Changeset 9611dd6 in sasview for src/sans


Ignore:
Timestamp:
Apr 27, 2014 3:33:24 PM (11 years ago)
Author:
Peter Parker
Branches:
master, ESS_GUI, ESS_GUI_Docs, ESS_GUI_batch_fitting, ESS_GUI_bumps_abstraction, ESS_GUI_iss1116, ESS_GUI_iss879, ESS_GUI_iss959, ESS_GUI_opencl, ESS_GUI_ordering, ESS_GUI_sync_sascalc, costrafo411, magnetic_scatt, release-4.1.1, release-4.1.2, release-4.2.2, release_4.0.1, ticket-1009, ticket-1094-headless, ticket-1242-2d-resolution, ticket-1243, ticket-1249, ticket885, unittest-saveload
Children:
a27b3df
Parents:
a110e37f
Message:

Fix greek letters.

File:
1 edited

Legend:

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

    ra110e37f r9611dd6  
    35863586<p>The 1D scattering intensity for this model is calculated according to the equations given by 
    35873587Nayuk and Huber (Nayuk, 2012).</p> 
    3588 <p>Assuming a hollow parallelepiped with infinitely thin walls, edge lengths <span class="formula"><i>A</i>†
     3588<p>Assuming a hollow parallelepiped with infinitely thin walls, edge lengths A &le; B &le; C 
     3589        <span class="formula"><i>A</i>†
    35893590≀†
    35903591<i>B</i>†
     
    35923593<i>C</i></span> 
    35933594 
    3594 and presenting an orientation with respect to the scattering vector given by Ξ and φ, 
    3595 where Ξ is the angle between the <em>z</em> axis and the longest axis of the parallelepiped <em>C</em>, and φ 
     3595and presenting an orientation with respect to the scattering vector given by &theta; and &phi;, 
     3596where &theta; is the angle between the <em>z</em> axis and the longest axis of the parallelepiped <em>C</em>, and &phi; 
    35963597is the angle between the scattering vector (lying in the <em>xy</em> plane) and the <em>y</em> axis, 
    35973598the form factor is given by:</p> 
     
    36153616<p style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="img/RectangularHollowPrismInfThinWalls_6.png" alt="" /></span></p> 
    36163617 
    3617 <p>where <em>V</em> is the volume of the rectangular prism, <span class="formula"><i>ρ</i><sub><span class="mbox">pipe</span></sub></span> 
     3618<p>where <em>V</em> is the volume of the rectangular prism, <span class="formula"><i>&rho;</i><sub><span class="mbox">pipe</span></sub></span> 
    36183619 is the scattering length of the 
    3619 parallelepiped, <span class="formula"><i>ρ</i><sub><span class="mbox">solvent</span></sub></span> 
     3620parallelepiped, <span class="formula"><i>&rho;</i><sub><span class="mbox">solvent</span></sub></span> 
    36203621 is the scattering length of the solvent, and 
    36213622(if the data are in absolute scale) scale represents the volume fraction (which is unitless) .</p> 
     
    36413642</tr> 
    36423643<tr><td>short_side</td> 
    3643 <td>Å</td> 
     3644<td>&Aring;</td> 
    36443645<td>35</td> 
    36453646</tr> 
     
    36533654</tr> 
    36543655<tr><td>sldPipe</td> 
    3655 <td>Å<sup>-2</sup></td> 
     3656<td>&Aring;<sup>-2</sup></td> 
    36563657<td>6.3e-6</td> 
    36573658</tr> 
    36583659<tr><td>sldSolv</td> 
    3659 <td>Å<sup>-2</sup></td> 
     3660<td>&Aring;<sup>-2</sup></td> 
    36603661<td>1.0e-6</td> 
    36613662</tr> 
     
    36973698but the implementation here is closer to the equations given by Nayuk and Huber (Nayuk, 2012).</p> 
    36983699<p>The scattering from a massive parallelepiped with an orientation with respect to the scattering vector 
    3699 given by Ξ and φ is given by:</p> 
     3700given by &theta; and &phi; is given by:</p> 
    37003701 
    37013702<p style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="img/RectangularPrism_1.png" alt="" /></span></p> 
    37023703 
    37033704<p>where <em>A</em>, <em>B</em> and <em>C</em> are the sides of the parallelepiped and must fulfill <span class="formula"><i>A</i>†
    3704 â‰€â€ 
     3705&le;†
    37053706<i>B</i>†
    3706 â‰€â€ 
     3707&le;†
    37073708<i>C</i></span> 
    37083709, 
    3709 Îž is the angle between the <em>z</em> axis and the longest axis of the parallelepiped <em>C</em>, and φ 
     3710&theta; is the angle between the <em>z</em> axis and the longest axis of the parallelepiped <em>C</em>, and &phi; 
    37103711is the angle between the scattering vector (lying in the <em>xy</em> plane) and the <em>y</em> axis.</p> 
    37113712<p>The normalized form factor in 1D is obtained averaging over all possible orientations:</p> 
     
    37173718<p style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="img/RectangularPrism_3.png" alt="" /></span></p> 
    37183719 
    3719 <p>where <em>V</em> is the volume of the rectangular prism, <span class="formula"><i>ρ</i><sub><span class="mbox">pipe</span></sub></span> 
     3720<p>where <em>V</em> is the volume of the rectangular prism, <span class="formula"><i>&rho;</i><sub><span class="mbox">pipe</span></sub></span> 
    37203721 is the scattering length of the 
    3721 parallelepiped, <span class="formula"><i>ρ</i><sub><span class="mbox">solvent</span></sub></span> 
     3722parallelepiped, <span class="formula"><i>&rho;</i><sub><span class="mbox">solvent</span></sub></span> 
    37223723 is the scattering length of the solvent, and 
    37233724(if the data are in absolute scale) scale represents the volume fraction (which is unitless) .</p> 
     
    37423743</tr> 
    37433744<tr><td>short_side</td> 
    3744 <td>Å</td> 
     3745<td>&Aring;</td> 
    37453746<td>35</td> 
    37463747</tr> 
     
    37543755</tr> 
    37553756<tr><td>sldPipe</td> 
    3756 <td>Å<sup>-2</sup></td> 
     3757<td>&Aring;<sup>-2</sup></td> 
    37573758<td>6.3e-6</td> 
    37583759</tr> 
    37593760<tr><td>sldSolv</td> 
    3760 <td>Å<sup>-2</sup></td> 
     3761<td>&Aring;<sup>-2</sup></td> 
    37613762<td>1.0e-6</td> 
    37623763</tr> 
     
    37933794<p>The 1D scattering intensity for this model is calculated by forming the difference of the 
    37943795amplitudes of two massive parallelepipeds differing in their outermost dimensions in 
    3795 each direction by the same length increment 2 Δ (Nayuk, 2012).</p> 
     3796each direction by the same length increment 2 &Delta; (Nayuk, 2012).</p> 
    37963797<p>As in the case of the massive parallelepiped, the scattering amplitude is computed for a particular 
    37973798orientation of the parallelepiped with respect to the scattering vector and then averaged over all 
     
    38003801<p style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="img/RectangularHollowPrism_1.png" alt="" /></span></p> 
    38013802 
    3802 <p>where Ξ is the angle between the <em>z</em> axis and the longest axis of the parallelepiped, φ 
     3803<p>where &theta; is the angle between the <em>z</em> axis and the longest axis of the parallelepiped, &phi; 
    38033804is the angle between the scattering vector (lying in the <em>xy</em> plane) and the <em>y</em> axis, and:</p> 
    38043805 
     
    38063807 
    38073808<p>where <em>A</em>, <em>B</em> and <em>C</em> are the external sides of the parallelepiped fulfilling <span class="formula"><i>A</i>†
    3808 â‰€â€ 
     3809&le;†
    38093810<i>B</i>†
    3810 â‰€â€ 
     3811&le;†
    38113812<i>C</i></span> 
    38123813, 
     
    38193820<p style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="img/RectangularHollowPrism_4.png" alt="" /></span></p> 
    38203821 
    3821 <p>where <span class="formula"><i>ρ</i><sub><span class="mbox">pipe</span></sub></span> 
     3822<p>where <span class="formula"><i>&rho;</i><sub><span class="mbox">pipe</span></sub></span> 
    38223823 is the scattering length of the 
    3823 parallelepiped, <span class="formula"><i>ρ</i><sub><span class="mbox">solvent</span></sub></span> 
     3824parallelepiped, <span class="formula"><i>&rho;</i><sub><span class="mbox">solvent</span></sub></span> 
    38243825 is the scattering length of the solvent, and 
    38253826(if the data are in absolute scale) scale represents the volume fraction (which is unitless) .</p> 
     
    38453846</tr> 
    38463847<tr><td>short_side</td> 
    3847 <td>Å</td> 
     3848<td>&Aring;</td> 
    38483849<td>35</td> 
    38493850</tr> 
     
    38573858</tr> 
    38583859<tr><td>thickness</td> 
    3859 <td>Å</td> 
     3860<td>&Aring;</td> 
    38603861<td>1</td> 
    38613862</tr> 
    38623863<tr><td>sldPipe</td> 
    3863 <td>Å<sup>-2</sup></td> 
     3864<td>&Aring;<sup>-2</sup></td> 
    38643865<td>6.3e-6</td> 
    38653866</tr> 
    38663867<tr><td>sldSolv</td> 
    3867 <td>Å<sup>-2</sup></td> 
     3868<td>&Aring;<sup>-2</sup></td> 
    38683869<td>1.0e-6</td> 
    38693870</tr> 
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