="" />&nbsp;&nbsp;&nbsp;&nbsp; (1)</p>
-<p style="margin-left: 0.25in;">Here n is the excluded volume parameter which is related to the Porod exponent m as <span style="font-family: Symbol;">n</span> = 1/m, a is the polymer chain statistical segment length and n is the degree of polymerization. This integral was later put into an &ldquo;almost&rdquo; analytical form (Hammouda, 1993) as follows:</p>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><img id="Picture 6" src="img/image207.jpg" alt="" />&nbsp;&nbsp;&nbsp; (2)</p>
-<p style="margin-left: 0.25in;">Here, <span style="font-family: Symbol;">g</span>(x,U) is the incomplete gamma function which is a built-in function in computer libraries.</p>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><img src="img/image208.jpg" alt="" /></p>
-<p style="margin-left: 0.25in;">The variable U is given in terms of the scattering variable Q as:</p>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><img src="img/image209.jpg" alt="" /></p>
-<p>The radius of gyration squared has been defined as:</p>
-<p style="text-align: center;" align="center"><span style="font-size: 14pt;"><img src="img/image210.jpg" alt="" /></span></p>
-<p>Note that this model describing polymer chains with excluded volume applies only in the mass fractal range ( 5/3 &lt;= m &lt;= 3) and does not apply to surface fractals ( 3 &lt; m &lt;= 4). It does not reproduce the rigid rod limit (m = 1) because it assumes chain flexibility from the outset.&nbsp; It may cover a portion of the semiflexible chain range ( 1 &lt; m &lt; 5/3).</p>
-<p>The low-Q expansion yields the Guinier form and the high-Q expansion yields the Porod form which is given by:</p>
-<p style="text-align: center;" align="center"><img src="img/image211.jpg" alt="" /></p>
-<p>Here <span style="font-family: Symbol;">G</span>(x) = <span style="font-family: Symbol;">g</span>(x,inf) is the gamma function. The asymptotic limit is dominated by the first term:</p>
-<p style="text-align: center;" align="center"><img src="img/image212.jpg" alt="" /></p>
-<p>The special case when <span style="font-family: Symbol;">n</span> = 0.5 (or m = 1/<span style="font-family: Symbol;">n</span> = 2) corresponds to Gaussian chains for which the form factor is given by the familiar Debye function.</p>
-<p style="text-align: center;" align="center"><img id="Picture 12" src="img/image213.jpg" alt="" /></p>
-<p>The form factor given by Eq. 2 is the calculated result, and is plotted below for the default parameter values.</p>
-<p>REFERENCE</p>
-<p>Benoit, H., Comptes Rendus (1957). 245, 2244-2247.</p>
-<p>Hammouda, B., &ldquo;SANS from Homogeneous Polymer Mixtures &shy; A Unified Overview&rdquo;, Advances in Polym. Sci. (1993), 106, 87-133.</p>
-<p style="margin-left: 0.25in;">For 2D plot, the wave transfer is defined as<span style="font-size: 12pt; font-family: 'Times New Roman','serif'; position: relative; top: 4.5pt;"><img src="img/image040.gif" alt="" /></span><span style="font-size: 14pt;">.</span></p>
-<p style="margin-left: 0.25in;">TEST DATASET</p>
-<p style="margin-left: 0.25in;">&nbsp;This example dataset is produced, using 200 data points, qmin = 0.001 &Aring;-1,&nbsp; qmax = 0.2 &Aring;-1&nbsp;&nbsp; and the default values below.</p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 19.25pt;">
-<td style="border: 1pt solid width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; vertical-align: top; width: 107pt; height: 19.25pt;">
-<p>Scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>None</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>1.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>rg</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>60.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>m(=Porod exponent)</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>3</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0.0</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="margin-left: 0.25in; text-align: center;" align="center">&nbsp;</p>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><img id="Picture 7" src="img/image214.jpg" alt="" width="479" height="333" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot using the default values (w/500 data points).</b></p>
-<p style="margin-left: 0.25in; text-align: center;" align="center">&nbsp;</p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.22.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b><span style="font-size: 14pt;">&nbsp; <a name="RPA10Model"></a>RPA10Model</span></b></p>
-<p style="margin-left: 0.25in;">Calculates the macroscopic scattering intensity (units of cm^-1) for a multicomponent homogeneous mixture of polymers using the Random Phase Approximation. This general formalism contains 10 specific cases:</p>
-<p style="margin-left: 0.25in;">Case 0: C/D Binary mixture of homopolymers</p>
-<p style="margin-left: 0.25in;">Case 1: C-D Diblock copolymer</p>
-<p style="margin-left: 0.25in;">Case 2: B/C/D Ternary mixture of homopolymers</p>
-<p style="margin-left: 0.25in;">Case 3: C/C-D Mixture of a homopolymer B and a diblock copolymer C-D</p>
-<p style="margin-left: 0.25in;">Case 4: B-C-D Triblock copolymer</p>
-<p style="margin-left: 0.25in;">Case 5: A/B/C/D Quaternary mixture of homopolymers</p>
-<p style="margin-left: 0.25in;">Case 6: A/B/C-D Mixture of two homopolymers A/B and a diblock C-D</p>
-<p style="margin-left: 0.25in;">Case 7: A/B-C-D Mixture of a homopolymer A and a triblock B-C-D</p>
-<p style="margin-left: 0.25in;">Case 8: A-B/C-D Mixture of two diblock copolymers A-B and C-D</p>
-<p style="margin-left: 0.25in;">Case 9: A-B-C-D Four-block copolymer</p>
-<p style="margin-left: 0.25in;">Note: the case numbers are different from the IGOR/NIST SANS package.</p>
-<p style="margin-left: 0.25in;"><b>&nbsp;</b></p>
-<p style="margin-left: 0.25in;">Only one case can be used at any one time.&nbsp; Plotting a different case will overwrite the original parameter waves.</p>
-<p style="margin-left: 0.25in;">The returned value is scaled to units of [cm-1].</p>
-<p style="margin-left: 0.25in;">Component D is assumed to be the "background" component (all contrasts are calculated with respect to component D).</p>
-<p style="margin-left: 0.25in;">Scattering contrast for a C/D blend= {SLD (component C) - SLD (component D)}2</p>
-<p style="margin-left: 0.25in;">Depending on what case is used, the number of fitting parameters varies. These represent the segment lengths (ba, bb, etc) and the Chi parameters (Kab, Kac, etc). The last one of these is a scaling factor to be held constant equal to unity.</p>
-<p style="margin-left: 0.25in;">The input parameters are the degree of polymerization, the volume fractions for each component the specific volumes and the neutron scattering length densities.</p>
-<p style="margin-left: 0.25in;">This RPA (mean field) formalism applies only when the multicomponent polymer mixture is in the homogeneous mixed-phase region.</p>
-<p style="margin-left: 0.25in;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; REFERENCE</p>
-<p style="margin-left: 0.25in;">A.Z. Akcasu, R. Klein and B. Hammouda, Macromolecules 26, 4136 (1993)</p>
-<p style="margin-left: 0.25in; text-align: center;" align="center">&nbsp;</p>
-<p style="margin-left: 0.25in; text-align: center;" align="center">Fitting parameters for Case0 Model</p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 19.25pt;">
-<td style="border: 1pt solid width: 127.5pt; height: 19.25pt;" valign="top" width="170">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 86.5pt; height: 19.25pt;" valign="top" width="115">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; vertical-align: top; width: 127.5pt; height: 19.25pt;">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 86.5pt; height: 19.25pt;" valign="top" width="115">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 127.5pt; height: 19.25pt;" valign="top" width="170">
-<p>scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 86.5pt; height: 19.25pt;" valign="top" width="115">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>1</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 127.5pt; height: 19.25pt;" valign="top" width="170">
-<p>bc(=Seg. Length bc)</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 86.5pt; height: 19.25pt;" valign="top" width="115">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>5</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 127.5pt; height: 19.25pt;" valign="top" width="170">
-<p>bd(=Seg. Length bd)</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 86.5pt; height: 19.25pt;" valign="top" width="115">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>5</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 127.5pt; height: 19.25pt;" valign="top" width="170">
-<p>Kcd(Chi Param. Kcd)</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 86.5pt; height: 19.25pt;" valign="top" width="115">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>-0.0004</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="margin-left: 0.25in;"><b><span style="font-size: 14pt;">&nbsp;</span></b></p>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><b><span style="font-size: 14pt;">&nbsp;</span></b></p>
-<p style="margin-left: 0.25in; text-align: center;" align="center">Fixed parameters for Case0 Model</p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 19.25pt;">
-<td style="border: 1pt solid width: 141pt; height: 19.25pt;" valign="top" width="188">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 73pt; height: 19.25pt;" valign="top" width="97">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 141pt; height: 19.25pt;" valign="top" width="188">
-<p>Lc(= Scatter. Length_c)</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 73pt; height: 19.25pt;" valign="top" width="97">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>1e-12</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 141pt; height: 19.25pt;" valign="top" width="188">
-<p>Ld(= Scatter. Length_d)</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 73pt; height: 19.25pt;" valign="top" width="97">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; vertical-align: top; width: 141pt; height: 19.25pt;">
-<p>Nc(=Deg.Polym.c)</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 73pt; height: 19.25pt;" valign="top" width="97">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>1000</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 141pt; height: 19.25pt;" valign="top" width="188">
-<p>Nd(=Deg.Polym.d)</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 73pt; height: 19.25pt;" valign="top" width="97">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>1000</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-style: none solid; border-width: medium 1pt; width: 141pt; height: 19.25pt;" valign="top" width="188">
-<p>Phic(=Vol. fraction of c)</p>
-</td>
-<td style="border-style: none solid none none; border-width: medium 1pt medium medium; width: 73pt; height: 19.25pt;" valign="top" width="97">&nbsp;</td>
-<td style="border-style: none solid none none; border-width: medium 1pt medium medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0.25</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-style: none solid; border-width: medium 1pt; width: 141pt; height: 19.25pt;" valign="top" width="188">
-<p>Phid(=Vol. fraction of d)</p>
-</td>
-<td style="border-style: none solid none none; border-width: medium 1pt medium medium; width: 73pt; height: 19.25pt;" valign="top" width="97">&nbsp;</td>
-<td style="border-style: none solid none none; border-width: medium 1pt medium medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0.25</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-style: none solid; border-width: medium 1pt; width: 141pt; height: 19.25pt;" valign="top" width="188">
-<p>vc(=Spec. vol. of c)</p>
-</td>
-<td style="border-style: none solid none none; border-width: medium 1pt medium medium; width: 73pt; height: 19.25pt;" valign="top" width="97">&nbsp;</td>
-<td style="border-style: none solid none none; border-width: medium 1pt medium medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>100</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-style: none solid; border-width: medium 1pt; width: 141pt; height: 19.25pt;" valign="top" width="188">
-<p>vd(=Spec. vol. of d)</p>
-</td>
-<td style="border-style: none solid none none; border-width: medium 1pt medium medium; width: 73pt; height: 19.25pt;" valign="top" width="97">&nbsp;</td>
-<td style="border-style: none solid none none; border-width: medium 1pt medium medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>100</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="margin-left: 0.25in;"><b><span style="font-size: 14pt;">&nbsp;</span></b></p>
-<p style="margin-left: 0.25in;"><b><span style="font-size: 14pt;">&nbsp;</span></b></p>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><img id="Picture 8" src="img/image215.jpg" alt="" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot using the default values (w/500 data points).</b></p>
-<p style="margin-left: 0.25in;"><b><span style="font-size: 14pt;">&nbsp;</span></b></p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.23.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b><span style="font-size: 14pt;">&nbsp;<a name="TwoLorentzian"></a>TwoLorentzian(Model)</span></b></p>
-<p style="margin-left: 0.25in;">Calculate an empirical functional form for SANS data characterized by a two Lorentzian functions.</p>
-<p style="margin-left: 0.25in;">The returned value is scaled to units of [cm-1sr-1], absolute scale.</p>
-<p style="margin-left: 0.25in;">The scattering intensity I(q) is calculated by:&nbsp;</p>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><span style="font-size: 14pt;"><img id="Picture 13" src="img/image216.jpg" alt="" /></span><span style="font-size: 14pt;">&nbsp;</span></p>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><span style="font-size: 14pt;">&nbsp;</span></p>
-<p style="margin-left: 0.25in;">A = Lorentzian scale #1</p>
-<p style="margin-left: 0.25in;">C = Lorentzian scale #2&nbsp;</p>
-<p style="margin-left: 0.25in;">where &lsquo;scale&rsquo; is the peak height centered at q0, and B refers to the standard deviation of the function.</p>
-<p style="margin-left: 0.25in;">The background term is added for data analysis.</p>
-<p style="margin-left: 0.25in;">For 2D plot, the wave transfer is defined as<span style="font-size: 12pt; font-family: 'Times New Roman','serif'; position: relative; top: 4.5pt;"><img src="img/image040.gif" alt="" /></span><span style="font-size: 14pt;">.</span></p>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><b>Default input parameter values</b></p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 19.25pt;">
-<td style="border: 1pt solid width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>scale_1(=A)</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>10</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>scale_2(=C)</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>1</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>1ength_1 (=Correlation length1)</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>100</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; vertical-align: top; width: 107pt; height: 19.25pt;">
-<p>1ength_2(=Correlation length2)</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>10</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>exponent_1(=n)</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>3</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>exponent_2(=m)</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>2</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Background(=B)</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0.1</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="margin-left: 0.5in;">&nbsp;</p>
-<p style="margin-left: 0.5in;">&nbsp;</p>
-<p style="margin-left: 0.5in; text-align: center;" align="center"><img id="Picture 9" src="img/image217.jpg" alt="" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot using the default values (w/500 data points).</b></p>
-<p style="margin-left: 0.5in; text-align: center;" align="center">&nbsp;</p>
-<p style="text-indent: 0.25in;"><b>REFERENCE: None</b></p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.24.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b><span style="font-size: 14pt;">&nbsp;<a name="TwoPowerLaw"></a>TwoPowerLaw(Model)</span></b></p>
-<p style="margin-left: 0.25in;">Calculate an empirical functional form for SANS data characterized by two power laws.</p>
-<p style="margin-left: 0.25in;">The returned value is scaled to units of [cm-1sr-1], absolute scale.</p>
-<p style="margin-left: 0.25in; text-align: center;" align="center">&nbsp;</p>
-<p style="margin-left: 0.25in;">The scattering intensity I(q) is calculated by:</p>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><span style="font-size: 14pt;"><img id="Picture 14" src="img/image218.jpg" alt="" /></span><span style="font-size: 14pt;">&nbsp;</span></p>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><span style="font-size: 14pt;">&nbsp;</span></p>
-<p style="margin-left: 0.25in;">qc is the location of the crossover from one slope to the other. The scaling A, sets the overall intensity of the lower Q power law region. The scaling of the second power law region is scaled to match the first. Be sure to enter the power law exponents as positive values.</p>
-<p style="margin-left: 0.25in;">For 2D plot, the wave transfer is defined as<span style="font-size: 12pt; font-family: 'Times New Roman','serif'; position: relative; top: 4.5pt;"><img src="img/image040.gif" alt="" /></span><span style="font-size: 14pt;">.</span></p>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><b>Default input parameter values</b></p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 19.25pt;">
-<td style="border: 1pt solid width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>coef_A</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>1.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>qc</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0.04</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; vertical-align: top; width: 107pt; height: 19.25pt;">
-<p>power_1(=m1)</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>4</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>power_2(=m2)</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>4</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0.0</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="margin-left: 0.5in;">&nbsp;</p>
-<p style="margin-left: 0.5in;">&nbsp;</p>
-<p style="margin-left: 0.5in; text-align: center;" align="center"><img id="Picture 10" src="img/image219.jpg" alt="" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot using the default values (w/500 data points).</b></p>
-<p style="margin-left: 0.5in; text-align: center;" align="center">&nbsp;</p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.25.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b><span style="font-size: 14pt;">&nbsp;<a name="UnifiedPowerRg"></a>UnifiedPower(Law and)Rg(Model)</span></b></p>
-<p style="margin-left: 0.25in;">The returned value is scaled to units of [cm-1sr-1], absolute scale.&nbsp;</p>
-<p style="margin-left: 0.25in;">Note that the level 0 is an extra function that is the inverse function; I (q) = scale/q + background.</p>
-<p style="margin-left: 0.25in;">Otherwise, program incorporates the empirical multiple level unified Exponential/Power-law fit method developed by G. Beaucage. Four functions are included so that One, Two, Three, or Four levels can be used.</p>
-<p style="margin-left: 0.25in;">The empirical expressions are able to reasonably approximate the scattering from many different types of particles, including fractal clusters, random coils (Debye equation), ellipsoidal particles, etc.&nbsp; The empirical fit function is&nbsp;</p>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><span style="font-size: 14pt;"><img id="Picture 15" src="img/image220.jpg" alt="" /></span></p>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><span style="font-size: 14pt;">&nbsp;</span></p>
-<p style="margin-left: 0.25in;">For each level, the four parameters Gi, Rg,i, Bi and Pi must be chosen.&nbsp;</p>
-<p style="margin-left: 0.25in;">For example, to approximate the scattering from random coils (Debye equation), set Rg,i as the Guinier radius, Pi = 2, and Bi = 2 Gi / Rg,i&nbsp;</p>
-<p style="margin-left: 0.25in;">See the listed references for further information on choosing the parameters.</p>
-<p style="margin-left: 0.25in;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</p>
-<p style="margin-left: 0.25in;">For 2D plot, the wave transfer is defined as<span style="font-size: 12pt; font-family: 'Times New Roman','serif'; position: relative; top: 4.5pt;"><img src="img/image040.gif" alt="" /></span><span style="font-size: 14pt;">.</span></p>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><b>Default input parameter values</b></p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 19.25pt;">
-<td style="border: 1pt solid width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>1.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; vertical-align: top; width: 107pt; height: 19.25pt;">
-<p>Rg2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>21</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>power2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>2</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>G2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>cm-1sr-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>3</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>B2</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>cm-1sr-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0.0006</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Rg1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>15.8</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>power1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>4</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>G1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>cm-1sr-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>400</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>B1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>cm-1sr-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>4.5e-006</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0.0</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="margin-left: 0.5in;">&nbsp;</p>
-<p style="margin-left: 0.5in;">&nbsp;</p>
-<p style="margin-left: 0.5in; text-align: center;" align="center"><img id="Picture 11" src="img/image221.jpg" alt="" width="470" height="336" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot using the default values (w/500 data points).</b></p>
-<p style="margin-left: 0.5in; text-align: center;" align="center">&nbsp;</p>
-<p style="margin-left: 0.25in;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; REFERENCES</p>
-<p style="margin-left: 0.25in;">G. Beaucage (1995).&nbsp; J. Appl. Cryst., vol. 28, p717-728.</p>
-<p style="margin-left: 0.25in;">G. Beaucage (1996).&nbsp; J. Appl. Cryst., vol. 29, p134-146.</p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.26.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b><span style="font-size: 14pt;">&nbsp;<a name="LineModel"></a> LineModel</span></b></p>
-<p style="margin-left: 0.25in;">This is a linear function that calculates:</p>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 5pt;"><img src="img/image222.PNG" alt="" /></span></p>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><span style="font-size: 14pt;">&nbsp;</span></p>
-<p style="margin-left: 0.25in;">where A and B are the coefficients of the first and second order terms.</p>
-<p style="margin-left: 0.25in;"><b>Note:</b> For 2D plot, I(q) = I(qx)*I(qy)&nbsp; which is defined differently from other shape independent models.</p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 19.25pt;">
-<td style="border: 1pt solid vertical-align: top; width: 107pt; height: 19.25pt;">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>A</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>1.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>B</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>1.0</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="margin-left: 0.55in; text-indent: -0.3in;">&nbsp;</p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.27.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="ReflectivityModel"></a><b><span style="font-size: 14pt;">ReflectivityModel</span></b></p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;">This model calculates the reflectivity and uses the Parrett algorithm. Up to nine film layers are supported between Bottom(substrate) and Medium(Superstrate where the neutron enters the first top film). Each layers are composed of [ &frac12; of the interface(from the previous layer or substrate) + flat portion + &frac12; of the interface(to the next layer or medium)]. Only two simple interfacial functions are selectable, error function and linear function. The each interfacial thickness is equivalent to (- 2.5 sigma to +2.5 sigma for the error function, sigma=roughness).</p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;">Note: This model was contributed by an interested user.</p>
-<p align="center"><img src="img/image231.bmp" alt="" /></p>
-<p style="text-align: center;" align="center"><b>Figure. Comparison (using the SLD profile below) with NISTweb calculation (circles): http://www.ncnr.nist.gov/resources/reflcalc.html.</b></p>
-<p align="center"><img src="img/image232.gif" alt="" /></p>
-<p style="text-align: center;" align="center"><b>Figure. SLD profile used for the calculation(above).</b></p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.28.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="ReflectivityIIModel"></a><b><span style="font-size: 14pt;">ReflectivityIIModel</span></b></p>
-<p>&nbsp;&nbsp;&nbsp; Same as the ReflectivityModel except that the it is more customizable. More interfacial functions are supplied. The number of points (npts_inter) for each interface can be choosen. &nbsp;&nbsp;&nbsp; The constant (A below but 'nu' as a parameter name of the model) for exp, erf, or power-law is an input. The SLD at the interface between layers, <em><span style="font-family: Symbol;">r</span>inter_i</em>, is calculated with a function chosen by a user, where the functions are:</p>
-<p style="margin-left: 0.55in;">1) Erf;</p>
-<p><img src="img/image051.gif" alt="" /></p>
-<p style="margin-left: 0.55in;">2) Power-Law;</p>
-<p><span><img src="img/image050.gif" alt="" /></span></p>
-<p>&nbsp;</p>
-<p>&nbsp;</p>
-<p style="margin-left: 0.55in;">3) Exp;</p>
-<p><span><img src="img/image049.gif" alt="" /></span></p>
-<p>&nbsp;</p>
-<p>&nbsp;&nbsp;&nbsp; Note: This model was implemented by an interested user.</p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.29.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="GelFitModel"></a><b><span style="font-size: 14pt;">GelFitModel</span></b></p>
-<p>&nbsp;&nbsp;&nbsp; Unlike a concentrated polymer solution, the fine-scale polymer distribution in a gel involves at least two characteristic length scales, a shorter correlation length (a1) to describe the rapid fluctuations in the position of the polymer chains that ensure thermodynamic equilibrium, and a longer distance (denoted here as a2) needed to account for the static accumulations of polymer pinned down by junction points or clusters of such points. The letter is derived from a simple Guinier function.</p>
-<p style="margin-left: 0.55in;">The scattered intensity I(Q) is then calculated as:</p>
-<p><img src="img/image233.gif" alt="" /></p>
-<p style="margin-left: 0.55in;">Where:</p>
-<p><span><img src="img/image234.gif" alt="" /></span></p>
-<p>&nbsp;</p>
-<p>&nbsp;</p>
-<p>&nbsp;&nbsp;&nbsp; Note the first term reduces to the Ornstein-Zernicke equation when D=2; ie, when the Flory exponent is 0.5 (theta conditions). &nbsp; In gels with significant hydrogen bonding D has been reported to be ~2.6 to 2.8.</p>
-<p>&nbsp;&nbsp;&nbsp; Note: This model was implemented by an interested user.</p>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><b>Default input parameter values</b></p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 19.25pt;">
-<td style="border: 1pt solid width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Background</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0.01</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; vertical-align: top; width: 107pt; height: 19.25pt;">
-<p>Guinier scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>1.7</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Lorentzian scale</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>cm-1</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>3.5</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Radius of gyration</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>104</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Fractal exponent</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>2</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Correlation length</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>16</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="margin-left: 0.5in;">&nbsp;</p>
-<p style="margin-left: 0.5in;">&nbsp;</p>
-<p style="margin-left: 0.5in; text-align: center;" align="center"><img id="Picture 11" src="img/image235.gif" alt="" width="470" height="336" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot using the default values (w/300 data points, qmin=0.001, and qmax=0.3).</b></p>
-<p style="margin-left: 0.5in; text-align: center;" align="center">&nbsp;</p>
-<p style="margin-left: 0.25in;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; REFERENCES</p>
-<p style="margin-left: 0.25in;">Mitsuhiro Shibayama, Toyoichi Tanaka, Charles C. Han, J. Chem. Phys. 1992, 97 (9), 6829-6841.</p>
-<p style="margin-left: 0.25in;">Simon Mallam, Ferenc Horkay, Anne-Marie Hecht, Adrian R. Rennie, Erik Geissler, Macromolecules 1991, 24, 543-548.</p>
-<p>&nbsp;</p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.30.</span></b> <b> <span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span> </b> <b> <span style="font-size: 14pt;"><a name="StarPolymer"></a><a name="StarPolymerModel"></a>Star Polymer with Gaussian Statistics</span> </b></p>
-<p style="margin-left: 0.25in;">For a star with <em>f</em> arms:</p>
-<p style="text-align: center;" align="center"><span style="font-size: 12pt; font-family: 'Times New Roman','serif'; position: relative; top: 4.5pt;"><img src="img/star1.png" alt="" /></span></p>
-<p style="text-align: center;" align="center"><span style="font-size: 12pt; font-family: 'Times New Roman','serif'; position: relative; top: 4.5pt;"><img src="img/star2.png" alt="" /></span></p>
-<p style="text-align: center;" align="center"><span style="font-size: 12pt; font-family: 'Times New Roman','serif'; position: relative; top: 4.5pt;"><img src="img/star3.png" alt="" /></span></p>
-<p style="margin-left: 0.25in;">where is the ensemble average radius of gyration squared of an arm.</p>
-<p style="margin-left: 0.25in; text-align: center;" align="center">&nbsp;</p>
-<p style="margin-left: 0.25in;">References:</p>
-<p style="margin-left: 0.25in; text-indent: 0.25in;">H. Benoit, &nbsp; J. Polymer Science.,&nbsp; 11, 596-599&nbsp; (1953)</p>
-<p>&nbsp;</p>
-<p>&nbsp;</p>
-<p style="margin-left: 0.25in; text-indent: -0.25in;"><b><span style="font-size: 16pt;">4.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp; </span></b><a name="Model"></a><b><span style="font-size: 16pt;">Customized Models </span></b></p>
-<p style="margin-left: 0.25in;"><b><span style="font-size: 14pt;">&nbsp;</span></b></p>
-<p style="margin-left: 0.25in;">Customized model functions can be redefined or added by users (See SansView tutorial for details).</p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">4.1.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span></b><a name="testmodel"></a><b><span style="font-size: 14pt;">testmodel</span></b></p>
-<p style="margin-left: 0.55in;"><b><span style="font-size: 14pt;">&nbsp;</span></b></p>
-<p>This function, as an example of a user defined function, calculates the intensity = A + Bcos(2q) + Csin(2q).</p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">4.2.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span></b><a name="testmodel_2"></a><b><span style="font-size: 14pt;">testmodel_2 </span></b></p>
-<p>This function, as an example of a user defined function, calculates the intensity =&nbsp; scale * sin(f)/f, where f = A + Bq + Cq2 + Dq3 + Eq4 + Fq5.</p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">4.3.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="sum_p1_p2"></a><b><span style="font-size: 14pt;">sum_p1_p2 </span></b></p>
-<p>This function, as an example of a user defined function, calculates the intensity =&nbsp; scale_factor * (CylinderModel + PolymerExclVolume model). To make your own sum(P1+P2) model, select 'Easy Custom Sum' from the Fitting menu, or modify and compile the file named 'sum_p1_p2.py' from 'Edit Custom Model' in the 'Fitting' menu. It works only for single functional models.</p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">4.4.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span></b><a name="sum_Ap1_1_Ap2"></a><b><span style="font-size: 14pt;">sum_Ap1_1_Ap2 </span></b></p>
-<p>This function, as an example of a user defined function, calculates the intensity =&nbsp; (scale_factor * CylinderModel + (1-scale_factor) * PolymerExclVolume model). To make your own A*p1+(1-A)*p2 model, modify and compile the file named 'sum_Ap1_1_Ap2.py' from 'Edit Custom Model' in the 'Fitting' menu. It works only for single functional models.</p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">4.5.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="polynomial5"></a><b><span style="font-size: 14pt;">polynomial5 </span></b></p>
-<p>This function, as an example of a user defined function, calculates the intensity =&nbsp; A + Bq + Cq2 + Dq3 + Eq4 + Fq5. This model can be modified and compiled from 'Edit Custom Model' in the 'Fitting' menu.</p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">4.6.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span></b><a name="sph_bessel_jn"></a><b><span style="font-size: 14pt;">sph_bessel_jn </span></b></p>
-<p>This function, as an example of a user defined function, calculates the intensity =&nbsp; C*sph_jn(Ax+B)+D where the sph_jn is spherical Bessel function of the order n. This model can be modified and compiled from 'Edit Custom Model' in the 'Fitting' menu.</p>
-<p style="margin-left: 0.25in; text-indent: -0.25in;"><b><span style="font-size: 16pt;">5.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp; </span></b><a name="Structure_Factors"></a><b><span style="font-size: 16pt;">Structure Factors</span></b></p>
-<p style="margin-left: 0.25in;">&nbsp;</p>
-<p style="margin-left: 0.25in;">The information in this section is originated from NIST SANS IgorPro package.</p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">5.1.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="HardsphereStructure"></a><b><span style="font-size: 14pt;">HardSphere Structure </span></b></p>
-<p>This calculates the interparticle structure factor for monodisperse spherical particles interacting through hard sphere (excluded volume) interactions. The calculation uses the Percus-Yevick closure where the interparticle potential is:</p>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 15pt;"><img src="img/image223.PNG" alt="" /></span></p>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><span style="font-size: 14pt;">&nbsp;</span></p>
-<p>where r is the distance from the center of the sphere of a radius R.</p>
-<p style="margin-left: 0.25in;">For 2D plot, the wave transfer is defined as<span style="font-size: 12pt; font-family: 'Times New Roman','serif'; position: relative; top: 4.5pt;"><img src="img/image040.gif" alt="" /></span><span style="font-size: 14pt;">.</span></p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 19.25pt;">
-<td style="border: 1pt solid width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; vertical-align: top; width: 107pt; height: 19.25pt;">
-<p>effect_radius</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>50.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>volfraction</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0.2</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">&nbsp;</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="text-align: center;" align="center"><img id="Picture 111" src="img/image224.jpg" alt="" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot using the default values (in linear scale).</b></p>
-<p>References:</p>
-<p style="margin-left: 0.5in;">Percus, J. K.; Yevick, J. Phys. Rev. 110, 1. (1958).</p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">5.2.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="SquareWellStructure"></a><b><span style="font-size: 14pt;">&nbsp;SquareWell Structure </span></b></p>
-<p>This calculates the interparticle structure factor for a squar well fluid spherical particles The mean spherical approximation (MSA) closure was used for this calculation, and is not the most appropriate closure for an attractive interparticle potential. This solution has been compared to Monte Carlo simulations for a square well fluid, showing this calculation to be limited in applicability to well depths e &lt; 1.5 kT and volume fractions f &lt; 0.08.</p>
-<p>Positive well depths correspond to an attractive potential well. Negative well depths correspond to a potential "shoulder", which may or may not be physically reasonable.</p>
-<p>The well width (l) is defined as multiples of the particle diameter (2*R)</p>
-<p>The interaction potential is:</p>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 22pt;"><img src="img/image225.PNG" alt="" /></span></p>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><span style="font-size: 14pt;">&nbsp;</span></p>
-<p>where r is the distance from the center of the sphere of a radius R.</p>
-<p style="margin-left: 0.25in;">For 2D plot, the wave transfer is defined as<span style="font-size: 12pt; font-family: 'Times New Roman','serif'; position: relative; top: 4.5pt;"><img src="img/image040.gif" alt="" /></span><span style="font-size: 14pt;">.</span></p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 19.25pt;">
-<td style="border: 1pt solid width: 108.5pt; height: 19.25pt;" valign="top" width="145">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 108.5pt; height: 19.25pt;" valign="top" width="145">
-<p>effect_radius</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>50.0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 108.5pt; height: 19.25pt;" valign="top" width="145">
-<p>volfraction</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0.04</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; vertical-align: top; width: 108.5pt; height: 19.25pt;">
-<p>welldepth</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>kT</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>1.5</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 108.5pt; height: 19.25pt;" valign="top" width="145">
-<p>wellwidth</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>diameters</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>1.2</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="text-align: center;" align="center"><img id="Picture 110" src="img/image226.jpg" alt="" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot using the default values (in linear scale).</b></p>
-<p>References:</p>
-<p style="margin-left: 0.5in;">Sharma, R. V.; Sharma, K. C. Physica, 89A, 213. (1977).</p>
-<p style="margin-left: 0.5in;">&nbsp;</p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">5.3.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="HayterMSAStructure"></a><b><span style="font-size: 14pt;">&nbsp;HayterMSA Structure </span></b></p>
-<p>This calculates the Structure factor (the Fourier transform of the pair correlation function g(r)) for a system of charged, spheroidal objects in a dielectric medium.&nbsp; When combined with an appropriate form factor (such as sphere, core+shell, ellipsoid etc&hellip;), this allows for inclusion of the interparticle interference effects due to screened coulomb repulsion between charged particles. This routine only works for charged particles.&nbsp; If the charge is set to zero the routine will self destruct.&nbsp; For non-charged particles use a hard sphere potential.</p>
-<p>The salt concentration is used to compute the ionic strength of the solution which in turn is used to compute the Debye screening length.&nbsp; At present there is no provision for entering the ionic strength directly nor for use of any multivalent salts.&nbsp; The counterions are also assumed to be monovalent.</p>
-<p style="margin-left: 0.25in;">For 2D plot, the wave transfer is defined as<span style="font-size: 12pt; font-family: 'Times New Roman','serif'; position: relative; top: 4.5pt;"><img src="img/image040.gif" alt="" /></span><span style="font-size: 14pt;">.</span></p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 19.25pt;">
-<td style="border: 1pt solid width: 108.5pt; height: 19.25pt;" valign="top" width="145">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 108.5pt; height: 19.25pt;" valign="top" width="145">
-<p>effect_radius</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>20.8</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 108.5pt; height: 19.25pt;" valign="top" width="145">
-<p>charge</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>19</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 108.5pt; height: 19.25pt;" valign="top" width="145">
-<p>volfraction</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0.2</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 108.5pt; height: 19.25pt;" valign="top" width="145">
-<p>temperature</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>K</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>318</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; vertical-align: top; width: 108.5pt; height: 19.25pt;">
-<p>salt conc</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>M</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 108.5pt; height: 19.25pt;" valign="top" width="145">
-<p>dielectconst</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>71.1</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="text-align: center;" align="center"><img id="Picture 112" src="img/image227.jpg" alt="" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot using the default values (in linear scale).</b></p>
-<p>References:</p>
-<p style="text-indent: 0.5in;">JP Hansen and JB Hayter, Molecular Physics 46, 651-656 (1982).</p>
-<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; JB Hayter and J Penfold, Molecular Physics 42, 109-118 (1981).</p>
-<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">5.4.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="StickyHSStructure"></a><b><span style="font-size: 14pt;">&nbsp;StickyHS Structure </span></b></p>
-<p>This calculates the interparticle structure factor for a hard sphere fluid with a narrow attractive well. A perturbative solution of the Percus-Yevick closure is used. The strength of the attractive well is described in terms of "stickiness" as defined below. The returned value is a dimensionless structure factor, S(q).</p>
-<p>The perturb (perturbation parameter), epsilon, should be held between 0.01 and 0.1. It is best to hold the perturbation parameter fixed and let the "stickiness" vary to adjust the interaction strength. The stickiness, tau, is defined in the equation below and is a function of both the perturbation parameter and the interaction strength. Tau and epsilon are defined in terms of the hard sphere diameter (sigma = 2R), the width of the square well, delta (same units as R), and the depth of the well, uo, in units of kT. From the definition, it is clear that smaller tau mean stronger attraction.</p>
-<p style="text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 22pt;"><img src="img/image228.PNG" alt="" /></span></p>
-<p style="text-align: center;" align="center"><span style="font-size: 14pt;">&nbsp;</span></p>
-<p style="text-align: center;" align="center"><span style="font-size: 14pt;">&nbsp;</span></p>
-<p>where the interaction potential is</p>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 23pt;"><img src="img/image229.PNG" alt="" /></span></p>
-<p style="margin-left: 0.25in; text-align: center;" align="center"><span style="font-size: 14pt;">&nbsp;</span></p>
-<p>The Percus-Yevick (PY) closure was used for this calculation, and is an adequate closure for an attractive interparticle potential. This solution has been compared to Monte Carlo simulations for a square well fluid, with good agreement.</p>
-<p>The true particle volume fraction, f, is not equal to h, which appears in most of the reference. The two are related in equation (24) of the reference. The reference also describes the relationship between this perturbation solution and the original sticky hard sphere (or adhesive sphere) model by Baxter.</p>
-<p>NOTES: The calculation can go haywire for certain combinations of the input parameters, producing unphysical solutions - in this case errors are reported to the command window and the S(q) is set to -1 (it will disappear on a log-log plot). Use tight bounds to keep the parameters to values that you know are physical (test them) and keep nudging them until the optimization does not hit the constraints.</p>
-<p style="margin-left: 0.25in;">For 2D plot, the wave transfer is defined as<span style="font-size: 12pt; font-family: 'Times New Roman','serif'; position: relative; top: 4.5pt;"><img src="img/image040.gif" alt="" /></span><span style="font-size: 14pt;">.</span></p>
-<div align="center">
-<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">
-<tbody>
-<tr style="height: 19.25pt;">
-<td style="border: 1pt solid width: 108.5pt; height: 19.25pt;" valign="top" width="145">
-<p>Parameter name</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Units</p>
-</td>
-<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>Default value</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 108.5pt; height: 19.25pt;" valign="top" width="145">
-<p>effect_radius</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>&Aring;</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>50</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; vertical-align: top; width: 108.5pt; height: 19.25pt;">
-<p>perturb</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0.05</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 108.5pt; height: 19.25pt;" valign="top" width="145">
-<p>volfraction</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">&nbsp;</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0.1</p>
-</td>
-</tr>
-<tr style="height: 19.25pt;">
-<td style="border-width: medium 1pt 1pt; width: 108.5pt; height: 19.25pt;" valign="top" width="145">
-<p>stickiness</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>K</p>
-</td>
-<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">
-<p>0.2</p>
-</td>
-</tr>
-</tbody>
-</table>
-</div>
-<p style="text-align: center;" align="center"><img id="Picture 113" src="img/image230.jpg" alt="" /></p>
-<p style="text-align: center;" align="center"><b>Figure. 1D plot using the default values (in linear scale).</b></p>
-<p>References:</p>
-<p style="text-indent: 0.5in;">Menon, S. V. G., Manohar, C. and K. Srinivas Rao J. Chem. Phys., 95(12), 9186-9190 (1991).</p>
-<p><a name="References"></a><b><span style="font-size: 14pt;">References</span></b></p>
-<p>Feigin, L. A, and D. I. Svergun (1987) "Structure Analysis by Small-Angle X-Ray and Neutron Scattering", Plenum Press, New York.</p>
-<p>Guinier, A. and G. Fournet (1955) "Small-Angle Scattering of X-Rays", John Wiley and Sons, New York.</p>
-<p>Kline, S. R. (2006) <em>J Appl. Cryst.</em> <b>39</b>(6), 895.</p>
-<p>Hansen, S., (1990)<em> J. Appl. Cryst. </em>23, 344-346.</p>
-<p>Henderson, S.J. (1996) <em>Biophys. J. </em>70, 1618-1627</p>
-<p>St&ouml;ckel, P., May, R., Strell, I., Cejka, Z., Hoppe, W., Heumann, H., Zillig, W. and Crespi, H. (1980) <em>Eur. J. Biochem. </em>112, 411-417.</p>
-<p>McAlister, B.C. and Grady, B.P., (1998) J. Appl. Cryst. 31, 594-599.</p>
-<p>Porod, G. (1982) in Small Angle X-ray Scattering, editors Glatter, O. and Kratky, O., Academic Press.</p>
-<p>*Also, see the references at the end of the each model function descriptions.</p>
-</body></html>
Index: src/sas/models/media/readme.txt
===================================================================
--- src/sas/models/media/readme.txt	(revision 794922220f2fb3b23dd08c648aabf87b4850596c)
+++ src/sas/models/media/readme.txt	(revision ae00b6fc81389d82c517e414b350781698733332)
@@ -2,5 +2,5 @@
 file from html to restructured text.
 
-model_functions.html is the help file distributed with SasView v2.2.1.
+model_functions_v0.html (if present) is the help file distributed with SasView v2.2.1.
 
 model_functions-2.html (if present) is the current html generated from the 
@@ -8,6 +8,6 @@
 
 NIST_IGOR_SANS_Model_Docs_v4.10.pdf should be used as the primary reference 
-for queries about the model descriptions, NOT model_functions.html.
+for queries about the model descriptions, NOT model_functions_v0.html.
 
 Steve King
-Apr 2014
+Feb 2015
Index: src/sas/perspectives/fitting/pagestate.py
===================================================================
--- src/sas/perspectives/fitting/pagestate.py	(revision b9a5f0eb8e8cbff8f8d934bbfa4ea18168141e13)
+++ src/sas/perspectives/fitting/pagestate.py	(revision d06ae30ac5ee253d15e9419032e938ebd5747771)
@@ -472,5 +472,5 @@
         Get the values (strings) from __str__ for report
         """
-        # Dictionary of teh report strings
+        # Dictionary of the report strings
         repo_time = ""
         model_name = ""
@@ -508,6 +508,14 @@
             if name == "value":
                 param_string += value + ','
+	    if name == "selected":
+		if value == u' False':
+		    fixed_parameter = True
+		else:
+		    fixed_parameter = False
             if name == "error value":
-                param_string += value + ','
+	        if fixed_parameter:
+		    param_string += '(fixed),'
+		else:
+                    param_string += value + ','
             if name == "parameter unit":
                 param_string += value + ':'
Index: src/sas/perspectives/fitting/report_dialog.py
===================================================================
--- src/sas/perspectives/fitting/report_dialog.py	(revision 794922220f2fb3b23dd08c648aabf87b4850596c)
+++ src/sas/perspectives/fitting/report_dialog.py	(revision d06ae30ac5ee253d15e9419032e938ebd5747771)
@@ -1,5 +1,5 @@
 """
 Dialog report panel to show and summarize the results of 
-the invariant calculation.
+the fitting calculation.
 """
 ################################################################################
