Changeset 30b60d2 in sasmodels for sasmodels/models


Ignore:
Timestamp:
Sep 5, 2017 2:39:41 PM (7 years ago)
Author:
Paul Kienzle <pkienzle@…>
Branches:
master, core_shell_microgels, costrafo411, magnetic_model, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests
Children:
3a45c2c
Parents:
64eecf7
Message:

allow build of both latex and html

Location:
sasmodels/models
Files:
9 edited

Legend:

Unmodified
Added
Removed

  • sasmodels/models/binary_hard_sphere.py

    r8f04da4 r30b60d2  
    2323    :nowrap: 
    2424 
    25     \begin{align} 
     25    \begin{align*} 
    2626    x &= \frac{(\phi_2 / \phi)\alpha^3}{(1-(\phi_2/\phi) + (\phi_2/\phi) 
    2727    \alpha^3)} \\ 
    2828    \phi &= \phi_1 + \phi_2 = \text{total volume fraction} \\ 
    2929    \alpha &= R_1/R_2 = \text{size ratio} 
    30     \end{align} 
     30    \end{align*} 
    3131 
    3232The 2D scattering intensity is the same as 1D, regardless of the orientation of 

  • sasmodels/models/core_shell_bicelle.py

    r64eecf7 r30b60d2  
    2525scattering length density variation along the cylinder axis is: 
    2626 
    27 .. 
    28  
    29   .. math:: 
     27.. math:: 
    3028 
    3129    \rho(r) = 
    … …  
    5048    :nowrap: 
    5149 
    52     \begin{align} 
     50    \begin{align*} 
    5351    F(Q,\alpha) = &\bigg[ 
    5452    (\rho_c - \rho_f) V_c \frac{2J_1(QRsin \alpha)}{QRsin\alpha}\frac{sin(QLcos\alpha/2)}{Q(L/2)cos\alpha} \\ 
    … …  
    5654    &+(\rho_r - \rho_s) V_t \frac{2J_1(Q(R+t_r)sin\alpha)}{Q(R+t_r)sin\alpha}\frac{sin(Q(L/2+t_f)cos\alpha)}{Q(L/2+t_f)cos\alpha} 
    5755    \bigg] 
    58     \end{align} 
     56    \end{align*} 
    5957 
    6058where $V_t$ is the total volume of the bicelle, $V_c$ the volume of the core, 

  • sasmodels/models/core_shell_bicelle_elliptical.py

    r64eecf7 r30b60d2  
    4949    :nowrap: 
    5050 
    51     \begin{align} 
     51    \begin{align*} 
    5252    F(Q,\alpha,\psi) = &\bigg[ 
    5353    (\rho_c - \rho_f) V_c \frac{2J_1(QR'sin \alpha)}{QR'sin\alpha}\frac{sin(QLcos\alpha/2)}{Q(L/2)cos\alpha} \\ 
    … …  
    5555    &+(\rho_r - \rho_s) V_t \frac{2J_1(Q(R'+t_r)sin\alpha)}{Q(R'+t_r)sin\alpha}\frac{sin(Q(L/2+t_f)cos\alpha)}{Q(L/2+t_f)cos\alpha} 
    5656    \bigg] 
    57     \end{align} 
     57    \end{align*} 
    5858 
    5959where 

  • sasmodels/models/core_shell_ellipsoid.py

    r64eecf7 r30b60d2  
    4646    :nowrap: 
    4747 
    48     \begin{align} 
     48    \begin{align*} 
    4949    F(q,\alpha) = &f(q,radius\_equat\_core,radius\_equat\_core.x\_core,\alpha) \\ 
    5050    &+ f(q,radius\_equat\_core + thick\_shell,radius\_equat\_core.x\_core + thick\_shell.x\_polar\_shell,\alpha) 
    51     \end{align} 
     51    \end{align*} 
    5252 
    5353where 

  • sasmodels/models/hollow_rectangular_prism.py

    r8f04da4 r30b60d2  
    3131  :nowrap: 
    3232 
    33   \begin{align} 
     33  \begin{align*} 
    3434  A_{P\Delta}(q) & =  A B C 
    3535    \left[\frac{\sin \bigl( q \frac{C}{2} \cos\theta \bigr)} 
    … …  
    4747    \left[ \frac{\sin \bigl[ q \bigl(\frac{B}{2}-\Delta\bigr) \sin\theta \cos\phi \bigr]} 
    4848    {q \bigl(\frac{B}{2}-\Delta\bigr) \sin\theta \cos\phi} \right] 
    49   \end{align} 
     49  \end{align*} 
    5050 
    5151where $A$, $B$ and $C$ are the external sides of the parallelepiped fulfilling 

  • sasmodels/models/parallelepiped.py

    r8f04da4 r30b60d2  
    2020   Parallelepiped with the corresponding definition of sides. 
    2121 
    22 .. note:: 
    23  
    24 The three dimensions of the parallelepiped (strictly here a cuboid) may be given in 
    25 $any$ size order. To avoid multiple fit solutions, especially 
    26 with Monte-Carlo fit methods, it may be advisable to restrict their ranges. There may 
    27 be a number of closely similar "best fits", so some trial and error, or fixing of some 
    28 dimensions at expected values, may help. 
     22The three dimensions of the parallelepiped (strictly here a cuboid) may be 
     23given in *any* size order. To avoid multiple fit solutions, especially 
     24with Monte-Carlo fit methods, it may be advisable to restrict their ranges. 
     25There may be a number of closely similar "best fits", so some trial and 
     26error, or fixing of some dimensions at expected values, may help. 
    2927 
    3028The 1D scattering intensity $I(q)$ is calculated as: 

  • sasmodels/models/rpa.py

    r4f9e288 r30b60d2  
    3030    These case numbers are different from those in the NIST SANS package! 
    3131 
    32 The models are based on the papers by Akcasu et al. [#Akcasu]_ and by 
    33 Hammouda [#Hammouda]_ assuming the polymer follows Gaussian statistics such 
     32The models are based on the papers by Akcasu *et al.* and by 
     33Hammouda assuming the polymer follows Gaussian statistics such 
    3434that $R_g^2 = n b^2/6$ where $b$ is the statistical segment length and $n$ is 
    3535the number of statistical segment lengths. A nice tutorial on how these are 
    3636constructed and implemented can be found in chapters 28 and 39 of Boualem 
    37 Hammouda's 'SANS Toolbox'[#toolbox]_. 
     37Hammouda's 'SANS Toolbox'. 
    3838 
    3939In brief the macroscopic cross sections are derived from the general forms 
    … …  
    4949  are calculated with respect to component D).** So the scattering contrast 
    5050  for a C/D blend = [SLD(component C) - SLD(component D)]\ :sup:`2`. 
    51 * Depending on which case is being used, the number of fitting parameters can  
     51* Depending on which case is being used, the number of fitting parameters can 
    5252  vary. 
    5353 
    … …  
    5757      component are obtained from other methods and held fixed while The *scale* 
    5858      parameter should be held equal to unity. 
    59     * The variables are normally the segment lengths (b\ :sub:`a`, b\ :sub:`b`, 
    60       etc) and $\chi$ parameters (K\ :sub:`ab`, K\ :sub:`ac`, etc). 
    61  
     59    * The variables are normally the segment lengths ($b_a$, $b_b$, 
     60      etc.) and $\chi$ parameters ($K_{ab}$, $K_{ac}$, etc). 
    6261 
    6362References 
    6463---------- 
    6564 
    66 .. [#Akcasu] A Z Akcasu, R Klein and B Hammouda, *Macromolecules*, 26 (1993) 
    67    4136. 
    68 .. [#Hammouda] B. Hammouda, *Advances in Polymer Science* 106 (1993) 87. 
    69 .. [#toolbox] https://www.ncnr.nist.gov/staff/hammouda/the_sans_toolbox.pdf 
     65A Z Akcasu, R Klein and B Hammouda, *Macromolecules*, 26 (1993) 4136. 
     66 
     67B. Hammouda, *Advances in Polymer Science* 106 (1993) 87. 
     68 
     69B. Hammouda, *SANS Toolbox* 
     70https://www.ncnr.nist.gov/staff/hammouda/the_sans_toolbox.pdf. 
    7071 
    7172Authorship and Verification 

  • sasmodels/models/star_polymer.py

    r142a8e2 r30b60d2  
    77emanating from a common central (in the case of this model) point.  It is 
    88derived as a special case of on the Benoit model for general branched 
    9 polymers\ [#CITBenoit]_ as also used by Richter ''et. al.''\ [#CITRichter]_ 
     9polymers\ [#CITBenoit]_ as also used by Richter *et al.*\ [#CITRichter]_ 
    1010 
    1111For a star with $f$ arms the scattering intensity $I(q)$ is calculated as 

  • sasmodels/models/surface_fractal.py

    r48462b0 r30b60d2  
    99 
    1010.. math:: 
     11    :nowrap: 
    1112 
     13    \begin{align*} 
    1214    I(q) &= \text{scale} \times P(q)S(q) + \text{background} \\ 
    1315    P(q) &= F(qR)^2 \\ 
    … …  
    1517    S(q) &= \Gamma(5-D_S)\xi^{\,5-D_S}\left[1+(q\xi)^2 \right]^{-(5-D_S)/2} 
    1618            \sin\left[-(5-D_S) \tan^{-1}(q\xi) \right] q^{-1} \\ 
    17     \text{scale} &= \text{scale_factor}\, N V^2(\rho_\text{particle} - \rho_\text{solvent})^2 \\ 
     19    \text{scale} &= \text{scale factor}\, N V^1(\rho_\text{particle} - \rho_\text{solvent})^2 \\ 
    1820    V &= \frac{4}{3}\pi R^3 
     21    \end{align*} 
    1922 
    2023where $R$ is the radius of the building block, $D_S$ is the **surface** fractal 
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