Changeset 6752950 in sasview for sansmodels/src
- Timestamp:
- Feb 9, 2012 12:02:49 PM (13 years ago)
- 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:
- 223a154
- Parents:
- 51da9dc
- Location:
- sansmodels/src/sans/models/media
- Files:
-
- 6 added
- 1 edited
-
mass_fractal_eq1.jpg (added)
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mass_fractal_fig1.jpg (added)
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masssurface_fractal_eq1.jpg (added)
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masssurface_fractal_fig1.jpg (added)
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model_functions.html (modified) (24 diffs)
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surface_fractal_eq1.gif (added)
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surface_fractal_fig1.jpg (added)
Legend:
- Unmodified
- Added
- Removed
-
sansmodels/src/sans/models/media/model_functions.html
rc053f23 r6752950 444 444 {margin-bottom:0in;} 445 445 --> 446 </style><title></title></head> 446 </style><title></title> 447 448 </head> 447 449 <body lang="EN-US" link="blue" vlink="purple"> 448 450 <div class="WordSection1"> … … 453 455 <li class="MsoNormal" style="line-height: 115%;"><a href="#Introduction"><b>Introduction</b></a> 454 456 </li> 455 <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>, <a href="#Core2ndMomentModel">Core2ndMomentModel</a>, 457 <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>, <a href="#Core2ndMomentModel">Core2ndMomentModel</a>, <a href="#CoreMultiShellModel">CoreMultiShellModel</a>, <a href="#VesicleModel">VesicleModel</a>, <a href="#MultiShellModel">MultiShellModel</a>, <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>, 456 458 <a href="#HollowCylinderModel">HollowCylinderModel</a>, 457 459 <a href="#FlexibleCylinderModel">FlexibleCylinderModel</a>, … … 469 471 <a href="#BEPolyelectrolyte">BEPolyelectrolyte</a>, 470 472 <a href="#BroadPeak">BroadPeak,<span style="text-decoration: none;"> </span><span style="color: windowtext; text-decoration: none;"><u><span style="color: blue;">CorrLength</span></u></span><span style="color: windowtext; text-decoration: none;">,</span></a> 471 <a href="#DAB_Model">DAB_Model</a>, <a href="#Debye">Debye</a>, <a href="#Number_Density_Fractal">FractalModel</a>, <a href="#FractalCoreShell">FractalCoreShell</a>, <a href="#GaussLorentzGel">GaussLorentzGel</a>, <a href="#Guinier">Guinier</a>, <a href="#GuinierPorod">GuinierPorod</a>, <a href="#Lorentz">Lorentz</a>, <a href="#Peak%20Gauss%20Model">PeakGaussModel</a>, <a href="#Peak%20Lorentz%20Model">PeakLorentzModel</a>, <a href="#Poly_GaussCoil">Poly_GaussCoil</a>, <a href="#PolymerExclVolume">PolyExclVolume</a>, <a href="#PorodModel">PorodModel</a>, <a href="#RPA10Model">RPA10Model</a>, <a href="#Teubner%20Strey">Teubner Strey</a>, <a href="#TwoLorentzian">TwoLorentzian</a>, <a href="#TwoPowerLaw">TwoPowerLaw</a>, <a href="#UnifiedPowerRg">UnifiedPowerRg</a>, <a href="#LineModel">LineModel</a>.</li> 473 <a href="#DAB_Model">DAB_Model</a>, <a href="#Debye">Debye</a>, <a href="#Number_Density_Fractal">FractalModel</a>, <a href="#FractalCoreShell">FractalCoreShell</a>, <a href="#GaussLorentzGel">GaussLorentzGel</a>, <a href="#Guinier">Guinier</a>, <a href="#GuinierPorod">GuinierPorod</a>, <a href="#Lorentz">Lorentz</a>, <a href="#Mass_Fractal">MassFractalModel</a>, <a href="#MassSurface_Fractal">MassSurfaceFractal</a>, <a href="#Peak%20Gauss%20Model">PeakGaussModel</a>, <a href="#Peak%20Lorentz%20Model">PeakLorentzModel</a>, <a href="#Poly_GaussCoil">Poly_GaussCoil</a>, <a href="#PolymerExclVolume">PolyExclVolume</a>, <a href="#PorodModel">PorodModel</a>, <a href="#RPA10Model">RPA10Model</a>, <a href="#Surface_Fractal">SurfaceFractalModel</a>, 474 <a href="#Teubner%20Strey">Teubner Strey</a>, <a href="#TwoLorentzian">TwoLorentzian</a>, <a href="#TwoPowerLaw">TwoPowerLaw</a>, <a href="#UnifiedPowerRg">UnifiedPowerRg</a>, <a href="#LineModel">LineModel</a>.</li> 472 475 <li class="MsoNormal" style="line-height: 115%;"><a href="#Model"><b>Customized Models</b></a>: 473 476 <a href="#A+Bcos%282x%29+Csin%282x%29">A+Bcos(2x)+Csin(2x)</a>, … … 1269 1272 fraction of the core paraticles, and Gamma and delta are the 1270 1273 adsorbed amount and the bulk density of the polymers respectively. The 1271 sigma is the second moment of the thickness distribution. </p><p class="MsoNormal"></p><p class="MsoNormal">Note 1274 sigma is the second moment of the thickness distribution. </p> 1275 <p class="MsoNormal"></p> 1276 <p class="MsoNormal">Note 1272 1277 that all parameters except the 1273 1278 'sigma' are correlated for fitting so that fitting those with 1274 more than one parameters will be generally failed. And note that 1279 more than one parameters will be generally failed. And note 1280 that 1275 1281 unlike other shape models, no volume normalization was applied to this 1276 1282 model. </p> … … 1393 1399 <p class="MsoNormal"></p> 1394 1400 <p class="MsoBodyText" style="text-align: center; page-break-after: avoid;" align="center"><img style="width: 526px; height: 333px;" src="secongm_fig1.jpg" alt="core_scondmoment_1D_validation"></p> 1395 1396 <p class="MsoNormal"> </p> 1397 1401 <p class="MsoNormal"> </p> 1398 1402 <p class="MsoNormal"> </p> 1399 1403 <p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.6.</span></b><b><span style="font-size: 7pt;"> … … 4924 4928 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 52pt;"><img src="image107.gif" height="144" width="288"></span></p> 4925 4929 <p class="MsoNormal"> </p> 4926 <p class="MsoNormal"> </p><p class="MsoNormal"></p><p class="MsoNormal"></p> 4930 <p class="MsoNormal"> </p> 4931 <p class="MsoNormal"></p> 4932 <p class="MsoNormal"></p> 4927 4933 <p class="MsoNormal">The < > brackets denote 4928 4934 an average of the structure … … 6236 6242 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 50pt;"><img src="image141.gif" height="133" width="252"></span></p> 6237 6243 <p class="MsoNormal" style="text-align: center;" align="center"> </p> 6238 <p class="MsoNormal" style="text-align: center;" align="center"> </p><p class="MsoNormal" style="text-align: center;" align="center"></p><p class="MsoNormal" style="text-align: center;" align="center"></p> 6244 <p class="MsoNormal" style="text-align: center;" align="center"> </p> 6245 <p class="MsoNormal" style="text-align: center;" align="center"></p> 6246 <p class="MsoNormal" style="text-align: center;" align="center"></p> 6239 6247 <p class="MsoNormal">Here d= (repeat) spacing, <span style="font-family: Symbol;">d</span> 6240 6248 = bilayer thickness, the contrast <span style="font-family: Symbol;">Dr</span> … … 8109 8117 the 8110 8118 Texiera reference. The value returned is in cm<sup>-1</sup>.</p> 8111 <p class="MsoNormal" style="margin-left: 0.25in;"> </p>8112 8119 <p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 85pt;"><img src="image186.gif"></span></p> 8120 <p class="MsoNormal" style="text-align: center;" align="center"></p> 8113 8121 <p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 14pt;"> </span></p> 8114 8122 <p class="MsoNormal"><b><span style="font-size: 14pt;"> </span></b></p> 8115 <p class="MsoNormal" style="margin-left: 0.25in;"></p><p class="MsoNormal" style="margin-left: 0.25in;"></p><p class="MsoNormal" style="margin-left: 0.25in;"></p><p class="MsoNormal" style="margin-left: 0.25in;"></p><p class="MsoNormal" style="margin-left: 0.25in;">The 8123 <p class="MsoNormal" style="margin-left: 0.25in;"></p> 8124 <p class="MsoNormal" style="margin-left: 0.25in;"></p> 8125 <p class="MsoNormal" style="margin-left: 0.25in;"></p> 8126 <p class="MsoNormal" style="margin-left: 0.25in;"></p> 8127 <p class="MsoNormal" style="margin-left: 0.25in;"></p> 8128 <p class="MsoNormal" style="margin-left: 0.25in;"></p> 8129 <p class="MsoNormal" style="margin-left: 0.25in;">The 8116 8130 scale 8117 8131 parameter is the volume fraction of the building blocks, R<sub>0</sub> … … 8237 8251 Teixeira, (1988) J. Appl. Cryst., vol. 21, p781-785</p> 8238 8252 <p class="MsoNormal"><b><span style="font-size: 14pt;"> </span></b></p> 8239 <p class="MsoNormal"><b><span style="font-size: 14pt;"> </span></b></p> 8253 <p class="MsoNormal"><b><span style="font-size: 14pt;"> </span></b><b><span style="font-size: 14pt;"></span></b> 8254 </p> 8240 8255 <p class="MsoNormal"><b><span style="font-size: 14pt;"> </span></b></p> 8241 8256 <p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.9.</span></b><b><span style="font-size: 7pt;"> 8257 </span></b><b><span style="font-size: 14pt;"><a name="Mass_Fractal"></a><a name="MassFractalModel">MassFractalModel</a></span></b></p> 8258 <p class="MsoNormal"><b><span style="font-size: 14pt;"> </span></b></p> 8259 <p class="MsoNormal" style="margin-left: 0.25in;">Calculates 8260 the scattering from 8261 fractal-like aggregates based on 8262 the Mildner reference (below). </p> 8263 <p class="MsoNormal" style="margin-left: 0.25in;"> </p> 8264 <p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 85pt;"><br> 8265 </span></p> 8266 <p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 12pt; font-family: "Times New Roman","serif"; position: relative; top: 4.5pt;"><img src="mass_fractal_eq1.jpg"></span><span style="font-size: 14pt;"> </span></p> 8267 <p class="MsoNormal"><b><span style="font-size: 14pt;"> </span></b></p> 8268 <p class="MsoNormal" style="margin-left: 0.25in;"></p> 8269 <p class="MsoNormal" style="margin-left: 0.25in;"></p> 8270 <p class="MsoNormal" style="margin-left: 0.25in;">The 8271 R 8272 is the 8273 radius of the building block, D<sub>m</sub> is the mass 8274 fractal 8275 dimension, ξ is 8276 the correlation (or cutt-off) length, <i>ρ<sub>solvent</sub></i> 8277 is the scattering 8278 length density of the solvent, and <i>ρ<small><small>particle</small></small></i> 8279 is the 8280 scattering length density of particles.</p> 8281 <p class="MsoNormal" style="margin-left: 0.25in;">Note: 8282 The mass fractal dimension is valid for 8283 1<mass_dim<6. </p> 8284 <p class="MsoNormal" style="margin-left: 0.25in;"> </p> 8285 <p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 14pt;"> </span></p> 8286 <div align="center"> 8287 <table class="MsoNormalTable" style="border-collapse: collapse;" border="2" cellpadding="0" cellspacing="0"> 8288 <tbody> 8289 <tr style="height: 19.25pt;"> 8290 <td style="border: 1pt solid windowtext; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 8291 <p class="MsoBodyText">Parameter name</p> 8292 </td> 8293 <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"> 8294 <p class="MsoBodyText">Units</p> 8295 </td> 8296 <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"> 8297 <p class="MsoBodyText">Default value</p> 8298 </td> 8299 </tr> 8300 <tr style="height: 19.25pt;"> 8301 <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;"> 8302 <p class="MsoBodyText">scale</p> 8303 </td> 8304 <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"> 8305 <p class="MsoBodyText">None</p> 8306 </td> 8307 <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"> 8308 <p class="MsoBodyText">1</p> 8309 </td> 8310 </tr> 8311 <tr style="height: 19.25pt;"> 8312 <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"> 8313 <p class="MsoBodyText">radius</p> 8314 </td> 8315 <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"> 8316 <p class="MsoBodyText">Å</p> 8317 </td> 8318 <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"> 8319 <p class="MsoBodyText">10.0</p> 8320 </td> 8321 </tr> 8322 <tr style="height: 19.25pt;"> 8323 <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"> 8324 <p class="MsoBodyText">mass_dim</p> 8325 </td> 8326 <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"> 8327 <p class="MsoBodyText">None</p> 8328 </td> 8329 <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"> 8330 <p class="MsoBodyText">1.9</p> 8331 </td> 8332 </tr> 8333 <tr style="height: 19.25pt;"> 8334 <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"> 8335 <p class="MsoBodyText">co_length</p> 8336 </td> 8337 <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"> 8338 <p class="MsoBodyText">Å</p> 8339 </td> 8340 <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"> 8341 <p class="MsoBodyText">100.0</p> 8342 </td> 8343 </tr> 8344 <tr style="height: 19.25pt;"> 8345 <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"> 8346 <p class="MsoBodyText">background</p> 8347 </td> 8348 <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> 8350 </td> 8351 <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"> 8352 <p class="MsoBodyText">0.0</p> 8353 </td> 8354 </tr> 8355 </tbody> 8356 </table> 8357 </div> 8358 <p class="MsoNormal" style="margin-left: 0.25in;"> </p> 8359 <p class="MsoNormal" style="margin-left: 0.25in; text-align: center;" align="center"><img style="width: 495px; height: 368px;" id="Picture 79" src="mass_fractal_fig1.jpg"></p> 8360 <p class="MsoNormal" style="text-align: center;" align="center"><b>Figure. 1D plot</b></p> 8361 <p class="MsoNormal" style="margin-left: 0.25in; text-align: center;" align="center"> </p> 8362 <p class="MsoNormal" style="margin-left: 0.25in; text-align: center;" align="center"> </p> 8363 <p class="MsoNormal" style="margin-left: 0.25in;">References: 8364 </p> 8365 <p class="MsoNormal" style="margin-left: 0.25in; text-indent: 0.25in;">D. 8366 Mildner, and P. Hall, J. Phys. D.: Appl. Phys., 19, 8367 1535-1545 (1986), Equation(9).</p> 8368 <p class="MsoNormal"><b><span style="font-size: 14pt;"> </span></b></p> 8369 <p class="MsoNormal"><b><span style="font-size: 14pt;"></span></b><b><span style="font-size: 14pt;"></span></b> </p> 8370 <p class="MsoNormal"></p> 8371 <p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.10.</span></b><b><span style="font-size: 7pt;"> 8372 </span></b><b><span style="font-size: 14pt;"><a name="Surface_Fractal"></a><a name="SurfaceFractalModel">SurfaceFractalModel</a></span></b></p> 8373 <p class="MsoNormal"><b><span style="font-size: 14pt;"> </span></b></p> 8374 <p class="MsoNormal" style="margin-left: 0.25in;">Calculates 8375 the scattering based on 8376 the Mildner reference (below). </p> 8377 <p class="MsoNormal" style="margin-left: 0.25in;"> </p> 8378 <p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 85pt;"><br> 8379 </span></p> 8380 <p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 12pt; font-family: "Times New Roman","serif"; position: relative; top: 4.5pt;"><img src="surface_fractal_eq1.gif"></span><span style="font-size: 14pt;"> </span></p> 8381 <p class="MsoNormal"><b><span style="font-size: 14pt;"> </span></b></p> 8382 <p class="MsoNormal" style="margin-left: 0.25in;"></p> 8383 <p class="MsoNormal" style="margin-left: 0.25in;"></p> 8384 <p class="MsoNormal" style="margin-left: 0.25in;">The 8385 R 8386 is the 8387 radius of the building block, D<sub>s</sub> is the surface 8388 fractal 8389 dimension, ξ is 8390 the correlation (or cutt-off) length, <i>ρ<sub>solvent</sub></i> 8391 is the scattering 8392 length density of the solvent, and <i>ρ<small><small>particle</small></small></i> 8393 is the 8394 scattering length density of particles. </p> 8395 <p class="MsoNormal" style="margin-left: 0.25in;"> Note: 8396 The surface fractal dimension is valid for 8397 1<surface_dim<3. Also it is valid in a limited q range (see the reference for details).</p> 8398 <p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 14pt;"> </span></p> 8399 <div align="center"> 8400 <table class="MsoNormalTable" style="border-collapse: collapse;" border="2" cellpadding="0" cellspacing="0"> 8401 <tbody> 8402 <tr style="height: 19.25pt;"> 8403 <td style="border: 1pt solid windowtext; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 8404 <p class="MsoBodyText">Parameter name</p> 8405 </td> 8406 <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"> 8407 <p class="MsoBodyText">Units</p> 8408 </td> 8409 <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"> 8410 <p class="MsoBodyText">Default value</p> 8411 </td> 8412 </tr> 8413 <tr style="height: 19.25pt;"> 8414 <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;"> 8415 <p class="MsoBodyText">scale</p> 8416 </td> 8417 <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"> 8418 <p class="MsoBodyText">None</p> 8419 </td> 8420 <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"> 8421 <p class="MsoBodyText">1</p> 8422 </td> 8423 </tr> 8424 <tr style="height: 19.25pt;"> 8425 <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"> 8426 <p class="MsoBodyText">radius</p> 8427 </td> 8428 <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"> 8429 <p class="MsoBodyText">Å</p> 8430 </td> 8431 <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"> 8432 <p class="MsoBodyText">10.0</p> 8433 </td> 8434 </tr> 8435 <tr style="height: 19.25pt;"> 8436 <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"> 8437 <p class="MsoBodyText">surface_dim</p> 8438 </td> 8439 <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"> 8440 <p class="MsoBodyText">None</p> 8441 </td> 8442 <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"> 8443 <p class="MsoBodyText">2.0</p> 8444 </td> 8445 </tr> 8446 <tr style="height: 19.25pt;"> 8447 <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"> 8448 <p class="MsoBodyText">co_length</p> 8449 </td> 8450 <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"> 8451 <p class="MsoBodyText">Å</p> 8452 </td> 8453 <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"> 8454 <p class="MsoBodyText">500.0</p> 8455 </td> 8456 </tr> 8457 <tr style="height: 19.25pt;"> 8458 <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"> 8459 <p class="MsoBodyText">background</p> 8460 </td> 8461 <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> 8463 </td> 8464 <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"> 8465 <p class="MsoBodyText">0.0</p> 8466 </td> 8467 </tr> 8468 </tbody> 8469 </table> 8470 </div> 8471 <p class="MsoNormal" style="margin-left: 0.25in;"> </p> 8472 <p class="MsoNormal" style="margin-left: 0.25in; text-align: center;" align="center"><img style="width: 507px; height: 375px;" id="Picture 79" src="surface_fractal_fig1.jpg"></p> 8473 <p class="MsoNormal" style="text-align: center;" align="center"><b>Figure. 1D plot</b></p> 8474 <p class="MsoNormal" style="margin-left: 0.25in; text-align: center;" align="center"> </p> 8475 <p class="MsoNormal" style="margin-left: 0.25in; text-align: center;" align="center"> </p> 8476 <p class="MsoNormal" style="margin-left: 0.25in;">References: 8477 </p> 8478 <p class="MsoNormal" style="margin-left: 0.25in; text-indent: 0.25in;">D. 8479 Mildner, and P. Hall, J. Phys. D.: Appl. Phys., 19, 8480 1535-1545 (1986), Equation(13).</p> 8481 <p class="MsoNormal"><b><span style="font-size: 14pt;"> </span></b></p> 8482 <p class="MsoNormal"><b><span style="font-size: 14pt;"></span></b></p> 8483 <p class="MsoNormal"></p> 8484 <p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.11.</span></b><b><span style="font-size: 7pt;"> 8485 </span></b><b><span style="font-size: 14pt;"><a name="MassSurface_Fractal"></a><a name="MassSurfaceFractal">MassSurfaceFractal</a></span></b></p> 8486 <p class="MsoNormal"><b><span style="font-size: 14pt;"> </span></b></p> 8487 <p class="MsoNormal" style="margin-left: 0.25in;">Calculates 8488 the scattering based on 8489 the Schmidt/Hurd references (below). </p> 8490 <p class="MsoNormal" style="margin-left: 0.25in;"> </p> 8491 <p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 85pt;"><br> 8492 </span></p> 8493 <p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 12pt; font-family: "Times New Roman","serif"; position: relative; top: 4.5pt;"><img src="masssurface_fractal_eq1.jpg"></span><span style="font-size: 14pt;"> </span></p> 8494 <p class="MsoNormal"><b><span style="font-size: 14pt;"> </span></b></p> 8495 <p class="MsoNormal" style="margin-left: 0.25in;"></p> 8496 <p class="MsoNormal" style="margin-left: 0.25in;"></p> 8497 <p class="MsoNormal" style="margin-left: 0.25in;">The 8498 R<small>g</small> 8499 is for the cluster, r<small>g</small> 8500 is for the primary, D<sub>s</sub> is the surface 8501 fractal 8502 dimension, D<sub>m</sub> is the mass 8503 fractal 8504 dimension, <i>ρ<sub>solvent</sub></i> 8505 is the scattering 8506 length density of the solvent, and <i>ρ<small><small>p</small></small></i> 8507 is the 8508 scattering length density of particles. </p> 8509 <p class="MsoNormal" style="margin-left: 0.25in;"> Note: 8510 The surface and mass fractal dimensions are valid for 8511 0<surface_dim<6, 0<mass_dim<6, and 8512 (surface_mass+mass_dim)<6. </p> 8513 <p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 14pt;"> </span></p> 8514 <div align="center"> 8515 <table class="MsoNormalTable" style="border-collapse: collapse;" border="2" cellpadding="0" cellspacing="0"> 8516 <tbody> 8517 <tr style="height: 19.25pt;"> 8518 <td style="border: 1pt solid windowtext; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 8519 <p class="MsoBodyText">Parameter name</p> 8520 </td> 8521 <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"> 8522 <p class="MsoBodyText">Units</p> 8523 </td> 8524 <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"> 8525 <p class="MsoBodyText">Default value</p> 8526 </td> 8527 </tr> 8528 <tr style="height: 19.25pt;"> 8529 <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;"> 8530 <p class="MsoBodyText">scale</p> 8531 </td> 8532 <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"> 8533 <p class="MsoBodyText">None</p> 8534 </td> 8535 <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"> 8536 <p class="MsoBodyText">1</p> 8537 </td> 8538 </tr> 8539 <tr style="height: 19.25pt;"> 8540 <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"> 8541 <p class="MsoBodyText">primary_rg</p> 8542 </td> 8543 <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"> 8544 <p class="MsoBodyText">Å</p> 8545 </td> 8546 <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"> 8547 <p class="MsoBodyText">4000.0</p> 8548 </td> 8549 </tr> 8550 <tr> 8551 <td> cluster_rg</td> 8552 <td> Å</td> 8553 <td> 86.7</td> 8554 </tr> 8555 <tr style="height: 19.25pt;"> 8556 <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"> 8557 <p class="MsoBodyText">surface_dim</p> 8558 </td> 8559 <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"> 8560 <p class="MsoBodyText">None</p> 8561 </td> 8562 <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"> 8563 <p class="MsoBodyText">2.3</p> 8564 </td> 8565 </tr> 8566 <tr> 8567 <td> mass_dim</td> 8568 <td> None</td> 8569 <td> 1.8</td> 8570 </tr> 8571 <tr style="height: 19.25pt;"> 8572 <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"> 8573 <p class="MsoBodyText">background</p> 8574 </td> 8575 <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> 8577 </td> 8578 <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"> 8579 <p class="MsoBodyText">0.0</p> 8580 </td> 8581 </tr> 8582 </tbody> 8583 </table> 8584 </div> 8585 <p class="MsoNormal" style="margin-left: 0.25in;"> </p> 8586 <p class="MsoNormal" style="margin-left: 0.25in; text-align: center;" align="center"><img style="width: 507px; height: 370px;" id="Picture 79" src="masssurface_fractal_fig1.jpg"></p> 8587 <p class="MsoNormal" style="text-align: center;" align="center"><b>Figure. 1D plot</b></p> 8588 <p class="MsoNormal" style="margin-left: 0.25in; text-align: center;" align="center"> </p> 8589 <p class="MsoNormal" style="margin-left: 0.25in; text-align: center;" align="center"> </p> 8590 <p class="MsoNormal" style="margin-left: 0.25in;">References: 8591 </p> 8592 <p class="MsoNormal" style="margin-left: 0.25in; text-indent: 0.25in;">P. 8593 Schmidt, J Appl. Cryst., 24, 414-435 (1991), Equation(19).</p> 8594 <p class="MsoNormal" style="margin-left: 0.25in; text-indent: 0.25in;">Hurd, 8595 Schaefer, Martin, Phys. Rev. A, 35, 2361-2364 (1987), Equation(2).</p> 8596 <p class="MsoNormal"><b><span style="font-size: 14pt;"> </span></b></p> 8597 <p class="MsoNormal"><b><span style="font-size: 14pt;"></span></b></p> 8598 <p class="MsoNormal"><b><span style="font-size: 14pt;"></span></b></p> 8599 <p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.12.</span></b><b><span style="font-size: 7pt;"> 8242 8600 </span></b><b><span style="font-size: 14pt;"> 8243 8601 <a name="FractalCoreShell">FractalCoreShell(Model)</a></span></b></p> … … 8389 8747 <p class="MsoNormal"><b><span style="font-size: 14pt;"> </span></b></p> 8390 8748 <p class="MsoNormal"><b><span style="font-size: 14pt;"> </span></b></p> 8391 <p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.1 0.</span></b><b><span style="font-size: 7pt;"> 8749 <p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.13.</span></b><b><span style="font-size: 7pt;"> 8392 8750 </span></b><b><span style="font-size: 14pt;"> 8393 8751 <a name="GaussLorentzGel">GaussLorentzGel(Model)</a></span></b></p> … … 8519 8877 Mortensen, H. Reynaers, Polymer 42 (2001) 2907-2913. </p> 8520 8878 <p class="MsoNormal"><b><span style="font-size: 14pt;"> </span></b></p> 8521 <p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.1 1.</span></b><b><span style="font-size: 7pt;"> 8879 <p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.14.</span></b><b><span style="font-size: 7pt;"> 8522 8880 </span></b><b><span style="font-size: 14pt;"> <a name="BEPolyelectrolyte"> 8523 8881 BEPolyelectrolyte Model</a></span></b></p> … … 8672 9030 <p class="MsoNormal"><b><span style="font-size: 14pt;"> </span></b></p> 8673 9031 <p class="MsoNormal" style="margin-left: 0.25in;"><b><span style="font-size: 14pt;"> </span></b></p> 8674 <p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.1 2.</span></b><b><span style="font-size: 7pt;"> 9032 <p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.15.</span></b><b><span style="font-size: 7pt;"> 8675 9033 </span></b><b><span style="font-size: 14pt;"> <a name="Guinier">Guinier 8676 9034 (Model)</a></span></b></p> … … 8732 9090 <p class="MsoNormal" style="margin-left: 0.25in;"><b><span style="font-size: 14pt;"> </span></b></p> 8733 9091 <p class="MsoNormal" style="margin-left: 0.25in;"> </p> 8734 <p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.1 3.</span></b><b><span style="font-size: 7pt;"> 9092 <p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.16.</span></b><b><span style="font-size: 7pt;"> 8735 9093 </span></b><b><span style="font-size: 14pt;"> <a name="GuinierPorod">GuinierPorod 8736 9094 (Model)</a></span></b></p> … … 8892 9250 <p class="MsoNormal" style="margin-left: 0.25in;"> </p> 8893 9251 <p class="MsoNormal" style="margin-left: 0.25in;"><b><span style="font-size: 14pt;"> </span></b></p> 8894 <p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.1 4.</span></b><b><span style="font-size: 7pt;"> 9252 <p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.17.</span></b><b><span style="font-size: 7pt;"> 8895 9253 </span></b><b><span style="font-size: 14pt;"> <a name="PorodModel">PorodModel</a></span></b></p> 8896 9254 <p class="MsoNormal"><b><span style="font-size: 14pt;"> </span></b></p> … … 8958 9316 <p class="MsoNormal"><b><span style="font-size: 14pt;"> </span></b></p> 8959 9317 <p class="MsoNormal"> </p> 8960 <p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.1 5.</span></b><b><span style="font-size: 7pt;"> 9318 <p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.18.</span></b><b><span style="font-size: 7pt;"> 8961 9319 </span></b><b><span style="font-size: 14pt;"> <a name="Peak Gauss Model">PeakGaussModel</a></span></b></p> 8962 9320 <p class="MsoNormal"><b><span style="font-size: 14pt;"> </span></b></p> … … 9049 9407 <p class="MsoBodyText"> </p> 9050 9408 <p class="MsoBodyText"> </p> 9051 <p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.1 6.</span></b><b><span style="font-size: 7pt;"> 9409 <p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.19.</span></b><b><span style="font-size: 7pt;"> 9052 9410 </span></b><b><span style="font-size: 14pt;"> <a name="Peak Lorentz Model">PeakLorentzModel</a></span></b></p> 9053 9411 <p class="MsoNormal"><b><span style="font-size: 14pt;"> </span></b></p> … … 9059 9417 <p class="MsoNormal" style="margin-left: 0.25in; text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 34pt;"><img src="image200.gif"></span></p> 9060 9418 <p class="MsoNormal" style="margin-left: 0.25in; text-align: center;" align="center"> </p> 9061 <p class="MsoNormal" style="margin-left: 0.25in;"></p><p class="MsoNormal" style="margin-left: 0.25in;">with 9419 <p class="MsoNormal" style="margin-left: 0.25in;"></p> 9420 <p class="MsoNormal" style="margin-left: 0.25in;">with 9062 9421 the peak having height of I0 9063 9422 centered at qpk having a hwhm (half-width-half-maximum) of B. … … 9137 9496 <p class="MsoBodyText"> </p> 9138 9497 <p class="MsoBodyText"> </p> 9139 <p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3. 17. 9498 <p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.20. 9140 9499 <a name="Poly_GaussCoil">Poly_GaussCoil </a>(Model)</span></b></p> 9141 9500 <p class="MsoNormal" style=""> </p> … … 9260 9619 <p class="MsoNormal" style=""> </p> 9261 9620 <p class="MsoBodyText"> </p> 9262 <p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3. 18. 9621 <p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.21. 9263 9622 <a name="PolymerExclVolume">PolymerExclVolume (Model)</a></span></b></p> 9264 9623 <p class="MsoNormal" style=""> </p> … … 9442 9801 <p class="MsoNormal" style="margin-left: 0.25in;"> </p> 9443 9802 <p class="MsoNormal" style="margin-left: 0.25in;"> </p> 9444 <p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3. 19.</span></b><b><span style="font-size: 7pt;"> 9803 <p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.22.</span></b><b><span style="font-size: 7pt;"> 9445 9804 </span></b><b><span style="font-size: 14pt;"> 9446 9805 <a name="RPA10Model">RPA10Model</a></span></b></p> … … 9699 10058 <p class="MsoNormal"><b><span style="font-size: 14pt;"> </span></b></p> 9700 10059 <p class="MsoNormal" style="margin-left: 0.25in;"><b><span style="font-size: 14pt;"> </span></b></p> 9701 <p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.2 0.</span></b><b><span style="font-size: 7pt;"> 10060 <p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.23.</span></b><b><span style="font-size: 7pt;"> 9702 10061 </span></b><b><span style="font-size: 14pt;"> <a name="TwoLorentzian">TwoLorentzian(Model)</a></span></b></p> 9703 10062 <p class="MsoNormal"><b><span style="font-size: 14pt;"> </span></b></p> … … 9832 10191 <p class="MsoNormal" style="text-indent: 0.25in;"><b> </b></p> 9833 10192 <p class="MsoNormal" style="text-indent: 0.25in;"><b> </b></p> 9834 <p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.2 1.</span></b><b><span style="font-size: 7pt;"> 10193 <p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.24.</span></b><b><span style="font-size: 7pt;"> 9835 10194 </span></b><b><span style="font-size: 14pt;"> <a name="TwoPowerLaw">TwoPowerLaw(Model)</a></span></b></p> 9836 10195 <p class="MsoNormal"><b><span style="font-size: 14pt;"> </span></b></p> … … 9940 10299 <p class="MsoNormal" style="text-indent: 0.25in;"><b> </b></p> 9941 10300 <p class="MsoNormal" style="text-indent: 0.25in;"><b> </b></p> 9942 <p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.2 2.</span></b><b><span style="font-size: 7pt;"> 10301 <p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.25.</span></b><b><span style="font-size: 7pt;"> 9943 10302 </span></b><b><span style="font-size: 14pt;"> <a name="UnifiedPowerRg">UnifiedPower(Law 9944 10303 and)Rg(Model)</a></span></b></p> … … 10129 10488 <p class="MsoNormal" style="text-indent: 0.25in;"><b> </b></p> 10130 10489 <p class="MsoNormal"> </p> 10131 <p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.2 3.</span></b><b><span style="font-size: 7pt;"> 10490 <p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.26.</span></b><b><span style="font-size: 7pt;"> 10132 10491 </span></b><b><span style="font-size: 14pt;"> <a name="LineModel"> LineModel</a></span></b></p> 10133 10492 <p class="MsoNormal"><b><span style="font-size: 14pt;"> </span></b></p>
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