Changeset 51b638f in sasview

Timestamp:

Sep 22, 2009 4:00:41 PM (15 years ago)

Author:

Jae Cho <jhjcho@…>

Branches:

master, ESS_GUI, ESS_GUI_Docs, ESS_GUI_batch_fitting, ESS_GUI_bumps_abstraction, ESS_GUI_iss1116, ESS_GUI_iss879, ESS_GUI_iss959, ESS_GUI_opencl, ESS_GUI_ordering, ESS_GUI_sync_sascalc, costrafo411, magnetic_scatt, release-4.1.1, release-4.1.2, release-4.2.2, release_4.0.1, ticket-1009, ticket-1094-headless, ticket-1242-2d-resolution, ticket-1243, ticket-1249, ticket885, unittest-saveload

Children:

49c5a36

Parents:

a0bc608

Message:

Model function doc and help update

Location:

sansview/doc

Files:

• Model Functions.docx (modified) (previous)
• Model Functions.pdf (added)
• model_functions.html (modified) (107 diffs)

sansview/doc/model_functions.html

@@ -9 +9 @@
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+        panose-1:2 11 6 9 2 2 4 3 2 4;}
+@font-face
+        {font-family:Constantia;
+        panose-1:2 3 6 2 5 3 6 3 3 3;}
+@font-face
+        {font-family:Corbel;
+        panose-1:2 11 5 3 2 2 4 2 2 4;}
+@font-face
+        {font-family:"Segoe UI";
+        panose-1:2 11 5 2 4 2 4 2 2 3;}
+@font-face
+        {font-family:"\@MS Mincho";
+        panose-1:2 2 6 9 4 2 5 8 3 4;}
  /* Style Definitions */
  p.MsoNormal, li.MsoNormal, div.MsoNormal
@@ -40 +627 @@
         font-size:12.0pt;
         font-family:"Times New Roman","serif";}
+a:link, span.MsoHyperlink
+        {color:blue;
+        text-decoration:underline;}
 a:visited, span.MsoHyperlinkFollowed
         {color:purple;
@@ -54 +644 @@
         font-size:8.0pt;
         font-family:"Tahoma","sans-serif";}
+p.MsoListParagraph, li.MsoListParagraph, div.MsoListParagraph
+        {margin-top:0in;
+        margin-right:0in;
+        margin-bottom:0in;
+        margin-left:.5in;
+        margin-bottom:.0001pt;
+        font-size:12.0pt;
+        font-family:"Times New Roman","serif";}
+p.MsoListParagraphCxSpFirst, li.MsoListParagraphCxSpFirst, div.MsoListParagraphCxSpFirst
+        {margin-top:0in;
+        margin-right:0in;
+        margin-bottom:0in;
+        margin-left:.5in;
+        margin-bottom:.0001pt;
+        font-size:12.0pt;
+        font-family:"Times New Roman","serif";}
+p.MsoListParagraphCxSpMiddle, li.MsoListParagraphCxSpMiddle, div.MsoListParagraphCxSpMiddle
+        {margin-top:0in;
+        margin-right:0in;
+        margin-bottom:0in;
+        margin-left:.5in;
+        margin-bottom:.0001pt;
+        font-size:12.0pt;
+        font-family:"Times New Roman","serif";}
+p.MsoListParagraphCxSpLast, li.MsoListParagraphCxSpLast, div.MsoListParagraphCxSpLast
+        {margin-top:0in;
+        margin-right:0in;
+        margin-bottom:0in;
+        margin-left:.5in;
+        margin-bottom:.0001pt;
+        font-size:12.0pt;
+        font-family:"Times New Roman","serif";}
 p.IUCrbodytext, li.IUCrbodytext, div.IUCrbodytext
         {mso-style-name:"IUCr body text";
@@ -100 +722 @@
         mso-style-link:"Balloon Text";
         font-family:"Tahoma","sans-serif";}
+span.msoIns
+        {mso-style-name:"";
+        text-decoration:underline;
+        color:teal;}
+span.msoDel
+        {mso-style-name:"";
+        text-decoration:line-through;
+        color:red;}
 .MsoPapDefault
         {margin-bottom:10.0pt;
@@ -118 +748 @@
 </head>
 
-<body lang=EN-US vlink=purple>
+<body lang=EN-US link=blue vlink=purple>
 
 <div class=Section1>
@@ -126 +756 @@
 <p class=MsoNormal>&nbsp;</p>
 
-<ul>
-<li><a href="#Introduction"><b>Introduction</b></a></li>
-<li><a href="#Shapes"><b>Shapes</b></a>:  
-<a href="#SphereModel">SphereModel</a>, 
-<a href="#CylinderModel">CylinderModel</a>, 
-<a href="#EllipsoidModel">EllipsoidModel</a>, 
-<a href="#CoreShellModel">CoreShellModel</a>, 
-<a href="#CoreShellCylinderModel">CoreShellCylinderModel</a>,
-<a href="#EllipticalCylinderModel">EllipticalCylinderModel</a>. 
-</li>
-<li><a href="#Shape-Independent"><b>Shape-Independent</b></a>: 
-<a href="#Debye">Debye</a>, 
-<a href="#Lorentz">Lorentz</a>, 
-<a href="#DAB_Model">DAB_Model</a>, 
-<a href="#Power_Law">Power_Law</a>,
-<a href="#Teubner Strey">Teubner Strey</a>,
-<a href="#BEPolyelectrolyte">BEPolyelectrolyte</a>,
-<a href="#Number Density Fractal">Number Density Fractal</a>,
-<a href="#Guinier">Guinier</a>,
-<a href="#PorodModel">PorodModel</a>. </li>
-<li><a href="#Customized Models"><b>Customized Models</b></a>:  
-<a href="#A+Bcos(2x)+Csin(2x)">A+Bcos(2x)+Csin(2x)</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 type=disc>
+ <li class=MsoNormal style='line-height:115%'><a href="#Introduction"><b>Introduction</b></a>
+     </li>
+ <li class=MsoNormal style='line-height:115%'><a href="#Shapes"><b>Shapes</b></a>:
+     <a href="#SphereModel">SphereModel</a>,
+     <a href="#CoreShellModel">CoreShellModel</a>,
+     <a href="#VesiclelModel">VesicleModel</a>,
+     <a href="#MultiShellModel">MultiShellModel</a>,
+     <a href="#BinaryHSModel">BinaryHSModel</a>,
+     <a href="#CylinderModel">CylinderModel</a>,
+     <a href="#CoreShellCylinderModel">CoreShellCylinderModel</a>,
+     <a href="#HollowCylinderModel">HollowCylinderModel</a>,
+     <a href="#FlexibleCylinderModel">FlexibleCylinderModel</a>,
+     <a href="#StackedDisksModel">StackedDisksModel</a>,
+     <a href="#ParallelepipedModel">ParallelepipedModel</a>,
+     <a href="#EllipticalCylinderModel">EllipticalCylinderModel</a>,
+     <a href="#EllipsoidModel">EllipsoidModel</a>,
+     <a href="#CoreShellEllipsoidModel">CoreShellEllipsoidModel</a>,
+     <a href="#TriaxialEllipsoidModel">TriaxialEllipsoidModel</a>,
+     <a href="#LamellarModel">LamellarModel</a>,
+     <a href="#LamellarFFHGModel">LamellarFFHGModel</a>,
+     <a href="#LamellarPSModel">LamellarPSModel</a>,
+     <a href="#LamellarPSHGModel">LamellarPSHGModel</a>.</li>
+ <li class=MsoNormal style='line-height:115%'><a href="#Shape-Independent"><b>Shape-Independent</b></a>:
+     <a href="#Debye">Debye</a>,
+     <a href="#Lorentz">Lorentz</a>,
+     <a href="#DAB_Model">DAB_Model</a>,
+     <a href="#Power_Law">Power_Law</a>,
+     <a href="#Teubner Strey">Teubner Strey</a>, 
+        <a href="#BEPolyelectrolyte">BEPolyelectrolyte</a>,
+     <a href="#Number Density Fractal">Number Density Fractal</a>, 
+     <a href="#Guinier">Guinier</a>,
+     <a href="#PorodModel">PorodModel</a>,
+     <a href="#Peak Gauss Model">Peak Gauss Model</a>, 
+<a href="#Peak Lorentz Model">Peak Lorentz Model</a>, 
+<a href="#LineModel">LineModel</a>.</li>
+ <li class=MsoNormal style='line-height:115%'>
+<a href="#Customized Models"><b>Customized
+     Models</b></a>: <a href="#A+Bcos(2x)+Csin(2x)">A+Bcos(2x)+Csin(2x)</a>,
+     <a href="#sin(poly)/poly">sin(poly)/poly</a>.</li>
+ <li class=MsoNormal style='line-height:115%'>
+<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 class=MsoNormal style='line-height:115%'>
+<a href="#References"><b>References</b></a>
+     </li>
 </ul>
 
+<p class=MsoNormal>&nbsp;</p>
+
 <p class=MsoNormal style='margin-left:.25in;text-indent:-.25in'><b><span
-style='font-size:14.0pt'>1.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;
-</span></span></b><b><span style='font-size:14.0pt'><a name="Introduction">Introduction</a></span></b></p>
+style='font-size:16.0pt'>1.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;
+</span></span></b><b><span style='font-size:16.0pt'><a name="Introduction"> Introduction </a></span></b></p>
 
 <p class=MsoNormal>The present text documents the modules made available by the
@@ -181 +836 @@
 <p class=MsoNormal><b>&nbsp;</b></p>
 
+<p class=MsoNormal><b>&nbsp;</b></p>
 
 <p class=MsoNormal style='margin-left:.25in;text-indent:-.25in'><b><span
-style='font-size:14.0pt'>2.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;
-</span></span></b><b><span style='font-size:14.0pt'><a name="Shapes">Shapes (Scattering intensity models)</a></span></b></p>
+style='font-size:16.0pt'>2.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;
+</span></span></b><b><span style='font-size:16.0pt'><a name="Shapes">Shapes (Scattering Intensity
+Models)</a></span></b></p>
 
 <p class=MsoNormal>&nbsp;</p>
@@ -203 +860 @@
 experiments, we normalize the form factors by the volume of the particle:</p>
 
-<p class=MsoNormal align=center style='text-align:center'><sub><img width=192
-height=43 src="../images/html/image001.gif"></sub>            (1)</p>
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:12.0pt'><img border=0 width=192 height=43
+src="../images/html/image001.png"></span>            (1)</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
 
 <p class=MsoNormal>with</p>
 
-<p class=MsoNormal align=center style='text-align:center'><sub><img width=159
-height=29 src="../images/html/image002.gif"></sub>        (2)</p>
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:8.0pt'><img border=0 width=159 height=29
+src="../images/html/image002.png"></span>        (2)</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
 
 <p class=MsoNormal>where <i>P</i><sub>0</sub><i>(<b>q</b>)</i> is the
@@ -220 +887 @@
 <p class=MsoNormal>For systems without inter-particle interference, the form
 factors we provide can be related to the scattering intensity by the particle
-volume fraction:<sub><img width=92 height=21
-src="../images/html/image003.gif"></sub>.</p>
+volume fraction:<span style='position:relative;top:5.0pt'><img border=0
+width=92 height=21 src="../images/html/image003.png"></span>.</p>
 
 <p class=MsoNormal>&nbsp;</p>
@@ -241 +908 @@
 <p class=MsoNormal>&nbsp;</p>
 
+<p class=MsoNormal>&nbsp;</p>
 
 <p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
 style='font-size:14.0pt'>2.1.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-</span></span></b><b><span style='font-size:14.0pt'><a name="SphereModel">SphereModel</a></span></b></p>
+</span></span></b><b><span style='font-size:14.0pt'><a name="SphereModel">Sphere Model</span></b></p>
 
 <p class=MsoNormal>&nbsp;</p>
@@ -254 +922 @@
 <p class=MsoNormal>&nbsp;</p>
 
-<p class=MsoNormal style='margin-left:.85in;text-indent:-.35in'><b>2.1.1.<span
-style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b>Definition</b></p>
-
-<p class=MsoNormal>&nbsp;</p>
-
-<p class=MsoNormal>The 1D scattering intensity is calculated in the following way
-(Guinier, 1955):</p>
-
-<p class=MsoNormal align=center style='text-align:center'><sub><img width=337
-height=53 src="../images/html/image004.gif"></sub>            (3)</p>
+<p class=MsoNormal style='margin-left:.85in;text-indent:-.35in'><b>1.1.<span
+style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b>Definition</b></p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>The 1D scattering intensity is calculated in the following
+way (Guinier, 1955):</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:16.0pt'><img border=0 width=337 height=53
+src="../images/html/image004.png"></span>            (3)</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
 
 <p class=MsoNormal>where <i>scale</i> is a scale factor, V is the volume of the
 scatterer, <i>r</i> is the radius of the sphere, <i>bkg</i> is the background
 level and <i><span style='font-family:"Arial","sans-serif"'>&#916;</span>&#961;</i>
-(contrast)  is the scattering length density difference between the scatterer
+(contrast)  is the scattering length density difference between the scatterer
 and the solvent it is in.</p>
 
@@ -280 +955 @@
 <p class=MsoNormal>The returned value is scaled to units of [cm<sup>-1</sup>]
 and the parameters of the sphere model are the following:</p>
+
+<p class=MsoNormal>&nbsp;</p>
 
 <div align=center>
@@ -369 +1046 @@
 <p class=MsoNormal>&nbsp;</p>
 
+<p class=MsoNormal>&nbsp;</p>
+
 <p class=MsoNormal>Our model uses the form factor calculations implemented in a
 c-library provided by the NIST Center for Neutron Research (Kline, 2006).</p>
@@ -374 +1053 @@
 <p class=MsoNormal>&nbsp;</p>
 
-
-<p class=MsoNormal style='margin-left:.85in;text-indent:-.35in'><b>2.1.2.<span
-style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b>Validation
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal style='margin-left:.85in;text-indent:-.35in'><b>2.1.<span
+style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b>Validation
 of the sphere model</b></p>
 
@@ -389 +1069 @@
 
 <p class=MsoBodyText align=center style='text-align:center;page-break-after:
-avoid'><img width=573 height=315 id="Picture 5"
+avoid'><img border=0 width=521 height=287 id="Picture 5"
 src="../images/html/image005.jpg" alt="sphere_1D_validation"></p>
+
+<p class=MsoBodyText align=center style='text-align:center;page-break-after:
+avoid'>&nbsp;</p>
 
 <p class=MsoCaption>Figure 1: Comparison of the DANSE scattering intensity for
@@ -399 +1082 @@
 <p class=MsoNormal>&nbsp;</p>
 
+<p class=MsoNormal><b>&nbsp;</b></p>
+
+<p class=MsoNormal><b>&nbsp;</b></p>
+
+<p class=MsoNormal><b>&nbsp;</b></p>
+
+
 
 <p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
 style='font-size:14.0pt'>2.2.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-</span></span></b><b><span style='font-size:14.0pt'><a name="CylinderModel">CylinderModel</a></span></b></p>
-
-<p class=MsoNormal>&nbsp;</p>
-
-<p class=MsoNormal>This model provides the form factor for a monodisperse right
-circular cylinder with uniform scattering length density. The form factor is
-normalized by the particle volume.</p>
-
-<p class=MsoNormal>&nbsp;</p>
-
-<p class=MsoNormal style='margin-left:.85in;text-indent:-.35in'><b>2.2.1.<span
-style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b>Definition</b></p>
+</span></span></b><b><span style='font-size:14.0pt'><a name="CoreShellModel">Core Shell (Sphere) Model</span></b></p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>This model provides the form factor, P(<i>q</i>), for a
+spherical particle with a core-shell structure. The form factor is normalized
+by the particle volume.</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal style='margin-left:.85in;text-indent:-.35in'><b>1.1.<span
+style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b>Definition</b></p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>The 1D scattering intensity is calculated in the following
+way (Guinier, 1955):</p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:16.0pt'><img border=0 width=642 height=55
+src="../images/html/image006.png"></span> (11)</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=right style='text-align:right'>&nbsp;</p>
+
+<p class=MsoNormal>where <i>scale</i> is a scale factor, <i>V<sub>s</sub></i>
+is the volume of the outer shell, <i>V<sub>c</sub></i> is the volume of the
+core, <i>r<sub>s</sub></i> is the radius of the shell, <i>r<sub>c</sub></i> is
+the radius of the core, <i>&#961;<sub>c</sub></i> is the scattering length
+density of the core, <i>&#961;<sub>s</sub></i> is the scattering length density
+of the shell, &#961;<sub>solv</sub> is the scattering length density of the
+solvent, and <i>bkg</i> is the background level. </p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>The 2D scattering intensity is the same as P(q) above,
+regardless of the orientation of the q vector.</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>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 class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>The returned value is scaled to units of [cm<sup>-1</sup>]
+and the parameters of the core-shell sphere model are the following:</p>
+
+<p class=MsoNormal>Here, radius = the radius of the core and thickness = the
+thickness of the shell.</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<div align=center>
+
+<table class=MsoTableGrid border=1 cellspacing=0 cellpadding=0
+ style='border-collapse:collapse;border:none'>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Parameter name</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Units</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Default value</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>scale</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>None</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>1.0</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>radius</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>60</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>thickness</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>10</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>core_sld</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å<sup> -2</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>1e-6</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>shell_sld</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å<sup> -2</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>2e-6</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>solvent_sld</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å<sup> -2</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>3e-6</p>
+  </td>
+ </tr>
+ <tr style='height:19.5pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.5pt'>
+  <p class=MsoBodyText>background</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:19.5pt'>
+  <p class=MsoBodyText>cm<sup>-1</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:19.5pt'>
+  <p class=MsoBodyText>0.001</p>
+  </td>
+ </tr>
+</table>
+
+</div>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>Our model uses the form factor calculations implemented in a
+c-library provided by the NIST Center for Neutron Research (Kline, 2006).</p>
+
+<p class=MsoNormal>            </p>
+
+<p class=MsoNormal>REFERENCE</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>Guinier, A. and G. Fournet, &quot;Small-Angle Scattering of
+X-Rays&quot;, John Wiley and Sons, New York, (1955).</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal style='margin-left:.85in;text-indent:-.35in'><b>2.1.<span
+style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b>Validation
+of the core-shell sphere model</b></p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>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 class=MsoNormal>&nbsp;</p>
+
+<p class=MsoBodyText align=center style='text-align:center;page-break-after:
+avoid'><img border=0 width=526 height=289 id="Picture 19"
+src="../images/html/image007.jpg" alt="core_shell_sphere_1D_validation"></p>
+
+<p class=MsoCaption>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 Å, Contrast=1e-6 Å<sup> -2</sup>,
+and Background=0.001 cm<sup> -1</sup>.</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal><b>&nbsp;</b></p>
+
+<p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
+style='font-size:14.0pt'>2.3.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span></b><b><span style='font-size:14.0pt'><a name="VesicleModel">VesicleModel</span></b></p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>This model provides the form factor, P(<i>q</i>), for an
+unilamellar vesicle. The form factor is normalized by the volume of the shell.</p>
+
+<p class=MsoNormal>The 1D scattering intensity is calculated in the following
+way (Guinier, 1955):</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:16.0pt'><img border=0 width=448 height=54
+src="../images/html/image008.png"></span> (11)</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=right style='text-align:right'>&nbsp;</p>
+
+<p class=MsoNormal>where <i>scale</i> is a scale factor, <i>V<sub>shell</sub></i>
+is the volume of the shell, <i>V<sub>1</sub></i> is the volume of the core, <i>V<sub>2</sub></i>
+is the total volume, <i>R<sub>1</sub></i> is the radius of the core, <i>r<sub>2</sub></i>
+is the outer radius of the shell, <i>&#961;<sub>1</sub></i> is the scattering
+length density of the core and the solvent, <i>&#961;<sub>2</sub></i> is the
+scattering length density of the shell, and <i>bkg</i> is the background level.
+And <i>J<sub>1</sub></i> = (sin<i>x </i>- <i>x</i>cos<i>x</i>)/<i>x</i><sup>2</sup>.
+The functional form is identical to a &quot;typical&quot; 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.  </p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><img border=0
+width=149 height=143 id="Picture 31" src="../images/html/image009.jpg"></p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal>The 2D scattering intensity is the same as <i>P</i>(<i>q</i>)
+above, regardless of the orientation of the <i>q</i> vector  which is defined
+as<span style='font-size:14.0pt;position:relative;top:8.0pt'><img border=0
+width=103 height=33 src="../images/html/image010.png"></span><span
+style='font-size:14.0pt;position:relative;top:6.0pt'>.</span></p>
+
+<p class=MsoNormal>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 class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>The returned value is scaled to units of [cm<sup>-1</sup>]
+and the parameters of the vesicle model are the following:</p>
+
+<p class=MsoNormal>In the parameters, the ‘radius’ represents the core radius
+(R<sub>1</sub>) and the ‘thickness’ (R<sub>2</sub> – R<sub>1</sub>) is the
+shell thickness.</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<div align=center>
+
+<table class=MsoTableGrid border=1 cellspacing=0 cellpadding=0
+ style='border-collapse:collapse;border:none'>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Parameter name</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Units</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Default value</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>scale</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>None</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>1.0</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>radius</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>100</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>thickness</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>30</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>core_sld</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å<sup> -2</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>6.3e-6</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>shell_sld</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å<sup> -2</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>0</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>background</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>cm<sup>-1</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>0.0</p>
+  </td>
+ </tr>
+</table>
+
+</div>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><img border=0
+width=454 height=356 id="Picture 158" src="../images/html/image011.png"></p>
+
+<p class=MsoNormal align=center style='text-align:center;text-autospace:none'><b>Figure.
+1D plot using the default values (w/200 data point).</b></p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal>Our model uses the form factor calculations implemented in a
+c-library provided by the NIST Center for Neutron Research (Kline, 2006).</p>
+
+<p class=MsoNormal>REFERENCE</p>
+
+<p class=MsoNormal>Guinier, A. and G. Fournet, &quot;Small-Angle Scattering of
+X-Rays&quot;, John Wiley and Sons, New York, (1955).</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoBodyText>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal><b>&nbsp;</b></p>
+
+<p class=MsoNormal><b>&nbsp;</b></p>
+
+
+<p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
+style='font-size:14.0pt'>2.4.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span></b><b><span style='font-size:14.0pt'><a name="MultiShellModel">MultiShellModel</span></b></p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>This model provides the form factor, P(<i>q</i>), 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 class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><img border=0
+width=255 height=224 id="Picture 32" src="../images/html/image012.jpg"></p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal>The 2D scattering intensity is the same as 1D, regardless of
+the orientation of the <i>q</i> vector which is defined as<span
+style='font-size:14.0pt;position:relative;top:8.0pt'><img border=0 width=103
+height=33 src="../images/html/image010.png"></span><span
+style='font-size:14.0pt;position:relative;top:6.0pt'>.</span></p>
+
+<p class=MsoNormal>For P*S: The outer most radius (= core_radius + n_pairs  *
+s_thickness  + (n_pairs -1) * w_thickness) is used as the effective radius
+toward S(Q) when P(Q)*S(Q) is applied. </p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>The returned value is scaled to units of [cm<sup>-1</sup>]
+and the parameters of the multi-shell model are the following:</p>
+
+<p class=MsoNormal>In the parameters, the ‘s_thickness’ is the shell thickness
+while the ‘w_thickness’ is the solvent thickness, and the n_pair is the number
+of shells.</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<div align=center>
+
+<table class=MsoTableGrid border=1 cellspacing=0 cellpadding=0
+ style='border-collapse:collapse;border:none'>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Parameter name</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Units</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Default value</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>scale</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>None</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>1.0</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>core_radius</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>60.0</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>n_pairs</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>None</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>2.0</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>core_sld</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å<sup> -2</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>6.3e-6</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>shell_sld</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å<sup> -2</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>0.0</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>background</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>cm<sup>-1</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>0.0</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>s_thickness</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>10</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>w_thickness</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>10</p>
+  </td>
+ </tr>
+</table>
+
+</div>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><img border=0
+width=447 height=340 id="Picture 173" src="../images/html/image013.jpg"></p>
+
+<p class=MsoNormal align=center style='text-align:center;text-autospace:none'><b>Figure.
+1D plot using the default values (w/200 data point).</b></p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal>Our model uses the form factor calculations implemented in a
+c-library provided by the NIST Center for Neutron Research (Kline, 2006).</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>REFERENCE</p>
+
+<p class=MsoNormal>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 class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal><b>&nbsp;</b></p>
+
+<p class=MsoNormal><b>&nbsp;</b></p>
+
+<p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
+style='font-size:14.0pt'>2.5.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span></b><b><span style='font-size:14.0pt'><a name="BinaryHSModel">BinaryHSModel</span></b></p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>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 class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:5.0pt'><img border=0 width=479 height=25
+src="../images/html/image014.png"></span></p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:16.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:16.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal><span style='position:relative;top:16.0pt'>where S<sub>ij</sub>
+are the partial structure factors and f<sub>i</sub> 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, (<i>x</i>
+=  n<sub>2</sub>/(n<sub>1</sub>+n<sub>2</sub>), n = the number density) is
+internally calculated based on:</span></p>
+
+<p class=MsoNormal><span style='position:relative;top:16.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:24.0pt'><img border=0 width=248 height=98
+src="../images/html/image015.png"></span><span style='position:relative;
+top:16.0pt'>.</span></p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:16.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:16.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>The 2D scattering intensity is the same as 1D, regardless of
+the orientation of the <i>q</i> vector which is defined as<span
+style='font-size:14.0pt;position:relative;top:8.0pt'><img border=0 width=103
+height=33 src="../images/html/image010.png"></span><span
+style='font-size:14.0pt;position:relative;top:6.0pt'>.</span></p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>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>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<div align=center>
+
+<table class=MsoTableGrid border=1 cellspacing=0 cellpadding=0
+ style='border-collapse:collapse;border:none'>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Parameter name</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Units</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Default value</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>background</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>cm<sup>-1</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>0.001</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>l_radius</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>100.0</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>ss_sld</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å<sup> -2</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>0.0</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>ls_sld</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å<sup> -2</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>3e-6</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>solvent_sld</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å<sup> -2</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>6e-6</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>s_radius</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>25.0</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>vol_frac_ls</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>0.1</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>vol_frac_ss</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>0.2</p>
+  </td>
+ </tr>
+</table>
+
+</div>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><img border=0
+width=484 height=361 id="Picture 197" src="../images/html/image016.png"></p>
+
+<p class=MsoNormal align=center style='text-align:center;text-autospace:none'><b>Figure.
+1D plot using the default values above (w/200 data point).</b></p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal>Our model uses the form factor calculations implemented in a
+c-library provided by the NIST Center for Neutron Research (Kline, 2006).</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>See the reference for details.</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>REFERENCE</p>
+
+<p class=MsoNormal>N. W. Ashcroft and D. C. Langreth, Physical Review, v. 156
+(1967) 685-692.</p>
+
+<p class=MsoNormal>[Errata found in Phys. Rev. 166 (1968) 934.]</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
+style='font-size:14.0pt'>2.6.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span></b><b><span style='font-size:14.0pt'><a name="CylinderModel">Cylinder Model</span></b></p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>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>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal style='margin-left:.85in;text-indent:-.35in'><b>1.1.<span
+style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b>Definition</b></p>
 
 <p class=MsoNormal>&nbsp;</p>
@@ -420 +2043 @@
 oriented cylinders is given by (Guinier, 1955):</p>
 
-<p class=MsoNormal align=center style='text-align:center'><sub><img width=184
-height=41 src="../images/html/image006.gif"></sub>  (4)</p>
-
-<p class=MsoNormal align=center style='text-align:center'><sub><img width=373
-height=45 src="../images/html/image007.gif"></sub>   (5)</p>
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:12.0pt'><img border=0 width=184 height=41
+src="../images/html/image017.png"></span>  (4)</p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:14.0pt'><img border=0 width=373 height=45
+src="../images/html/image018.png"></span>   (5)</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
 
 <p class=MsoNormal>where <span style='font-family:"Arial","sans-serif"'>&#945;</span>
@@ -435 +2068 @@
 <p class=MsoNormal>&nbsp;</p>
 
-<p class=MsoNormal>To provide easy access to the orientation of the cylinder, we
-define the axis of the cylinder using two angles &#952; and <span
-style='font-family:"Arial","sans-serif"'>&#966;</span>. Those angles are
-defined on Figure 2.</p>
+<p class=MsoNormal>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 class=MsoNormal>&nbsp;</p>
 
 <p class=MsoNormal align=center style='text-align:center;page-break-after:avoid'><img
-width=300 height=281 id="Picture 8" src="../images/html/image008.jpg"
-alt=angles></p>
+border=0 width=478 height=258 id="Picture 14"
+src="../images/html/image019.jpg" alt=cylinderangles.gif></p>
 
 <p class=MsoCaption align=center style='text-align:center'><a
-name="_Ref173306040"></a><a name="_Ref173213915">Figure </a>2: Definition of the angles for oriented cylinders.</p>
-
-<p class=MsoNormal>&nbsp;</p>
-
+name="_Ref173306040"></a><a name="_Ref173213915">Figure </a>2a. Definition of the angles for oriented cylinders.</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><img border=0
+width=409 height=276 src="../images/html/image020.jpg"
+alt=cylinderangles2.gif></p>
+
+<p class=MsoCaption align=center style='text-align:center'>Figure 2b. Examples of the angles for oriented cylinders against the detector plane.</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal>For P*S: The 2<sup>nd</sup> 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 class=MsoNormal>&nbsp;</p>
 
 <p class=MsoNormal>The returned value is scaled to units of [cm<sup>-1</sup>]
 and the parameters of the cylinder model are the following:</p>
+
+<p class=MsoNormal>&nbsp;</p>
 
 <p class=MsoNormal>&nbsp;</p>
@@ -476 +2129 @@
   <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
   border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.85pt'>
-  <p class=MsoBodyText>Scale</p>
+  <p class=MsoBodyText>scale</p>
   </td>
   <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
@@ -492 +2145 @@
   <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
   border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.85pt'>
-  <p class=MsoBodyText>Radius</p>
+  <p class=MsoBodyText>radius</p>
   </td>
   <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
@@ -508 +2161 @@
   <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
   border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.85pt'>
-  <p class=MsoBodyText>Length</p>
+  <p class=MsoBodyText>length</p>
   </td>
   <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
@@ -524 +2177 @@
   <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
   border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.85pt'>
-  <p class=MsoBodyText>Contrast</p>
+  <p class=MsoBodyText>contrast</p>
   </td>
   <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
@@ -540 +2193 @@
   <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
   border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.85pt'>
-  <p class=MsoBodyText>Background</p>
+  <p class=MsoBodyText>background</p>
   </td>
   <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
@@ -556 +2209 @@
   <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
   border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.85pt'>
-  <p class=MsoBodyText>Cyl_theta</p>
+  <p class=MsoBodyText>cyl_theta</p>
   </td>
   <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
@@ -572 +2225 @@
   <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
   border-top:none;padding:0in 5.4pt 0in 5.4pt;height:20.6pt'>
-  <p class=MsoBodyText>Cyl_phi</p>
+  <p class=MsoBodyText>cyl_phi</p>
   </td>
   <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
@@ -591 +2244 @@
 <p class=MsoNormal>&nbsp;</p>
 
+<p class=MsoNormal>&nbsp;</p>
+
 <p class=MsoNormal>The output of the 1D scattering intensity function for
 randomly oriented cylinders is then given by:</p>
 
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
 <p class=MsoNormal align=center style='text-align:center'><a
-name="_Ref173306479"></a><a name="_Ref173306528"><sub><img width=253 height=56
-src="../images/html/image009.gif"></sub>         (</a>6)</p>
+name="_Ref173306479"></a><a name="_Ref173306528"><span style='position:relative;
+top:16.0pt'><img border=0 width=253 height=56
+src="../images/html/image021.png"></span>         (</a>6)</p>
 
 <p class=MsoNormal>&nbsp;</p>
@@ -606 +2266 @@
 <p class=MsoNormal>&nbsp;</p>
 
-
-<p class=MsoNormal>&nbsp;</p>
-
-<p class=MsoNormal style='margin-left:.85in;text-indent:-.35in'><b>2.2.2.<span
-style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b>Validation
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal style='margin-left:.85in;text-indent:-.35in'><b>2.1.<span
+style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b>Validation
 of the cylinder model</b></p>
 
@@ -625 +2288 @@
 done by evaluating the following:</p>
 
-<p class=MsoNormal align=center style='text-align:center'><sub><img width=244
-height=51 src="../images/html/image010.gif"></sub>           (7)</p>
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:16.0pt'><img border=0 width=244 height=51
+src="../images/html/image022.png"></span>           (7)</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
 
 <p class=MsoNormal>where <i>p(&#952;,</i><i><span style='font-family:"Arial","sans-serif"'>&#966;</span>)</i>
@@ -639 +2309 @@
 <p class=MsoNormal>&nbsp;</p>
 
-<p class=MsoNormal style='page-break-after:avoid'><img width=573 height=315
-id="Picture 11" src="../images/html/image011.jpg"
-alt="cylinder_1D_validation"></p>
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center;page-break-after:avoid'><img
+border=0 width=512 height=282 id="Picture 11"
+src="../images/html/image023.jpg" alt="cylinder_1D_validation"></p>
+
+<p class=MsoNormal align=center style='text-align:center;page-break-after:avoid'>&nbsp;</p>
 
 <p class=MsoCaption><a name="_Ref173211049"></a><a name="_Ref173211066">Figure </a>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 Å,
-Length=400 Å, Contrast=3e-6 Å<sup> -2</sup>, and Background=0.01 cm<sup> -1</sup>.</p>
+NIST SANS analysis software. The parameters were set to: Scale=1.0, Radius=20
+Å, Length=400 Å, Contrast=3e-6 Å<sup> -2</sup>, and Background=0.01 cm<sup> -1</sup>.</p>
+
+<p class=MsoNormal>&nbsp;</p>
 
 <p class=MsoCaption>&nbsp;</p>
 
-<p class=MsoNormal style='page-break-after:avoid'><img width=573 height=315
-id="Picture 12" src="../images/html/image012.jpg"
-alt="cylinder_2D_average"></p>
+<p class=MsoNormal align=center style='text-align:center;page-break-after:avoid'><img
+border=0 width=521 height=287 id="Picture 12"
+src="../images/html/image024.jpg" alt="cylinder_2D_average"></p>
+
+<p class=MsoNormal align=center style='text-align:center;page-break-after:avoid'>&nbsp;</p>
 
 <p class=MsoCaption><a name="_Ref173213305">Figure </a>4: Comparison of the
@@ -661 +2339 @@
 <p class=MsoCaption>&nbsp;</p>
 
-<p class=MsoNormal>&nbsp;</p>
-
+<p class=MsoNormal><b>&nbsp;</b></p>
+
+<p class=MsoNormal><b>&nbsp;</b></p>
 
 <p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
-style='font-size:14.0pt'>2.3.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-</span></span></b><b><span style='font-size:14.0pt'><a name="EllipsoidModel">EllipsoidModel</a></span></b></p>
-
-<p class=MsoNormal>&nbsp;</p>
-
-<p class=MsoNormal>This model provides the form factor for a monodisperse
-ellipsoid (ellipsoid of revolution) with uniform scattering length density. The
-form factor is normalized by the particle volume.</p>
-
-<p class=MsoNormal>&nbsp;</p>
-
-<p class=MsoNormal style='margin-left:.85in;text-indent:-.35in'><b>2.3.1.<span
-style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b>Definition</b></p>
-
-<p class=MsoNormal>&nbsp;</p>
-
-<p class=MsoNormal>The output of the 2D scattering intensity function for
-oriented ellipsoids is given by (Feigin, 1987):</p>
-
-<p class=MsoCaption align=center style='text-align:center'><sub><img width=184
-height=41 src="../images/html/image006.gif"></sub>   <span
-style='font-size:12.0pt;font-weight:normal'>(8)</span></p>
-
-<p class=MsoCaption align=center style='text-align:center'><sub><img width=371
-height=47 src="../images/html/image013.gif"></sub>    <span
-style='font-size:12.0pt;font-weight:normal'>(9)</span></p>
-
-<p class=MsoCaption align=center style='text-align:center'><sub><img width=272
-height=29 src="../images/html/image014.gif"></sub>     <span
-style='font-size:12.0pt;font-weight:normal'>(10)</span></p>
-
-<p class=MsoNormal>where <span style='font-family:"Arial","sans-serif"'>&#945;</span>
-is the angle between the axis of the ellipsoid and the q-vector, V is the
-volume of the ellipsoid, R<sub>a</sub> is the radius along the rotation axis of
-the ellipsoid, R<sub>b</sub> is the radius perpendicular to the rotation axis of
-the ellipsoid and <i><span style='font-family:"Arial","sans-serif"'>&#916;</span>&#961;</i>
-(contrast) is the scattering length density difference between the scatterer
-and the solvent. </p>
-
-<p class=MsoNormal>&nbsp;</p>
-
-<p class=MsoNormal>To provide easy access to the orientation of the ellipsoid,
-we define the rotation axis of the ellipsoid using two angles &#952; and <span
-style='font-family:"Arial","sans-serif"'>&#966;</span>. Similarly to the case
-of the cylinder, those angles are defined on Figure 2. For the ellipsoid,
-&#952; is the angle between the rotation axis and the z-axis. </p>
-
-<p class=MsoNormal>&nbsp;</p>
-
-<p class=MsoNormal>The returned value is scaled to units of [cm<sup>-1</sup>]
-and the parameters of the ellipsoid model are the following:</p>
-
-<p class=MsoNormal>&nbsp;</p>
-
-<div align=center>
-
-<table class=MsoTableGrid border=1 cellspacing=0 cellpadding=0
- style='border-collapse:collapse;border:none'>
- <tr style='height:19.85pt'>
-  <td width=180 valign=top style='width:135.1pt;border:solid windowtext 1.0pt;
-  padding:0in 5.4pt 0in 5.4pt;height:19.85pt'>
-  <p class=MsoBodyText>Parameter name</p>
-  </td>
-  <td width=105 valign=top style='width:78.9pt;border:solid windowtext 1.0pt;
-  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:19.85pt'>
-  <p class=MsoBodyText>Units</p>
-  </td>
-  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
-  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:19.85pt'>
-  <p class=MsoBodyText>Default value</p>
-  </td>
- </tr>
- <tr style='height:19.85pt'>
-  <td width=180 valign=top style='width:135.1pt;border:solid windowtext 1.0pt;
-  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.85pt'>
-  <p class=MsoBodyText>Scale</p>
-  </td>
-  <td width=105 valign=top style='width:78.9pt;border-top:none;border-left:
-  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
-  padding:0in 5.4pt 0in 5.4pt;height:19.85pt'>
-  <p class=MsoBodyText>None</p>
-  </td>
-  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
-  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
-  padding:0in 5.4pt 0in 5.4pt;height:19.85pt'>
-  <p class=MsoBodyText>1.0</p>
-  </td>
- </tr>
- <tr style='height:19.85pt'>
-  <td width=180 valign=top style='width:135.1pt;border:solid windowtext 1.0pt;
-  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.85pt'>
-  <p class=MsoBodyText>Radius_a (parallel)</p>
-  </td>
-  <td width=105 valign=top style='width:78.9pt;border-top:none;border-left:
-  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
-  padding:0in 5.4pt 0in 5.4pt;height:19.85pt'>
-  <p class=MsoBodyText>Å</p>
-  </td>
-  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
-  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
-  padding:0in 5.4pt 0in 5.4pt;height:19.85pt'>
-  <p class=MsoBodyText>20.0</p>
-  </td>
- </tr>
- <tr style='height:19.85pt'>
-  <td width=180 valign=top style='width:135.1pt;border:solid windowtext 1.0pt;
-  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.85pt'>
-  <p class=MsoBodyText>Radius_b (perpendicular)</p>
-  </td>
-  <td width=105 valign=top style='width:78.9pt;border-top:none;border-left:
-  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
-  padding:0in 5.4pt 0in 5.4pt;height:19.85pt'>
-  <p class=MsoBodyText>Å</p>
-  </td>
-  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
-  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
-  padding:0in 5.4pt 0in 5.4pt;height:19.85pt'>
-  <p class=MsoBodyText>400.0</p>
-  </td>
- </tr>
- <tr style='height:19.85pt'>
-  <td width=180 valign=top style='width:135.1pt;border:solid windowtext 1.0pt;
-  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.85pt'>
-  <p class=MsoBodyText>Contrast</p>
-  </td>
-  <td width=105 valign=top style='width:78.9pt;border-top:none;border-left:
-  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
-  padding:0in 5.4pt 0in 5.4pt;height:19.85pt'>
-  <p class=MsoBodyText>Å<sup> -2</sup></p>
-  </td>
-  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
-  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
-  padding:0in 5.4pt 0in 5.4pt;height:19.85pt'>
-  <p class=MsoBodyText>3.0e-6</p>
-  </td>
- </tr>
- <tr style='height:19.85pt'>
-  <td width=180 valign=top style='width:135.1pt;border:solid windowtext 1.0pt;
-  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.85pt'>
-  <p class=MsoBodyText>Background</p>
-  </td>
-  <td width=105 valign=top style='width:78.9pt;border-top:none;border-left:
-  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
-  padding:0in 5.4pt 0in 5.4pt;height:19.85pt'>
-  <p class=MsoBodyText>cm<sup>-1</sup></p>
-  </td>
-  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
-  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
-  padding:0in 5.4pt 0in 5.4pt;height:19.85pt'>
-  <p class=MsoBodyText>0.0</p>
-  </td>
- </tr>
- <tr style='height:19.85pt'>
-  <td width=180 valign=top style='width:135.1pt;border:solid windowtext 1.0pt;
-  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.85pt'>
-  <p class=MsoBodyText>Axis_theta</p>
-  </td>
-  <td width=105 valign=top style='width:78.9pt;border-top:none;border-left:
-  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
-  padding:0in 5.4pt 0in 5.4pt;height:19.85pt'>
-  <p class=MsoBodyText>Radian</p>
-  </td>
-  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
-  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
-  padding:0in 5.4pt 0in 5.4pt;height:19.85pt'>
-  <p class=MsoBodyText>1.57</p>
-  </td>
- </tr>
- <tr style='height:20.6pt'>
-  <td width=180 valign=top style='width:135.1pt;border:solid windowtext 1.0pt;
-  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:20.6pt'>
-  <p class=MsoBodyText>Axis_phi</p>
-  </td>
-  <td width=105 valign=top style='width:78.9pt;border-top:none;border-left:
-  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
-  padding:0in 5.4pt 0in 5.4pt;height:20.6pt'>
-  <p class=MsoBodyText>Radian</p>
-  </td>
-  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
-  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
-  padding:0in 5.4pt 0in 5.4pt;height:20.6pt'>
-  <p class=MsoBodyText>0.0</p>
-  </td>
- </tr>
-</table>
-
-</div>
-
-<p class=MsoNormal>&nbsp;</p>
-
-<p class=MsoNormal>The output of the 1D scattering intensity function for
-randomly oriented ellipsoids is then given by equation 6.</p>
-
-<p class=MsoNormal>&nbsp;</p>
-
-<p class=MsoNormal>The <i>axis_theta</i> and axis<i>_phi</i> 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 class=MsoNormal>&nbsp;</p>
-
-
-<p class=MsoNormal style='margin-left:.85in;text-indent:-.35in'><b>2.3.2.<span
-style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b>Validation
-of the ellipsoid model</b></p>
-
-<p class=MsoNormal>&nbsp;</p>
-
-<p class=MsoNormal>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 class=MsoNormal>&nbsp;</p>
-
-<p class=MsoNormal>Averaging over a distribution of orientation is done by
-evaluating equation 7. 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 <i>p(&#952;,</i><i><span
-style='font-family:"Arial","sans-serif"'>&#966;</span>)</i> = 1.0.  Figure 6 shows the result of such a cross-check.</p>
-
-<p class=MsoNormal align=center style='text-align:center'><b><i><span
-style='color:#3366FF'>&nbsp;</span></i></b></p>
-
-<p class=MsoNormal>The discrepancy above q=0.3 Å<sup> -1</sup> 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
-(equation 6). 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"'>&#945;</span>.
-Our result was found to be stable over the range of q shown for a number of
-points higher than 500.</p>
-
-<p class=MsoNormal style='page-break-after:avoid'><b><img width=573 height=315
-id="Picture 16" src="../images/html/image015.jpg"
-alt="ellipsoid_1D_validation"></b></p>
-
-<p class=MsoCaption><a name="_Ref173222904">Figure </a>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 Å, Radius_b=400
-Å, </p>
-
-<p class=MsoCaption>Contrast=3e-6 Å<sup> -2</sup>, and Background=0.01 cm<sup>
--1</sup>.</p>
-
-<p class=MsoNormal><b>&nbsp;</b></p>
-
-
-<p class=MsoNormal style='page-break-after:avoid'><img width=573 height=315
-id="Picture 17" src="../images/html/image016.jpg"
-alt="ellipsoid_2D_average"></p>
-
-<p class=MsoCaption><a name="_Ref173223004">Figure </a>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 Å, Radius_b=400 Å, Contrast=3e-6 Å<sup> -2</sup>, and
-Background=0.0 cm<sup> -1</sup>.</p>
-
-<p class=MsoCaption>&nbsp;</p>
-
-<p class=MsoNormal><b>&nbsp;</b></p>
-
-<p class=MsoNormal><b>&nbsp;</b></p>
-
-<p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
-style='font-size:14.0pt'>2.4.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-</span></span></b><b><span style='font-size:14.0pt'><a name="CoreShellModel">CoreShell(Sphere)Model</a></span></b></p>
-
-<p class=MsoNormal>&nbsp;</p>
-
-<p class=MsoNormal>This model provides the form factor, P(<i>q</i>), for a
-monodisperse spherical particle with a core-shell structure. The form factor is
+style='font-size:14.0pt'>2.7.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span></b><b><span style='font-size:14.0pt'><a name="CoreShellCylinderModel">Core-Shell Cylinder Model</span></b></p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>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 class=MsoNormal>&nbsp;</p>
 
-<p class=MsoNormal style='margin-left:.85in;text-indent:-.35in'><b>2.4.1.<span
-style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b>Definition</b></p>
-
-<p class=MsoNormal>&nbsp;</p>
-
-<p class=MsoNormal>The 1D scattering intensity is calculated in the following
-way (Guinier, 1955):</p>
-
-<p class=MsoNormal align=right style='text-align:right'><sub><img width=643
-height=55 src="../images/html/image017.gif"></sub> (11)</p>
-
-<p class=MsoNormal>where <i>scale</i> is a scale factor, <i>V<sub>s</sub></i>
-is the volume of the outer shell, <i>V<sub>c</sub></i> is the volume of the
-core, <i>r<sub>s</sub></i> is the radius of the shell, <i>r<sub>c</sub></i> is
-the radius of the core, <i>&#961;<sub>c</sub></i> is the scattering length
-density of the core, <i>&#961;<sub>s</sub></i> is the scattering length density
-of the shell, &#961;<sub>solv</sub> is the scattering length density of the
-solvent, and <i>bkg</i> is the background level.</p>
-
-<p class=MsoNormal>&nbsp;</p>
-
-<p class=MsoNormal>The 2D scattering intensity is the same as P(q) above,
-regardless of the orientation of the q vector.</p>
-
-<p class=MsoNormal>&nbsp;</p>
-
-<p class=MsoNormal>The returned value is scaled to units of [cm<sup>-1</sup>]
-and the parameters of the core-shell sphere model are the following:</p>
-
-<p class=MsoNormal>&nbsp;</p>
-
-<div align=center>
-
-<table class=MsoTableGrid border=1 cellspacing=0 cellpadding=0
- style='border-collapse:collapse;border:none'>
- <tr style='height:18.8pt'>
-  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
-  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
-  <p class=MsoBodyText>Parameter name</p>
-  </td>
-  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
-  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
-  <p class=MsoBodyText>Units</p>
-  </td>
-  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
-  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
-  <p class=MsoBodyText>Default value</p>
-  </td>
- </tr>
- <tr style='height:18.8pt'>
-  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
-  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
-  <p class=MsoBodyText>Scale</p>
-  </td>
-  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
-  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
-  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
-  <p class=MsoBodyText>None</p>
-  </td>
-  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
-  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
-  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
-  <p class=MsoBodyText>1.0</p>
-  </td>
- </tr>
- <tr style='height:18.8pt'>
-  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
-  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
-  <p class=MsoBodyText>Radius</p>
-  </td>
-  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
-  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
-  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
-  <p class=MsoBodyText>Å</p>
-  </td>
-  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
-  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
-  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
-  <p class=MsoBodyText>60</p>
-  </td>
- </tr>
- <tr style='height:18.8pt'>
-  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
-  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
-  <p class=MsoBodyText>Thickness</p>
-  </td>
-  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
-  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
-  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
-  <p class=MsoBodyText>Å</p>
-  </td>
-  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
-  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
-  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
-  <p class=MsoBodyText>10</p>
-  </td>
- </tr>
- <tr style='height:18.8pt'>
-  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
-  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
-  <p class=MsoBodyText>Core_sld</p>
-  </td>
-  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
-  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
-  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
-  <p class=MsoBodyText>Å<sup> -2</sup></p>
-  </td>
-  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
-  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
-  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
-  <p class=MsoBodyText>1e-6</p>
-  </td>
- </tr>
- <tr style='height:18.8pt'>
-  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
-  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
-  <p class=MsoBodyText>Shell_sld</p>
-  </td>
-  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
-  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
-  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
-  <p class=MsoBodyText>Å<sup> -2</sup></p>
-  </td>
-  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
-  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
-  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
-  <p class=MsoBodyText>2e-6</p>
-  </td>
- </tr>
- <tr style='height:18.8pt'>
-  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
-  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
-  <p class=MsoBodyText>Solvent_sld</p>
-  </td>
-  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
-  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
-  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
-  <p class=MsoBodyText>Å<sup> -2</sup></p>
-  </td>
-  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
-  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
-  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
-  <p class=MsoBodyText>3e-6</p>
-  </td>
- </tr>
- <tr style='height:19.5pt'>
-  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
-  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.5pt'>
-  <p class=MsoBodyText>Background</p>
-  </td>
-  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
-  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
-  padding:0in 5.4pt 0in 5.4pt;height:19.5pt'>
-  <p class=MsoBodyText>cm<sup>-1</sup></p>
-  </td>
-  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
-  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
-  padding:0in 5.4pt 0in 5.4pt;height:19.5pt'>
-  <p class=MsoBodyText>0.001</p>
-  </td>
- </tr>
-</table>
-
-</div>
-
-<p class=MsoNormal>&nbsp;</p>
-
-<p class=MsoNormal>Our model uses the form factor calculations implemented in a
-c-library provided by the NIST Center for Neutron Research (Kline, 2006).</p>
-
-<p class=MsoNormal>&nbsp;</p>
-
-
-<p class=MsoNormal style='margin-left:.85in;text-indent:-.35in'><b>2.4.2.<span
-style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b>Validation
-of the core-shell sphere model</b></p>
-
-<p class=MsoNormal>&nbsp;</p>
-
-<p class=MsoNormal>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 class=MsoNormal>&nbsp;</p>
-
-<p class=MsoBodyText align=center style='text-align:center;page-break-after:
-avoid'><img width=573 height=315 id="Picture 19"
-src="../images/html/image018.jpg" alt="core_shell_sphere_1D_validation"></p>
-
-<p class=MsoCaption>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 Å, Contrast=1e-6 Å<sup> -2</sup>,
-and Background=0.001 cm<sup> -1</sup>.</p>
-
-<p class=MsoBodyText>&nbsp;</p>
-
-<p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
-style='font-size:14.0pt'>2.5.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-</span></span></b><b><span style='font-size:14.0pt'><a name="CoreShellCylinderModel">CoreShellCylinderModel</a></span></b></p>
-
-<p class=MsoNormal>&nbsp;</p>
-
-<p class=MsoNormal>This model provides the form factor for a monodisperse,
-circular cylinder with a core-shell scattering length density profile. The form
-factor is normalized by the particle volume.</p>
-
-<p class=MsoNormal>&nbsp;</p>
-
-<p class=MsoNormal style='margin-left:.85in;text-indent:-.35in'><b>2.5.1.<span
-style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b>Definition</b></p>
+<p class=MsoNormal style='margin-left:.85in;text-indent:-.35in'><b>1.1.<span
+style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b>Definition</b></p>
 
 <p class=MsoNormal>&nbsp;</p>
@@ -1159 +2363 @@
 oriented core-shell cylinders is given by (Kline, 2006):</p>
 
-<p class=MsoNormal align=center style='text-align:center'><sub><img width=184
-height=45 src="../images/html/image019.gif"></sub> (12)</p>
-
-<p class=MsoNormal align=center style='text-align:center'><sub><img width=476
-height=93 src="../images/html/image020.gif"></sub> (13)</p>
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:15.0pt'><img border=0 width=184 height=45
+src="../images/html/image025.png"></span> (12)</p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:32.0pt'><img border=0 width=476 height=93
+src="../images/html/image026.png"></span> (13)</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
 
 <p class=MsoNormal>where <span style='font-family:"Arial","sans-serif"'>&#945;</span>
@@ -1178 +2392 @@
 <p class=MsoNormal>&nbsp;</p>
 
-<p class=MsoNormal>To provide easy access to the orientation of the core-shell cylinder,
-we define the axis of the cylinder using two angles &#952; and <span
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><img border=0
+width=384 height=196 id="Picture 34" src="../images/html/image027.jpg"></p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal>To provide easy access to the orientation of the core-shell
+cylinder, we define the axis of the cylinder using two angles &#952; and <span
 style='font-family:"Arial","sans-serif"'>&#966;</span>. Similarly to the case
 of the cylinder, those angles are defined on Figure 2.</p>
@@ -1185 +2408 @@
 <p class=MsoNormal>&nbsp;</p>
 
+<p class=MsoNormal>For P*S: The 2<sup>nd</sup> 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 class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
 <p class=MsoNormal>The returned value is scaled to units of [cm<sup>-1</sup>]
 and the parameters of the core-shell cylinder model are the following:</p>
@@ -1211 +2443 @@
   <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
   border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
-  <p class=MsoBodyText>Scale</p>
+  <p class=MsoBodyText>scale</p>
   </td>
   <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
@@ -1227 +2459 @@
   <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
   border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
-  <p class=MsoBodyText>Radius</p>
+  <p class=MsoBodyText>radius</p>
   </td>
   <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
@@ -1243 +2475 @@
   <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
   border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
-  <p class=MsoBodyText>Thickness</p>
+  <p class=MsoBodyText>thickness</p>
   </td>
   <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
@@ -1259 +2491 @@
   <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
   border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
-  <p class=MsoBodyText>Length</p>
+  <p class=MsoBodyText>length</p>
   </td>
   <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
@@ -1275 +2507 @@
   <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
   border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
-  <p class=MsoBodyText>Core_sld</p>
+  <p class=MsoBodyText>core_sld</p>
   </td>
   <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
@@ -1291 +2523 @@
   <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
   border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
-  <p class=MsoBodyText>Shell_sld</p>
+  <p class=MsoBodyText>shell_sld</p>
   </td>
   <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
@@ -1307 +2539 @@
   <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
   border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
-  <p class=MsoBodyText>Solvent_sld</p>
+  <p class=MsoBodyText>solvent_sld</p>
   </td>
   <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
@@ -1323 +2555 @@
   <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
   border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
-  <p class=MsoBodyText>Background</p>
+  <p class=MsoBodyText>background</p>
   </td>
   <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
@@ -1339 +2571 @@
   <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
   border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
-  <p class=MsoBodyText>Axis_theta</p>
+  <p class=MsoBodyText>axis_theta</p>
   </td>
   <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
@@ -1355 +2587 @@
   <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
   border-top:none;padding:0in 5.4pt 0in 5.4pt;height:20.0pt'>
-  <p class=MsoBodyText>Axis_phi</p>
+  <p class=MsoBodyText>axis_phi</p>
   </td>
   <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
@@ -1385 +2617 @@
 <p class=MsoNormal>&nbsp;</p>
 
-<p class=MsoNormal style='margin-left:.85in;text-indent:-.35in'><b>2.5.2.<span
-style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b>Validation
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal style='margin-left:.85in;text-indent:-.35in'><b>2.1.<span
+style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b>Validation
 of the core-shell cylinder model</b></p>
 
@@ -1404 +2638 @@
 style='font-family:"Arial","sans-serif"'>&#966;</span>)</i> = 1.0.  Figure 9 shows the result of such a cross-check.</p>
 
-<p class=MsoNormal style='page-break-after:avoid'><img width=573 height=315
-id="Picture 22" src="../images/html/image021.jpg"
-alt="core_shell_cylinder_1D_validation"></p>
+<p class=MsoNormal align=center style='text-align:center;page-break-after:avoid'><img
+border=0 width=509 height=280 id="Picture 22"
+src="../images/html/image028.jpg" alt="core_shell_cylinder_1D_validation"></p>
+
+<p class=MsoNormal align=center style='text-align:center;page-break-after:avoid'>&nbsp;</p>
 
 <p class=MsoCaption><a name="_Ref173307149">Figure </a>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 Å,
-Thickness=10 Å, Length=400 Å, Core_sld=1e-6 Å<sup> -2</sup>, Shell_sld=4e-6 Å<sup>
+NIST SANS analysis software. The parameters were set to: Scale=1.0, Radius=20
+Å, Thickness=10 Å, Length=400 Å, Core_sld=1e-6 Å<sup> -2</sup>, Shell_sld=4e-6 Å<sup>
 -2</sup>, Solvent_sld=1e-6 Å<sup> -2</sup>, and Background=0.01 cm<sup> -1</sup>.</p>
 
@@ -1418 +2654 @@
 <p class=MsoNormal>&nbsp;</p>
 
-<p class=MsoNormal style='page-break-after:avoid'><img width=573 height=315
-id="Picture 23" src="../images/html/image022.jpg"
-alt="core_shell_cylinder_2D_average"></p>
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center;page-break-after:avoid'><img
+border=0 width=518 height=285 id="Picture 23"
+src="../images/html/image029.jpg" alt="core_shell_cylinder_2D_average"></p>
+
+<p class=MsoNormal align=center style='text-align:center;page-break-after:avoid'>&nbsp;</p>
 
 <p class=MsoCaption><a name="_Ref173307204">Figure </a>9: Comparison of the
@@ -1430 +2670 @@
 
 <p class=MsoNormal>&nbsp;</p>
-<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal><b>&nbsp;</b></p>
+
+<p class=MsoNormal><b>&nbsp;</b></p>
+
 
 <p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
-style='font-size:14.0pt'>2.6.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-</span></span></b><b><span style='font-size:14.0pt'><a name="EllipticalCylinderModel">EllipticalCylinderModel</a></span></b></p>
+style='font-size:14.0pt'>2.8.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span></b><b><span style='font-size:14.0pt'><a name="HollowCylinderModel">HollowCylinderModel</span></b></p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>This model provides the form factor, P(<i>q</i>), for a
+monodisperse hollow right angle circular cylinder (tube) where the form factor
+is normalized by the volume of the tube:</p>
+
+<p class=MsoNormal>P(q) = scale*&lt;f^2&gt;/V<sub>shell</sub>+background where
+the averaging &lt; &gt; id applied only for the 1D calculation.  The inside and
+outside of the hollow cylinder have the same SLD.</p>
+
+<p class=MsoNormal>The 1D scattering intensity is calculated in the following
+way (Guinier, 1955):</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:44.0pt'><img border=0 width=514 height=176
+src="../images/html/image030.png"></span> (11)</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=right style='text-align:right'>&nbsp;</p>
+
+<p class=MsoNormal>where <i>scale</i> is a scale factor, <i>J<sub>1</sub></i>
+is the 1<sup>st</sup> order Bessel function, <i>J<sub>1</sub></i> (x)= (sin<i>x
+</i>- <i>x</i>cos<i>x</i>)/<i>x</i><sup>2</sup>. </p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><img border=0
+width=393 height=217 id="Picture 33" src="../images/html/image031.jpg"></p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal>To provide easy access to the orientation of the core-shell
+cylinder, we define the axis of the cylinder using two angles &#952; and <span
+style='font-family:"Arial","sans-serif"'>&#966;</span>. Similarly to the case
+of the cylinder, those angles are defined on Figure 2 of CylinderModel.</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>For P*S: The 2<sup>nd</sup> 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 class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>In the parameters, the ‘contrast’ represents SLD (shell) -
+SLD (solvent) and the radius = R<sub>hell</sub> while core_radius = R<sub>core</sub>.</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal><sub>&nbsp;</sub></p>
+
+<div align=center>
+
+<table class=MsoTableGrid border=1 cellspacing=0 cellpadding=0
+ style='border-collapse:collapse;border:none'>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Parameter name</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Units</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Default value</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>scale</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>None</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>1.0</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>radius</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>30</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>length</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>400</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>core_radius</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>20</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>contrast</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å<sup> -2</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>5e-06</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>background</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>cm<sup>-1</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>0.01</p>
+  </td>
+ </tr>
+</table>
+
+</div>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><img border=0
+width=468 height=344 id="Picture 220" src="../images/html/image032.png"></p>
+
+<p class=MsoNormal align=center style='text-align:center;text-autospace:none'><b>Figure.
+1D plot using the default values (w/1000 data point).</b></p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal>Our model uses the form factor calculations implemented in a
+c-library provided by the NIST Center for Neutron Research (Kline, 2006).</p>
+
+<p class=MsoBodyText>&nbsp;</p>
+
+<p class=MsoBodyText>REFERENCE</p>
+
+<p class=MsoBodyText>Feigin, L. A, and D. I. Svergun, &quot;Structure Analysis
+by Small-Angle X-Ray and Neutron Scattering&quot;, Plenum Press, New York,
+(1987).</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal><b>&nbsp;</b></p>
+
+<p class=MsoNormal><b>&nbsp;</b></p>
+
+<p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
+style='font-size:14.0pt'>2.9.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span></b><b><span style='font-size:14.0pt'><a name="FlexibleCylinderModel">FlexibleCylinderModel</span></b></p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>This model provides the form factor, P(<i>q</i>), 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;  is applied over
+all orientation for 1D.  The 2D scattering intensity is the same as 1D,
+regardless of the orientation of the <i>q</i> vector which is defined as<span
+style='font-size:14.0pt;position:relative;top:8.0pt'><img border=0 width=103
+height=33 src="../images/html/image010.png"></span><span
+style='font-size:14.0pt;position:relative;top:6.0pt'>.</span></p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><img border=0
+width=329 height=150 id="Picture 35" src="../images/html/image033.jpg"></p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal>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 ‘contrast’ represents SLD (chain) -
+SLD (solvent).</p>
+
+<p class=MsoNormal><sub>&nbsp;</sub></p>
+
+<p class=MsoNormal><sub>&nbsp;</sub></p>
+
+<div align=center>
+
+<table class=MsoTableGrid border=1 cellspacing=0 cellpadding=0
+ style='border-collapse:collapse;border:none'>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Parameter name</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Units</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Default value</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>scale</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>None</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>1.0</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>radius</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>20</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>length</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>1000</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>contrast</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å<sup> -2</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>5e-06</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>background</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>cm<sup>-1</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>0.01</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>kuhn_length</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>100</p>
+  </td>
+ </tr>
+</table>
+
+</div>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><img border=0
+width=434 height=322 id="Picture 228" src="../images/html/image034.jpg"></p>
+
+<p class=MsoNormal align=center style='text-align:center;text-autospace:none'><b>Figure.
+1D plot using the default values (w/1000 data point).</b></p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal>Our model uses the form factor calculations implemented in a
+c-library provided by the NIST Center for Neutron Research (Kline, 2006):</p>
+
+<p class=MsoNormal>From the reference, &quot;Method 3 With Excluded
+Volume&quot; 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.  See equations (13,26-27) in the
+original reference for the details.</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoBodyText>REFERENCE</p>
+
+<p class=MsoNormal>Pedersen, J. S. and P. Schurtenberger (1996). “Scattering
+functions of semiflexible polymers with and without excluded volume effects.”
+Macromolecules 29: 7602-7612. </p>
+
+<p class=MsoNormal>Correction of the formula can be found in:</p>
+
+<p class=MsoNormal>Wei-Ren Chen, Paul D. Butler, and Linda J. Magid,
+&quot;Incorporating Intermicellar Interactions in the Fitting of SANS Data from
+Cationic Wormlike Micelles&quot; Langmuir, August 2006.</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal><b>&nbsp;</b></p>
+
+<p class=MsoNormal><b>&nbsp;</b></p>
+
+
+<p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
+style='font-size:14.0pt'>2.10.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span></b><b><span style='font-size:14.0pt'><a name="StackedDisksModel"> StackedDisksModel </a></span></b></p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>This model provides the form factor, P(<i>q</i>), for stacked
+discs (tactoids) with a core/layer structure where the form factor is
+normalized by the volume of the cylinder.  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 class=MsoNormal>The 2D scattering intensity is the same as 1D, regardless of
+the orientation of the <i>q</i> vector which is defined as<span
+style='font-size:14.0pt;position:relative;top:8.0pt'><img border=0 width=103
+height=33 src="../images/html/image010.png"></span><span
+style='font-size:14.0pt;position:relative;top:6.0pt'>.</span></p>
+
+<p class=MsoNormal><span style='font-size:14.0pt;position:relative;top:6.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>         <img
+border=0 width=214 height=93 id="Picture 36"
+src="../images/html/image035.png"></p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><img border=0
+width=173 height=136 id="Picture 37" src="../images/html/image036.png"></p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal>The returned value is in units of [cm<sup>-1</sup> sr<sup>-1</sup>],
+on absolute scale. </p>
+
+<p class=MsoNormal>The scattering intensity I(q) is:</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:9.0pt'><img border=0 width=514 height=38
+src="../images/html/image037.png"></span></p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:16.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal>where the contrast,</p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:6.0pt'><img border=0 width=115 height=24
+src="../images/html/image038.png"></span></p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:16.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal><span style='position:relative;top:16.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal><span style='position:relative;top:16.0pt'>N is the number
+of discs per unit volume, </span><span style='font-family:Symbol;position:relative;
+top:16.0pt'>a</span><span style='position:relative;top:16.0pt'> 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.</span></p>
+
+<p class=MsoNormal><span style='position:relative;top:16.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal><span style='position:relative;top:16.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:39.0pt'><img border=0 width=424 height=113
+src="../images/html/image039.png"></span></p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:16.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:16.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal>where d = thickness of the layer (layer_thick), 2h= core
+thickness (core_thick),  and R = radius of the disc (radius).</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:14.0pt'><img border=0 width=399 height=46
+src="../images/html/image040.png"></span></p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:16.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal><span style='position:relative;top:16.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal><span style='position:relative;top:16.0pt'>where n = the
+total number of the disc stacked (n_stacking), D=the next neighbor center to
+cent distance (d-spacing), and </span><span style='font-family:Symbol;
+position:relative;top:16.0pt'>s</span><sub><span style='position:relative;
+top:16.0pt'>D</span></sub><span style='position:relative;top:16.0pt'> = the
+Gaussian standard deviation of the d-spacing (sigma_d).</span></p>
+
+<p class=MsoNormal><span style='position:relative;top:16.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal>To provide easy access to the orientation of the stackeddisks,
+we define the axis of the cylinder using two angles &#952; and <span
+style='font-family:"Arial","sans-serif"'>&#966;</span>. Similarly to the case
+of the cylinder, those angles are defined on Figure 2 of CylinderModel.</p>
+
+<p class=MsoNormal><span style='position:relative;top:16.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal><span style='position:relative;top:16.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal><span style='position:relative;top:16.0pt'> </span>For P*S:
+The 2<sup>nd</sup> 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>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<div align=center>
+
+<table class=MsoTableGrid border=1 cellspacing=0 cellpadding=0
+ style='border-collapse:collapse;border:none'>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Parameter name</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Units</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Default value</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>background</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>cm<sup>-1</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>0.001</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>core_sld</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å<sup> -2</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>4e-006</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>core_thick</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>10</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>layer_sld</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å<sup> -2</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>0</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>layer_thick</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>15</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>n_stacking</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>&nbsp;</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>1</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>radius</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>3e+003</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>scale</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>&nbsp;</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>0.01</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>sigma_d</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>&nbsp;</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>0</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>solvent_sld</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å<sup> -2</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>5e-006</p>
+  </td>
+ </tr>
+</table>
+
+</div>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><img border=0
+width=451 height=334 id="Picture 233" src="../images/html/image041.png"></p>
+
+<p class=MsoNormal align=center style='text-align:center;text-autospace:none'><b>Figure.
+1D plot using the default values (w/1000 data point).</b></p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><img border=0
+width=377 height=215 id="Picture 251" src="../images/html/image042.jpg"
+alt=stackdiskangles.gif></p>
+
+<p class=MsoCaption align=center style='text-align:center'>Figure. Examples of
+the angles for oriented stackeddisks against the detector plane.</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal>Our model uses the form factor calculations implemented in a
+c-library provided by the NIST Center for Neutron Research (Kline, 2006):</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoBodyText>REFERENCE</p>
+
+<p class=MsoNormal>Guinier, A. and Fournet, G., &quot;Small-Angle Scattering of
+X-Rays&quot;, John Wiley and Sons, New York, 1955.</p>
+
+<p class=MsoNormal>Kratky, O. and Porod, G., J. Colloid Science, 4, 35, 1949. </p>
+
+<p class=MsoNormal>Higgins, J.S. and Benoit, H.C., &quot;Polymers and Neutron
+Scattering&quot;, Clarendon, Oxford, 1994.</p>
+
+<p class=MsoNormal><b>&nbsp;</b></p>
+
+<p class=MsoNormal><b>&nbsp;</b></p>
+
+<p class=MsoNormal><b>&nbsp;</b></p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal><b>&nbsp;</b></p>
+
+<p class=MsoNormal><b>&nbsp;</b></p>
+
+<p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
+style='font-size:14.0pt'>2.11.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span></b><b><span style='font-size:14.0pt'><a name="ParallelepipedModel">ParallelepipedModel</span></b></p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>This model provides the form factor, P(<i>q</i>), 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;  is applied over all orientation for 1D.  </p>
+
+<p class=MsoNormal><span style='font-size:14.0pt;position:relative;top:6.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal align=center style='text-align:center'><img border=0
+width=326 height=247 id="Picture 38" src="../images/html/image043.jpg"></p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal>The side of the solid must be satisfied the condition of
+A&lt;B&lt;C in order for the calculation to be correct: where A = short_a,
+B=short_b, and C=long_c for the fitting parameters.</p>
+
+<p class=MsoNormal>By this definition, assuming </p>
+
+<p class=MsoNormal>a = A/B&lt;1; b=B/B=1; c=C/B&gt;1, the form factor,</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:48.0pt'><img border=0 width=360 height=145
+src="../images/html/image044.png"></span></p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:16.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal>The contrast is defined as</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:6.0pt'><img border=0 width=117 height=24
+src="../images/html/image045.png"></span></p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:16.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal><span style='position:relative;top:16.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal><span style='position:relative;top:16.0pt'>The scattering
+intensity per unit volume is returned in the unit of [cm<sup>-1</sup>];  I(q) =
+</span><span style='font-family:Symbol;position:relative;top:16.0pt'>f</span><span
+style='position:relative;top:16.0pt'>P(q).</span></p>
+
+<p class=MsoNormal><span style='position:relative;top:16.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal>For P*S: The 2<sup>nd</sup> virial coefficient of the solid
+cylinder is calculate based on the averaged 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 class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>To provide easy access to the orientation of the parallelepiped,
+we define the axis of the cylinder using two angles &#952; , <span
+style='font-family:"Arial","sans-serif"'>&#966; </span>and<span
+style='font-family:"Arial","sans-serif"'> </span><span style='font-family:Symbol'>Y</span><span
+style='font-family:"Arial","sans-serif"'> </span>. Similarly to the case of the
+cylinder, those angles, &#952;  and <span style='font-family:"Arial","sans-serif"'>&#966;,</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 class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><img border=0
+width=352 height=264 id="Picture 243" src="../images/html/image046.jpg"
+alt=pprangles.gif></p>
+
+<p class=MsoNormal align=center style='text-align:center'><b>Figure. Definition
+of angels for 2D</b>.</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><img border=0
+width=379 height=256 src="../images/html/image047.jpg"
+alt=cylinderangles2.gif></p>
+
+<p class=MsoCaption align=center style='text-align:center'>Figure. Examples of
+the angles for oriented elliptical cylinders against the detector plane.</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<div align=center>
+
+<table class=MsoTableGrid border=1 cellspacing=0 cellpadding=0
+ style='border-collapse:collapse;border:none'>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Parameter name</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Units</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Default value</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>background</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>cm<sup>-1</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>0.0</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>contrast</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å<sup> -2</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>5e-006</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>long_c</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>400</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>short_a</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å<sup> -2</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>35</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>short_b</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>75</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>scale</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>&nbsp;</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>1</p>
+  </td>
+ </tr>
+</table>
+
+</div>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><img border=0
+width=431 height=332 id="Picture 492" src="../images/html/image048.jpg"></p>
+
+<p class=MsoNormal align=center style='text-align:center;text-autospace:none'><b>Figure.
+1D plot using the default values (w/1000 data point).</b></p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoListParagraph style='margin-left:1.35in;text-indent:-.25in'><span
+style='font-family:Symbol'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span><b>Validation of the parallelepiped 2D model</b></p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>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 class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><img border=0
+width=481 height=299 id="Picture 693" src="../images/html/image049.png"></p>
+
+<p class=MsoNormal align=center style='text-align:center;text-autospace:none'><b>Figure.
+Comparison between 1D and averaged 2D.</b></p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal>Our model uses the form factor calculations implemented in a
+c-library provided by the NIST Center for Neutron Research (Kline, 2006):</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoBodyText>REFERENCE</p>
+
+<p class=MsoNormal>Mittelbach and Porod, Acta Physica Austriaca 14 (1961)
+185-211.</p>
+
+<p class=MsoNormal>Equations (1), (13-14). (in German)</p>
+
+<p class=MsoNormal><b>&nbsp;</b></p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
+style='font-size:14.0pt'>2.12.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span></b><b><span style='font-size:14.0pt'><a name="EllipticalCylinderModel">Elliptical Cylinder Model</span></b></p>
 
 <p class=MsoNormal>&nbsp;</p>
 
 <p class=MsoNormal>This function calculates the scattering from an oriented
-elliptical cylinder. 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 (or all) of the orientation angles, and also for the minor
-radius and the ratio of the ellipse radii.</p>
+elliptical cylinder. </p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal><b>For 2D (orientated system):</b></p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>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 class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><img border=0
+width=352 height=172 id="Picture 40" src="../images/html/image050.png"></p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-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 class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
 
 <p class=MsoNormal>The function calculated is:</p>
 
-<p class=MsoNormal align=center style='text-align:center'><span
-style='position:relative;top:16.0pt'><img width=377 height=46
-src="../images/html/image023.gif"></span> </p>
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:16.0pt'><img border=0 width=377 height=46
+src="../images/html/image051.png"></span> </p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
 
 <p class=MsoNormal>with the functions:</p>
 
-<p class=MsoNormal align=center style='text-align:center'><span
-style='position:relative;top:39.0pt'><img width=297 height=114
-src="../images/html/image024.gif"></span>          (13)</p>
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:39.0pt'><img border=0 width=297 height=114
+src="../images/html/image052.png"></span>          (13)</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
 
 <p class=MsoNormal>and the angle psi is defined as the orientation of the major
@@ -1462 +3821 @@
 <p class=MsoNormal>&nbsp;</p>
 
-<p class=MsoNormal>The returned value is scaled to units of [cm<sup>-1</sup>]
-and the parameters are the following:</p>
+<p class=MsoNormal><b>For 1D (no preferred orientation):</b></p>
+
+<p class=MsoNormal>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 class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>The returned value is scaled to units of [cm<sup>-1</sup>]. </p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>To provide easy access to the orientation of the elliptical,
+we define the axis of the cylinder using two angles &#952; , <span
+style='font-family:"Arial","sans-serif"'>&#966; </span>and<span
+style='font-family:"Arial","sans-serif"'> </span><span style='font-family:Symbol'>Y</span><span
+style='font-family:"Arial","sans-serif"'> </span>. Similarly to the case of the
+cylinder, those angles, &#952;  and <span style='font-family:"Arial","sans-serif"'>&#966;,</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 class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>All angle parameters are valid and given only for 2D calculation
+(Oriented system).</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><img border=0
+width=370 height=277 id="Picture 239" src="../images/html/image053.jpg"
+alt=ellcylinderangles.gif></p>
+
+<p class=MsoNormal align=center style='text-align:center'><b>Figure. Definition
+of angels for 2D</b>.</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><img border=0
+width=379 height=256 src="../images/html/image047.jpg"
+alt=cylinderangles2.gif></p>
+
+<p class=MsoCaption align=center style='text-align:center'>Figure. Examples of
+the angles for oriented elliptical cylinders against the detector plane.</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal><b>&nbsp;</b></p>
+
+<p class=MsoNormal><b>For P*S</b>: The 2<sup>nd</sup> virial coefficient of the
+solid cylinder is calculate based on the averaged radius
+(=sqrt(r_minor^2*r_ratio))  and length values, and used as the effective radius
+toward S(Q) when P(Q)*S(Q) is applied. </p>
+
+<p class=MsoNormal>&nbsp;</p>
 
 <p class=MsoNormal>&nbsp;</p>
@@ -1634 +4050 @@
 
 <p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><img border=0
+width=443 height=328 id="Picture 503" src="../images/html/image054.jpg"></p>
+
+<p class=MsoNormal align=center style='text-align:center;text-autospace:none'><b>Figure.
+1D plot using the default values (w/1000 data point).</b></p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoListParagraph style='margin-left:1.35in;text-indent:-.25in'><span
+style='font-family:Symbol'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span><b>Validation of the elliptical cylinder 2D model</b></p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>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 class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><img border=0
+width=448 height=278 id="Picture 692" src="../images/html/image055.png"></p>
+
+<p class=MsoNormal align=center style='text-align:center;text-autospace:none'><b>Figure.
+Comparison between 1D and averaged 2D.</b></p>
+
+<p class=MsoNormal style='text-autospace:none'><b>&nbsp;</b></p>
+
+<p class=MsoNormal style='text-autospace:none'>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 class=MsoNormal style='text-autospace:none'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center;text-autospace:none'><img
+border=0 width=409 height=303 id="Picture 690"
+src="../images/html/image056.png"></p>
+
+<p class=MsoNormal align=center style='text-align:center;text-autospace:none'><b>Figure.
+The intensities averaged from 2D over different number of points of binning of
+angles.</b></p>
+
+<p class=MsoNormal align=center style='text-align:center;text-autospace:none'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
 
 <p class=MsoNormal>REFERENCE</p>
@@ -1645 +4116 @@
 <p class=MsoNormal>&nbsp;</p>
 
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
+style='font-size:14.0pt'>2.13.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span></b><b><span style='font-size:14.0pt'><a name="EllipsoidModel">Ellipsoid Model</span></b></p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>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 class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal style='margin-left:.85in;text-indent:-.35in'><b>1.1.<span
+style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b>Definition</b></p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>The output of the 2D scattering intensity function for
+oriented ellipsoids is given by (Feigin, 1987):</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoCaption align=center style='text-align:center'><span
+style='position:relative;top:12.0pt'><img border=0 width=184 height=41
+src="../images/html/image017.png"></span>   <span style='font-size:12.0pt;
+font-weight:normal'>(8)</span></p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoCaption align=center style='text-align:center'><span
+style='position:relative;top:15.0pt'><img border=0 width=371 height=47
+src="../images/html/image057.png"></span>    <span style='font-size:
+12.0pt;font-weight:normal'>(9)</span></p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoCaption align=center style='text-align:center'><span
+style='position:relative;top:6.0pt'><img border=0 width=272 height=29
+src="../images/html/image058.png"></span>     <span style='font-size:
+12.0pt;font-weight:normal'>(10)</span></p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>where <span style='font-family:"Arial","sans-serif"'>&#945;</span>
+is the angle between the axis of the ellipsoid and the q-vector, V is the
+volume of the ellipsoid, R<sub>a</sub> is the radius along the rotation axis of
+the ellipsoid, R<sub>b</sub> is the radius perpendicular to the rotation axis
+of the ellipsoid and <i><span style='font-family:"Arial","sans-serif"'>&#916;</span>&#961;</i>
+(contrast) is the scattering length density difference between the scatterer
+and the solvent. </p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>To provide easy access to the orientation of the ellipsoid,
+we define the rotation axis of the ellipsoid using two angles &#952; and <span
+style='font-family:"Arial","sans-serif"'>&#966;</span>. Similarly to the case
+of the cylinder, those angles are defined on Figure 2. For the ellipsoid,
+&#952; is the angle between the rotation axis and the z-axis. </p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>For P*S: The 2<sup>nd</sup> 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 class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>The returned value is scaled to units of [cm<sup>-1</sup>]
+and the parameters of the ellipsoid model are the following:</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<div align=center>
+
+<table class=MsoTableGrid border=1 cellspacing=0 cellpadding=0
+ style='border-collapse:collapse;border:none'>
+ <tr style='height:19.85pt'>
+  <td width=180 valign=top style='width:135.1pt;border:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:19.85pt'>
+  <p class=MsoBodyText>Parameter name</p>
+  </td>
+  <td width=105 valign=top style='width:78.9pt;border:solid windowtext 1.0pt;
+  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:19.85pt'>
+  <p class=MsoBodyText>Units</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:19.85pt'>
+  <p class=MsoBodyText>Default value</p>
+  </td>
+ </tr>
+ <tr style='height:19.85pt'>
+  <td width=180 valign=top style='width:135.1pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.85pt'>
+  <p class=MsoBodyText>scale</p>
+  </td>
+  <td width=105 valign=top style='width:78.9pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:19.85pt'>
+  <p class=MsoBodyText>None</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:19.85pt'>
+  <p class=MsoBodyText>1.0</p>
+  </td>
+ </tr>
+ <tr style='height:19.85pt'>
+  <td width=180 valign=top style='width:135.1pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.85pt'>
+  <p class=MsoBodyText>radius_a (polar)</p>
+  </td>
+  <td width=105 valign=top style='width:78.9pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:19.85pt'>
+  <p class=MsoBodyText>Å</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:19.85pt'>
+  <p class=MsoBodyText>20.0</p>
+  </td>
+ </tr>
+ <tr style='height:19.85pt'>
+  <td width=180 valign=top style='width:135.1pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.85pt'>
+  <p class=MsoBodyText>radius_b (equatorial)</p>
+  </td>
+  <td width=105 valign=top style='width:78.9pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:19.85pt'>
+  <p class=MsoBodyText>Å</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:19.85pt'>
+  <p class=MsoBodyText>400.0</p>
+  </td>
+ </tr>
+ <tr style='height:19.85pt'>
+  <td width=180 valign=top style='width:135.1pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.85pt'>
+  <p class=MsoBodyText>contrast</p>
+  </td>
+  <td width=105 valign=top style='width:78.9pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:19.85pt'>
+  <p class=MsoBodyText>Å<sup> -2</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:19.85pt'>
+  <p class=MsoBodyText>3.0e-6</p>
+  </td>
+ </tr>
+ <tr style='height:19.85pt'>
+  <td width=180 valign=top style='width:135.1pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.85pt'>
+  <p class=MsoBodyText>background</p>
+  </td>
+  <td width=105 valign=top style='width:78.9pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:19.85pt'>
+  <p class=MsoBodyText>cm<sup>-1</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:19.85pt'>
+  <p class=MsoBodyText>0.0</p>
+  </td>
+ </tr>
+ <tr style='height:19.85pt'>
+  <td width=180 valign=top style='width:135.1pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.85pt'>
+  <p class=MsoBodyText>axis_theta</p>
+  </td>
+  <td width=105 valign=top style='width:78.9pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:19.85pt'>
+  <p class=MsoBodyText>Radian</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:19.85pt'>
+  <p class=MsoBodyText>1.57</p>
+  </td>
+ </tr>
+ <tr style='height:20.6pt'>
+  <td width=180 valign=top style='width:135.1pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:20.6pt'>
+  <p class=MsoBodyText>axis_phi</p>
+  </td>
+  <td width=105 valign=top style='width:78.9pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:20.6pt'>
+  <p class=MsoBodyText>Radian</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:20.6pt'>
+  <p class=MsoBodyText>0.0</p>
+  </td>
+ </tr>
+</table>
+
+</div>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>The output of the 1D scattering intensity function for
+randomly oriented ellipsoids is then given by equation 6.</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>The <i>axis_theta</i> and axis<i>_phi</i> 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 class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><img border=0
+width=396 height=297 src="../images/html/image059.jpg"
+alt=ellipsoangles.gif></p>
+
+<p class=MsoCaption align=center style='text-align:center'>Figure. Examples of
+the angles for oriented ellipsoid against the detector plane.</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal style='margin-left:.85in;text-indent:-.35in'><b>2.1.<span
+style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b>Validation
+of the ellipsoid model</b></p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>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 class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>Averaging over a distribution of orientation is done by
+evaluating equation 7. 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 <i>p(&#952;,</i><i><span
+style='font-family:"Arial","sans-serif"'>&#966;</span>)</i> = 1.0.  Figure 6 shows the result of such a cross-check.</p>
+
+<p class=MsoNormal align=center style='text-align:center'><b><i><span
+style='color:#3366FF'>&nbsp;</span></i></b></p>
+
+<p class=MsoNormal>The discrepancy above q=0.3 Å<sup> -1</sup> 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 (equation 6). 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"'>&#945;</span>. Our result was found to be stable over the
+range of q shown for a number of points higher than 500.</p>
+
+<p class=MsoNormal align=center style='text-align:center;page-break-after:avoid'><b><img
+border=0 width=469 height=258 id="Picture 16"
+src="../images/html/image060.jpg" alt="ellipsoid_1D_validation"></b></p>
+
+<p class=MsoCaption><a name="_Ref173222904">Figure </a>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 Å,
+Radius_b=400 Å, </p>
+
+<p class=MsoCaption>Contrast=3e-6 Å<sup> -2</sup>, and Background=0.01 cm<sup>
+-1</sup>.</p>
+
+<p class=MsoNormal><b>&nbsp;</b></p>
+
+<p class=MsoNormal><b>&nbsp;</b></p>
+
+<p class=MsoNormal align=center style='text-align:center;page-break-after:avoid'><img
+border=0 width=450 height=247 id="Picture 17"
+src="../images/html/image061.jpg" alt="ellipsoid_2D_average"></p>
+
+<p class=MsoCaption><a name="_Ref173223004">Figure </a>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 Å, Radius_b=400 Å, Contrast=3e-6 Å<sup> -2</sup>, and
+Background=0.0 cm<sup> -1</sup>.</p>
+
+<p class=MsoCaption>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal><b>&nbsp;</b></p>
+
+<p class=MsoNormal><b>&nbsp;</b></p>
+
+<p class=MsoNormal><b>&nbsp;</b></p>
+
+
+
+<p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
+style='font-size:14.0pt'>2.14.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span></b><b><span style='font-size:14.0pt'><a name="CoreShellEllipsoidModel"> CoreShellEllipsoidModel </a></span></b></p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>This model provides the form factor, P(<i>q</i>), 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*r<sub>maj</sub>*r<sub>min</sub><sup>2</sup>
+and the averaging &lt; &gt;  is applied over all orientation for 1D.  </p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>   <img border=0
+width=246 height=131 id="Picture 41" src="../images/html/image062.png"></p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal>The returned value is in units of [cm<sup>-1</sup>], on
+absolute scale. </p>
+
+<p class=MsoNormal>The form factor calculated is:</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:48.0pt'><img border=0 width=334 height=137
+src="../images/html/image063.png"></span></p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:16.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>To provide easy access to the orientation of the coreshell
+ellipsoid, we define the axis of the solid ellipsoid using two angles &#952; , <span
+style='font-family:"Arial","sans-serif"'>&#966;</span>. Similarly to the case
+of the cylinder, those angles, &#952;  and <span style='font-family:"Arial","sans-serif"'>&#966;,</span>
+are defined on Figure 2 of CylinderModel. </p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>The contrast is defined as SLD(core) – SLD(shell) or
+SLD(shell – solvent). In the parameters, equat_core = equatorial radius of the
+core, polar_core = polar radius of the core, equat_shell = r<sub>min</sub> (or
+equatorial radius of the shell), and polar_shell = = r<sub>maj</sub> (or polar
+radius of the shell).</p>
+
+<p class=MsoNormal><span style='position:relative;top:16.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal>For P*S: The 2<sup>nd</sup> 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 class=MsoNormal><sub>&nbsp;</sub></p>
+
+<div align=center>
+
+<table class=MsoTableGrid border=1 cellspacing=0 cellpadding=0
+ style='border-collapse:collapse;border:none'>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Parameter name</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Units</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Default value</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>background</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>cm<sup>-1</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>0.001</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>equat_core</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>200</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>equat_shell</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>250</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>sld_solvent</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å<sup> -2</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>6e-006</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>ploar_shell</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>30</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>ploar_core</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>20</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>scale</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>&nbsp;</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>1</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>contrast</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å<sup> -2</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>1e-006</p>
+  </td>
+ </tr>
+</table>
+
+</div>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><img border=0
+width=426 height=333 id="Picture 526" src="../images/html/image064.jpg"></p>
+
+<p class=MsoNormal align=center style='text-align:center;text-autospace:none'><b>Figure.
+1D plot using the default values (w/1000 data point).</b></p>
+
+<p class=MsoNormal align=center style='text-align:center;text-autospace:none'><b>&nbsp;</b></p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><img border=0
+width=396 height=297 id="Picture 245" src="../images/html/image059.jpg"
+alt=ellipsoangles.gif></p>
+
+<p class=MsoNormal align=center style='text-align:center'>Figure. Examples of
+the angles for oriented coreshellellipsoid against the detector plane where a
+=polar axis.</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal>Our model uses the form factor calculations implemented in a
+c-library provided by the NIST Center for Neutron Research (Kline, 2006):</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoBodyText>REFERENCE</p>
+
+<p class=MsoNormal>Kotlarchyk, M.; Chen, S.-H. J. Chem. Phys., 1983, 79, 2461.</p>
+
+<p class=MsoNormal>Berr, S.  J. Phys. Chem., 1987, 91, 4760.</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal><b>&nbsp;</b></p>
+
+<p class=MsoNormal><b>&nbsp;</b></p>
+
+<p class=MsoNormal><b>&nbsp;</b></p>
+
+<p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
+style='font-size:14.0pt'>2.15.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span></b><b><span style='font-size:14.0pt'><a name="TriaxialEllipsoidModel">TriaxialEllipsoidModel</span></b></p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>This model provides the form factor, P(<i>q</i>), for an
+ellipsoid (below) where all three axes are of different lengths, i.e.,  R<sub>a</sub>
+=&lt; R<sub>b</sub> =&lt; R<sub>c</sub> (Note that users should maintains this
+inequality for the all calculations).  P(q) = scale*&lt;f^2&gt;/V+background
+where the volume V= 4pi/3*R<sub>a</sub>*R<sub>b</sub>*R<sub>c</sub>, and the
+averaging &lt; &gt;  is applied over all orientation for 1D.  </p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>   <img border=0
+width=261 height=157 id="Picture 42" src="../images/html/image065.jpg"></p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal>The returned value is in units of [cm<sup>-1</sup>], on
+absolute scale. </p>
+
+<p class=MsoNormal>The form factor calculated is:</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:33.0pt'><img border=0 width=472 height=97
+src="../images/html/image066.png"></span></p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:16.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal><span style='position:relative;top:16.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>To provide easy access to the orientation of the triaxial
+ellipsoid, we define the axis of the cylinder using the angles &#952; , <span
+style='font-family:"Arial","sans-serif"'>&#966; </span>and<span
+style='font-family:"Arial","sans-serif"'> </span><span style='font-family:Symbol'>Y</span><span
+style='font-family:"Arial","sans-serif"'> </span>. Similarly to the case of the
+cylinder, those angles, &#952;  and <span style='font-family:"Arial","sans-serif"'>&#966;,</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 class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>The radius of gyration for this system is R<sub>g</sub><sup>2</sup>
+= (R<sub>a</sub><sup>2</sup>*R<sub>b</sub><sup>2</sup>*R<sub>c</sub><sup>2</sup>)/5. 
+The contrast is defined as SLD(ellipsoid) – SLD(solvent). In the parameters, semi_axisA
+= R<sub>a</sub> (or minor equatorial radius), semi_axisB = R<sub>b</sub> (or
+major equatorial radius), and semi_axisC = R<sub>c</sub> (or polar radius of
+the ellipsoid).</p>
+
+<p class=MsoNormal><span style='position:relative;top:16.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal>For P*S: The 2<sup>nd</sup> virial coefficient of the solid
+ellipsoid is calculate based on the radius_a (=semi_axisC) and radius_b (=sqrt(semi_axisA*
+semi_axisB))  values, and used as the effective radius toward S(Q) when
+P(Q)*S(Q) is applied. </p>
+
+<p class=MsoNormal><sub>&nbsp;</sub></p>
+
+<p class=MsoNormal><sub>&nbsp;</sub></p>
+
+<div align=center>
+
+<table class=MsoTableGrid border=1 cellspacing=0 cellpadding=0
+ style='border-collapse:collapse;border:none'>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Parameter name</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Units</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Default value</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>background</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>cm<sup>-1</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>0.0</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>semi_axisA</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>35</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>semi_axisB</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>100</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>semi_axisC</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å<sup> </sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>400</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>scale</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>&nbsp;</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>1</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>contrast</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å<sup> -2</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>5e-006</p>
+  </td>
+ </tr>
+</table>
+
+</div>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><img border=0
+width=439 height=341 id="Picture 545" src="../images/html/image067.png"></p>
+
+<p class=MsoNormal align=center style='text-align:center;text-autospace:none'><b>Figure.
+1D plot using the default values (w/1000 data point).</b></p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoListParagraph style='margin-left:1.35in;text-indent:-.25in'><span
+style='font-family:Symbol'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span><b>Validation of the triaxialellipsoid 2D model</b></p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>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 class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><img border=0
+width=438 height=272 id="Picture 691" src="../images/html/image068.png"></p>
+
+<p class=MsoNormal align=center style='text-align:center;text-autospace:none'><b>Figure.
+Comparison between 1D and averaged 2D.</b></p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><img border=0
+width=396 height=297 id="Picture 248" src="../images/html/image069.jpg"
+alt=triellrangles.gif></p>
+
+<p class=MsoCaption align=center style='text-align:center'>Figure. Examples of
+the angles for oriented ellipsoid against the detector plane.</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>Our model uses the form factor calculations implemented in a
+c-library provided by the NIST Center for Neutron Research (Kline, 2006):</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoBodyText>REFERENCE</p>
+
+<p class=MsoNormal>L. A. Feigin and D. I. Svergun “Structure Analysis by
+Small-Angle X-Ray and Neutron Scattering”, Plenum, New York, 1987.</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal><b>&nbsp;</b></p>
+
+<p class=MsoNormal><b>&nbsp;</b></p>
+
+<p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
+style='font-size:14.0pt'>2.16.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span></b><b><span style='font-size:14.0pt'><a name="LamellarModel">LamellarModel</span></b></p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>This model provides the scattering intensity, I(<i>q</i>),
+for a lyotropic lamellar phase where a uniform SLD and random distribution in
+solution are assumed.  The ploydispersion in the bilayer thickness can be
+applied from the GUI.</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>The scattering intensity I(q) is:</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:15.0pt'><img border=0 width=103 height=46
+src="../images/html/image070.png"></span></p>
+
+<p class=MsoNormal>The form factor is,</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:15.0pt'><img border=0 width=174 height=48
+src="../images/html/image071.png"></span></p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:16.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal>where <span style='font-family:Symbol'>d</span> = bilayer
+thickness.</p>
+
+<p class=MsoNormal>The 2D scattering intensity is calculated in the same way as
+1D, where the <i>q</i> vector is defined as<span style='font-size:14.0pt;
+position:relative;top:8.0pt'><img border=0 width=103 height=33
+src="../images/html/image010.png"></span><span style='font-size:14.0pt;
+position:relative;top:6.0pt'>.</span></p>
+
+<p class=MsoNormal><span style='font-size:14.0pt;position:relative;top:6.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal>The returned value is in units of [cm<sup>-1</sup>], 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 class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal><sub>&nbsp;</sub></p>
+
+<div align=center>
+
+<table class=MsoTableGrid border=1 cellspacing=0 cellpadding=0
+ style='border-collapse:collapse;border:none'>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Parameter name</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Units</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Default value</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>background</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>cm<sup>-1</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>0.0</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>sld_bi</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å<sup> -2</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>1e-006</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>bi_thick</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>50</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>sld_sol</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å<sup> -2</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>6e-006</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>scale</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>&nbsp;</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>1</p>
+  </td>
+ </tr>
+</table>
+
+</div>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><img border=0
+width=476 height=351 id="Picture 571" src="../images/html/image072.png"></p>
+
+<p class=MsoNormal align=center style='text-align:center;text-autospace:none'><b>Figure.
+1D plot using the default values (w/1000 data point).</b></p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal>Our model uses the form factor calculations implemented in a
+c-library provided by the NIST Center for Neutron Research (Kline, 2006):</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoBodyText>REFERENCE</p>
+
+<p class=MsoNormal>Nallet, Laversanne, and Roux, J. Phys. II France, 3, (1993)
+487-502.</p>
+
+<p class=MsoNormal>            also in J. Phys. Chem. B, 105, (2001)
+11081-11088.</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal><b>&nbsp;</b></p>
+
+<p class=MsoNormal><b>&nbsp;</b></p>
+
+
+
+<p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
+style='font-size:14.0pt'>2.17.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span></b><b><span style='font-size:14.0pt'><a name="LamellarFFHGModel">LamellarFFHGModel</span></b></p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>This model provides the scattering intensity, I(<i>q</i>),
+for a lyotropic lamellar phase where a random distribution in solution are
+assumed.  The SLD of the head region is taken to be different from the SLD of
+the tail region.</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>The scattering intensity I(q) is:</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:15.0pt'><img border=0 width=151 height=46
+src="../images/html/image073.png"></span></p>
+
+<p class=MsoNormal>The form factor is</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:15.0pt'><img border=0 width=174 height=48
+src="../images/html/image071.png"></span></p>
+
+<p class=MsoNormal><span style='position:relative;top:16.0pt'>And the structure
+is </span></p>
+
+<p class=MsoNormal><span style='position:relative;top:16.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal><span style='position:relative;top:16.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:16.0pt'><img border=0 width=334 height=51
+src="../images/html/image074.png"></span></p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:16.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal><span style='position:relative;top:16.0pt'>where </span></p>
+
+<p class=MsoNormal><span style='position:relative;top:16.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal><span style='position:relative;top:16.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:50.0pt'><img border=0 width=252 height=133
+src="../images/html/image075.png"></span></p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:16.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:16.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal>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 class=MsoNormal>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 class=MsoNormal>The 2D scattering intensity is calculated in the same way as
+1D, where the <i>q</i> vector is defined as<span style='font-size:14.0pt;
+position:relative;top:8.0pt'><img border=0 width=103 height=33
+src="../images/html/image010.png"></span><span style='font-size:14.0pt;
+position:relative;top:6.0pt'>.</span></p>
+
+<p class=MsoNormal>The returned value is in units of [cm<sup>-1</sup>], on
+absolute scale. </p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal><sub>&nbsp;</sub></p>
+
+<div align=center>
+
+<table class=MsoTableGrid border=1 cellspacing=0 cellpadding=0
+ style='border-collapse:collapse;border:none'>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Parameter name</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Units</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Default value</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>background</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>cm<sup>-1</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>0.0</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>contrast</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å<sup> -2</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>5e-006</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>scale</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>&nbsp;</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>1</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>delta</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>30</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>n_plates</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>&nbsp;</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>20</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>spacing</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>400</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>caille</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å<sup> -2</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>0.1</p>
+  </td>
+ </tr>
+</table>
+
+</div>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><img border=0
+width=439 height=348 id="Picture 659" src="../images/html/image076.jpg"></p>
+
+<p class=MsoNormal align=center style='text-align:center;text-autospace:none'><b>Figure.
+1D plot using the default values (w/6000 data point).</b></p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal>Our model uses the form factor calculations implemented in a
+c-library provided by the NIST Center for Neutron Research (Kline, 2006):</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoBodyText>REFERENCE</p>
+
+<p class=MsoNormal>Nallet, Laversanne, and Roux, J. Phys. II France, 3, (1993)
+487-502.</p>
+
+<p class=MsoNormal>            also in J. Phys. Chem. B, 105, (2001)
+11081-11088.</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal><b>&nbsp;</b></p>
+
+<p class=MsoNormal><b>&nbsp;</b></p>
+
+
+<p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
+style='font-size:14.0pt'>2.18.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span></b><b><span style='font-size:14.0pt'><a name="LamellarPSModel">LamellarPSModel</span></b></p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>This model provides the scattering intensity (<b>form factor</b>
+<b>*</b> <b>structure factor</b>), I(<i>q</i>), for a lyotropic lamellar phase where
+a random distribution in solution are assumed.  The SLD of the head region is
+taken to be different from the SLD of the tail region.</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>The scattering intensity I(q) is:</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:15.0pt'><img border=0 width=133 height=46
+src="../images/html/image077.png"></span></p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:16.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal>The form factor is,</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:15.0pt'><img border=0 width=398 height=46
+src="../images/html/image078.png"></span></p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:16.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal>where <span style='font-family:Symbol'>d<sub>T</sub></span>
+= tail length (or t_length), <span style='font-family:Symbol'>d<sub>H</sub></span>
+= heasd thickness (or h_thickness) , <span style='font-family:Symbol'>Dr</span><sub>H</sub>
+= SLD (headgroup) - SLD(solvent), and <span style='font-family:Symbol'>Dr</span><sub>T</sub>
+= SLD (tail) - SLD(headgroup).</p>
+
+<p class=MsoNormal>The 2D scattering intensity is calculated in the same way as
+1D, where the <i>q</i> vector is defined as<span style='font-size:14.0pt;
+position:relative;top:8.0pt'><img border=0 width=103 height=33
+src="../images/html/image010.png"></span><span style='font-size:14.0pt;
+position:relative;top:6.0pt'>.</span></p>
+
+<p class=MsoNormal><span style='font-size:14.0pt;position:relative;top:6.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal>The returned value is in units of [cm<sup>-1</sup>], on
+absolute scale. In the parameters, sld_tail = SLD of the tail group, and
+sld_head = SLD of the head group.</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal><sub>&nbsp;</sub></p>
+
+<div align=center>
+
+<table class=MsoTableGrid border=1 cellspacing=0 cellpadding=0
+ style='border-collapse:collapse;border:none'>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Parameter name</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Units</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Default value</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>background</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>cm<sup>-1</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>0.0</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>sld_head</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å<sup> -2</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>3e-006</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>scale</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>&nbsp;</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>1</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>sld_solvent</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å<sup> -2</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>6e-006</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>h_thickness</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>10</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>t_length</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>15</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>sld_tail</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å<sup> -2</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>0</p>
+  </td>
+ </tr>
+</table>
+
+</div>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><img border=0
+width=444 height=343 src="../images/html/image079.png"></p>
+
+<p class=MsoNormal align=center style='text-align:center;text-autospace:none'><b>Figure.
+1D plot using the default values (w/1000 data point).</b></p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal>Our model uses the form factor calculations implemented in a
+c-library provided by the NIST Center for Neutron Research (Kline, 2006):</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoBodyText>REFERENCE</p>
+
+<p class=MsoNormal>Nallet, Laversanne, and Roux, J. Phys. II France, 3, (1993)
+487-502.</p>
+
+<p class=MsoNormal>            also in J. Phys. Chem. B, 105, (2001)
+11081-11088.</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal><b>&nbsp;</b></p>
+
+<p class=MsoNormal><b>&nbsp;</b></p>
+
+
+<p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
+style='font-size:14.0pt'>2.19.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span></b><b><span style='font-size:14.0pt'><a name="LamellarPSHGModel">LamellarPSHGModel</span></b></p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>This model provides the scattering intensity (<b>form factor</b>
+<b>*</b> <b>structure factor</b>), I(<i>q</i>), for a lyotropic lamellar phase where
+a random distribution in solution are assumed.  The SLD of the head region is
+taken to be different from the SLD of the tail region.</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>The scattering intensity I(q) is:</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:15.0pt'><img border=0 width=133 height=46
+src="../images/html/image077.png"></span></p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:16.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal>The form factor is,</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:15.0pt'><img border=0 width=398 height=46
+src="../images/html/image078.png"></span></p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:16.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal>The structure factor is</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:16.0pt'><img border=0 width=334 height=51
+src="../images/html/image074.png"></span></p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:16.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal><span style='position:relative;top:16.0pt'>where </span></p>
+
+<p class=MsoNormal><span style='position:relative;top:16.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:50.0pt'><img border=0 width=252 height=133
+src="../images/html/image075.png"></span></p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:16.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:16.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>where <span style='font-family:Symbol'>d<sub>T</sub></span>
+= tail length (or t_length), <span style='font-family:Symbol'>d<sub>H</sub></span>
+= heasd thickness (or h_thickness) , <span style='font-family:Symbol'>Dr</span><sub>H</sub>
+= SLD (headgroup) - SLD(solvent), and <span style='font-family:Symbol'>Dr</span><sub>T</sub>
+= 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 class=MsoNormal>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 class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>The 2D scattering intensity is calculated in the same way as
+1D, where the <i>q</i> vector is defined as<span style='font-size:14.0pt;
+position:relative;top:8.0pt'><img border=0 width=103 height=33
+src="../images/html/image010.png"></span><span style='font-size:14.0pt;
+position:relative;top:6.0pt'>.</span></p>
+
+<p class=MsoNormal><span style='font-size:14.0pt;position:relative;top:6.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal>The returned value is in units of [cm<sup>-1</sup>], 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 class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal><sub>&nbsp;</sub></p>
+
+<div align=center>
+
+<table class=MsoTableGrid border=1 cellspacing=0 cellpadding=0
+ style='border-collapse:collapse;border:none'>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Parameter name</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Units</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Default value</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>background</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>cm<sup>-1</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>0.001</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>sld_head</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å<sup> -2</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>2e-006</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>scale</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>&nbsp;</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>1</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>sld_solvent</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å<sup> -2</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>6e-006</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>deltaH</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>2</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>deltaT</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>10</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>sld_tail</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å<sup> -2</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>0</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>n_plates</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>&nbsp;</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>30</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>spacing</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>40</p>
+  </td>
+ </tr>
+ <tr style='height:18.8pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>caille</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>Å<sup> -2</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'>
+  <p class=MsoBodyText>0.001</p>
+  </td>
+ </tr>
+</table>
+
+</div>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><img border=0
+width=463 height=360 id="Picture 687" src="../images/html/image080.png"></p>
+
+<p class=MsoNormal align=center style='text-align:center;text-autospace:none'><b>Figure.
+1D plot using the default values (w/6000 data point).</b></p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal>Our model uses the form factor calculations implemented in a
+c-library provided by the NIST Center for Neutron Research (Kline, 2006):</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoBodyText>REFERENCE</p>
+
+<p class=MsoNormal>Nallet, Laversanne, and Roux, J. Phys. II France, 3, (1993)
+487-502.</p>
+
+<p class=MsoNormal>            also in J. Phys. Chem. B, 105, (2001)
+11081-11088.</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
 <p class=MsoNormal style='margin-left:.25in;text-indent:-.25in'><b><span
-style='font-size:14.0pt'>3.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;
-</span></span></b><b><span style='font-size:14.0pt'><a name="Shape-Independent">Shape-Independent</a></span></b></p>
+style='font-size:16.0pt'>3.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;
+</span></span></b><b><span style='font-size:16.0pt'><a name="Shape-Independent">Shape-Independent Models </a></span></b></p>
 
 <p class=MsoBodyText>&nbsp;</p>
@@ -1658 +5959 @@
 <p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
 style='font-size:14.0pt'>3.1.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-</span></span></b><b><span style='font-size:14.0pt'> <a name="Debye">Debye (Model)</a></span></b></p>
+</span></span></b><b><span style='font-size:14.0pt'> <a name="Debye">Debye (Model)</span></b></p>
 
 <p class=MsoNormal style='text-autospace:none'>&nbsp;</p>
@@ -1667 +5968 @@
 are included in the calculation. </p>
 
+<p class=MsoNormal style='margin-left:.25in;text-autospace:none'>&nbsp;</p>
+
 <p class=MsoNormal><span style='font-size:14.0pt'>&nbsp;</span></p>
 
 <p class=MsoNormal align=center style='text-align:center'><span
-style='font-size:14.0pt'><sub><img width=188 height=76
-src="../images/html/image025.gif"></sub></span></p>
+style='font-size:14.0pt;position:relative;top:27.0pt'><img border=0 width=188
+height=76 src="../images/html/image081.png"></span></p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='font-size:14.0pt;position:relative;top:27.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='font-size:14.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal style='margin-left:.25in'>For 2D plot, the wave transfer is
+defined as <span style='font-size:14.0pt;position:relative;top:8.0pt'><img
+border=0 width=103 height=33 src="../images/html/image010.png"></span><span
+style='font-size:14.0pt;position:relative;top:6.0pt'>.</span></p>
 
 <p class=MsoNormal><span style='font-size:14.0pt'>&nbsp;</span></p>
@@ -1741 +6055 @@
   </td>
  </tr>
+ <tr style='height:19.25pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
+  <p class=MsoBodyText>&nbsp;</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
+  <p class=MsoBodyText>&nbsp;</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
+  <p class=MsoBodyText>&nbsp;</p>
+  </td>
+ </tr>
 </table>
 
@@ -1754 +6084 @@
 <p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
 style='font-size:14.0pt'>3.2.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-</span></span></b><b><span style='font-size:14.0pt'> <a name="Lorentz">(Ornstein-Zernicke)
-Lorentz (Model)</span></b></p>
+</span></span></b><b><span style='font-size:14.0pt'> <a name="Lorentz">(Ornstein-Zernicke) Lorentz
+(Model)</span></b></p>
 
 <p class=MsoNormal style='text-autospace:none'>&nbsp;</p>
@@ -1765 +6095 @@
 
 <p class=MsoNormal align=center style='text-align:center'><span
-style='font-size:14.0pt'><sub><img width=212 height=24
-src="../images/html/image026.gif"></sub></span></p>
+style='font-size:14.0pt;position:relative;top:5.0pt'><img border=0 width=212
+height=24 src="../images/html/image082.png"></span></p>
 
 <p class=MsoNormal><span style='font-size:14.0pt'>&nbsp;</span></p>
@@ -1773 +6103 @@
 the screening length.</p>
 
+<p class=MsoNormal style='text-indent:.25in'>&nbsp;</p>
+
+<p class=MsoNormal style='margin-left:.25in'>For 2D plot, the wave transfer is
+defined as <span style='font-size:14.0pt;position:relative;top:8.0pt'><img
+border=0 width=103 height=33 src="../images/html/image010.png"></span><span
+style='font-size:14.0pt;position:relative;top:6.0pt'>.</span></p>
+
+<p class=MsoNormal style='text-indent:.25in'>&nbsp;</p>
+
 <p class=MsoNormal><span style='font-size:14.0pt'>&nbsp;</span></p>
 
@@ -1849 +6188 @@
 <p class=MsoNormal><b><span style='font-size:14.0pt'>&nbsp;</span></b></p>
 
+<p class=MsoNormal><b><span style='font-size:14.0pt'>&nbsp;</span></b></p>
+
+<p class=MsoNormal><b><span style='font-size:14.0pt'>&nbsp;</span></b></p>
 
 <p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
 style='font-size:14.0pt'>3.3.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-</span></span></b><b><span style='font-size:14.0pt'> <a name="DAB_Model">DAB(Debye-Anderson-Brumberger)_
-Model)</a></span></b></p>
+</span></span></b><b><span style='font-size:14.0pt'> <a name="DAB_Model">DAB (Debye-Anderson-Brumberger)_Model</span></b></p>
+
+<p class=MsoNormal style='margin-left:.55in'><b><span style='font-size:14.0pt'>&nbsp;</span></b></p>
 
 <p class=MsoNormal style='margin-left:.25in;text-autospace:none'>Calculates the
@@ -1867 +6210 @@
 
 <p class=MsoNormal align=center style='text-align:center'><span
-style='font-size:14.0pt'><sub><img width=221 height=28
-src="../images/html/image027.gif"></sub></span></p>
+style='font-size:14.0pt;position:relative;top:5.0pt'><img border=0 width=221
+height=28 src="../images/html/image083.png"></span></p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='font-size:14.0pt'>&nbsp;</span></p>
 
 <p class=MsoNormal align=center style='text-align:center'><span
@@ -1875 +6221 @@
 <p class=MsoNormal style='margin-left:.25in;text-autospace:none'>The parameter
 L is referred to as the correlation length.</p>
+
+<p class=MsoNormal style='margin-left:.25in;text-autospace:none'>&nbsp;</p>
+
+<p class=MsoNormal style='margin-left:.25in'>For 2D plot, the wave transfer is
+defined as <span style='font-size:14.0pt;position:relative;top:8.0pt'><img
+border=0 width=103 height=33 src="../images/html/image010.png"></span><span
+style='font-size:14.0pt;position:relative;top:6.0pt'>.</span></p>
+
+<p class=MsoNormal style='margin-left:.25in;text-autospace:none'>&nbsp;</p>
 
 <p class=MsoNormal align=center style='text-align:center'><span
@@ -1968 +6323 @@
 <p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
 style='font-size:14.0pt'>3.4.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-</span></span></b><b><span style='font-size:14.0pt'> <a name="Power_Law">Power_Law</a></span></b></p>
+</span></span></b><b><span style='font-size:14.0pt'> <a name="Power_Law"> Power_Law </a></span></b></p>
 
 <p class=MsoNormal><b><span style='font-size:14.0pt'>&nbsp;</span></b></p>
@@ -1978 +6333 @@
 
 <p class=MsoNormal align=center style='text-align:center'><span
-style='font-size:14.0pt'><sub><img width=161 height=24
-src="../images/html/image028.gif"></sub></span></p>
+style='font-size:14.0pt;position:relative;top:5.0pt'><img border=0 width=149
+height=24 src="../images/html/image084.png"></span></p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='font-size:14.0pt'>&nbsp;</span></p>
 
 <p class=MsoNormal align=center style='text-align:center'><span
@@ -2064 +6422 @@
 <p class=MsoNormal><b><span style='font-size:14.0pt'>&nbsp;</span></b></p>
 
+<p class=MsoNormal><b><span style='font-size:14.0pt'>&nbsp;</span></b></p>
+
 <p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
 style='font-size:14.0pt'>3.5.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-</span></span></b><b><span style='font-size:14.0pt'><a name="Teubner Strey"> Teubner Strey (Model) </a></span></b></p>
+</span></span></b><b><span style='font-size:14.0pt'> <a name="Teubner Strey">Teubner Strey (Model)</a></span></b></p>
 
 <p class=MsoNormal><b><span style='font-size:14.0pt'>&nbsp;</span></b></p>
@@ -2076 +6436 @@
 
 <p class=MsoNormal align=center style='text-align:center'><span
-style='font-size:14.0pt'><sub><img width=213 height=45
-src="../images/html/image029.gif"></sub></span></p>
+style='font-size:14.0pt;position:relative;top:15.0pt'><img border=0 width=213
+height=45 src="../images/html/image085.png"></span></p>
 
 <p class=MsoNormal align=center style='text-align:center'><span
@@ -2084 +6444 @@
 <p class=MsoNormal align=center style='text-align:center'><span
 style='font-size:14.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal style='margin-left:.25in'>For 2D plot, the wave transfer is
+defined as <span style='font-size:14.0pt;position:relative;top:8.0pt'><img
+border=0 width=103 height=33 src="../images/html/image010.png"></span><span
+style='font-size:14.0pt;position:relative;top:6.0pt'>.</span></p>
+
+<p class=MsoNormal><span style='font-size:14.0pt'>&nbsp;</span></p>
 
 <div align=center>
@@ -2187 +6554 @@
 <p class=MsoNormal><b><span style='font-size:14.0pt'>&nbsp;</span></b></p>
 
+<p class=MsoNormal><b><span style='font-size:14.0pt'>&nbsp;</span></b></p>
 
 <p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
 style='font-size:14.0pt'>3.6.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-</span></span></b><b><span style='font-size:14.0pt'><a name="Number Density Fractal"> Number Density Fractal (Model)</a></span></b></p>
+</span></span></b><b><span style='font-size:14.0pt'> <a name="Number Density Fractal">Number Density Fractal (Model)</a></span></b></p>
 
 <p class=MsoNormal><b><span style='font-size:14.0pt'>&nbsp;</span></b></p>
@@ -2200 +6568 @@
 <p class=MsoNormal style='margin-left:.25in'>&nbsp;</p>
 
-
-<p class=MsoNormal align=center style='text-align:center'><span
-style='font-size:14.0pt'><sub><img width=380 height=188
-src="../images/html/image030.gif"></sub></span></p>
+<p class=MsoNormal style='margin-left:.25in'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='font-size:14.0pt;position:relative;top:85.0pt'><img border=0 width=332
+height=188 src="../images/html/image086.png"></span></p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='font-size:14.0pt;position:relative;top:85.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='font-size:14.0pt'>&nbsp;</span></p>
 
 <p class=MsoNormal><b><span style='font-size:14.0pt'>&nbsp;</span></b></p>
@@ -2216 +6591 @@
 <p class=MsoNormal style='margin-left:.25in;text-autospace:none'>&nbsp;</p>
 
+<p class=MsoNormal style='margin-left:.25in'>For 2D plot, the wave transfer is
+defined as <span style='font-size:14.0pt;position:relative;top:8.0pt'><img
+border=0 width=103 height=33 src="../images/html/image010.png"></span><span
+style='font-size:14.0pt;position:relative;top:6.0pt'>.</span></p>
+
+<p class=MsoNormal style='margin-left:.25in;text-autospace:none'>&nbsp;</p>
+
+<p class=MsoNormal style='text-autospace:none'>&nbsp;</p>
+
 <p class=MsoNormal align=center style='text-align:center'><span
 style='font-size:14.0pt'>&nbsp;</span></p>
@@ -2256 +6640 @@
   <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
   border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
-  <p class=MsoBodyText>Radius</p>
+  <p class=MsoBodyText>radius</p>
   </td>
   <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
@@ -2272 +6656 @@
   <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
   border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
-  <p class=MsoBodyText>Fractal_dim</p>
+  <p class=MsoBodyText>fractal_dim</p>
   </td>
   <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
@@ -2288 +6672 @@
   <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
   border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
-  <p class=MsoBodyText>Corr_length</p>
+  <p class=MsoBodyText>corr_length</p>
   </td>
   <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
@@ -2304 +6688 @@
   <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
   border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
-  <p class=MsoBodyText>Block_sld</p>
+  <p class=MsoBodyText>block_sld</p>
   </td>
   <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
@@ -2320 +6704 @@
   <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
   border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
-  <p class=MsoBodyText>Solvent_sld</p>
+  <p class=MsoBodyText>solvent_sld</p>
   </td>
   <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
@@ -2336 +6720 @@
   <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
   border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
-  <p class=MsoBodyText>Background</p>
+  <p class=MsoBodyText>background</p>
   </td>
   <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
@@ -2353 +6737 @@
 </div>
 
+<p class=MsoNormal style='margin-left:.25in;text-autospace:none'>&nbsp;</p>
 
 <p class=MsoNormal style='margin-left:.25in;text-autospace:none'>&nbsp;</p>
@@ -2367 +6752 @@
 <p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
 style='font-size:14.0pt'>3.7.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-</span></span></b><b><span style='font-size:14.0pt'> <a name="BEPolyelectrolyte">BEPolyelectrolyte Model</a></span></b></p>
+</span></span></b><b><span style='font-size:14.0pt'> <a name="BEPolyelectrolyte"> BEPolyelectrolyte Model</span></b></p>
 
 <p class=MsoNormal><b><span style='font-size:14.0pt'>&nbsp;</span></b></p>
@@ -2378 +6763 @@
 
 <p class=MsoNormal align=center style='text-align:center'><span
-style='font-size:14.0pt'><sub><img width=365 height=125
-src="../images/html/image031.gif"></sub></span></p>
+style='font-size:14.0pt;position:relative;top:43.0pt'><img border=0 width=420
+height=125 src="../images/html/image087.png"></span></p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='font-size:14.0pt;position:relative;top:43.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='font-size:14.0pt'>&nbsp;</span></p>
 
 <p class=MsoNormal style='margin-left:.25in'>&nbsp;</p>
@@ -2387 +6778 @@
 the monomer length, C<sub>s</sub> is the concentration of monovalent salt,
 &#945; is the ionization degree, C<sub>a</sub> is the polymer molar
-concentration, and bck is the incoherent background.</p>
+concentration, and background is the incoherent background.</p>
+
+<p class=MsoNormal style='margin-left:.25in'>&nbsp;</p>
+
+<p class=MsoNormal style='margin-left:.25in'>For 2D plot, the wave transfer is
+defined as <span style='font-size:14.0pt;position:relative;top:8.0pt'><img
+border=0 width=103 height=33 src="../images/html/image010.png"></span><span
+style='font-size:14.0pt;position:relative;top:6.0pt'>.</span></p>
+
+<p class=MsoNormal style='margin-left:.25in'>&nbsp;</p>
 
 <p class=MsoNormal><b><span style='font-size:14.0pt'>&nbsp;</span></b></p>
@@ -2492 +6892 @@
   <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
   border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
-  <p class=MsoBodyText>Alpha</p>
+  <p class=MsoBodyText>alpha</p>
   </td>
   <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
@@ -2524 +6924 @@
   <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
   border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
-  <p class=MsoBodyText>Background</p>
+  <p class=MsoBodyText>background</p>
   </td>
   <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
@@ -2565 +6965 @@
 <p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
 style='font-size:14.0pt'>3.8.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-</span></span></b><b><span style='font-size:14.0pt'><a name="Guinier"> Guinier (Model)</a></span></b></p>
+</span></span></b><b><span style='font-size:14.0pt'> <a name="Guinier">Guinier (Model)</span></b></p>
 
 <p class=MsoNormal><b><span style='font-size:14.0pt'>&nbsp;</span></b></p>
 
-<p class=MsoNormal style='margin-left:.25in'>A Guinier analysis is done by linearizing
-the data at low q by plotting it as log(I) versus Q<sup>2</sup>. The Guinier
-radius R<sub>g</sub> can be obtained by fitting the following model:</p>
+<p class=MsoNormal style='margin-left:.25in'>A Guinier analysis is done by
+linearizing the data at low q by plotting it as log(I) versus Q<sup>2</sup>.
+The Guinier radius R<sub>g</sub> can be obtained by fitting the following
+model:</p>
 
 <p class=MsoNormal style='margin-left:.25in'>&nbsp;</p>
 
+<p class=MsoNormal style='margin-left:.25in'>&nbsp;</p>
+
 <p class=MsoNormal align=center style='margin-left:.25in;text-align:center'><span
-style='font-size:14.0pt'><sub><img width=183 height=28
-src="../images/html/image032.gif"></sub></span></p>
+style='font-size:14.0pt;position:relative;top:7.0pt'><img border=0 width=183
+height=28 src="../images/html/image088.png"></span></p>
+
+<p class=MsoNormal align=center style='margin-left:.25in;text-align:center'><span
+style='font-size:14.0pt'>&nbsp;</span></p>
 
 <p class=MsoNormal align=center style='margin-left:.25in;text-align:center'><b><span
 style='font-size:14.0pt'>&nbsp;</span></b></p>
 
+<p class=MsoNormal style='margin-left:.25in'>For 2D plot, the wave transfer is
+defined as <span style='font-size:14.0pt;position:relative;top:8.0pt'><img
+border=0 width=103 height=33 src="../images/html/image010.png"></span><span
+style='font-size:14.0pt;position:relative;top:6.0pt'>.</span></p>
+
+<p class=MsoNormal align=center style='margin-left:.25in;text-align:center'><b><span
+style='font-size:14.0pt'>&nbsp;</span></b></p>
+
 <div align=center>
 
@@ -2629 +7043 @@
   none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
   padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
-  <p class=MsoBodyText>60</p>
+  <p class=MsoBodyText>0.1</p>
   </td>
  </tr>
@@ -2637 +7051 @@
 
 <p class=MsoNormal style='margin-left:.25in'><b><span style='font-size:14.0pt'>&nbsp;</span></b></p>
-<p class=MsoNormal style='margin-left:.25in'><b><span style='font-size:14.0pt'>&nbsp;</span></b></p>
+
 <p class=MsoNormal style='margin-left:.25in'><b><span style='font-size:14.0pt'>&nbsp;</span></b></p>
 
 <p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
 style='font-size:14.0pt'>3.9.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-</span></span></b><b><span style='font-size:14.0pt'> <a name="PorodModel">PorodModel</a></span></b></p>
+</span></span></b><b><span style='font-size:14.0pt'> <a name="PorodModel">PorodModel</span></b></p>
 
 <p class=MsoNormal><b><span style='font-size:14.0pt'>&nbsp;</span></b></p>
@@ -2653 +7067 @@
 
 <p class=MsoNormal align=center style='margin-left:.25in;text-align:center'><span
-style='font-size:14.0pt'><sub><img width=368 height=25
-src="../images/html/image033.gif"></sub></span></p>
+style='font-size:14.0pt;position:relative;top:6.0pt'><img border=0 width=368
+height=25 src="../images/html/image089.png"></span></p>
+
+<p class=MsoNormal align=center style='margin-left:.25in;text-align:center'><span
+style='font-size:14.0pt'>&nbsp;</span></p>
 
 <p class=MsoNormal align=center style='margin-left:.25in;text-align:center'><span
@@ -2663 +7080 @@
 is the contrast factor. </p>
 
-<p class=MsoNormal style='margin-left:.25in'>&nbsp;</p>
-
 <p class=MsoNormal style='margin-left:.25in'>The background term is added for
 data analysis.</p>
 
+<p class=MsoNormal style='margin-left:.25in'>&nbsp;</p>
+
+<p class=MsoNormal style='margin-left:.25in'>For 2D plot, the wave transfer is
+defined as <span style='font-size:14.0pt;position:relative;top:8.0pt'><img
+border=0 width=103 height=33 src="../images/html/image010.png"></span><span
+style='font-size:14.0pt;position:relative;top:6.0pt'>.</span></p>
+
+<p class=MsoNormal style='margin-left:.25in'>&nbsp;</p>
+
 <p class=MsoNormal align=center style='margin-left:.25in;text-align:center'><b><span
 style='font-size:14.0pt'>&nbsp;</span></b></p>
@@ -2692 +7116 @@
   <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
   border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
-  <p class=MsoBodyText>Scale</p>
+  <p class=MsoBodyText>scale</p>
   </td>
   <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
@@ -2708 +7132 @@
   <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
   border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
-  <p class=MsoBodyText>Background</p>
+  <p class=MsoBodyText>background</p>
   </td>
   <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
@@ -2727 +7151 @@
 <p class=MsoNormal><b><span style='font-size:14.0pt'>&nbsp;</span></b></p>
 
+<p class=MsoNormal style='margin-left:.5in;text-autospace:none'>&nbsp;</p>
+
+<p class=MsoNormal style='margin-left:.25in;text-autospace:none'>&nbsp;</p>
+
 <p class=MsoNormal><b><span style='font-size:14.0pt'>&nbsp;</span></b></p>
 
+
+
+<p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
+style='font-size:14.0pt'>3.10.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span></b><b><span style='font-size:14.0pt'><a name="Peak Gauss Model"> Peak Gauss Model</span></b></p>
+
 <p class=MsoNormal><b><span style='font-size:14.0pt'>&nbsp;</span></b></p>
 
-
-
+<p class=MsoNormal style='margin-left:.25in'>This Gaussian peak model with a
+flat background calculates:</p>
+
+<p class=MsoNormal style='margin-left:.25in'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='margin-left:.25in;text-align:center'><span
+style='font-size:14.0pt;position:relative;top:6.0pt'><img border=0 width=334
+height=25 src="../images/html/image090.png"></span></p>
+
+<p class=MsoNormal align=center style='margin-left:.25in;text-align:center'><span
+style='font-size:14.0pt;position:relative;top:7.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal align=center style='margin-left:.25in;text-align:center'><span
+style='font-size:14.0pt;position:relative;top:7.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal style='margin-left:.25in'><span style='position:relative;
+top:7.0pt'>where ‘scale’ is the peak height centered at q<sub>0</sub>, and B
+refers to the standard deviation of the function (equivalently, the FWHM is
+2.54*B).</span></p>
+
+<p class=MsoNormal style='margin-left:.25in'>The background term is added for
+data analysis. </p>
+
+<p class=MsoNormal style='margin-left:.25in'>&nbsp;</p>
+
+<p class=MsoNormal style='margin-left:.25in'>For 2D plot, the wave transfer is
+defined as <span style='font-size:14.0pt;position:relative;top:8.0pt'><img
+border=0 width=103 height=33 src="../images/html/image010.png"></span><span
+style='font-size:14.0pt;position:relative;top:6.0pt'>.</span></p>
+
+<p class=MsoNormal style='margin-left:.25in'>&nbsp;</p>
+
+<p class=MsoNormal style='margin-left:.25in'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='margin-left:.25in;text-align:center'><b><span
+style='font-size:14.0pt'>&nbsp;</span></b></p>
+
+<div align=center>
+
+<table class=MsoTableGrid border=1 cellspacing=0 cellpadding=0
+ style='border-collapse:collapse;border:none'>
+ <tr style='height:19.25pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
+  <p class=MsoBodyText>Parameter name</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
+  <p class=MsoBodyText>Units</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
+  <p class=MsoBodyText>Default value</p>
+  </td>
+ </tr>
+ <tr style='height:19.25pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
+  <p class=MsoBodyText>scale</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
+  <p class=MsoBodyText>cm<sup>-1</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
+  <p class=MsoBodyText>100</p>
+  </td>
+ </tr>
+ <tr style='height:19.25pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
+  <p class=MsoBodyText>B</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
+  <p class=MsoBodyText>Å<sup>-1</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
+  <p class=MsoBodyText>0.005</p>
+  </td>
+ </tr>
+ <tr style='height:19.25pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
+  <p class=MsoBodyText>q<sub>0</sub></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
+  <p class=MsoBodyText>Å<sup>-1</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
+  <p class=MsoBodyText>0.05</p>
+  </td>
+ </tr>
+ <tr style='height:19.25pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
+  <p class=MsoBodyText>background</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
+  <p class=MsoBodyText>cm<sup>-1</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
+  <p class=MsoBodyText>1.0</p>
+  </td>
+ </tr>
+</table>
+
+</div>
+
+<p class=MsoNormal style='margin-left:.25in'><b><span style='font-size:14.0pt'>&nbsp;</span></b></p>
+
+<p class=MsoNormal style='margin-left:.25in'><b><span style='font-size:14.0pt'>&nbsp;</span></b></p>
+
+<p class=MsoNormal style='margin-left:.25in'><b><span style='font-size:14.0pt'>&nbsp;</span></b></p>
+
+<p class=MsoNormal style='margin-left:.25in'><b><span style='font-size:14.0pt'>&nbsp;</span></b></p>
+
+<p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
+style='font-size:14.0pt'>3.11.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span></b><b><span style='font-size:14.0pt'> <a name="Peak Lorentz Model">Peak Lorentz Model</span></b></p>
+
+<p class=MsoNormal><b><span style='font-size:14.0pt'>&nbsp;</span></b></p>
+
+<p class=MsoNormal style='margin-left:.25in'>This Lorentzean peak model with a
+flat background calculates:</p>
+
+<p class=MsoNormal style='margin-left:.25in'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='margin-left:.25in;text-align:center'><span
+style='font-size:14.0pt;position:relative;top:34.0pt'><img border=0 width=241
+height=70 src="../images/html/image091.png"></span></p>
+
+<p class=MsoNormal align=center style='margin-left:.25in;text-align:center'><span
+style='font-size:14.0pt;position:relative;top:6.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal align=center style='margin-left:.25in;text-align:center'><span
+style='font-size:14.0pt;position:relative;top:6.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal align=center style='margin-left:.25in;text-align:center'><span
+style='font-size:14.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal style='margin-left:.25in'><span style='position:relative;
+top:7.0pt'>where ‘scale’ is the peak height centered at q<sub>0</sub>, and B
+refers to the standard deviation of the function.</span></p>
+
+<p class=MsoNormal style='margin-left:.25in'>The background term is added for
+data analysis. </p>
+
+<p class=MsoNormal style='margin-left:.25in'>&nbsp;</p>
+
+<p class=MsoNormal style='margin-left:.25in'>For 2D plot, the wave transfer is
+defined as<span style='font-size:14.0pt;position:relative;top:8.0pt'><img
+border=0 width=103 height=33 src="../images/html/image010.png"></span><span
+style='font-size:14.0pt;position:relative;top:6.0pt'>.</span></p>
+
+<p class=MsoNormal align=center style='margin-left:.25in;text-align:center'><b><span
+style='font-size:14.0pt'>&nbsp;</span></b></p>
+
+<div align=center>
+
+<table class=MsoTableGrid border=1 cellspacing=0 cellpadding=0
+ style='border-collapse:collapse;border:none'>
+ <tr style='height:19.25pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
+  <p class=MsoBodyText>Parameter name</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
+  <p class=MsoBodyText>Units</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
+  <p class=MsoBodyText>Default value</p>
+  </td>
+ </tr>
+ <tr style='height:19.25pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
+  <p class=MsoBodyText>scale</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
+  <p class=MsoBodyText>cm<sup>-1</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
+  <p class=MsoBodyText>100</p>
+  </td>
+ </tr>
+ <tr style='height:19.25pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
+  <p class=MsoBodyText>B</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
+  <p class=MsoBodyText>Å<sup>-1</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
+  <p class=MsoBodyText>0.005</p>
+  </td>
+ </tr>
+ <tr style='height:19.25pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
+  <p class=MsoBodyText>q<sub>0</sub></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
+  <p class=MsoBodyText>Å<sup>-1</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
+  <p class=MsoBodyText>0.05</p>
+  </td>
+ </tr>
+ <tr style='height:19.25pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
+  <p class=MsoBodyText>background</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
+  <p class=MsoBodyText>cm<sup>-1</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
+  <p class=MsoBodyText>1.0</p>
+  </td>
+ </tr>
+</table>
+
+</div>
+
+<p class=MsoNormal style='margin-left:.5in;text-autospace:none'>&nbsp;</p>
+
+<p class=MsoNormal style='margin-left:.25in;text-autospace:none'>&nbsp;</p>
+
+<p class=MsoNormal><b><span style='font-size:14.0pt'>&nbsp;</span></b></p>
+
+<p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
+style='font-size:14.0pt'>3.12.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span></b><b><span style='font-size:14.0pt'> <a name="LineModel"> LineModel</span></b></p>
+
+<p class=MsoNormal><b><span style='font-size:14.0pt'>&nbsp;</span></b></p>
+
+<p class=MsoNormal style='margin-left:.25in'>This is a linear function that
+calculates:</p>
+
+<p class=MsoNormal style='margin-left:.25in'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='margin-left:.25in;text-align:center'><span
+style='font-size:14.0pt;position:relative;top:5.0pt'><img border=0 width=92
+height=21 src="../images/html/image092.png"></span></p>
+
+<p class=MsoNormal align=center style='margin-left:.25in;text-align:center'><span
+style='font-size:14.0pt;position:relative;top:7.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal align=center style='margin-left:.25in;text-align:center'><span
+style='font-size:14.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal style='margin-left:.25in'>where A and B are the coefficients
+of the first and second order terms.</p>
+
+<p class=MsoNormal style='margin-left:.25in'>Note: For 2D plot, I(q) = I(q<sub>x</sub>)*I(q<sub>y</sub>) 
+which is defined differently from other shape independent models.</p>
+
+<p class=MsoNormal style='margin-left:.25in'>&nbsp;</p>
+
+<div align=center>
+
+<table class=MsoTableGrid border=1 cellspacing=0 cellpadding=0
+ style='border-collapse:collapse;border:none'>
+ <tr style='height:19.25pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
+  <p class=MsoBodyText>Parameter name</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
+  <p class=MsoBodyText>Units</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
+  <p class=MsoBodyText>Default value</p>
+  </td>
+ </tr>
+ <tr style='height:19.25pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
+  <p class=MsoBodyText>A</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
+  <p class=MsoBodyText>cm<sup>-1</sup></p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
+  <p class=MsoBodyText>1.0</p>
+  </td>
+ </tr>
+ <tr style='height:19.25pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
+  <p class=MsoBodyText>B</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
+  <p class=MsoBodyText>Å</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
+  <p class=MsoBodyText>1.0</p>
+  </td>
+ </tr>
+</table>
+
+</div>
+
+<p class=MsoNormal style='margin-left:.25in'><b><span style='font-size:14.0pt'>&nbsp;</span></b></p>
+
+<p class=MsoNormal><b><span style='font-size:14.0pt'>&nbsp;</span></b></p>
+
+<p class=MsoNormal><b><span style='font-size:14.0pt'>&nbsp;</span></b></p>
 
 <p class=MsoNormal style='margin-left:.25in;text-indent:-.25in'><b><span
-style='font-size:14.0pt'>4.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;
-</span></span></b><b><span style='font-size:14.0pt'><a name="Customized Models">Customized Models</a></span></b></p>
-
-<p class=MsoBodyText>&nbsp;</p>
-
-<p class=MsoBodyText>These models are defined by users (See SansView tutorial for details). </p>
-
-<p class=MsoBodyText>&nbsp;</p>
-
-<p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
+style='font-size:16.0pt'>4.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;
+</span></span></b><b><span style='font-size:16.0pt'><a name="Customized Models">Customized Models </a></span></b></p>
+
+<p class=MsoNormal style='margin-left:.25in'><b><span style='font-size:14.0pt'>&nbsp;</span></b></p>
+
+<p class=MsoBodyText style='margin-left:.25in'>These model functions can be redefined
+by users (See SansView tutorial for details). </p>
+
+<p class=MsoBodyText style='margin-left:.25in'>&nbsp;</p>
+
+<p class=MsoListParagraphCxSpFirst style='margin-left:.55in;text-indent:-.3in'><b><span
 style='font-size:14.0pt'>4.1.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-</span></span></b><b><span style='font-size:14.0pt'> <a name="A+Bcos(2x)+Csin(2x)">A+Bcos(2x)+Csin(2x)</a></span></b></p>
-
-<p class=MsoNormal style='text-autospace:none'>&nbsp;</p>
-
-<p class=MsoNormal style='margin-left:.25in;text-autospace:none'>This function, as an example function, calculates intensity = A + Bcos(2Q) + Csin(2Q). </p>
-
-
-<p class=MsoNormal><b><span style='font-size:14.0pt'>&nbsp;</span></b></p>
-<p class=MsoListParagraphCxSpMiddle style='margin-left:.25in;text-indent:-.25in'><b><span
-style='font-size:14.0pt'>5.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;
-</span></span></b><b><span style='font-size:14.0pt'><a name="Structure Factors">Structure Factors</a></span></b></p>
+</span></span></b><b><span style='font-size:14.0pt'><a name="A+Bcos(2x)+Csin(2x)"> A+Bcos(2x)+Csin(2x)</a></span></b></p>
+
+<p class=MsoListParagraphCxSpLast style='margin-left:.55in'><b><span
+style='font-size:14.0pt'>&nbsp;</span></b></p>
+
+<p class=MsoNormal>This function, as a sample function, calculates the intensity
+= A + Bcos(2q) + Csin(2q).</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+
+<p class=MsoListParagraphCxSpLast style='margin-left:.55in;text-indent:-.3in'><b><span
+style='font-size:14.0pt'>4.2.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span></b><b><span style='font-size:14.0pt'><a name ="sin(poly)/poly"> sin(poly)/poly </a></span></b></p>
+
+<p class=MsoNormal><b>&nbsp;</b></p>
+
+<p class=MsoNormal>This function calculates the intensity =  scale * sin(f)/f,
+where f = A + Bq + Cq<sup>2</sup> + Dq<sup>3 </sup>+ Eq<sup>4</sup> + Fq<sup>5</sup>.</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoListParagraphCxSpFirst style='margin-left:.25in;text-indent:-.25in'><b><span
+style='font-size:16.0pt'>5.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;
+</span></span></b><b><span style='font-size:16.0pt'><a name="Structure Factors"> Structure Factors</a></span></b></p>
 
 <p class=MsoListParagraphCxSpMiddle style='margin-left:.25in'>&nbsp;</p>
@@ -2765 +7570 @@
 <p class=MsoBodyText>&nbsp;</p>
 
-<p class=MsoListParagraph style='margin-left:.55in;text-indent:-.3in'><b><span
-style='font-size:14.0pt'>5.1.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-</span></span></b><b><span style='font-size:14.0pt'> <a name="HardSphereStructure">HardSphere Structure</a></span></b></p>
+<p class=MsoBodyText>&nbsp;</p>
+
+<p class=MsoListParagraph style='margin-left:.55in;text-indent:-.3in'><b>
+<span style='font-size:14.0pt'>5.1.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span></b><b><span style='font-size:14.0pt'><a name="HardsphereStructure"> HardSphere Structure </a></span></b></p>
 
 <p class=MsoNormal>&nbsp;</p>
@@ -2778 +7585 @@
 <p class=MsoNormal>&nbsp;</p>
 
+<p class=MsoNormal>&nbsp;</p>
+
 <p class=MsoNormal align=center style='margin-left:.25in;text-align:center'><span
-style='font-size:14.0pt;position:relative;top:15.0pt'><img width=122 height=48
-src="../images/html/image034.gif"></span></p>
+style='font-size:14.0pt;position:relative;top:15.0pt'><img border=0 width=122
+height=48 src="../images/html/image093.png"></span></p>
 
 <p class=MsoNormal align=center style='margin-left:.25in;text-align:center'><span
 style='font-size:14.0pt;position:relative;top:7.0pt'>&nbsp;</span></p>
 
+<p class=MsoNormal align=center style='margin-left:.25in;text-align:center'><span
+style='font-size:14.0pt;position:relative;top:7.0pt'>&nbsp;</span></p>
+
 <p class=MsoNormal><span style='position:relative;top:7.0pt'>where r is the
 distance from the center of the sphere of a radius R.</span></p>
 
+<p class=MsoNormal><span style='position:relative;top:7.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal style='margin-left:.25in'>For 2D plot, the wave transfer is
+defined as<span style='font-size:14.0pt;position:relative;top:8.0pt'><img
+border=0 width=103 height=33 src="../images/html/image010.png"></span><span
+style='font-size:14.0pt;position:relative;top:6.0pt'>.</span></p>
+
+<p class=MsoNormal><span style='position:relative;top:7.0pt'>&nbsp;</span></p>
+
 <p class=MsoNormal>&nbsp;</p>
 
@@ -2813 +7634 @@
   <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
   border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
-  <p class=MsoBodyText>radius</p>
+  <p class=MsoBodyText>effect_radius</p>
   </td>
   <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
@@ -2842 +7663 @@
   </td>
  </tr>
+ <tr style='height:19.25pt'>
+  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt;
+  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
+  <p class=MsoBodyText>&nbsp;</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
+  <p class=MsoBodyText>&nbsp;</p>
+  </td>
+  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
+  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
+  padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
+  <p class=MsoBodyText>&nbsp;</p>
+  </td>
+ </tr>
 </table>
 
 </div>
 
-<p class=MsoNormal><img width=579 height=273 id="Picture 43"
-src="../images/html/image035.gif"></p>
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><img border=0
+width=484 height=331 id="Picture 111" src="../images/html/image094.png"></p>
 
 <p class=MsoNormal style='text-autospace:none'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center;text-autospace:none'><b>Figure.
+1D plot using the default values (in linear scale).</b></p>
 
 <p class=MsoNormal style='text-autospace:none'>&nbsp;</p>
@@ -2866 +7708 @@
 <p class=MsoListParagraph style='margin-left:.55in;text-indent:-.3in'><b><span
 style='font-size:14.0pt'>5.2.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-</span></span></b><b><span style='font-size:14.0pt'><a name="SquareWellStructure"> SquareWell Structure</a></span></b></p>
+</span></span></b><b><span style='font-size:14.0pt'><a name="SquareWellStructure"> SquareWell Structure </a></span></b></p>
 
 <p class=MsoNormal>&nbsp;</p>
@@ -2893 +7735 @@
 <p class=MsoNormal>The interaction potential is:</p>
 
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
 <p class=MsoNormal align=center style='margin-left:.25in;text-align:center'><span
-style='font-size:14.0pt;position:relative;top:22.0pt'><img width=174 height=67
-src="../images/html/image036.gif"></span></p>
+style='font-size:14.0pt;position:relative;top:22.0pt'><img border=0 width=174
+height=67 src="../images/html/image095.png"></span></p>
 
 <p class=MsoNormal align=center style='margin-left:.25in;text-align:center'><span
 style='font-size:14.0pt;position:relative;top:7.0pt'>&nbsp;</span></p>
 
+<p class=MsoNormal align=center style='margin-left:.25in;text-align:center'><span
+style='font-size:14.0pt;position:relative;top:7.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal align=center style='margin-left:.25in;text-align:center'><span
+style='font-size:14.0pt;position:relative;top:7.0pt'>&nbsp;</span></p>
+
 <p class=MsoNormal><span style='position:relative;top:7.0pt'>where r is the
 distance from the center of the sphere of a radius R.</span></p>
 
+<p class=MsoNormal><span style='position:relative;top:7.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal style='margin-left:.25in'>For 2D plot, the wave transfer is
+defined as<span style='font-size:14.0pt;position:relative;top:8.0pt'><img
+border=0 width=103 height=33 src="../images/html/image010.png"></span><span
+style='font-size:14.0pt;position:relative;top:6.0pt'>.</span></p>
+
 <p class=MsoNormal>&nbsp;</p>
 
@@ -2928 +7787 @@
   <td width=145 valign=top style='width:108.5pt;border:solid windowtext 1.0pt;
   border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
-  <p class=MsoBodyText>radius</p>
+  <p class=MsoBodyText>effect_radius</p>
   </td>
   <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
@@ -2954 +7813 @@
   none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
   padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
-  <p class=MsoBodyText>0.2</p>
+  <p class=MsoBodyText>0.04</p>
   </td>
  </tr>
@@ -2995 +7854 @@
 <p class=MsoNormal>&nbsp;</p>
 
-<p class=MsoNormal><img width=546 height=296 id="Picture 53"
-src="../images/html/image037.gif"></p>
+<p class=MsoNormal align=center style='text-align:center'><img border=0
+width=510 height=346 id="Picture 110" src="../images/html/image096.png"></p>
 
 <p class=MsoNormal style='text-autospace:none'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center;text-autospace:none'><b>Figure.
+1D plot using the default values (in linear scale).</b></p>
 
 <p class=MsoNormal style='text-autospace:none'>&nbsp;</p>
@@ -3007 +7869 @@
 Sharma, K. C. Physica, 89A, 213. (1977).</p>
 
+<p class=MsoNormal style='margin-left:.5in;text-autospace:none'>&nbsp;</p>
+
 <p class=MsoNormal style='text-autospace:none'>&nbsp;</p>
 
 <p class=MsoListParagraph style='margin-left:.55in;text-indent:-.3in'><b><span
 style='font-size:14.0pt'>5.3.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-</span></span></b><b><span style='font-size:14.0pt'><a name="HayterMSAStructure"> HayterMSA Structure</a></span></b></p>
+</span></span></b><b><span style='font-size:14.0pt'><a name="HayterMSAStructure"> HayterMSA Structure </a></span></b></p>
 
 <p class=MsoNormal>&nbsp;</p>
@@ -3030 +7894 @@
 of the solution which in turn is used to compute the Debye screening length. 
 At present there is no provision for entering the ionic strength directly nor
-for use of any multivalent salts.  The counterions are also assumed to be monovalent.</p>
+for use of any multivalent salts.  The counterions are also assumed to be
+monovalent.</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal style='margin-left:.25in'>For 2D plot, the wave transfer is
+defined as<span style='font-size:14.0pt;position:relative;top:8.0pt'><img
+border=0 width=103 height=33 src="../images/html/image010.png"></span><span
+style='font-size:14.0pt;position:relative;top:6.0pt'>.</span></p>
 
 <p class=MsoNormal>&nbsp;</p>
@@ -3057 +7929 @@
   <td width=145 valign=top style='width:108.5pt;border:solid windowtext 1.0pt;
   border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
-  <p class=MsoBodyText>radius</p>
+  <p class=MsoBodyText>effect_radius</p>
   </td>
   <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
@@ -3156 +8028 @@
 <p class=MsoNormal>&nbsp;</p>
 
-<p class=MsoNormal><img width=548 height=354 id="Picture 56"
-src="../images/html/image038.gif"></p>
+<p class=MsoNormal align=center style='text-align:center'><img border=0
+width=498 height=333 id="Picture 112" src="../images/html/image097.png"></p>
 
 <p class=MsoNormal style='text-autospace:none'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center;text-autospace:none'><b>Figure.
+1D plot using the default values (in linear scale).</b></p>
 
 <p class=MsoNormal style='text-autospace:none'>&nbsp;</p>
@@ -3175 +8050 @@
 <p class=MsoNormal style='text-autospace:none'>&nbsp;</p>
 
+<p class=MsoNormal style='text-autospace:none'>&nbsp;</p>
+
 <p class=MsoListParagraph style='margin-left:.55in;text-indent:-.3in'><b><span
 style='font-size:14.0pt'>5.4.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-</span></span></b><b><span style='font-size:14.0pt'><a name="StickyHSStructure"> StickyHS Structure</a></span></b></p>
+</span></span></b><b><span style='font-size:14.0pt'> <a name="StickyHSStructure">StickyHS Structure </a></span></b></p>
 
 <p class=MsoNormal>&nbsp;</p>
@@ -3199 +8076 @@
 attraction.</p>
 
-<p class=MsoNormal align=center style='text-align:center'><span
-style='font-size:14.0pt;position:relative;top:22.0pt'><img width=135 height=67
-src="../images/html/image039.gif"></span></p>
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='font-size:14.0pt;position:relative;top:22.0pt'><img border=0 width=135
+height=67 src="../images/html/image098.png"></span></p>
 
 <p class=MsoNormal align=center style='text-align:center'><span
 style='font-size:14.0pt;position:relative;top:27.0pt'>&nbsp;</span></p>
 
+<p class=MsoNormal align=center style='text-align:center'><span
+style='font-size:14.0pt;position:relative;top:27.0pt'>&nbsp;</span></p>
+
 <p class=MsoNormal>where the interaction potential is</p>
 
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
 <p class=MsoNormal align=center style='margin-left:.25in;text-align:center'><span
-style='font-size:14.0pt;position:relative;top:23.0pt'><img width=186 height=69
-src="../images/html/image040.gif"></span></p>
+style='font-size:14.0pt;position:relative;top:23.0pt'><img border=0 width=186
+height=69 src="../images/html/image099.png"></span></p>
+
+<p class=MsoNormal align=center style='margin-left:.25in;text-align:center'><span
+style='font-size:14.0pt;position:relative;top:7.0pt'>&nbsp;</span></p>
+
+<p class=MsoNormal align=center style='margin-left:.25in;text-align:center'><span
+style='font-size:14.0pt;position:relative;top:7.0pt'>&nbsp;</span></p>
 
 <p class=MsoNormal>The Percus-Yevick (PY) closure was used for this
@@ -3236 +8130 @@
 <p class=MsoNormal>&nbsp;</p>
 
+<p class=MsoNormal style='margin-left:.25in'>For 2D plot, the wave transfer is
+defined as<span style='font-size:14.0pt;position:relative;top:8.0pt'><img
+border=0 width=103 height=33 src="../images/html/image010.png"></span><span
+style='font-size:14.0pt;position:relative;top:6.0pt'>.</span></p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
 <div align=center>
 
@@ -3257 +8160 @@
   <td width=145 valign=top style='width:108.5pt;border:solid windowtext 1.0pt;
   border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
-  <p class=MsoBodyText>radius</p>
+  <p class=MsoBodyText>effect_radius</p>
   </td>
   <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
@@ -3267 +8170 @@
   none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
   padding:0in 5.4pt 0in 5.4pt;height:19.25pt'>
-  <p class=MsoBodyText>20.8</p>
+  <p class=MsoBodyText>50</p>
   </td>
  </tr>
@@ -3324 +8227 @@
 <p class=MsoNormal>&nbsp;</p>
 
-<p class=MsoNormal><img width=524 height=359 id="Picture 111"
-src="../images/html/image041.gif"></p>
+<p class=MsoNormal align=center style='text-align:center'><img border=0
+width=502 height=328 id="Picture 113" src="../images/html/image100.png"></p>
+
+<p class=MsoNormal align=center style='text-align:center;text-autospace:none'><b>Figure.
+1D plot using the default values (in linear scale).</b></p>
 
 <p class=MsoNormal style='text-autospace:none'>&nbsp;</p>
@@ -3336 +8242 @@
 G., Manohar, C. and K. Srinivas Rao J. Chem. Phys., 95(12), 9186-9190 (1991).</p>
 
-
-
 <p class=MsoNormal><b><span style='font-size:14.0pt'>&nbsp;</span></b></p>
 
 <p class=MsoNormal><b><span style='font-size:14.0pt'>&nbsp;</span></b></p>
 
-
-<p class=MsoBodyText><b><span style='font-size:14.0pt'><a name="References">References</a></span></b></p>
+<p class=MsoBodyText><b><span style='font-size:14.0pt'>References</span></b></p>
 
 <p class=MsoBodyText>Feigin, L. A, and D. I. Svergun (1987) &quot;Structure
-Analysis by Small-Angle X-Ray and Neutron Scattering&quot;, Plenum Press, New York.</p>
+Analysis by Small-Angle X-Ray and Neutron Scattering&quot;, Plenum Press, New
+York.</p>
 
 <p class=MsoBodyText>Guinier, A. and G. Fournet (1955) &quot;Small-Angle