Changeset 28c9e5a in sasview

Timestamp:

Aug 22, 2011 5:06:45 PM (13 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:

8cf19e9

Parents:

b21d32b

Message:

added pearlnecklace model in doc

Files:

• sansmodels/src/sans/models/media/model_functions.html (modified) (30 diffs)
• sansmodels/src/sans/models/media/pearl_eq1.gif (added)
• sansmodels/src/sans/models/media/pearl_eq2.gif (added)
• sansmodels/src/sans/models/media/pearl_eq3.gif (added)
• sansmodels/src/sans/models/media/pearl_eq4.gif (added)
• sansmodels/src/sans/models/media/pearl_eq5.gif (added)
• sansmodels/src/sans/models/media/pearl_eq6.gif (added)
• sansmodels/src/sans/models/media/pearl_eq7.gif (added)
• sansmodels/src/sans/models/media/pearl_fig.jpg (added)
• sansmodels/src/sans/models/media/pearl_plot.jpg (added)
• sansview/media/Model Functions.pdf (modified) (previous)

sansmodels/src/sans/models/media/model_functions.html

@@ -468 +468 @@
      href="#VesicleModel">VesicleModel</a>, <a href="#MultiShellModel">MultiShellModel</a>,
       <a href="#OnionExpShellModel">OnionExpShellModel</a>, <a
-     href="#SphericalSLDModel">SphericalSLDModel</a>, <a href="#CylinderModel">CylinderModel</a>,
+     href="#SphericalSLDModel">SphericalSLDModel</a>, <a
+     href="#PearlNecklaceModel">PearlNecklaceModel</a>
+     , <a href="#CylinderModel">CylinderModel</a>,
      <a href="#CoreShellCylinderModel">CoreShellCylinderModel</a>, <a
      href="#HollowCylinderModel">HollowCylinderModel</a>, <a
@@ -656 +658 @@
 <p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
 
-<p class=MsoNormal>where <i>scale</i> is a scale factor* volume fraction, 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)&nbsp; is the scattering length density (SLD) &nbsp;difference
-between the scatterer and the solvent it is in.</p>
+<p class=MsoNormal>where scale is a scale factor* volume fraction, 
+V is the volume of the scatterer, r is the radius of the sphere, 
+bkg is the background level and sldXXX is the scattering length density 
+(SLD)  of  the scatterer or the solvent.  </p>
+<p>
+Note that if your data is in absolute scale, 
+the 'scale' should represent the volume fraction (unitless) if you have a good fit.  
+If not, it should represent the volume fraction * a factor 
+(by which your data might need to be rescaled).</p>
 
 <p class=MsoNormal>&nbsp;</p>
@@ -3238 +3244 @@
 
 <p class=MsoNormal>&nbsp;</p>
-
 <p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
 style='font-size:14.0pt'>2.10.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></b><b><a name=PearlNecklaceModel><span style='font-size:14.0pt'>PearlNecklaceModel</span></b></p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>This model provides the form factor for a pearl necklace composed
+of two elements: N pearls (homogeneous spheres) freely jointed by M rods (like
+strings) (with a total mass M<sub>w</sub> = M *m<sub>r</sub> + N * m<sub>s</sub>,
+the radius R and the string segment length (or edge separation) l (= A- 2R)).
+The A is the center to center pearl separation distance.</p>
+<p/>
+<center><img src="pearl_fig.jpg"></center>
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal style='margin-left:.85in;text-indent:-.35in'><b>1.1.</b><b><span
+style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp; </span>Definition</b></p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>The output of the scattering intensity function for the
+pearlnecklace model is given by (Schweins, 2004):</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 
+src="pearl_eq1.gif"></span>&nbsp; </p>
+
+<p class=MsoNormal>where</p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:16.0pt'><img 
+src="pearl_eq2.gif"></span><span
+style='position:relative;top:14.0pt'>,</span>&nbsp;&nbsp; </p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:17.0pt'><img 
+src="pearl_eq3.gif"></span><span
+style='position:relative;top:14.0pt'>,</span></p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:16.0pt'><img 
+src="pearl_eq4.gif"></span><span
+style='position:relative;top:14.0pt'>,</span></p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:15.0pt'><img 
+src="pearl_eq5.gif"></span>&nbsp;,</p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:14.0pt'><img 
+src="pearl_eq6.gif">,</span></p>
+
+<p class=MsoNormal><span style='position:relative;top:14.0pt'>and</span></p>
+
+<p class=MsoNormal align=center style='text-align:center'><span
+style='position:relative;top:14.0pt'><img 
+src="pearl_eq7.gif">.</span></p>
+<p/>
+<p class=MsoNormal>where the mass m<sub>i </sub> is (sld(of i) – sld(of
+solvent)) * (volume of the N pearls/rods), V is the total volume of the necklace.</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 sphere model are the following:</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<div align=center>
+
+<table class=MsoNormalTable border=0 cellspacing=0 cellpadding=0
+ style='border-collapse:collapse'>
+ <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>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:19.25pt'>
+  <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>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: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>80.0</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>edge_separation</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>350.0</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>num_pearls</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>(integer)</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>3</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>sld_pearl</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> -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:19.25pt'>
+  <p class=MsoBodyText>1e-6</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>sld_solv</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> -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:19.25pt'>
+  <p class=MsoBodyText>6.3e-6</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>sld_string</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> -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:19.25pt'>
+  <p class=MsoBodyText>1e-6</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>thick_string</p>
+  <p class=MsoBodyText>(=rod diameter)</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>2.5</p>
+  </td>
+ </tr>
+ <tr style='height:20.0pt'>
+  <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>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:20.0pt'>
+  <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:20.0pt'>
+  <p class=MsoBodyText>0.0</p>
+  </td>
+ </tr>
+</table>
+
+</div>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal align=center style='text-align:center'><img 
+src="pearl_plot.jpg"></p>
+
+<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p>
+
+<p class=MsoNormal>&nbsp;</p>
+
+<p class=MsoNormal>REFERENCE</p>
+
+<p class=MsoNormal>R. Schweins and K. Huber, ‘Particle Scattering Factor of
+Pearl Necklace Chains’, Macromol. Symp., 211, 25-42, 2004.</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'>2.11.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><a name=CylinderModel><b><span style='font-size:14.0pt'>Cylinder
 Model</span></b></a></p>
@@ -3433 +3700 @@
   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>
+  <p class=MsoBodyText>degree</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>
+  <p class=MsoBodyText>60</p>
   </td>
  </tr>
@@ -3449 +3716 @@
   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>
+  <p class=MsoBodyText>degree</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>1.0</p>
+  <p class=MsoBodyText>60</p>
   </td>
  </tr>
@@ -3565 +3832 @@
 
 <p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
-style='font-size:14.0pt'>2.11.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+style='font-size:14.0pt'>2.12.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><a name=CoreShellCylinderModel><b><span style='font-size:14.0pt'>Core-Shell
 Cylinder Model</span></b></a></p>
@@ -3796 +4063 @@
   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>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:19.25pt'>
-  <p class=MsoBodyText>1.57</p>
+  <p class=MsoBodyText>degree</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>90</p>
   </td>
  </tr>
@@ -3812 +4079 @@
   none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
   padding:0in 5.4pt 0in 5.4pt;height:20.0pt'>
-  <p class=MsoBodyText>Radian</p>
+  <p class=MsoBodyText>degree</p>
   </td>
   <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
@@ -3901 +4168 @@
 
 <p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
-style='font-size:14.0pt'>2.12.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+style='font-size:14.0pt'>2.13.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><a name=HollowCylinderModel><b><span style='font-size:14.0pt'>HollowCylinderModel</span></b></a></p>
 
@@ -4137 +4404 @@
 
 <p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
-style='font-size:14.0pt'>2.13.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+style='font-size:14.0pt'>2.14.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><a name=FlexibleCylinderModel></a><b><span style='font-size:14.0pt'>FlexibleCylinderModel</span></b></p>
 
@@ -4356 +4623 @@
 
 <p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
-style='font-size:14.0pt'>2.14.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+style='font-size:14.0pt'>2.15.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><b><span style='font-size:14.0pt'>FlexCylEllipXMo<a
 name=FlexCylEllipXModel></a>del</span></b></p>
@@ -4643 +4910 @@
 
 <p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
-style='font-size:14.0pt'>2.15.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+style='font-size:14.0pt'>2.16.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><a name=StackedDisksModel><b><span style='font-size:14.0pt'>StackedDisksModel
 </span></b></a></p>
@@ -5004 +5271 @@
 
 <p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
-style='font-size:14.0pt'>2.16.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+style='font-size:14.0pt'>2.17.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><a name=ParallelepipedModel><b><span style='font-size:14.0pt'>ParallelepipedModel</span></b></a></p>
 
@@ -5291 +5558 @@
 
 <p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
-style='font-size:14.0pt'>2.17.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+style='font-size:14.0pt'>2.18.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><b><span style='font-size:14.0pt'><a
 name=CSParallelepipedModel>CSParallelepipedModel</a></span></b></p>
@@ -5719 +5986 @@
 
 <p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
-style='font-size:14.0pt'>2.18.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+style='font-size:14.0pt'>2.19.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><a name=EllipticalCylinderModel><b><span style='font-size:14.0pt'>Elliptical
 Cylinder Model</span></b></a></p>
@@ -6060 +6327 @@
 
 <p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
-style='font-size:14.0pt'>2.19.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+style='font-size:14.0pt'>2.20.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><a name=BarBellModel><b><span style='font-size:14.0pt'>BarBell(/DumBell)Model</span></b></a></p>
 
@@ -6359 +6626 @@
 
 <p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
-style='font-size:14.0pt'>2.20.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+style='font-size:14.0pt'>2.21.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><a name=CappedCylinderModel><b><span style='font-size:14.0pt'>CappedCylinder(/ConvexLens)Model</span></b></a></p>
 
@@ -6651 +6918 @@
 
 <p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
-style='font-size:14.0pt'>2.21.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+style='font-size:14.0pt'>2.22.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><a name=EllipsoidModel><b><span style='font-size:14.0pt'>Ellipsoid
 Model</span></b></a></p>
@@ -6853 +7120 @@
   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>
+  <p class=MsoBodyText>degree</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>
+  <p class=MsoBodyText>90</p>
   </td>
  </tr>
@@ -6869 +7136 @@
   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>
+  <p class=MsoBodyText>degree</p>
   </td>
   <td width=143 valign=top style='width:107.0pt;border-top:none;border-left:
@@ -6991 +7258 @@
 
 <p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
-style='font-size:14.0pt'>2.22.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+style='font-size:14.0pt'>2.23.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><a name=CoreShellEllipsoidModel><b><span style='font-size:14.0pt'>CoreShellEllipsoidModel
 </span></b></a></p>
@@ -7268 +7535 @@
 
 <p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
-style='font-size:14.0pt'>2.23.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+style='font-size:14.0pt'>2.24.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><a name=TriaxialEllipsoidModel><b><span style='font-size:14.0pt'>TriaxialEllipsoidModel</span></b></a></p>
 
@@ -7543 +7810 @@
 
 <p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
-style='font-size:14.0pt'>2.24.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+style='font-size:14.0pt'>2.25.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><a name=LamellarModel><b><span style='font-size:14.0pt'>LamellarModel</span></b></a></p>
 
@@ -7730 +7997 @@
 
 <p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
-style='font-size:14.0pt'>2.25.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+style='font-size:14.0pt'>2.26.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><a name=LamellarFFHGModel><b><span style='font-size:14.0pt'>LamellarFFHGModel</span></b></a></p>
 
@@ -7959 +8226 @@
 
 <p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
-style='font-size:14.0pt'>2.26.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+style='font-size:14.0pt'>2.27.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><a name=LamellarPSModel><b><span style='font-size:14.0pt'>LamellarPSModel</span></b></a></p>
 
@@ -8206 +8473 @@
 
 <p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
-style='font-size:14.0pt'>2.27.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+style='font-size:14.0pt'>2.28.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><a name=LamellarPSHGModel><b><span style='font-size:14.0pt'>LamellarPSHGModel</span></b></a></p>
 
@@ -8508 +8775 @@
 
 <p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
-style='font-size:14.0pt'>2.28.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+style='font-size:14.0pt'>2.29.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><a name=LamellarPCrystalModel><b><span style='font-size:14.0pt'>LamellarPCrystalModel</span></b></a></p>
 
@@ -8762 +9029 @@
 
 <p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
-style='font-size:14.0pt'>2.29.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+style='font-size:14.0pt'>2.30.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><a name=SCCrystalModel><b><span style='font-size:14.0pt'>SC(Simple
 Cubic Para-)CrystalModel</span></b></a></p>
@@ -9074 +9341 @@
 
 <p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
-style='font-size:14.0pt'>2.30.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+style='font-size:14.0pt'>2.31.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><a name=FCCrystalModel><b><span style='font-size:14.0pt'>FC(Face
 Centered Cubic Para-)CrystalModel</span></b></a></p>
@@ -9388 +9655 @@
 
 <p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span
-style='font-size:14.0pt'>2.31.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+style='font-size:14.0pt'>2.32.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><a name=BCCrystalModel><b><span style='font-size:14.0pt'>BC(Body
 Centered Cubic Para-)CrystalModel</span></b></a></p>