Ignore:
Timestamp:
Aug 22, 2011 5:06:45 PM (13 years ago)
Author:
Jae Cho <jhjcho@…>
Branches:
master, ESS_GUI, ESS_GUI_Docs, ESS_GUI_batch_fitting, ESS_GUI_bumps_abstraction, ESS_GUI_iss1116, ESS_GUI_iss879, ESS_GUI_iss959, ESS_GUI_opencl, ESS_GUI_ordering, ESS_GUI_sync_sascalc, costrafo411, magnetic_scatt, release-4.1.1, release-4.1.2, release-4.2.2, release_4.0.1, ticket-1009, ticket-1094-headless, ticket-1242-2d-resolution, ticket-1243, ticket-1249, ticket885, unittest-saveload
Children:
8cf19e9
Parents:
b21d32b
Message:

added pearlnecklace model in doc

File:
1 edited

Legend:

Unmodified
Added
Removed

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

    r76b5220 r28c9e5a  
    468468     href="#VesicleModel">VesicleModel</a>, <a href="#MultiShellModel">MultiShellModel</a>, 
    469469      <a href="#OnionExpShellModel">OnionExpShellModel</a>, <a 
    470      href="#SphericalSLDModel">SphericalSLDModel</a>, <a href="#CylinderModel">CylinderModel</a>, 
     470     href="#SphericalSLDModel">SphericalSLDModel</a>, <a 
     471     href="#PearlNecklaceModel">PearlNecklaceModel</a> 
     472     , <a href="#CylinderModel">CylinderModel</a>, 
    471473     <a href="#CoreShellCylinderModel">CoreShellCylinderModel</a>, <a 
    472474     href="#HollowCylinderModel">HollowCylinderModel</a>, <a 
    … …  
    656658<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p> 
    657659 
    658 <p class=MsoNormal>where <i>scale</i> is a scale factor* volume fraction, V is 
    659 the volume of the scatterer, <i>r</i> is the radius of the sphere, <i>bkg</i> 
    660 is the background level and <i><span style='font-family:"Arial","sans-serif"'>&#916;</span>&#961;</i> 
    661 (contrast)&nbsp; is the scattering length density (SLD) &nbsp;difference 
    662 between the scatterer and the solvent it is in.</p> 
     660<p class=MsoNormal>where scale is a scale factor* volume fraction,  
     661V is the volume of the scatterer, r is the radius of the sphere,  
     662bkg is the background level and sldXXX is the scattering length density  
     663(SLD)  of  the scatterer or the solvent.  </p> 
     664<p> 
     665Note that if your data is in absolute scale,  
     666the 'scale' should represent the volume fraction (unitless) if you have a good fit.   
     667If not, it should represent the volume fraction * a factor  
     668(by which your data might need to be rescaled).</p> 
    663669 
    664670<p class=MsoNormal>&nbsp;</p> 
    … …  
    32383244 
    32393245<p class=MsoNormal>&nbsp;</p> 
    3240  
    32413246<p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span 
    32423247style='font-size:14.0pt'>2.10.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     3248</span></b><b><a name=PearlNecklaceModel><span style='font-size:14.0pt'>PearlNecklaceModel</span></b></p> 
     3249 
     3250<p class=MsoNormal>&nbsp;</p> 
     3251 
     3252<p class=MsoNormal>This model provides the form factor for a pearl necklace composed 
     3253of two elements: N pearls (homogeneous spheres) freely jointed by M rods (like 
     3254strings) (with a total mass M<sub>w</sub> = M *m<sub>r</sub> + N * m<sub>s</sub>, 
     3255the radius R and the string segment length (or edge separation) l (= A- 2R)). 
     3256The A is the center to center pearl separation distance.</p> 
     3257<p/> 
     3258<center><img src="pearl_fig.jpg"></center> 
     3259<p class=MsoNormal>&nbsp;</p> 
     3260 
     3261<p class=MsoNormal style='margin-left:.85in;text-indent:-.35in'><b>1.1.</b><b><span 
     3262style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp; </span>Definition</b></p> 
     3263 
     3264<p class=MsoNormal>&nbsp;</p> 
     3265 
     3266<p class=MsoNormal>The output of the scattering intensity function for the 
     3267pearlnecklace model is given by (Schweins, 2004):</p> 
     3268 
     3269<p class=MsoNormal>&nbsp;</p> 
     3270 
     3271<p class=MsoNormal>&nbsp;</p> 
     3272 
     3273<p class=MsoNormal align=center style='text-align:center'><span 
     3274style='position:relative;top:15.0pt'><img  
     3275src="pearl_eq1.gif"></span>&nbsp; </p> 
     3276 
     3277<p class=MsoNormal>where</p> 
     3278 
     3279<p class=MsoNormal align=center style='text-align:center'><span 
     3280style='position:relative;top:16.0pt'><img  
     3281src="pearl_eq2.gif"></span><span 
     3282style='position:relative;top:14.0pt'>,</span>&nbsp;&nbsp; </p> 
     3283 
     3284<p class=MsoNormal align=center style='text-align:center'><span 
     3285style='position:relative;top:17.0pt'><img  
     3286src="pearl_eq3.gif"></span><span 
     3287style='position:relative;top:14.0pt'>,</span></p> 
     3288 
     3289<p class=MsoNormal align=center style='text-align:center'><span 
     3290style='position:relative;top:16.0pt'><img  
     3291src="pearl_eq4.gif"></span><span 
     3292style='position:relative;top:14.0pt'>,</span></p> 
     3293 
     3294<p class=MsoNormal align=center style='text-align:center'><span 
     3295style='position:relative;top:15.0pt'><img  
     3296src="pearl_eq5.gif"></span>&nbsp;,</p> 
     3297 
     3298<p class=MsoNormal align=center style='text-align:center'><span 
     3299style='position:relative;top:14.0pt'><img  
     3300src="pearl_eq6.gif">,</span></p> 
     3301 
     3302<p class=MsoNormal><span style='position:relative;top:14.0pt'>and</span></p> 
     3303 
     3304<p class=MsoNormal align=center style='text-align:center'><span 
     3305style='position:relative;top:14.0pt'><img  
     3306src="pearl_eq7.gif">.</span></p> 
     3307<p/> 
     3308<p class=MsoNormal>where the mass m<sub>i </sub> is (sld(of i) – sld(of 
     3309solvent)) * (volume of the N pearls/rods), V is the total volume of the necklace.</p> 
     3310 
     3311<p class=MsoNormal>&nbsp;</p> 
     3312 
     3313<p class=MsoNormal>The 2D scattering intensity is the same as P(q) above, 
     3314regardless of the orientation of the q vector.</p> 
     3315 
     3316<p class=MsoNormal>&nbsp;</p> 
     3317 
     3318<p class=MsoNormal>The returned value is scaled to units of [cm<sup>-1</sup>] 
     3319and the parameters of the sphere model are the following:</p> 
     3320 
     3321<p class=MsoNormal>&nbsp;</p> 
     3322 
     3323<div align=center> 
     3324 
     3325<table class=MsoNormalTable border=0 cellspacing=0 cellpadding=0 
     3326 style='border-collapse:collapse'> 
     3327 <tr style='height:19.25pt'> 
     3328  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt; 
     3329  padding:0in 5.4pt 0in 5.4pt;height:19.25pt'> 
     3330  <p class=MsoBodyText>Parameter name</p> 
     3331  </td> 
     3332  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt; 
     3333  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'> 
     3334  <p class=MsoBodyText>Units</p> 
     3335  </td> 
     3336  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt; 
     3337  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'> 
     3338  <p class=MsoBodyText>Default value</p> 
     3339  </td> 
     3340 </tr> 
     3341 <tr style='height:19.25pt'> 
     3342  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt; 
     3343  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'> 
     3344  <p class=MsoBodyText>scale</p> 
     3345  </td> 
     3346  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
     3347  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
     3348  padding:0in 5.4pt 0in 5.4pt;height:19.25pt'> 
     3349  <p class=MsoBodyText>None</p> 
     3350  </td> 
     3351  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
     3352  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
     3353  padding:0in 5.4pt 0in 5.4pt;height:19.25pt'> 
     3354  <p class=MsoBodyText>1.0</p> 
     3355  </td> 
     3356 </tr> 
     3357 <tr style='height:19.25pt'> 
     3358  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt; 
     3359  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'> 
     3360  <p class=MsoBodyText>radius</p> 
     3361  </td> 
     3362  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
     3363  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
     3364  padding:0in 5.4pt 0in 5.4pt;height:19.25pt'> 
     3365  <p class=MsoBodyText>Å</p> 
     3366  </td> 
     3367  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
     3368  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
     3369  padding:0in 5.4pt 0in 5.4pt;height:19.25pt'> 
     3370  <p class=MsoBodyText>80.0</p> 
     3371  </td> 
     3372 </tr> 
     3373 <tr style='height:19.25pt'> 
     3374  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt; 
     3375  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'> 
     3376  <p class=MsoBodyText>edge_separation</p> 
     3377  </td> 
     3378  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
     3379  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
     3380  padding:0in 5.4pt 0in 5.4pt;height:19.25pt'> 
     3381  <p class=MsoBodyText>Å</p> 
     3382  </td> 
     3383  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
     3384  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
     3385  padding:0in 5.4pt 0in 5.4pt;height:19.25pt'> 
     3386  <p class=MsoBodyText>350.0</p> 
     3387  </td> 
     3388 </tr> 
     3389 <tr style='height:19.25pt'> 
     3390  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt; 
     3391  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'> 
     3392  <p class=MsoBodyText>num_pearls</p> 
     3393  </td> 
     3394  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
     3395  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
     3396  padding:0in 5.4pt 0in 5.4pt;height:19.25pt'> 
     3397  <p class=MsoBodyText>(integer)</p> 
     3398  </td> 
     3399  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
     3400  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
     3401  padding:0in 5.4pt 0in 5.4pt;height:19.25pt'> 
     3402  <p class=MsoBodyText>3</p> 
     3403  </td> 
     3404 </tr> 
     3405 <tr style='height:19.25pt'> 
     3406  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt; 
     3407  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'> 
     3408  <p class=MsoBodyText>sld_pearl</p> 
     3409  </td> 
     3410  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
     3411  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
     3412  padding:0in 5.4pt 0in 5.4pt;height:19.25pt'> 
     3413  <p class=MsoBodyText>Å<sup> -2</sup></p> 
     3414  </td> 
     3415  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
     3416  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
     3417  padding:0in 5.4pt 0in 5.4pt;height:19.25pt'> 
     3418  <p class=MsoBodyText>1e-6</p> 
     3419  </td> 
     3420 </tr> 
     3421 <tr style='height:19.25pt'> 
     3422  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt; 
     3423  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'> 
     3424  <p class=MsoBodyText>sld_solv</p> 
     3425  </td> 
     3426  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
     3427  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
     3428  padding:0in 5.4pt 0in 5.4pt;height:19.25pt'> 
     3429  <p class=MsoBodyText>Å<sup> -2</sup></p> 
     3430  </td> 
     3431  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
     3432  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
     3433  padding:0in 5.4pt 0in 5.4pt;height:19.25pt'> 
     3434  <p class=MsoBodyText>6.3e-6</p> 
     3435  </td> 
     3436 </tr> 
     3437 <tr style='height:19.25pt'> 
     3438  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt; 
     3439  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'> 
     3440  <p class=MsoBodyText>sld_string</p> 
     3441  </td> 
     3442  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
     3443  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
     3444  padding:0in 5.4pt 0in 5.4pt;height:19.25pt'> 
     3445  <p class=MsoBodyText>Å<sup> -2</sup></p> 
     3446  </td> 
     3447  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
     3448  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
     3449  padding:0in 5.4pt 0in 5.4pt;height:19.25pt'> 
     3450  <p class=MsoBodyText>1e-6</p> 
     3451  </td> 
     3452 </tr> 
     3453 <tr style='height:19.25pt'> 
     3454  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt; 
     3455  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:19.25pt'> 
     3456  <p class=MsoBodyText>thick_string</p> 
     3457  <p class=MsoBodyText>(=rod diameter)</p> 
     3458  </td> 
     3459  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
     3460  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
     3461  padding:0in 5.4pt 0in 5.4pt;height:19.25pt'> 
     3462  <p class=MsoBodyText>Å</p> 
     3463  </td> 
     3464  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
     3465  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
     3466  padding:0in 5.4pt 0in 5.4pt;height:19.25pt'> 
     3467  <p class=MsoBodyText>2.5</p> 
     3468  </td> 
     3469 </tr> 
     3470 <tr style='height:20.0pt'> 
     3471  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt; 
     3472  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:20.0pt'> 
     3473  <p class=MsoBodyText>background</p> 
     3474  </td> 
     3475  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
     3476  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
     3477  padding:0in 5.4pt 0in 5.4pt;height:20.0pt'> 
     3478  <p class=MsoBodyText>cm<sup>-1</sup></p> 
     3479  </td> 
     3480  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
     3481  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
     3482  padding:0in 5.4pt 0in 5.4pt;height:20.0pt'> 
     3483  <p class=MsoBodyText>0.0</p> 
     3484  </td> 
     3485 </tr> 
     3486</table> 
     3487 
     3488</div> 
     3489 
     3490<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p> 
     3491 
     3492<p class=MsoNormal align=center style='text-align:center'><img  
     3493src="pearl_plot.jpg"></p> 
     3494 
     3495<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p> 
     3496 
     3497<p class=MsoNormal>&nbsp;</p> 
     3498 
     3499<p class=MsoNormal>REFERENCE</p> 
     3500 
     3501<p class=MsoNormal>R. Schweins and K. Huber, ‘Particle Scattering Factor of 
     3502Pearl Necklace Chains’, Macromol. Symp., 211, 25-42, 2004.</p> 
     3503 
     3504<p class=MsoNormal>&nbsp;</p> 
     3505 
     3506<p class=MsoNormal>&nbsp;</p> 
     3507 
     3508<p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span 
     3509style='font-size:14.0pt'>2.11.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    32433510</span></b><a name=CylinderModel><b><span style='font-size:14.0pt'>Cylinder 
    32443511Model</span></b></a></p> 
    … …  
    34333700  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
    34343701  padding:0in 5.4pt 0in 5.4pt;height:19.85pt'> 
    3435   <p class=MsoBodyText>Radian</p> 
     3702  <p class=MsoBodyText>degree</p> 
    34363703  </td> 
    34373704  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
    34383705  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
    34393706  padding:0in 5.4pt 0in 5.4pt;height:19.85pt'> 
    3440   <p class=MsoBodyText>1.0</p> 
     3707  <p class=MsoBodyText>60</p> 
    34413708  </td> 
    34423709 </tr> 
    … …  
    34493716  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
    34503717  padding:0in 5.4pt 0in 5.4pt;height:20.6pt'> 
    3451   <p class=MsoBodyText>Radian</p> 
     3718  <p class=MsoBodyText>degree</p> 
    34523719  </td> 
    34533720  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
    34543721  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
    34553722  padding:0in 5.4pt 0in 5.4pt;height:20.6pt'> 
    3456   <p class=MsoBodyText>1.0</p> 
     3723  <p class=MsoBodyText>60</p> 
    34573724  </td> 
    34583725 </tr> 
    … …  
    35653832 
    35663833<p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span 
    3567 style='font-size:14.0pt'>2.11.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     3834style='font-size:14.0pt'>2.12.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    35683835</span></b><a name=CoreShellCylinderModel><b><span style='font-size:14.0pt'>Core-Shell 
    35693836Cylinder Model</span></b></a></p> 
    … …  
    37964063  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
    37974064  padding:0in 5.4pt 0in 5.4pt;height:19.25pt'> 
    3798   <p class=MsoBodyText>Radian</p> 
    3799   </td> 
    3800   <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
    3801   none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
    3802   padding:0in 5.4pt 0in 5.4pt;height:19.25pt'> 
    3803   <p class=MsoBodyText>1.57</p> 
     4065  <p class=MsoBodyText>degree</p> 
     4066  </td> 
     4067  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
     4068  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
     4069  padding:0in 5.4pt 0in 5.4pt;height:19.25pt'> 
     4070  <p class=MsoBodyText>90</p> 
    38044071  </td> 
    38054072 </tr> 
    … …  
    38124079  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
    38134080  padding:0in 5.4pt 0in 5.4pt;height:20.0pt'> 
    3814   <p class=MsoBodyText>Radian</p> 
     4081  <p class=MsoBodyText>degree</p> 
    38154082  </td> 
    38164083  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
    … …  
    39014168 
    39024169<p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span 
    3903 style='font-size:14.0pt'>2.12.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     4170style='font-size:14.0pt'>2.13.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    39044171</span></b><a name=HollowCylinderModel><b><span style='font-size:14.0pt'>HollowCylinderModel</span></b></a></p> 
    39054172 
    … …  
    41374404 
    41384405<p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span 
    4139 style='font-size:14.0pt'>2.13.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     4406style='font-size:14.0pt'>2.14.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    41404407</span></b><a name=FlexibleCylinderModel></a><b><span style='font-size:14.0pt'>FlexibleCylinderModel</span></b></p> 
    41414408 
    … …  
    43564623 
    43574624<p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span 
    4358 style='font-size:14.0pt'>2.14.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     4625style='font-size:14.0pt'>2.15.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    43594626</span></b><b><span style='font-size:14.0pt'>FlexCylEllipXMo<a 
    43604627name=FlexCylEllipXModel></a>del</span></b></p> 
    … …  
    46434910 
    46444911<p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span 
    4645 style='font-size:14.0pt'>2.15.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     4912style='font-size:14.0pt'>2.16.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    46464913</span></b><a name=StackedDisksModel><b><span style='font-size:14.0pt'>StackedDisksModel 
    46474914</span></b></a></p> 
    … …  
    50045271 
    50055272<p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span 
    5006 style='font-size:14.0pt'>2.16.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     5273style='font-size:14.0pt'>2.17.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    50075274</span></b><a name=ParallelepipedModel><b><span style='font-size:14.0pt'>ParallelepipedModel</span></b></a></p> 
    50085275 
    … …  
    52915558 
    52925559<p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span 
    5293 style='font-size:14.0pt'>2.17.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     5560style='font-size:14.0pt'>2.18.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    52945561</span></b><b><span style='font-size:14.0pt'><a 
    52955562name=CSParallelepipedModel>CSParallelepipedModel</a></span></b></p> 
    … …  
    57195986 
    57205987<p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span 
    5721 style='font-size:14.0pt'>2.18.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     5988style='font-size:14.0pt'>2.19.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    57225989</span></b><a name=EllipticalCylinderModel><b><span style='font-size:14.0pt'>Elliptical 
    57235990Cylinder Model</span></b></a></p> 
    … …  
    60606327 
    60616328<p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span 
    6062 style='font-size:14.0pt'>2.19.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     6329style='font-size:14.0pt'>2.20.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    60636330</span></b><a name=BarBellModel><b><span style='font-size:14.0pt'>BarBell(/DumBell)Model</span></b></a></p> 
    60646331 
    … …  
    63596626 
    63606627<p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span 
    6361 style='font-size:14.0pt'>2.20.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     6628style='font-size:14.0pt'>2.21.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    63626629</span></b><a name=CappedCylinderModel><b><span style='font-size:14.0pt'>CappedCylinder(/ConvexLens)Model</span></b></a></p> 
    63636630 
    … …  
    66516918 
    66526919<p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span 
    6653 style='font-size:14.0pt'>2.21.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     6920style='font-size:14.0pt'>2.22.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    66546921</span></b><a name=EllipsoidModel><b><span style='font-size:14.0pt'>Ellipsoid 
    66556922Model</span></b></a></p> 
    … …  
    68537120  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
    68547121  padding:0in 5.4pt 0in 5.4pt;height:19.85pt'> 
    6855   <p class=MsoBodyText>Radian</p> 
     7122  <p class=MsoBodyText>degree</p> 
    68567123  </td> 
    68577124  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
    68587125  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
    68597126  padding:0in 5.4pt 0in 5.4pt;height:19.85pt'> 
    6860   <p class=MsoBodyText>1.57</p> 
     7127  <p class=MsoBodyText>90</p> 
    68617128  </td> 
    68627129 </tr> 
    … …  
    68697136  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
    68707137  padding:0in 5.4pt 0in 5.4pt;height:20.6pt'> 
    6871   <p class=MsoBodyText>Radian</p> 
     7138  <p class=MsoBodyText>degree</p> 
    68727139  </td> 
    68737140  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
    … …  
    69917258 
    69927259<p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span 
    6993 style='font-size:14.0pt'>2.22.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     7260style='font-size:14.0pt'>2.23.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    69947261</span></b><a name=CoreShellEllipsoidModel><b><span style='font-size:14.0pt'>CoreShellEllipsoidModel 
    69957262</span></b></a></p> 
    … …  
    72687535 
    72697536<p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span 
    7270 style='font-size:14.0pt'>2.23.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     7537style='font-size:14.0pt'>2.24.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    72717538</span></b><a name=TriaxialEllipsoidModel><b><span style='font-size:14.0pt'>TriaxialEllipsoidModel</span></b></a></p> 
    72727539 
    … …  
    75437810 
    75447811<p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span 
    7545 style='font-size:14.0pt'>2.24.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     7812style='font-size:14.0pt'>2.25.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    75467813</span></b><a name=LamellarModel><b><span style='font-size:14.0pt'>LamellarModel</span></b></a></p> 
    75477814 
    … …  
    77307997 
    77317998<p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span 
    7732 style='font-size:14.0pt'>2.25.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     7999style='font-size:14.0pt'>2.26.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    77338000</span></b><a name=LamellarFFHGModel><b><span style='font-size:14.0pt'>LamellarFFHGModel</span></b></a></p> 
    77348001 
    … …  
    79598226 
    79608227<p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span 
    7961 style='font-size:14.0pt'>2.26.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     8228style='font-size:14.0pt'>2.27.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    79628229</span></b><a name=LamellarPSModel><b><span style='font-size:14.0pt'>LamellarPSModel</span></b></a></p> 
    79638230 
    … …  
    82068473 
    82078474<p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span 
    8208 style='font-size:14.0pt'>2.27.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     8475style='font-size:14.0pt'>2.28.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    82098476</span></b><a name=LamellarPSHGModel><b><span style='font-size:14.0pt'>LamellarPSHGModel</span></b></a></p> 
    82108477 
    … …  
    85088775 
    85098776<p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span 
    8510 style='font-size:14.0pt'>2.28.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     8777style='font-size:14.0pt'>2.29.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    85118778</span></b><a name=LamellarPCrystalModel><b><span style='font-size:14.0pt'>LamellarPCrystalModel</span></b></a></p> 
    85128779 
    … …  
    87629029 
    87639030<p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span 
    8764 style='font-size:14.0pt'>2.29.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     9031style='font-size:14.0pt'>2.30.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    87659032</span></b><a name=SCCrystalModel><b><span style='font-size:14.0pt'>SC(Simple 
    87669033Cubic Para-)CrystalModel</span></b></a></p> 
    … …  
    90749341 
    90759342<p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span 
    9076 style='font-size:14.0pt'>2.30.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     9343style='font-size:14.0pt'>2.31.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    90779344</span></b><a name=FCCrystalModel><b><span style='font-size:14.0pt'>FC(Face 
    90789345Centered Cubic Para-)CrystalModel</span></b></a></p> 
    … …  
    93889655 
    93899656<p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span 
    9390 style='font-size:14.0pt'>2.31.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     9657style='font-size:14.0pt'>2.32.</span></b><b><span style='font-size:7.0pt'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    93919658</span></b><a name=BCCrystalModel><b><span style='font-size:14.0pt'>BC(Body 
    93929659Centered Cubic Para-)CrystalModel</span></b></a></p> 
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