Changeset 1d3a2e7 in sasview for sansmodels/src/sans/models/media


Ignore:
Timestamp:
Aug 2, 2012 9:03:36 AM (12 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:
808da5e
Parents:
8037f4b
Message:

more cleanups

File:
1 edited

Legend:

Unmodified
Added
Removed
  • sansmodels/src/sans/models/media/model_functions.html

    r8037f4b r1d3a2e7  
    260260<p  style="text-align: center; page-break-after: avoid;" align="center"><img src="image005.jpg" alt="sphere_1D_validation" height="315" width="573"></p> 
    261261<p  style="text-align: center; page-break-after: avoid;" align="center">&nbsp;</p> 
    262 <p class="MsoCaption">Figure 1: Comparison of the DANSE 
     262<p>Figure 1: Comparison of the DANSE 
    263263scattering intensity for 
    264264a sphere with the output of the NIST SANS analysis software. The 
     
    940940 
    941941<p  style="text-align: center; page-break-after: avoid;" align="center"><img src="image014.jpg" alt="core_shell_sphere_1D_validation" height="315" width="573"></p> 
    942 <p class="MsoCaption">Figure 7: Comparison of the DANSE 
     942<p>Figure 7: Comparison of the DANSE 
    943943scattering intensity for 
    944944a core-shell sphere with the output of the NIST SANS analysis software. 
     
    20032003function chosen by an user, where the functions are:</p> 
    20042004 
    2005 <p class="MsoListParagraph" style="text-indent: -0.25in;">1)<span style="font-family: &quot;Times New Roman&quot;; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     2005<p style="text-indent: -0.25in;">1)<span style="font-family: &quot;Times New Roman&quot;; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    20062006</span>Exp;&nbsp;&nbsp;&nbsp; </p> 
    20072007<p ><span style="font-size: 12pt; font-family: &quot;Times New Roman&quot;,&quot;serif&quot;;"><img src="image049.gif"></span></p> 
    20082008 
    2009 <p class="MsoListParagraph" style="text-indent: -0.25in;">2)<span style="font-family: &quot;Times New Roman&quot;; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     2009<p style="text-indent: -0.25in;">2)<span style="font-family: &quot;Times New Roman&quot;; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    20102010</span>Power-Law;</p> 
    20112011 
    2012 <p class="MsoListParagraph">&nbsp;</p> 
     2012<p >&nbsp;</p> 
    20132013<p ><span style="font-size: 12pt; font-family: &quot;Times New Roman&quot;,&quot;serif&quot;;"><img src="image050.gif"></span></p> 
    20142014 
    20152015 
    2016 <p class="MsoListParagraph" style="text-indent: -0.25in;">3)<span style="font-family: &quot;Times New Roman&quot;; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     2016<p style="text-indent: -0.25in;">3)<span style="font-family: &quot;Times New Roman&quot;; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    20172017</span>Erf;</p> 
    20182018 
    2019 <p class="MsoListParagraph"><span style="font-size: 12pt; font-family: &quot;Times New Roman&quot;,&quot;serif&quot;;"><img src="image051.gif"></span></p> 
    2020 <p class="MsoListParagraph">&nbsp;</p> 
    2021 <p class="MsoListParagraph">&nbsp;</p> 
     2019<p ><span style="font-size: 12pt; font-family: &quot;Times New Roman&quot;,&quot;serif&quot;;"><img src="image051.gif"></span></p> 
     2020<p >&nbsp;</p> 
     2021<p >&nbsp;</p> 
    20222022<p >Then the functions are normalized so 
    20232023that it varies between 
     
    26012601 
    26022602<p  style="text-align: center; page-break-after: avoid;" align="center"><img src="image061.jpg" alt="cylinderangles.gif" height="258" width="478"></p> 
    2603 <p class="MsoCaption" style="text-align: center;" align="center"><a name="_Ref173213915"></a><a name="_Ref173306040"></a>Figure 2a. Definition of 
     2603<p style="text-align: center;" align="center"><a name="_Ref173213915"></a><a name="_Ref173306040"></a>Figure 2a. Definition of 
    26042604the angles for oriented cylinders.</p> 
    26052605 
    26062606 
    26072607<p  style="text-align: center;" align="center"><img src="image062.jpg" alt="cylinderangles2.gif" height="313" width="464"></p> 
    2608 <p class="MsoCaption" style="text-align: center;" align="center">Figure 2b. Examples 
     2608<p style="text-align: center;" align="center">Figure 2b. Examples 
    26092609of the angles for oriented cylinders against the detector plane.</p> 
    26102610 
     
    27682768<p  style="text-align: center; page-break-after: avoid;" align="center"><img src="image065.jpg" alt="cylinder_1D_validation" height="315" width="573"></p> 
    27692769<p  style="text-align: center; page-break-after: avoid;" align="center">&nbsp;</p> 
    2770 <p class="MsoCaption"><a name="_Ref173211066"></a><a name="_Ref173211049"></a>Figure 
     2770<p><a name="_Ref173211066"></a><a name="_Ref173211049"></a>Figure 
    277127713: Comparison of the DANSE scattering intensity for a cylinder with the 
    27722772output 
     
    27772777cm<sup> -1</sup>.</p> 
    27782778 
    2779 <p class="MsoCaption">&nbsp;</p> 
     2779<p>&nbsp;</p> 
    27802780<p  style="text-align: center; page-break-after: avoid;" align="center"><img src="image066.jpg" alt="cylinder_2D_average" height="315" width="573"></p> 
    27812781<p  style="text-align: center; page-break-after: avoid;" align="center">&nbsp;</p> 
    2782 <p class="MsoCaption"><a name="_Ref173213305">Figure 
     2782<p><a name="_Ref173213305">Figure 
    27832783</a>4: Comparison of the 
    27842784intensity for uniformly distributed cylinders calculated from our 2D 
     
    27892789and 
    27902790Background=0.0 cm<sup> -1</sup>.</p> 
    2791 <p class="MsoCaption">&nbsp;</p> 
     2791<p>&nbsp;</p> 
    27922792 
    27932793 
     
    30173017<p  style="text-align: center; page-break-after: avoid;" align="center"><img src="image070.jpg" alt="core_shell_cylinder_1D_validation" height="315" width="573"></p> 
    30183018<p  style="text-align: center; page-break-after: avoid;" align="center">&nbsp;</p> 
    3019 <p class="MsoCaption"><a name="_Ref173307149">Figure 
     3019<p><a name="_Ref173307149">Figure 
    30203020</a>8: Comparison of the 
    30213021DANSE scattering intensity for a core-shell cylinder with the output of 
     
    30283028and Background=0.01 cm<sup> 
    30293029-1</sup>.</p> 
    3030 <p class="MsoCaption">&nbsp;</p> 
     3030<p>&nbsp;</p> 
    30313031 
    30323032 
    30333033<p  style="text-align: center; page-break-after: avoid;" align="center"><img id="Picture 23" src="image071.jpg" alt="core_shell_cylinder_2D_average" height="315" width="573"></p> 
    30343034<p  style="text-align: center; page-break-after: avoid;" align="center">&nbsp;</p> 
    3035 <p class="MsoCaption"><a name="_Ref173307204">Figure 
     3035<p><a name="_Ref173307204">Figure 
    30363036</a>9: Comparison of the 
    30373037intensity for uniformly distributed core-shell cylinders calculated 
     
    39993999 
    40004000<p  style="text-align: center;" align="center"><img id="Picture 101" src="image086.jpg" height="215" width="377"></p> 
    4001 <p class="MsoCaption" style="text-align: center;" align="center">Figure. Examples of 
     4001<p style="text-align: center;" align="center">Figure. Examples of 
    40024002the angles for oriented stackeddisks against the detector plane.</p> 
    40034003 
     
    40854085 
    40864086<p  style="text-align: center;" align="center"><img src="image091.jpg" height="256" width="379"></p> 
    4087 <p class="MsoCaption" style="text-align: center;" align="center">Figure. Examples of 
     4087<p style="text-align: center;" align="center">Figure. Examples of 
    40884088the angles for oriented pp against the detector plane.</p> 
    40894089 
     
    41814181 
    41824182 
    4183 <p class="MsoListParagraph" style="margin-left: 1.35in; text-indent: -0.25in;"><span style="font-family: Symbol;">·</span><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     4183<p style="margin-left: 1.35in; text-indent: -0.25in;"><span style="font-family: Symbol;">·</span><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    41844184</span><b>Validation of the parallelepiped 2D model</b></p> 
    41854185 
     
    43254325 
    43264326<p  style="text-align: center;" align="center"><img id="Picture 103" src="image091.jpg" height="256" width="379"></p> 
    4327 <p class="MsoCaption" style="text-align: center;" align="center">Figure. Examples of 
     4327<p style="text-align: center;" align="center">Figure. Examples of 
    43284328the angles for oriented cspp against the detector plane.</p> 
    43294329 
     
    46014601 
    46024602<p  style="text-align: center;" align="center"><img id="Picture 114" src="image091.jpg" height="256" width="379"></p> 
    4603 <p class="MsoCaption" style="text-align: center;" align="center"><span style="font-size: 12pt;">Figure. 
     4603<p style="text-align: center;" align="center"><span style="font-size: 12pt;">Figure. 
    46044604Examples of the angles for oriented elliptical 
    46054605cylinders </span></p> 
    4606 <p class="MsoCaption" style="text-align: center;" align="center"><span style="font-size: 12pt;">against 
     4606<p style="text-align: center;" align="center"><span style="font-size: 12pt;">against 
    46074607the detector plane.</span></p> 
    46084608 
     
    47174717 
    47184718 
    4719 <p class="MsoListParagraph" style="margin-left: 1.35in; text-indent: -0.25in;"><span style="font-family: Symbol;">·</span><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     4719<p style="margin-left: 1.35in; text-indent: -0.25in;"><span style="font-family: Symbol;">·</span><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    47204720</span><b>Validation of the elliptical cylinder 2D model</b></p> 
    47214721 
     
    51855185 
    51865186 
    5187 <p class="MsoCaption" style="text-align: center;" align="center"><span style="position: relative; top: 12pt;"><img src="image059.PNG"></span>&nbsp;&nbsp; 
     5187<p style="text-align: center;" align="center"><span style="position: relative; top: 12pt;"><img src="image059.PNG"></span>&nbsp;&nbsp; 
    51885188</p> 
    51895189 
    5190 <p class="MsoCaption" style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="image119.PNG"></span>&nbsp;&nbsp;&nbsp; 
     5190<p style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="image119.PNG"></span>&nbsp;&nbsp;&nbsp; 
    51915191</p> 
    51925192 
    5193 <p class="MsoCaption" style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="image120.PNG"></span>&nbsp;&nbsp;&nbsp;&nbsp; 
     5193<p style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="image120.PNG"></span>&nbsp;&nbsp;&nbsp;&nbsp; 
    51945194</p> 
    51955195 
     
    53485348 
    53495349<p  style="text-align: center;" align="center"><img src="image122.jpg" height="297" width="396"></p> 
    5350 <p class="MsoCaption" style="text-align: center;" align="center"><span style="font-size: 12pt;">Figure. 
     5350<p style="text-align: center;" align="center"><span style="font-size: 12pt;">Figure. 
    53515351Examples of the angles for oriented ellipsoid </span></p> 
    5352 <p class="MsoCaption" style="text-align: center;" align="center"><span style="font-size: 12pt;">against 
     5352<p style="text-align: center;" align="center"><span style="font-size: 12pt;">against 
    53535353the detector plane</span>.</p> 
    53545354 
     
    53945394 
    53955395<p  style="text-align: center; page-break-after: avoid;" align="center"><b><img id="Picture 16" src="image123.jpg" alt="ellipsoid_1D_validation" height="315" width="573"></b></p> 
    5396 <p class="MsoCaption"><a name="_Ref173222904">Figure 
     5396<p><a name="_Ref173222904">Figure 
    53975397</a>5: Comparison of the 
    53985398DANSE scattering intensity for an ellipsoid with the output of the NIST 
     
    54015401Å, 
    54025402Radius_b=400 Å, </p> 
    5403 <p class="MsoCaption">Contrast=3e-6 Å<sup> -2</sup>, 
     5403<p>Contrast=3e-6 Å<sup> -2</sup>, 
    54045404and Background=0.01 cm<sup> 
    54055405-1</sup>.</p> 
     
    54085408<p  style="text-align: center; page-break-after: avoid;" align="center"><img src="image124.jpg" alt="ellipsoid_2D_average" height="315" width="573"></p> 
    54095409<p  style="text-align: center; page-break-after: avoid;" align="center">&nbsp;</p> 
    5410 <p class="MsoCaption"><a name="_Ref173223004">Figure 
     5410<p><a name="_Ref173223004">Figure 
    54115411</a>6: Comparison of the 
    54125412intensity for uniformly distributed ellipsoids calculated from our 2D 
     
    54175417and 
    54185418Background=0.0 cm<sup> -1</sup>.</p> 
    5419 <p class="MsoCaption">&nbsp;</p> 
     5419<p>&nbsp;</p> 
    54205420 
    54215421 
     
    57745774 
    57755775 
    5776 <p class="MsoListParagraph" style="margin-left: 1.35in; text-indent: -0.25in;"><span style="font-family: Symbol;">·</span><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     5776<p style="margin-left: 1.35in; text-indent: -0.25in;"><span style="font-family: Symbol;">·</span><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    57775777</span><b>Validation of the triaxialellipsoid 2D model</b></p> 
    57785778 
     
    57965796 
    57975797<p  style="text-align: center;" align="center"><img src="image132.jpg" height="297" width="396"></p> 
    5798 <p class="MsoCaption" style="text-align: center;" align="center">Figure. Examples of 
     5798<p style="text-align: center;" align="center">Figure. Examples of 
    57995799the angles for oriented ellipsoid against the detector plane.</p> 
    58005800 
     
    1039810398</div> 
    1039910399 
    10400 <p class="MsoListParagraph" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;"></span></b></p> 
    10401 <p class="MsoListParagraph" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.27.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     10400<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;"></span></b></p> 
     10401<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.27.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    1040210402</span></b><a name="ReflectivityModel"><b><span style="font-size: 14pt;">ReflectivityModel</span></b></a></p> 
    1040310403 
    10404 <p class="MsoListParagraph" style="margin-left: 0.55in; text-indent: -0.3in;">This 
     10404<p style="margin-left: 0.55in; text-indent: -0.3in;">This 
    1040510405model calculates the reflectivity and uses the Parrett algorithm. Up to 
    1040610406nine 
     
    1041710417the error 
    1041810418function, sigma=roughness).</p> 
    10419 <p class="MsoListParagraph" style="margin-left: 0.55in; text-indent: -0.3in;">Note: 
     10419<p style="margin-left: 0.55in; text-indent: -0.3in;">Note: 
    1042010420This model was contributed by an interested user. </p> 
    1042110421 
     
    1043510435 
    1043610436 
    10437 <p class="MsoListParagraph" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.28.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     10437<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.28.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    1043810438</span></b><a name="ReflectivityIIModel"><b><span style="font-size: 14pt;">ReflectivityIIModel</span></b></a></p> 
    1043910439 
     
    1045010450the interface between layers, <i><span style="font-family: Symbol;">r</span><sub>inter_i</sub></i>, 
    1045110451is calculated with a function chosen by a user, where the functions are:</p> 
    10452 <p class="MsoListParagraph" style="margin-left: 0.55in;">1) 
     10452<p style="margin-left: 0.55in;">1) 
    1045310453Erf; </p> 
    1045410454<p> <img src="image051.gif"></p> 
    10455 <p class="MsoListParagraph" style="margin-left: 0.55in;">2) 
     10455<p style="margin-left: 0.55in;">2) 
    1045610456Power-Law; </p> 
    1045710457<p> <span><img src="image050.gif"></span></p> 
    1045810458<p> </p> 
    1045910459<p> </p> 
    10460 <p class="MsoListParagraph" style="margin-left: 0.55in;">3) 
     10460<p style="margin-left: 0.55in;">3) 
    1046110461Exp; </p> 
    1046210462<p> <span><img src="image049.gif"></span></p> 
     
    1047010470 
    1047110471 
    10472 <p class="MsoListParagraph" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.28.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     10472<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.28.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    1047310473</span></b><a name="GelFitModel"><b><span style="font-size: 14pt;">GelFitModel</span></b></a></p> 
    1047410474 
     
    1047810478accumulations of polymer pinned down by junction points or clusters of such points. The letter is derived from a simple Guinier function.</p> 
    1047910479 
    10480 <p class="MsoListParagraph" style="margin-left: 0.55in;"> 
     10480<p style="margin-left: 0.55in;"> 
    1048110481The scattered intensity I(Q) is then calculated as: </p> 
    1048210482<p> <img src="image233.gif"></p> 
    10483 <p class="MsoListParagraph" style="margin-left: 0.55in;"> 
     10483<p style="margin-left: 0.55in;"> 
    1048410484Where: </p> 
    1048510485<p> <span><img src="image234.gif"></span></p> 
     
    1062410624 
    1062510625 
    10626 <p class="MsoListParagraph" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.30.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     10626<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.30.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    1062710627</span></b><a name="FractalO_Z"><b><span style="font-size: 14pt;">FractalO_Z</span></b></a></p> 
    1062810628 
     
    1063810638</p> 
    1063910639 
    10640 <p class="MsoListParagraph" style="margin-left: 0.55in;"> 
     10640<p style="margin-left: 0.55in;"> 
    1064110641The scattered intensity I(Q) is then calculated using a modified Ornstein-Zernicke equation: </p> 
    1064210642<p> <img src="image236.gif"></p> 
    10643 <p class="MsoListParagraph" style="margin-left: 0.55in;"> 
     10643<p style="margin-left: 0.55in;"> 
    1064410644Where: </p> 
    1064510645<p> <span><img src="image237.gif"></span></p> 
     
    1075610756redefined or added by users (See SansView tutorial for details). </p> 
    1075710757 
    10758 <p class="MsoListParagraph" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">4.1.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span></b><a name="testmodel"><b><span style="font-size: 14pt;">testmodel</span></b></a></p> 
    10759 <p class="MsoListParagraph" style="margin-left: 0.55in;"><b><span style="font-size: 14pt;">&nbsp;</span></b></p> 
     10758<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">4.1.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span></b><a name="testmodel"><b><span style="font-size: 14pt;">testmodel</span></b></a></p> 
     10759<p style="margin-left: 0.55in;"><b><span style="font-size: 14pt;">&nbsp;</span></b></p> 
    1076010760<p >This function, as an example of a 
    1076110761user defined function, calculates 
     
    1076310763 
    1076410764 
    10765 <p class="MsoListParagraph" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">4.2.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span></b><a name="testmodel_2"><b><span style="font-size: 14pt;">testmodel_2 
     10765<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">4.2.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span></b><a name="testmodel_2"><b><span style="font-size: 14pt;">testmodel_2 
    1076610766</span></b></a></p> 
    1076710767 
     
    1077310773 
    1077410774 
    10775 <p class="MsoListParagraph" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">4.3.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     10775<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">4.3.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    1077610776</span></b><a name="sum_p1_p2"><b><span style="font-size: 14pt;">sum_p1_p2 
    1077710777</span></b></a></p> 
     
    1078810788 
    1078910789 
    10790 <p class="MsoListParagraph" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">4.4.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span></b><a name="sum_Ap1_1_Ap2"><b><span style="font-size: 14pt;">sum_Ap1_1_Ap2 
     10790<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">4.4.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span></b><a name="sum_Ap1_1_Ap2"><b><span style="font-size: 14pt;">sum_Ap1_1_Ap2 
    1079110791</span></b></a></p> 
    1079210792 
     
    1080110801 
    1080210802 
    10803 <p class="MsoListParagraph" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">4.5.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     10803<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">4.5.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    1080410804</span></b><a name="polynomial5"><b><span style="font-size: 14pt;">polynomial5 
    1080510805</span></b></a></p> 
     
    1081410814 
    1081510815 
    10816 <p class="MsoListParagraph" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">4.6.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span></b><a name="sph_bessel_jn"><b><span style="font-size: 14pt;">sph_bessel_jn 
     10816<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">4.6.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span></b><a name="sph_bessel_jn"><b><span style="font-size: 14pt;">sph_bessel_jn 
    1081710817</span></b></a></p> 
    1081810818 
     
    1082510825</p> 
    1082610826 
    10827 <p class="MsoListParagraph" style="margin-left: 0.25in; text-indent: -0.25in;"><b><span style="font-size: 16pt;">5.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp; 
     10827<p style="margin-left: 0.25in; text-indent: -0.25in;"><b><span style="font-size: 16pt;">5.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp; 
    1082810828</span></b><a name="Structure_Factors"><b><span style="font-size: 16pt;">Structure 
    1082910829Factors</span></b></a></p> 
    10830 <p class="MsoListParagraph" style="margin-left: 0.25in;">&nbsp;</p> 
    10831 <p class="MsoListParagraph" style="margin-left: 0.25in;">The 
     10830<p style="margin-left: 0.25in;">&nbsp;</p> 
     10831<p style="margin-left: 0.25in;">The 
    1083210832information in this 
    1083310833section is originated from NIST SANS IgorPro package.</p> 
    1083410834 
    1083510835 
    10836 <p class="MsoListParagraph" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">5.1.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     10836<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">5.1.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    1083710837</span></b><a name="HardsphereStructure"><b><span style="font-size: 14pt;">HardSphere 
    1083810838Structure </span></b></a></p> 
     
    1092110921 
    1092210922 
    10923 <p class="MsoListParagraph" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">5.2.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     10923<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">5.2.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    1092410924</span></b><a name="SquareWellStructure"><b><span style="font-size: 14pt;">&nbsp;SquareWell 
    1092510925Structure </span></b></a></p> 
     
    1103511035<p  style="margin-left: 0.5in;">&nbsp;</p> 
    1103611036 
    11037 <p class="MsoListParagraph" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">5.3.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     11037<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">5.3.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    1103811038</span></b><a name="HayterMSAStructure"><b><span style="font-size: 14pt;">&nbsp;HayterMSA 
    1103911039Structure </span></b></a></p> 
     
    1116811168 
    1116911169 
    11170 <p class="MsoListParagraph" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">5.4.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     11170<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">5.4.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    1117111171</span></b><a name="StickyHSStructure"><b><span style="font-size: 14pt;">&nbsp;StickyHS Structure </span></b></a></p> 
    1117211172 
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