Ignore:
Timestamp:
Feb 27, 2012 6:27:47 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:
996c643
Parents:
015eb2b
Message:

Added coreshellbicelle model

File:
1 edited

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

    r6752950 r543d1bd  
    456456</li> 
    457457<li class="MsoNormal" style="line-height: 115%;"><a href="#Shapes"><b>Shapes</b></a>: <a href="#SphereModel">SphereModel</a>, <a href="#BinaryHSModel">BinaryHSModel</a>, <a href="#FuzzySphereModel">FuzzySphereModel</a>, <a href="#CoreShellModel">CoreShellModel</a>,&nbsp;<a href="#Core2ndMomentModel">Core2ndMomentModel</a>, <a href="#CoreMultiShellModel">CoreMultiShellModel</a>, <a href="#VesicleModel">VesicleModel</a>, <a href="#MultiShellModel">MultiShellModel</a>, &nbsp;<a href="#OnionExpShellModel">OnionExpShellModel</a>, <a href="#SphericalSLDModel">SphericalSLDModel</a>, <a href="#LinearPearlsModel">LinearPearlsModel</a>, <a href="#PearlNecklaceModel">PearlNecklaceModel</a> , <a href="#CylinderModel">CylinderModel</a>, <a href="#CoreShellCylinderModel">CoreShellCylinderModel</a>, 
    458 <a href="#HollowCylinderModel">HollowCylinderModel</a>, 
     458<a href="#CoreShellBicelleModel">CoreShellBicelleModel</a>,<a href="#HollowCylinderModel">HollowCylinderModel</a>, 
    459459<a href="#FlexibleCylinderModel">FlexibleCylinderModel</a>, 
    460460<a href="#FlexibleCylinderModel">FlexCylEllipXModel</a>, 
     
    33403340<p class="MsoNormal">&nbsp;</p> 
    33413341<p class="MsoNormal">&nbsp;</p> 
     3342<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.15.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     3343</span></b><a name="CoreShellBicelleModel"><b><span style="font-size: 14pt;">Core-Shell (Cylinder) Bicelle Model</span></b></a></p> 
     3344<p class="MsoNormal">&nbsp;</p> 
     3345<p class="MsoNormal">This model provides the form factor 
     3346for a circular cylinder 
     3347with a core-shell scattering length density profile. The form factor is 
     3348normalized by the particle volume. This model is a more general case of 
     3349<a href="#CoreShellCylinderModel"> 
     3350core-shell cylinder model </a> (see&nbsp;above and reference below) in 
     3351that the parameters of the shell are separated into a face-shell and 
     3352a rim-shell so that users can set different values of the thicknesses 
     3353and slds.&nbsp;</p> 
     3354<p class="MsoNormal"></p> 
     3355<p class="MsoNormal">The returned value is scaled to units 
     3356of [cm<sup>-1</sup>] 
     3357and the parameters of the core-shell cylinder model are the following:</p> 
     3358<p class="MsoNormal">&nbsp;</p> 
     3359<div align="center"> 
     3360<table class="MsoNormalTable" style="border-collapse: collapse;" border="2" cellpadding="0" cellspacing="0"> 
     3361<tbody> 
     3362<tr style="height: 19.25pt;"> 
     3363<td style="border: 1pt solid windowtext; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
     3364<p class="MsoBodyText">Parameter name</p> 
     3365</td> 
     3366<td style="border-style: solid solid solid none; border-color: windowtext windowtext windowtext -moz-use-text-color; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
     3367<p class="MsoBodyText">Units</p> 
     3368</td> 
     3369<td style="border-style: solid solid solid none; border-color: windowtext windowtext windowtext -moz-use-text-color; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
     3370<p class="MsoBodyText">Default value</p> 
     3371</td> 
     3372</tr> 
     3373<tr style="height: 19.25pt;"> 
     3374<td style="border-style: none solid solid; border-color: -moz-use-text-color windowtext windowtext; border-width: medium 1pt 1pt; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
     3375<p class="MsoBodyText">scale</p> 
     3376</td> 
     3377<td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
     3378<p class="MsoBodyText">None</p> 
     3379</td> 
     3380<td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
     3381<p class="MsoBodyText">1.0</p> 
     3382</td> 
     3383</tr> 
     3384<tr style="height: 19.25pt;"> 
     3385<td style="border-style: none solid solid; border-color: -moz-use-text-color windowtext windowtext; border-width: medium 1pt 1pt; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
     3386<p class="MsoBodyText">radius</p> 
     3387</td> 
     3388<td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
     3389<p class="MsoBodyText">Å</p> 
     3390</td> 
     3391<td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
     3392<p class="MsoBodyText">20.0</p> 
     3393</td> 
     3394</tr> 
     3395<tr style="height: 19.25pt;"> 
     3396<td style="border-style: none solid solid; border-color: -moz-use-text-color windowtext windowtext; border-width: medium 1pt 1pt; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
     3397<p class="MsoBodyText">rim_thick</p> 
     3398</td> 
     3399<td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
     3400<p class="MsoBodyText">Å</p> 
     3401</td> 
     3402<td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
     3403<p class="MsoBodyText">10.0</p> 
     3404</td> 
     3405</tr> 
     3406<tr> 
     3407<td>face_thick</td> 
     3408<td>Å</td> 
     3409<td>10.0</td> 
     3410</tr> 
     3411<tr style="height: 19.25pt;"> 
     3412<td style="border-style: none solid solid; border-color: -moz-use-text-color windowtext windowtext; border-width: medium 1pt 1pt; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
     3413<p class="MsoBodyText">length</p> 
     3414</td> 
     3415<td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
     3416<p class="MsoBodyText">Å</p> 
     3417</td> 
     3418<td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
     3419<p class="MsoBodyText">400.0</p> 
     3420</td> 
     3421</tr> 
     3422<tr style="height: 19.25pt;"> 
     3423<td style="border-style: none solid solid; border-color: -moz-use-text-color windowtext windowtext; border-width: medium 1pt 1pt; padding: 0in 5.4pt; vertical-align: top; width: 107pt; height: 19.25pt;"> 
     3424<p class="MsoBodyText">core_sld</p> 
     3425</td> 
     3426<td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
     3427<p class="MsoBodyText">Å<sup> -2</sup></p> 
     3428</td> 
     3429<td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
     3430<p class="MsoBodyText">1e-6</p> 
     3431</td> 
     3432</tr> 
     3433<tr style="height: 19.25pt;"> 
     3434<td style="border-style: none solid solid; border-color: -moz-use-text-color windowtext windowtext; border-width: medium 1pt 1pt; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
     3435<p class="MsoBodyText">rim_sld</p> 
     3436</td> 
     3437<td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
     3438<p class="MsoBodyText">Å<sup> -2</sup></p> 
     3439</td> 
     3440<td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
     3441<p class="MsoBodyText">4e-6</p> 
     3442</td> 
     3443</tr> 
     3444<tr> 
     3445<td>face_sld</td> 
     3446<td>Å<sup> -2</sup></td> 
     3447<td>4e-6</td> 
     3448</tr> 
     3449<tr style="height: 19.25pt;"> 
     3450<td style="border-style: none solid solid; border-color: -moz-use-text-color windowtext windowtext; border-width: medium 1pt 1pt; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
     3451<p class="MsoBodyText">solvent_sld</p> 
     3452</td> 
     3453<td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
     3454<p class="MsoBodyText">Å<sup> -2</sup></p> 
     3455</td> 
     3456<td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
     3457<p class="MsoBodyText">1e-6</p> 
     3458</td> 
     3459</tr> 
     3460<tr style="height: 19.25pt;"> 
     3461<td style="border-style: none solid solid; border-color: -moz-use-text-color windowtext windowtext; border-width: medium 1pt 1pt; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
     3462<p class="MsoBodyText">background</p> 
     3463</td> 
     3464<td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
     3465<p class="MsoBodyText">cm<sup>-1</sup></p> 
     3466</td> 
     3467<td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
     3468<p class="MsoBodyText">0.0</p> 
     3469</td> 
     3470</tr> 
     3471<tr style="height: 19.25pt;"> 
     3472<td style="border-style: none solid solid; border-color: -moz-use-text-color windowtext windowtext; border-width: medium 1pt 1pt; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
     3473<p class="MsoBodyText">axis_theta</p> 
     3474</td> 
     3475<td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
     3476<p class="MsoBodyText">degree</p> 
     3477</td> 
     3478<td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
     3479<p class="MsoBodyText">90</p> 
     3480</td> 
     3481</tr> 
     3482<tr style="height: 20pt;"> 
     3483<td style="border-style: none solid solid; border-color: -moz-use-text-color windowtext windowtext; border-width: medium 1pt 1pt; padding: 0in 5.4pt; width: 107pt; height: 20pt;" valign="top" width="143"> 
     3484<p class="MsoBodyText">axis_phi</p> 
     3485</td> 
     3486<td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 20pt;" valign="top" width="143"> 
     3487<p class="MsoBodyText">degree</p> 
     3488</td> 
     3489<td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 20pt;" valign="top" width="143"> 
     3490<p class="MsoBodyText">0.0</p> 
     3491</td> 
     3492</tr> 
     3493</tbody> 
     3494</table> 
     3495</div> 
     3496<p class="MsoNormal">&nbsp;</p> 
     3497<p class="MsoNormal">The output of the 1D scattering 
     3498intensity function for 
     3499randomly oriented cylinders is then given by the equation above.</p> 
     3500<p class="MsoNormal">&nbsp;</p> 
     3501<p class="MsoNormal">The <i>axis_theta</i> 
     3502and axis<i>_phi</i> parameters are not 
     3503used for the 1D output. Our implementation of the scattering kernel and 
     3504the 1D 
     3505scattering intensity use the c-library from NIST.</p> 
     3506<p class="MsoNormal"></p> 
     3507<p class="MsoNormal">&nbsp;</p> 
     3508<p class="MsoNormal">&nbsp;</p> 
     3509<p class="MsoNormal" style="text-align: center;" align="center"><img style="width: 512px; height: 377px;" id="cscylbicelle" src="cscylbicelle_pic.jpg"></p> 
     3510<p class="MsoNormal" style="text-align: center;" align="center"><b>Figure. 
     35111D plot using the default values (w/200 data point).</b></p> 
     3512<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p> 
     3513<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p> 
     3514<p class="MsoNormal">&nbsp;REFERENCE<br> 
     3515Feigin, L. A, and D. I. Svergun, "Structure Analysis by Small-Angle 
     3516X-Ray and Neutron Scattering", Plenum Press, New York, (1987).</p> 
    33423517<p class="MsoNormal"><b>&nbsp;</b></p> 
    33433518<p class="MsoNormal"><b>&nbsp;</b></p> 
    3344 <p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.15.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     3519<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.16.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    33453520</span></b><a name="HollowCylinderModel"><b><span style="font-size: 14pt;">HollowCylinderModel</span></b></a></p> 
    33463521<p class="MsoNormal">&nbsp;</p> 
     
    35093684<p class="MsoNormal"><b>&nbsp;</b></p> 
    35103685<p class="MsoNormal"><b>&nbsp;</b></p> 
    3511 <p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.16.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     3686<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.17.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    35123687</span></b><a name="FlexibleCylinderModel"></a><b><span style="font-size: 14pt;">FlexibleCylinderModel</span></b></p> 
    35133688<p class="MsoNormal">&nbsp;</p> 
     
    36723847<p class="MsoNormal">&nbsp;</p> 
    36733848<p class="MsoNormal">&nbsp;</p> 
    3674 <p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.17.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     3849<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.18.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    36753850</span></b><b><span style="font-size: 14pt;">FlexCylEllipXMo<a name="FlexCylEllipXModel"></a>del</span></b></p> 
    36763851<p class="MsoNormal">&nbsp;</p> 
     
    38994074<p class="MsoNormal">&nbsp;</p> 
    39004075<p class="MsoNormal"><b>&nbsp;</b></p> 
    3901 <p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.18.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     4076<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.19.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    39024077</span></b><a name="StackedDisksModel"><b><span style="font-size: 14pt;">StackedDisksModel 
    39034078</span></b></a></p> 
     
    41434318<p class="MsoNormal"><b>&nbsp;</b></p> 
    41444319<p class="MsoNormal"><b>&nbsp;</b></p> 
    4145 <p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.19.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     4320<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.20.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    41464321</span></b><a name="ParallelepipedModel"><b><span style="font-size: 14pt;">ParallelepipedModel</span></b></a></p> 
    41474322<p class="MsoNormal">&nbsp;</p> 
     
    43384513<p class="MsoNormal"><b>&nbsp;</b></p> 
    43394514<p class="MsoNormal"><b>&nbsp;</b></p> 
    4340 <p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.20.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     4515<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.21.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    43414516</span></b><b><span style="font-size: 14pt;"><a name="CSParallelepipedModel">CSParallelepipedModel</a></span></b></p> 
    43424517<p class="MsoNormal">&nbsp;</p> 
     
    46474822<p class="MsoNormal">&nbsp;</p> 
    46484823<p class="MsoNormal">&nbsp;</p> 
    4649 <p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.21.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     4824<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.22.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    46504825</span></b><a name="EllipticalCylinderModel"><b><span style="font-size: 14pt;">Elliptical 
    46514826Cylinder Model</span></b></a></p> 
     
    48815056<p class="MsoNormal">&nbsp;</p> 
    48825057<p class="MsoNormal">&nbsp;</p> 
    4883 <p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.22.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     5058<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.23.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    48845059</span></b><a name="BarBellModel"><b><span style="font-size: 14pt;">BarBell(/DumBell)Model</span></b></a></p> 
    48855060<p class="MsoNormal">&nbsp;</p> 
     
    50895264<p class="MsoNormal">&nbsp;</p> 
    50905265<p class="MsoNormal">&nbsp;</p> 
    5091 <p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.23.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     5266<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.24.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    50925267</span></b><a name="CappedCylinderModel"><b><span style="font-size: 14pt;">CappedCylinder(/ConvexLens)Model</span></b></a></p> 
    50935268<p class="MsoNormal">&nbsp;</p> 
     
    52925467<p class="MsoNormal">&nbsp;</p> 
    52935468<p class="MsoNormal">&nbsp;</p> 
    5294 <p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.24.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     5469<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.25.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    52955470</span></b><a name="EllipsoidModel"><b><span style="font-size: 14pt;">Ellipsoid 
    52965471Model</span></b></a></p> 
     
    55485723<p class="MsoNormal"><b>&nbsp;</b></p> 
    55495724<p class="MsoNormal"><b>&nbsp;</b></p> 
    5550 <p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.25.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     5725<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.26.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    55515726</span></b><a name="CoreShellEllipsoidModel"><b><span style="font-size: 14pt;">CoreShellEllipsoidModel 
    55525727</span></b></a></p> 
     
    57455920<p class="MsoNormal"><b>&nbsp;</b></p> 
    57465921<p class="MsoNormal"><b>&nbsp;</b></p> 
    5747 <p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.26.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     5922<p class="MsoNormal" 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; 
    57485923</span></b><a name="TriaxialEllipsoidModel"><b><span style="font-size: 14pt;">TriaxialEllipsoidModel</span></b></a></p> 
    57495924<p class="MsoNormal">&nbsp;</p> 
     
    59426117<p class="MsoNormal"><b>&nbsp;</b></p> 
    59436118<p class="MsoNormal"><b>&nbsp;</b></p> 
    5944 <p class="MsoNormal" 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; 
     6119<p class="MsoNormal" 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; 
    59456120</span></b><a name="LamellarModel"><b><span style="font-size: 14pt;">LamellarModel</span></b></a></p> 
    59466121<p class="MsoNormal">&nbsp;</p> 
     
    60666241<p class="MsoNormal"><b>&nbsp;</b></p> 
    60676242<p class="MsoNormal"><b>&nbsp;</b></p> 
    6068 <p class="MsoNormal" 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; 
     6243<p class="MsoNormal" 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; 
    60696244</span></b><a name="LamellarFFHGModel"><b><span style="font-size: 14pt;">LamellarFFHGModel</span></b></a></p> 
    60706245<p class="MsoNormal">&nbsp;</p> 
     
    62196394<p class="MsoNormal"><b>&nbsp;</b></p> 
    62206395<p class="MsoNormal"><b>&nbsp;</b></p> 
    6221 <p class="MsoNormal" 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; 
     6396<p class="MsoNormal" 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; 
    62226397</span></b><a name="LamellarPSModel"><b><span style="font-size: 14pt;">LamellarPSModel</span></b></a></p> 
    62236398<p class="MsoNormal">&nbsp;</p> 
     
    63856560<p class="MsoNormal"><b>&nbsp;</b></p> 
    63866561<p class="MsoNormal"><b>&nbsp;</b></p> 
    6387 <p class="MsoNormal" 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; 
     6562<p class="MsoNormal" 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; 
    63886563</span></b><a name="LamellarPSHGModel"><b><span style="font-size: 14pt;">LamellarPSHGModel</span></b></a></p> 
    63896564<p class="MsoNormal">&nbsp;</p> 
     
    65896764<p class="MsoNormal"><b>&nbsp;</b></p> 
    65906765<p class="MsoNormal"><b>&nbsp;</b></p> 
    6591 <p class="MsoNormal" 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;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     6766<p class="MsoNormal" 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;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    65926767</span></b><a name="LamellarPCrystalModel"><b><span style="font-size: 14pt;">LamellarPCrystalModel</span></b></a></p> 
    65936768<p class="MsoNormal">&nbsp;</p> 
     
    67626937<p class="MsoNormal"><b>&nbsp;</b></p> 
    67636938<p class="MsoNormal"><b>&nbsp;</b></p> 
    6764 <p class="MsoNormal" 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; 
     6939<p class="MsoNormal" 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; 
    67656940</span></b><a name="SCCrystalModel"><b><span style="font-size: 14pt;">SC(Simple 
    67666941Cubic Para-)CrystalModel</span></b></a></p> 
     
    69807155<p class="MsoNormal">&nbsp;</p> 
    69817156<p class="MsoNormal"><b>&nbsp;</b></p> 
    6982 <p class="MsoNormal" 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; 
     7157<p class="MsoNormal" 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; 
    69837158</span></b><a name="FCCrystalModel"><b><span style="font-size: 14pt;">FC(Face 
    69847159Centered Cubic Para-)CrystalModel</span></b></a></p> 
     
    72047379<p class="MsoNormal">&nbsp;</p> 
    72057380<p class="MsoNormal"><b>&nbsp;</b></p> 
    7206 <p class="MsoNormal" 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; 
     7381<p class="MsoNormal" 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; 
    72077382</span></b><a name="BCCrystalModel"><b><span style="font-size: 14pt;">BC(Body 
    72087383Centered Cubic Para-)CrystalModel</span></b></a></p> 
     
    83478522</td> 
    83488523<td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
    8349 <p class="MsoBodyText"><br><sup></sup></p> 
     8524<p class="MsoBodyText"><br> 
     8525</p> 
    83508526</td> 
    83518527<td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
     
    83958571<p class="MsoNormal" style="margin-left: 0.25in;">&nbsp;Note: 
    83968572&nbsp;The surface fractal dimension is valid for 
    8397 1&lt;surface_dim&lt;3. &nbsp;Also it is valid in a limited q range (see the reference for details).</p> 
     85731&lt;surface_dim&lt;3. &nbsp;Also it is valid in a limited 
     8574q range (see the reference for details).</p> 
    83988575<p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 14pt;">&nbsp;</span></p> 
    83998576<div align="center"> 
     
    84608637</td> 
    84618638<td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
    8462 <p class="MsoBodyText"><br><sup></sup></p> 
     8639<p class="MsoBodyText"><br> 
     8640</p> 
    84638641</td> 
    84648642<td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
     
    85748752</td> 
    85758753<td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
    8576 <p class="MsoBodyText"><br><sup></sup></p> 
     8754<p class="MsoBodyText"><br> 
     8755</p> 
    85778756</td> 
    85788757<td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
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