Changeset a110e37f in sasview for src


Ignore:
Timestamp:
Apr 27, 2014 1:12:49 PM (11 years ago)
Author:
Peter Parker
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:
9611dd6
Parents:
3600c12
Message:

Add documentation for Miguel and Richard's new models.

Location:
src/sans/models/media
Files:
13 added
1 edited

Legend:

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

    ra857c0a ra110e37f  
    88<li><a href="#Introduction"><b>Introduction</b></a></li> 
    99<li><a href="#Shapes"><b>Shapes</b></a>:  
    10         <ul> 
    11         <li>Sphere based:<br/> 
    12         <a href="#SphereModel">SphereModel (Magnetic 2D Model)</a>,  
    13         <a href="#BinaryHSModel">BinaryHSModel</a>,  
    14         <a href="#FuzzySphereModel">FuzzySphereModel</a>,  
    15         <a href="#RaspBerryModel">RaspBerryModel</a>,  
    16         <a href="#CoreShellModel">CoreShellModel (Magnetic 2D Model)</a>, 
    17         <a href="#Core2ndMomentModel">Core2ndMomentModel</a>,  
    18         <a href="#CoreMultiShellModel">CoreMultiShellModel (Magnetic 2D Model)</a>,  
    19         <a href="#VesicleModel">VesicleModel</a>,  
    20         <a href="#MultiShellModel">MultiShellModel</a>,  
    21         <a href="#OnionExpShellModel">OnionExpShellModel</a>,  
    22         <a href="#SphericalSLDModel">SphericalSLDModel</a>,  
    23         <a href="#LinearPearlsModel">LinearPearlsModel</a>,  
    24         <a href="#PearlNecklaceModel">PearlNecklaceModel</a> 
    25         </li> 
    26         <li>Cylinder based:<br/> 
    27         <a href="#CylinderModel">CylinderModel (Magnetic 2D Model)</a>,  
    28         <a href="#CoreShellCylinderModel">CoreShellCylinderModel</a>,  
    29         <a href="#CoreShellBicelleModel">CoreShellBicelleModel</a>, 
    30         <a href="#HollowCylinderModel">HollowCylinderModel</a>, 
    31         <a href="#FlexibleCylinderModel">FlexibleCylinderModel</a>, 
    32         <a href="#FlexibleCylinderModel">FlexCylEllipXModel</a>, 
    33         <a href="#StackedDisksModel">StackedDisksModel</a>, 
    34         <a href="#EllipticalCylinderModel">EllipticalCylinderModel</a>,  
    35         <a href="#BarBellModel">BarBellModel</a>,  
    36         <a href="#CappedCylinderModel">CappedCylinderModel</a>, 
    37         <a href="#PringleModel">PringleModel</a>  
    38         </li> 
    39         <li>Parallelpipeds:<br/> 
    40         <a href="#ParallelepipedModel">ParallelepipedModel (Magnetic 2D Model)</a>, 
    41         <a href="#CSParallelepipedModel">CSParallelepipedModel</a> 
    42         </li> 
    43         <li>Ellipsoids:<br/> 
    44         <a href="#EllipsoidModel">EllipsoidModel</a>,  
    45         <a href="#CoreShellEllipsoidModel">CoreShellEllipsoidModel</a>,  
    46         <a href="#TriaxialEllipsoidModel">TriaxialEllipsoidModel</a> 
    47         </li> 
    48         <li>Lamellar:<br/>  
    49         <a href="#LamellarModel">LamellarModel</a>,  
    50         <a href="#LamellarFFHGModel">LamellarFFHGModel</a>,  
    51         <a href="#LamellarPSModel">LamellarPSModel</a>,  
    52         <a href="#LamellarPSHGModel">LamellarPSHGModel</a> 
    53         </li> 
    54         <li>Paracrystals:<br/> 
    55         <a href="#LamellarPCrystalModel">LamellarPCrystalModel</a>,  
    56         <a href="#SCCrystalModel">SCCrystalModel</a>,  
    57         <a href="#FCCrystalModel">FCCrystalModel</a>,  
    58         <a href="#BCCrystalModel">BCCrystalModel</a> 
    59         </li> 
    60         </ul> 
     10    <ul> 
     11    <li>Sphere based:<br/> 
     12    <a href="#SphereModel">SphereModel (Magnetic 2D Model)</a>,  
     13    <a href="#BinaryHSModel">BinaryHSModel</a>,  
     14    <a href="#FuzzySphereModel">FuzzySphereModel</a>,  
     15    <a href="#RaspBerryModel">RaspBerryModel</a>,  
     16    <a href="#CoreShellModel">CoreShellModel (Magnetic 2D Model)</a>, 
     17    <a href="#Core2ndMomentModel">Core2ndMomentModel</a>,  
     18    <a href="#CoreMultiShellModel">CoreMultiShellModel (Magnetic 2D Model)</a>,  
     19    <a href="#VesicleModel">VesicleModel</a>,  
     20    <a href="#MultiShellModel">MultiShellModel</a>,  
     21    <a href="#OnionExpShellModel">OnionExpShellModel</a>,  
     22    <a href="#SphericalSLDModel">SphericalSLDModel</a>,  
     23    <a href="#LinearPearlsModel">LinearPearlsModel</a>,  
     24    <a href="#PearlNecklaceModel">PearlNecklaceModel</a> 
     25    </li> 
     26    <li>Cylinder based:<br/> 
     27    <a href="#CylinderModel">CylinderModel (Magnetic 2D Model)</a>,  
     28    <a href="#CoreShellCylinderModel">CoreShellCylinderModel</a>,  
     29    <a href="#CoreShellBicelleModel">CoreShellBicelleModel</a>, 
     30    <a href="#HollowCylinderModel">HollowCylinderModel</a>, 
     31    <a href="#FlexibleCylinderModel">FlexibleCylinderModel</a>, 
     32    <a href="#FlexibleCylinderModel">FlexCylEllipXModel</a>, 
     33    <a href="#StackedDisksModel">StackedDisksModel</a>, 
     34    <a href="#EllipticalCylinderModel">EllipticalCylinderModel</a>,  
     35    <a href="#BarBellModel">BarBellModel</a>,  
     36    <a href="#CappedCylinderModel">CappedCylinderModel</a>, 
     37    <a href="#PringleModel">PringleModel</a>  
     38    </li> 
     39    <li>Parallelpipeds:<br/> 
     40    <a href="#ParallelepipedModel">ParallelepipedModel (Magnetic 2D Model)</a>, 
     41    <a href="#CSParallelepipedModel">CSParallelepipedModel</a>, 
     42    <a href="#RectangularHollowPrismInfThinWallsModel">RectangularHollowPrismInfThinWallsModel</a>, 
     43    <a href="#RectangularPrismModel">RectangularPrismModel</a>, 
     44    <a href="#RectangularHollowPrismModel">RectangularHollowPrismModel</a> 
     45    </li> 
     46    <li>Ellipsoids:<br/> 
     47    <a href="#EllipsoidModel">EllipsoidModel</a>,  
     48    <a href="#CoreShellEllipsoidModel">CoreShellEllipsoidModel</a>,  
     49    <a href="#CoreShellEllipsoidXTModel">CoreShellEllipsoidXTModel</a>,  
     50    <a href="#TriaxialEllipsoidModel">TriaxialEllipsoidModel</a> 
     51    </li> 
     52    <li>Lamellar:<br/>  
     53    <a href="#LamellarModel">LamellarModel</a>,  
     54    <a href="#LamellarFFHGModel">LamellarFFHGModel</a>,  
     55    <a href="#LamellarPSModel">LamellarPSModel</a>,  
     56    <a href="#LamellarPSHGModel">LamellarPSHGModel</a> 
     57    </li> 
     58    <li>Paracrystals:<br/> 
     59    <a href="#LamellarPCrystalModel">LamellarPCrystalModel</a>,  
     60    <a href="#SCCrystalModel">SCCrystalModel</a>,  
     61    <a href="#FCCrystalModel">FCCrystalModel</a>,  
     62    <a href="#BCCrystalModel">BCCrystalModel</a> 
     63    </li> 
     64    </ul> 
    6165<li><a href="#Shape-Independent"><b>Shape-Independent</b></a>:  
    62         <a href="#Absolute%20Power_Law">AbsolutePower_Law</a>,  
    63         <a href="#BEPolyelectrolyte">BEPolyelectrolyte</a>,  
    64         <a href="#BroadPeakModel">BroadPeakModel</a>, 
    65         <a href="#CorrLength">CorrLength</a>,  
    66         <a href="#DABModel">DABModel</a>,  
    67         <a href="#Debye">Debye</a>,  
    68         <a href="#Number_Density_Fractal">FractalModel</a>,  
    69         <a href="#FractalCoreShell">FractalCoreShell</a>,  
    70         <a href="#GaussLorentzGel">GaussLorentzGel</a>,  
    71         <a href="#Guinier">Guinier</a>,  
    72         <a href="#GuinierPorod">GuinierPorod</a>,  
    73         <a href="#Lorentz">Lorentz</a>,  
    74         <a href="#Mass_Fractal">MassFractalModel</a>,  
    75         <a href="#MassSurface_Fractal">MassSurfaceFractal</a>,  
    76         <a href="#Peak%20Gauss%20Model">PeakGaussModel</a>,  
    77         <a href="#Peak%20Lorentz%20Model">PeakLorentzModel</a>,  
    78         <a href="#Poly_GaussCoil">Poly_GaussCoil</a>,  
    79         <a href="#PolymerExclVolume">PolyExclVolume</a>,  
    80         <a href="#PorodModel">PorodModel</a>,  
    81         <a href="#RPA10Model">RPA10Model</a>,  
    82         <a href="#StarPolymer">StarPolymer</a>,  
    83         <a href="#Surface_Fractal">SurfaceFractalModel</a>,  
    84         <a href="#TeubnerStreyModel">Teubner Strey</a>,  
    85         <a href="#TwoLorentzian">TwoLorentzian</a>,  
    86         <a href="#TwoPowerLaw">TwoPowerLaw</a>,  
    87         <a href="#UnifiedPowerRg">UnifiedPowerRg</a>,  
    88         <a href="#LineModel">LineModel</a>,  
    89         <a href="#ReflectivityModel">ReflectivityModel</a>,  
    90         <a href="#ReflectivityIIModel">ReflectivityIIModel</a>,  
    91         <a href="#GelFitModel">GelFitModel</a>.</li> 
    92          
     66    <a href="#Absolute%20Power_Law">AbsolutePower_Law</a>,  
     67    <a href="#BEPolyelectrolyte">BEPolyelectrolyte</a>,  
     68    <a href="#BroadPeakModel">BroadPeakModel</a>, 
     69    <a href="#CorrLength">CorrLength</a>,  
     70    <a href="#DABModel">DABModel</a>,  
     71    <a href="#Debye">Debye</a>,  
     72    <a href="#Number_Density_Fractal">FractalModel</a>,  
     73    <a href="#FractalCoreShell">FractalCoreShell</a>,  
     74    <a href="#GaussLorentzGel">GaussLorentzGel</a>,  
     75    <a href="#Guinier">Guinier</a>,  
     76    <a href="#GuinierPorod">GuinierPorod</a>,  
     77    <a href="#Lorentz">Lorentz</a>,  
     78    <a href="#Mass_Fractal">MassFractalModel</a>,  
     79    <a href="#MassSurface_Fractal">MassSurfaceFractal</a>,  
     80    <a href="#Peak%20Gauss%20Model">PeakGaussModel</a>,  
     81    <a href="#Peak%20Lorentz%20Model">PeakLorentzModel</a>,  
     82    <a href="#Poly_GaussCoil">Poly_GaussCoil</a>,  
     83    <a href="#PolymerExclVolume">PolyExclVolume</a>,  
     84    <a href="#PorodModel">PorodModel</a>,  
     85    <a href="#RPA10Model">RPA10Model</a>,  
     86    <a href="#StarPolymer">StarPolymer</a>,  
     87    <a href="#Surface_Fractal">SurfaceFractalModel</a>,  
     88    <a href="#TeubnerStreyModel">Teubner Strey</a>,  
     89    <a href="#TwoLorentzian">TwoLorentzian</a>,  
     90    <a href="#TwoPowerLaw">TwoPowerLaw</a>,  
     91    <a href="#UnifiedPowerRg">UnifiedPowerRg</a>,  
     92    <a href="#LineModel">LineModel</a>,  
     93    <a href="#ReflectivityModel">ReflectivityModel</a>,  
     94    <a href="#ReflectivityIIModel">ReflectivityIIModel</a>,  
     95    <a href="#GelFitModel">GelFitModel</a>.</li> 
     96     
    9397<li><a href="#Model"><b>Customized Models</b></a>:  
    94         <a href="#testmodel">testmodel</a>,  
    95         <a href="#testmodel_2">testmodel_2</a>,  
    96         <a href="#sum_p1_p2">sum_p1_p2</a>,  
    97         <a href="#sum_Ap1_1_Ap2">sum_Ap1_1_Ap2</a>,  
    98         <a href="#polynomial5">polynomial5</a>,  
    99         <a href="#sph_bessel_jn">sph_bessel_jn</a>.</li> 
    100          
     98    <a href="#testmodel">testmodel</a>,  
     99    <a href="#testmodel_2">testmodel_2</a>,  
     100    <a href="#sum_p1_p2">sum_p1_p2</a>,  
     101    <a href="#sum_Ap1_1_Ap2">sum_Ap1_1_Ap2</a>,  
     102    <a href="#polynomial5">polynomial5</a>,  
     103    <a href="#sph_bessel_jn">sph_bessel_jn</a>.</li> 
     104     
    101105<li><a href="#Structure_Factors"><b>Structure Factors</b></a>:  
    102         <a href="#HardsphereStructure">HardSphereStructure</a>,  
    103         <a href="#SquareWellStructure">SquareWellStructure</a>,  
    104         <a href="#HayterMSAStructure">HayterMSAStructure</a>,  
    105         <a href="#StickyHSStructure">StickyHSStructure</a>.</li> 
    106          
     106    <a href="#HardsphereStructure">HardSphereStructure</a>,  
     107    <a href="#SquareWellStructure">SquareWellStructure</a>,  
     108    <a href="#HayterMSAStructure">HayterMSAStructure</a>,  
     109    <a href="#StickyHSStructure">StickyHSStructure</a>.</li> 
     110     
    107111<li><a href="#References"><b>References</b></a></li> 
    108112</ul> 
     
    35753579 
    35763580 
    3577  
    3578 <p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.27.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="EllipsoidModel"></a><b><span style="font-size: 14pt;">Ellipsoid Model</span></b></p> 
     3581<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.27.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b><span style="font-size: 14pt;"><a name="RectangularHollowPrismInfThinWallsModel"></a>RectangularHollowPrismInfThinWallsModel</span></b></p> 
     3582 
     3583<p>This model provides the form factor, P( <em>q</em>), for a hollow rectangular prism 
     3584with infinitely thin walls.</p> 
     3585<p><em>Definition</em></p> 
     3586<p>The 1D scattering intensity for this model is calculated according to the equations given by 
     3587Nayuk and Huber (Nayuk, 2012).</p> 
     3588<p>Assuming a hollow parallelepiped with infinitely thin walls, edge lengths <span class="formula"><i>A</i>†
     3589≀†
     3590<i>B</i>†
     3591≀†
     3592<i>C</i></span> 
     3593 
     3594and presenting an orientation with respect to the scattering vector given by Ξ and φ, 
     3595where Ξ is the angle between the <em>z</em> axis and the longest axis of the parallelepiped <em>C</em>, and φ 
     3596is the angle between the scattering vector (lying in the <em>xy</em> plane) and the <em>y</em> axis, 
     3597the form factor is given by:</p> 
     3598 
     3599<p style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="img/RectangularHollowPrismInfThinWalls_1.png" alt="" /></span></p> 
     3600 
     3601<p>where</p> 
     3602 
     3603<p style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="img/RectangularHollowPrismInfThinWalls_2.png" alt="" /></span></p> 
     3604 
     3605<p style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="img/RectangularHollowPrismInfThinWalls_3.png" alt="" /></span></p> 
     3606 
     3607<p style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="img/RectangularHollowPrismInfThinWalls_4.png" alt="" /></span></p> 
     3608 
     3609<p>and</p> 
     3610 
     3611<p style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="img/RectangularHollowPrismInfThinWalls_5.png" alt="" /></span></p> 
     3612 
     3613<p>The 1D scattering intensity is calculated as:</p> 
     3614 
     3615<p style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="img/RectangularHollowPrismInfThinWalls_6.png" alt="" /></span></p> 
     3616 
     3617<p>where <em>V</em> is the volume of the rectangular prism, <span class="formula"><i>ρ</i><sub><span class="mbox">pipe</span></sub></span> 
     3618 is the scattering length of the 
     3619parallelepiped, <span class="formula"><i>ρ</i><sub><span class="mbox">solvent</span></sub></span> 
     3620 is the scattering length of the solvent, and 
     3621(if the data are in absolute scale) scale represents the volume fraction (which is unitless) .</p> 
     3622<p>The 2D scattering intensity is not computed by this model.</p> 
     3623<p>The returned value is scaled to units of cm<sup>-1</sup> and the parameters of the RectangularHollowPrismInfThinWallModel 
     3624are the following:</p> 
     3625<table border="1" class="docutils"> 
     3626<colgroup> 
     3627<col width="40%" /> 
     3628<col width="23%" /> 
     3629<col width="37%" /> 
     3630</colgroup> 
     3631<thead valign="bottom"> 
     3632<tr><th class="head">Parameter name</th> 
     3633<th class="head">Units</th> 
     3634<th class="head">Default value</th> 
     3635</tr> 
     3636</thead> 
     3637<tbody valign="top"> 
     3638<tr><td>scale</td> 
     3639<td>None</td> 
     3640<td>1</td> 
     3641</tr> 
     3642<tr><td>short_side</td> 
     3643<td>Å</td> 
     3644<td>35</td> 
     3645</tr> 
     3646<tr><td>b2a_ratio</td> 
     3647<td>None</td> 
     3648<td>1</td> 
     3649</tr> 
     3650<tr><td>c2a_ratio</td> 
     3651<td>None</td> 
     3652<td>1</td> 
     3653</tr> 
     3654<tr><td>sldPipe</td> 
     3655<td>Å<sup>-2</sup></td> 
     3656<td>6.3e-6</td> 
     3657</tr> 
     3658<tr><td>sldSolv</td> 
     3659<td>Å<sup>-2</sup></td> 
     3660<td>1.0e-6</td> 
     3661</tr> 
     3662<tr><td>background</td> 
     3663<td>cm<sup>-1</sup></td> 
     3664<td>0</td> 
     3665</tr> 
     3666</tbody> 
     3667</table> 
     3668<p>REFERENCES</p> 
     3669<ol class="upperalpha simple" start="18"> 
     3670<li>Nayuk and K. Huber, <em>Z. Phys. Chem.</em> 226 (2012) 837-854.</li> 
     3671</ol> 
     3672<p><em>Validation of the RectangularHollowPrismInfThinWallsModel</em></p> 
     3673<p>Validation of the code was done qualitatively by comparing the output of the 1D model to the curves 
     3674shown in (Nayuk, 2012).</p> 
     3675 
     3676 
     3677 
     3678 
     3679 
     3680 
     3681 
     3682 
     3683 
     3684 
     3685 
     3686 
     3687<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.28.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b><span style="font-size: 14pt;"><a name="RectangularPrismModel"></a>RectangularPrismModel</span></b></p> 
     3688<p>This model provides the form factor, P( <em>q</em>), for a rectangular prism.</p> 
     3689<p>Note that this model is almost totally equivalent to the existing 
     3690ParallelepipedModel. The only difference is that the way the 
     3691relevant parameters are defined here (<em>a</em>, <em>b/a</em>, <em>c/a</em> instead of <em>a</em>, <em>b</em>, <em>c</em>) 
     3692allows to use polydispersity with this model while keeping the shape 
     3693of the prism (e.g. setting <em>b/a</em> = 1 and <em>c/a</em> = 1 and applying polydispersity 
     3694to <em>a</em> will generate a distribution of cubes of different sizes).</p> 
     3695<p><em>Definition</em></p> 
     3696<p>The 1D scattering intensity for this model was calculated by Mittelbach and Porod (Mittelbach, 1961), 
     3697but the implementation here is closer to the equations given by Nayuk and Huber (Nayuk, 2012).</p> 
     3698<p>The scattering from a massive parallelepiped with an orientation with respect to the scattering vector 
     3699given by Ξ and φ is given by:</p> 
     3700 
     3701<p style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="img/RectangularPrism_1.png" alt="" /></span></p> 
     3702 
     3703<p>where <em>A</em>, <em>B</em> and <em>C</em> are the sides of the parallelepiped and must fulfill <span class="formula"><i>A</i>†
     3704≀†
     3705<i>B</i>†
     3706≀†
     3707<i>C</i></span> 
     3708, 
     3709Ξ is the angle between the <em>z</em> axis and the longest axis of the parallelepiped <em>C</em>, and φ 
     3710is the angle between the scattering vector (lying in the <em>xy</em> plane) and the <em>y</em> axis.</p> 
     3711<p>The normalized form factor in 1D is obtained averaging over all possible orientations:</p> 
     3712 
     3713<p style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="img/RectangularPrism_2.png" alt="" /></span></p> 
     3714 
     3715<p>The 1D scattering intensity is calculated as:</p> 
     3716 
     3717<p style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="img/RectangularPrism_3.png" alt="" /></span></p> 
     3718 
     3719<p>where <em>V</em> is the volume of the rectangular prism, <span class="formula"><i>ρ</i><sub><span class="mbox">pipe</span></sub></span> 
     3720 is the scattering length of the 
     3721parallelepiped, <span class="formula"><i>ρ</i><sub><span class="mbox">solvent</span></sub></span> 
     3722 is the scattering length of the solvent, and 
     3723(if the data are in absolute scale) scale represents the volume fraction (which is unitless) .</p> 
     3724<p>The 2D scattering intensity is not computed by this model.</p> 
     3725<p>The returned value is scaled to units of cm<sup>-1</sup> and the parameters of the RectangularPrismModel are the following:</p> 
     3726<table border="1" class="docutils"> 
     3727<colgroup> 
     3728<col width="40%" /> 
     3729<col width="23%" /> 
     3730<col width="37%" /> 
     3731</colgroup> 
     3732<thead valign="bottom"> 
     3733<tr><th class="head">Parameter name</th> 
     3734<th class="head">Units</th> 
     3735<th class="head">Default value</th> 
     3736</tr> 
     3737</thead> 
     3738<tbody valign="top"> 
     3739<tr><td>scale</td> 
     3740<td>None</td> 
     3741<td>1</td> 
     3742</tr> 
     3743<tr><td>short_side</td> 
     3744<td>Å</td> 
     3745<td>35</td> 
     3746</tr> 
     3747<tr><td>b2a_ratio</td> 
     3748<td>None</td> 
     3749<td>1</td> 
     3750</tr> 
     3751<tr><td>c2a_ratio</td> 
     3752<td>None</td> 
     3753<td>1</td> 
     3754</tr> 
     3755<tr><td>sldPipe</td> 
     3756<td>Å<sup>-2</sup></td> 
     3757<td>6.3e-6</td> 
     3758</tr> 
     3759<tr><td>sldSolv</td> 
     3760<td>Å<sup>-2</sup></td> 
     3761<td>1.0e-6</td> 
     3762</tr> 
     3763<tr><td>background</td> 
     3764<td>cm<sup>-1</sup></td> 
     3765<td>0</td> 
     3766</tr> 
     3767</tbody> 
     3768</table> 
     3769<p>REFERENCES</p> 
     3770<ol class="upperalpha simple" start="16"> 
     3771<li>Mittelbach and G. Porod, <em>Acta Physica Austriaca</em> 14 (1961) 185-211.</li> 
     3772</ol> 
     3773<ol class="upperalpha simple" start="18"> 
     3774<li>Nayuk and K. Huber, <em>Z. Phys. Chem.</em> 226 (2012) 837-854.</li> 
     3775</ol> 
     3776<p><em>Validation of the RectangularPrismModel</em></p> 
     3777<p>Validation of the code was done by comparing the output of the 1D model to the output of the existing 
     3778parallelepiped model.</p> 
     3779 
     3780 
     3781 
     3782 
     3783 
     3784 
     3785 
     3786 
     3787 
     3788 
     3789<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.29.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><b><span style="font-size: 14pt;"><a name="RectangularHollowPrismModel"></a>RectangularHollowPrismModel</span></b></p> 
     3790<p>This model provides the form factor, P( <em>q</em>), for a hollow rectangular parallelepiped 
     3791with a wall thickness Δ.</p> 
     3792<p><em>Definition</em></p> 
     3793<p>The 1D scattering intensity for this model is calculated by forming the difference of the 
     3794amplitudes of two massive parallelepipeds differing in their outermost dimensions in 
     3795each direction by the same length increment 2 Δ (Nayuk, 2012).</p> 
     3796<p>As in the case of the massive parallelepiped, the scattering amplitude is computed for a particular 
     3797orientation of the parallelepiped with respect to the scattering vector and then averaged over all 
     3798possible orientations, giving:</p> 
     3799 
     3800<p style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="img/RectangularHollowPrism_1.png" alt="" /></span></p> 
     3801 
     3802<p>where Ξ is the angle between the <em>z</em> axis and the longest axis of the parallelepiped, φ 
     3803is the angle between the scattering vector (lying in the <em>xy</em> plane) and the <em>y</em> axis, and:</p> 
     3804 
     3805<p style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="img/RectangularHollowPrism_2.png" alt="" /></span></p> 
     3806 
     3807<p>where <em>A</em>, <em>B</em> and <em>C</em> are the external sides of the parallelepiped fulfilling <span class="formula"><i>A</i>†
     3808≀†
     3809<i>B</i>†
     3810≀†
     3811<i>C</i></span> 
     3812, 
     3813and the volume <em>V</em> of the parallelepiped is:</p> 
     3814 
     3815<p style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="img/RectangularHollowPrism_3.png" alt="" /></span></p> 
     3816 
     3817<p>The 1D scattering intensity is calculated as:</p> 
     3818 
     3819<p style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="img/RectangularHollowPrism_4.png" alt="" /></span></p> 
     3820 
     3821<p>where <span class="formula"><i>ρ</i><sub><span class="mbox">pipe</span></sub></span> 
     3822 is the scattering length of the 
     3823parallelepiped, <span class="formula"><i>ρ</i><sub><span class="mbox">solvent</span></sub></span> 
     3824 is the scattering length of the solvent, and 
     3825(if the data are in absolute scale) scale represents the volume fraction (which is unitless) .</p> 
     3826<p>The 2D scattering intensity is not computed by this model.</p> 
     3827<p>The returned value is scaled to units of cm<sup>-1</sup> and the parameters of the RectangularHollowPrismModel 
     3828are the following:</p> 
     3829<table border="1" class="docutils"> 
     3830<colgroup> 
     3831<col width="40%" /> 
     3832<col width="23%" /> 
     3833<col width="37%" /> 
     3834</colgroup> 
     3835<thead valign="bottom"> 
     3836<tr><th class="head">Parameter name</th> 
     3837<th class="head">Units</th> 
     3838<th class="head">Default value</th> 
     3839</tr> 
     3840</thead> 
     3841<tbody valign="top"> 
     3842<tr><td>scale</td> 
     3843<td>None</td> 
     3844<td>1</td> 
     3845</tr> 
     3846<tr><td>short_side</td> 
     3847<td>Å</td> 
     3848<td>35</td> 
     3849</tr> 
     3850<tr><td>b2a_ratio</td> 
     3851<td>None</td> 
     3852<td>1</td> 
     3853</tr> 
     3854<tr><td>c2a_ratio</td> 
     3855<td>None</td> 
     3856<td>1</td> 
     3857</tr> 
     3858<tr><td>thickness</td> 
     3859<td>Å</td> 
     3860<td>1</td> 
     3861</tr> 
     3862<tr><td>sldPipe</td> 
     3863<td>Å<sup>-2</sup></td> 
     3864<td>6.3e-6</td> 
     3865</tr> 
     3866<tr><td>sldSolv</td> 
     3867<td>Å<sup>-2</sup></td> 
     3868<td>1.0e-6</td> 
     3869</tr> 
     3870<tr><td>background</td> 
     3871<td>cm<sup>-1</sup></td> 
     3872<td>0</td> 
     3873</tr> 
     3874</tbody> 
     3875</table> 
     3876<p>REFERENCES</p> 
     3877<ol class="upperalpha simple" start="18"> 
     3878<li>Nayuk and K. Huber, <em>Z. Phys. Chem.</em> 226 (2012) 837-854.</li> 
     3879</ol> 
     3880<p><em>Validation of the RectangularHollowPrismModel</em></p> 
     3881<p>Validation of the code was done qualitatively by comparing the output of the 1D model to the curves 
     3882shown in (Nayuk, 2012).</p> 
     3883 
     3884 
     3885 
     3886 
     3887 
     3888 
     3889 
     3890 
     3891 
     3892 
     3893 
     3894 
     3895 
     3896 
     3897 
     3898 
     3899 
     3900 
     3901<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.30.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="EllipsoidModel"></a><b><span style="font-size: 14pt;">Ellipsoid Model</span></b></p> 
    35793902<p>This model provides the form factor for an ellipsoid (ellipsoid of revolution) with uniform scattering length density. The form factor is normalized by the particle volume.</p> 
    35803903<p style="margin-left: 0.85in; text-indent: -0.35in;"><b>1.1.</b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp; </span>Definition</b></p> 
     
    37104033<p><a name="_Ref173223004"></a>Figure 6: Comparison of the intensity for uniformly distributed ellipsoids calculated from our 2D model and the intensity from the NIST SANS analysis software. The parameters used were: Scale=1.0, Radius_a=20 &Aring;, Radius_b=400 &Aring;, Contrast=3e-6 &Aring; -2, and Background=0.0 cm -1.</p> 
    37114034<p>&nbsp;</p> 
    3712 <p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.28.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="CoreShellEllipsoidModel"></a><b><span style="font-size: 14pt;">CoreShellEllipsoidModel </span></b></p> 
     4035<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.31.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="CoreShellEllipsoidModel"></a><b><span style="font-size: 14pt;">CoreShellEllipsoidModel </span></b></p> 
    37134036<p>This model provides the form factor, P(<em>q</em>), for a core shell ellipsoid (below) where the form factor is normalized by the volume of the cylinder. P(q) = scale*&lt;f^2&gt;/V+background where the volume V= 4pi/3*rmaj*rmin2 and the averaging &lt; &gt;&nbsp; is applied over all orientation for 1D. &nbsp;</p> 
    37144037<p style="text-align: center;" align="center">&nbsp;&nbsp;<img id="Picture 41" src="img/image125.gif" alt="" width="335" height="179" /></p> 
     
    38494172 
    38504173 
    3851 <p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.29.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="TriaxialEllipsoidModel"></a><b><span style="font-size: 14pt;">TriaxialEllipsoidModel</span></b></p> 
     4174 
     4175 
     4176 
     4177 
     4178 
     4179 
     4180<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.32.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="CoreShellEllipsoidXTModel"></a><b><span style="font-size: 14pt;">CoreShellEllipsoidXTModel </span></b></p> 
     4181 
     4182<p>An alternative version of P( *q*) for the core plus shell ellipsoid (see  
     4183CoreShellEllipsoidModel), having as  
     4184parameters the core axial ratio X and a shell thickness, which are more often  
     4185what we would like to determine and behave better when polydispersity is  
     4186applied than the four independent radii in the original model.</p> 
     4187 
     4188<p>The geometric parameters are: equat_core = equatorial core radius = Rminor_core,  
     4189X_core = polar_core/equat_core = Rmajor_core/Rminor_core 
     4190T_shell = equat_outer - equat_core = Rminor_outer - Rminor_core, 
     4191XpolarShell = Tpolar_shell/T_shell = (Rmajor_outer - Rmajor_core)/(Rminor_outer - Rminor_core)</p> 
     4192 
     4193<p>In terms of the original radii: 
     4194polar_core = equat_core * X_core,  equat_shell = equat_core + T_shell 
     4195polar_shell = equat_core * X_core  + T_shell*XpolarShell 
     4196(where we note that "shell" perhaps confusingly, relates to the outer radius).</p> 
     4197 
     4198<p>When X_core &lt; 1 the core is oblate, when X_core &gt; 1  it is prolate,  
     4199X_core =1 is a spherical core. For a fixed shell thickness XpolarShell = 1, to scale the  
     4200shell thickness pro-rata with the radius XpolarShell = X_core.</p> 
     4201 
     4202<p>When including and S(Q), the radius in S(Q) is calculated to be that of a 
     4203 sphere with the same 2nd virial coefficient of the outr surface of the ellipsoid.  
     4204 This may have some undesirable effects if the aspect ratio of the ellipsoid is  
     4205 large ( X&lt;&lt;1 or X&gt;&gt;1), when the S(Q) which assumes spheres wil not in any case be valid.</p> 
     4206  
     4207<p>If SANS data are in absolute units, and sld's are correct, then "scale" should be the total  
     4208volume fraction of the "outer particle". When S(Q) is introduced this moves to the S(Q)  
     4209volume fraction, and "scale" should then be 1.0, or contain some ther units conversion factor  
     4210if you have say Xray data.</p> 
     4211 
     4212 
     4213<div align="center"> 
     4214<table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0"> 
     4215<tbody> 
     4216<tr style="height: 18.8pt;"> 
     4217<td style="border: 1pt solid width: 107pt; height: 18.8pt;" valign="top" width="143"> 
     4218<p>Parameter name</p> 
     4219</td> 
     4220<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143"> 
     4221<p>Units</p> 
     4222</td> 
     4223<td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143"> 
     4224<p>Default value</p> 
     4225</td> 
     4226</tr> 
     4227<tr style="height: 18.8pt;"> 
     4228<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143"> 
     4229<p>background</p> 
     4230</td> 
     4231<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143"> 
     4232<p>cm-1</p> 
     4233</td> 
     4234<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143"> 
     4235<p>0.001</p> 
     4236</td> 
     4237</tr> 
     4238<tr style="height: 18.8pt;"> 
     4239<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143"> 
     4240<p>equat_core</p> 
     4241</td> 
     4242<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143"> 
     4243<p>&Aring;</p> 
     4244</td> 
     4245<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143"> 
     4246<p>20</p> 
     4247</td> 
     4248</tr> 
     4249<tr style="height: 18.8pt;"> 
     4250<td style="border-width: medium 1pt 1pt; vertical-align: top; width: 107pt; height: 18.8pt;"> 
     4251<p>scale</p> 
     4252</td> 
     4253<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143"> 
     4254<p></p> 
     4255</td> 
     4256<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143"> 
     4257<p>0.05</p> 
     4258</td> 
     4259</tr> 
     4260<tr style="height: 18.8pt;"> 
     4261<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143"> 
     4262<p>sld_core</p> 
     4263</td> 
     4264<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143"> 
     4265<p>&Aring; -2</p> 
     4266</td> 
     4267<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143"> 
     4268<p>2.0e-6</p> 
     4269</td> 
     4270</tr> 
     4271<tr style="height: 18.8pt;"> 
     4272<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143"> 
     4273<p>sld_shell</p> 
     4274</td> 
     4275<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143"> 
     4276<p>&Aring; -2</p> 
     4277</td> 
     4278<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143"> 
     4279<p>1.0e-6</p> 
     4280</td> 
     4281</tr> 
     4282<tr style="height: 18.8pt;"> 
     4283<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143"> 
     4284<p>sld_solv</p> 
     4285</td> 
     4286<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143"> 
     4287<p>&Aring; -2</p> 
     4288</td> 
     4289<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143"> 
     4290<p>6.3e-6</p> 
     4291</td> 
     4292</tr> 
     4293<tr style="height: 18.8pt;"> 
     4294<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143"> 
     4295<p>T_shell</p> 
     4296</td> 
     4297<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143"> 
     4298<p>&Aring;</p> 
     4299</td> 
     4300<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143"> 
     4301<p>30</p> 
     4302</td> 
     4303</tr> 
     4304<tr style="height: 18.8pt;"> 
     4305<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143"> 
     4306<p>X_core</p> 
     4307</td> 
     4308<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143"> 
     4309<p></p> 
     4310</td> 
     4311<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143"> 
     4312<p>3.0</p> 
     4313</td> 
     4314</tr> 
     4315<tr style="height: 18.8pt;"> 
     4316<td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143"> 
     4317<p>XpolarShell</p> 
     4318</td> 
     4319<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143"></td> 
     4320<td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143"> 
     4321<p>1.0</p> 
     4322</td> 
     4323</tr> 
     4324</tbody> 
     4325</table> 
     4326</div> 
     4327 
     4328 
     4329 
     4330 
     4331 
     4332 
     4333 
     4334 
     4335 
     4336<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.33.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="TriaxialEllipsoidModel"></a><b><span style="font-size: 14pt;">TriaxialEllipsoidModel</span></b></p> 
    38524337<p>This model provides the form factor, P(<em>q</em>), for an ellipsoid (below) where all three axes are of different lengths, i.e.,&nbsp; Ra =&lt; Rb =&lt; Rc (Note that users should maintains this inequality for the all calculations).&nbsp; P(q) = scale*&lt;f^2&gt;/V+background where the volume V= 4pi/3*Ra*Rb*Rc, and the averaging &lt; &gt;&nbsp; is applied over all orientation for 1D. &nbsp;</p> 
    38534338<p style="text-align: center;" align="center">&nbsp;&nbsp;<img id="Picture 42" src="img/image128.jpg" alt="" width="376" height="226" /></p> 
     
    39704455 
    39714456 
    3972 <p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.30.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="LamellarModel"></a><b><span style="font-size: 14pt;">LamellarModel</span></b></p> 
     4457<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.34.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="LamellarModel"></a><b><span style="font-size: 14pt;">LamellarModel</span></b></p> 
    39734458<p>This model provides the scattering intensity, I(<em>q</em>), for a lyotropic lamellar phase where a uniform SLD and random distribution in solution are assumed. &nbsp;The ploydispersion in the bilayer thickness can be applied from the GUI.</p> 
    39744459<p>The scattering intensity I(q) is:</p> 
     
    40574542<p>Nallet, Laversanne, and Roux, J. Phys. II France, 3, (1993) 487-502.</p> 
    40584543<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; also in J. Phys. Chem. B, 105, (2001) 11081-11088.</p> 
    4059 <p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.31.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="LamellarFFHGModel"></a><b><span style="font-size: 14pt;">LamellarFFHGModel</span></b></p> 
     4544<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.35.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="LamellarFFHGModel"></a><b><span style="font-size: 14pt;">LamellarFFHGModel</span></b></p> 
    40604545<p>This model provides the scattering intensity, I(<em>q</em>), for a lyotropic lamellar phase where a random distribution in solution are assumed. &nbsp;The SLD of the head region is taken to be different from the SLD of the tail region.</p> 
    40614546<p>The scattering intensity I(q) is:</p> 
     
    41664651<p>Nallet, Laversanne, and Roux, J. Phys. II France, 3, (1993) 487-502.</p> 
    41674652<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; also in J. Phys. Chem. B, 105, (2001) 11081-11088.</p> 
    4168 <p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.32.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="LamellarPSModel"></a><b><span style="font-size: 14pt;">LamellarPSModel</span></b></p> 
     4653<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.36.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="LamellarPSModel"></a><b><span style="font-size: 14pt;">LamellarPSModel</span></b></p> 
    41694654<p>This model provides the scattering intensity (<b>form factor</b> <b>*</b> <b>structure factor</b>), I(<em>q</em>), for a lyotropic lamellar phase where a random distribution in solution are assumed.</p> 
    41704655<p>The scattering intensity I(q) is:</p> 
     
    42794764<p>Nallet, Laversanne, and Roux, J. Phys. II France, 3, (1993) 487-502.</p> 
    42804765<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; also in J. Phys. Chem. B, 105, (2001) 11081-11088.</p> 
    4281 <p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.33.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="LamellarPSHGModel"></a><b><span style="font-size: 14pt;">LamellarPSHGModel</span></b></p> 
     4766<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.37.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="LamellarPSHGModel"></a><b><span style="font-size: 14pt;">LamellarPSHGModel</span></b></p> 
    42824767<p>This model provides the scattering intensity (<b>form factor</b> <b>*</b> <b>structure factor</b>), I(<em>q</em>), for a lyotropic lamellar phase where a random distribution in solution are assumed. &nbsp;The SLD of the head region is taken to be different from the SLD of the tail region.</p> 
    42834768<p>The scattering intensity I(q) is:</p> 
     
    44264911<p>Nallet, Laversanne, and Roux, J. Phys. II France, 3, (1993) 487-502.</p> 
    44274912<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; also in J. Phys. Chem. B, 105, (2001) 11081-11088.</p> 
    4428 <p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.34.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="LamellarPCrystalModel"></a><b><span style="font-size: 14pt;">LamellarPCrystalModel</span></b></p> 
     4913<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.38.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="LamellarPCrystalModel"></a><b><span style="font-size: 14pt;">LamellarPCrystalModel</span></b></p> 
    44294914<p>Lamella ParaCrystal Model: Calculates the scattering from a stack of repeating lamellar structures. The stacks of lamellae (infinite in lateral dimension) are treated as a paracrystal to account for the repeating spacing. The repeat distance is further characterized by a Gaussian polydispersity. This model can be used for large multilamellar vesicles.</p> 
    44304915<p>The scattering intensity I(q) is calculated as:</p> 
     
    45425027<p>REFERENCE</p> 
    45435028<p>M. Bergstrom, J. S. Pedersen, P. Schurtenberger, S. U. Egelhaaf, J. Phys. Chem. B, 103 (1999) 9888-9897.</p> 
    4544 <p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.35.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="SCCrystalModel"></a><b><span style="font-size: 14pt;">SC(Simple Cubic Para-)CrystalModel</span></b></p> 
     5029<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.39.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="SCCrystalModel"></a><b><span style="font-size: 14pt;">SC(Simple Cubic Para-)CrystalModel</span></b></p> 
    45455030<p>Calculates the scattering from a simple cubic lattice with paracrystalline distortion. Thermal vibrations are considered to be negligible, and the size of the paracrystal is infinitely large. Paracrystalline distortion is assumed to be isotropic and characterized by a Gaussian distribution.</p> 
    45465031<p>The returned value is scaled to units of [cm-1sr-1], absolute scale.</p> 
     
    46665151<p style="text-align: center;" align="center"><b><img src="img/image157.jpg" alt="" width="447" height="322" /></b></p> 
    46675152<p style="text-align: center;" align="center"><b>Figure. 2D plot using the default values (w/200X200 pixels).</b></p> 
    4668 <p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.36.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="FCCrystalModel"></a><b><span style="font-size: 14pt;">FC(Face Centered Cubic Para-)CrystalModel</span></b></p> 
     5153<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.40.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="FCCrystalModel"></a><b><span style="font-size: 14pt;">FC(Face Centered Cubic Para-)CrystalModel</span></b></p> 
    46695154<p>Calculates the scattering from a face-centered cubic lattice with paracrystalline distortion. Thermal vibrations are considered to be negligible, and the size of the paracrystal is infinitely large. Paracrystalline distortion is assumed to be isotropic and characterized by a Gaussian distribution.&nbsp;</p> 
    46705155<p>The returned value is scaled to units of [cm-1sr-1], absolute scale.</p> 
     
    47915276<p style="text-align: center;" align="center"><img src="img/image166.jpg" alt="" width="473" height="352" /></p> 
    47925277<p style="text-align: center;" align="center"><b>Figure. 2D plot using the default values (w/200X200 pixels).</b></p> 
    4793 <p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.37.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="BCCrystalModel"></a><b><span style="font-size: 14pt;">BC(Body Centered Cubic Para-)CrystalModel</span></b></p> 
     5278<p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.41.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></b><a name="BCCrystalModel"></a><b><span style="font-size: 14pt;">BC(Body Centered Cubic Para-)CrystalModel</span></b></p> 
    47945279<p>Calculates the scattering from a body-centered cubic lattice with paracrystalline distortion. Thermal vibrations are considered to be negligible, and the size of the paracrystal is infinitely large. Paracrystalline distortion is assumed to be isotropic and characterized by a Gaussian distribution.The returned value is scaled to units of [cm-1sr-1], absolute scale.</p> 
    47955280<p>The scattering intensity I(q) is calculated as:</p> 
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