Changeset e5a8f33 in sasmodels


Ignore:
Timestamp:
Mar 27, 2019 6:29:26 AM (4 months ago)
Author:
smk78
Branches:
master, core_shell_microgels, magnetic_model, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests
Children:
81d0b9b
Parents:
db1c84b
Message:

Fixed missing/poor rst/latex markup

File:
1 edited

Legend:

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  • sasmodels/models/core_shell_ellipsoid.py

    r0507e09 re5a8f33  
    33---------- 
    44 
    5 Parameters for this model are the core axial ratio X and a shell thickness, 
    6 which are more often what we would like to determine and makes the model 
    7 better behaved, particularly when polydispersity is applied than the four 
    8 independent radii used in the original parameterization of this model. 
     5Parameters for this model are the core axial ratio $X_{core}$ and a shell  
     6thickness $t_{shell}$, which are more often what we would like to determine  
     7and make the model better behaved, particularly when polydispersity is  
     8applied, than the four independent radii used in the original parameterization  
     9of this model. 
    910 
    1011 
     
    1516the poles, of a prolate ellipsoid. 
    1617 
    17 When *X_core < 1* the core is oblate; when *X_core > 1* it is prolate. 
    18 *X_core = 1* is a spherical core. 
    19  
    20 For a fixed shell thickness *XpolarShell = 1*, to scale the shell thickness 
    21 pro-rata with the radius set or constrain *XpolarShell = X_core*. 
    22  
    23 When including an $S(q)$, the radius in $S(q)$ is calculated to be that of 
    24 a sphere with the same 2nd virial coefficient of the outer surface of the 
    25 ellipsoid. This may have some undesirable effects if the aspect ratio of the 
    26 ellipsoid is large (ie, if $X << 1$ or $X >> 1$ ), when the $S(q)$ 
    27 - which assumes spheres - will not in any case be valid.  Generating a 
    28 custom product model will enable separate effective volume fraction and 
    29 effective radius in the $S(q)$. 
     18When $X_{core}$ < 1 the core is oblate; when $X_{core}$ > 1 it is prolate. 
     19$X_{core}$ = 1 is a spherical core. 
     20 
     21For a fixed shell thickness $X_{polar shell}$ = 1, to scale $t_{shell}$  
     22pro-rata with the radius set or constrain $X_{polar shell}$ = $X_{core}$. 
     23 
     24.. note:: 
     25 
     26   When including an $S(q)$, the radius in $S(q)$ is calculated to be that of 
     27   a sphere with the same 2nd virial coefficient of the outer surface of the 
     28   ellipsoid. This may have some undesirable effects if the aspect ratio of the 
     29   ellipsoid is large (ie, if $X << 1$ or $X >> 1$), when the $S(q)$ 
     30   - which assumes spheres - will not in any case be valid.  Generating a 
     31   custom product model will enable separate effective volume fraction and 
     32   effective radius in the $S(q)$. 
    3033 
    3134If SAS data are in absolute units, and the SLDs are correct, then scale should 
     
    4346where 
    4447 
     48.. In following equation SK changed radius\_equat\_core to R_e 
     49   
    4550.. math:: 
    4651    :nowrap: 
    4752 
    4853    \begin{align*} 
    49     F(q,\alpha) = &f(q,radius\_equat\_core,radius\_equat\_core.x\_core,\alpha) \\ 
    50     &+ f(q,radius\_equat\_core + thick\_shell, 
    51          radius\_equat\_core.x\_core + thick\_shell.x\_polar\_shell,\alpha) 
     54    F(q,\alpha) = &f(q,R_e,R_e.x_{core},\alpha) \\ 
     55    &+ f(q,R_e + t_{shell}, 
     56         R_e.x_{core} + t_{shell}.x_{polar shell},\alpha) 
    5257    \end{align*} 
    5358 
     
    7176$V = (4/3)\pi R_pR_e^2$ is the volume of the ellipsoid , $R_p$ is the 
    7277polar radius along the rotational axis of the ellipsoid, $R_e$ is the 
    73 equatorial radius perpendicular to the rotational axis of the ellipsoid 
    74 and $\Delta \rho$ (contrast) is the scattering length density difference, 
    75 either $(sld\_core - sld\_shell)$ or $(sld\_shell - sld\_solvent)$. 
     78equatorial radius perpendicular to the rotational axis of the ellipsoid,  
     79$t_{shell}$ is the thickness of the shell at the equator,  
     80and $\Delta \rho$ (the contrast) is the scattering length density difference, 
     81either $(\rho_{core} - \rho_{shell})$ or $(\rho_{shell} - \rho_{solvent})$. 
    7682 
    7783For randomly oriented particles: 
     
    104110* **Author:** NIST IGOR/DANSE **Date:** pre 2010 
    105111* **Last Modified by:** Richard Heenan (reparametrised model) **Date:** 2015 
    106 * **Last Reviewed by:** Richard Heenan **Date:** October 6, 2016 
     112* **Last Reviewed by:** Steve King **Date:** March 27, 2019 
    107113* **Source added by :** Steve King **Date:** March 25, 2019 
    108114""" 
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