Changeset ca04add in sasmodels


Ignore:
Timestamp:
Sep 13, 2017 7:29:11 AM (7 years ago)
Author:
lewis
Branches:
master, core_shell_microgels, costrafo411, magnetic_model, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests
Children:
dd4f5ed
Parents:
2ba5ba5
Message:

Modify model docs to render correctly on marketplace

Location:
sasmodels/models
Files:
8 edited

Legend:

Unmodified
Added
Removed

  • sasmodels/models/fractal_core_shell.py

    r64eecf7 rca04add  
    2222    \frac{\sin(qr_c)-qr_c\cos(qr_c)}{(qr_c)^3}+ 
    2323    3V_s(\rho_s-\rho_{solv}) 
    24     \frac{\sin(qr_s)-qr_s\cos(qr_s)}{(qr_s)^3}\right]^2 
    25  
     24    \frac{\sin(qr_s)-qr_s\cos(qr_s)}{(qr_s)^3}\right]^2 \\ 
    2625    S(q) &= 1 + \frac{D_f\ \Gamma\!(D_f-1)}{[1+1/(q\xi)^2]^{(D_f-1)/2}} 
    2726    \frac{\sin[(D_f-1)\tan^{-1}(q\xi)]}{(qr_s)^{D_f}} 

  • sasmodels/models/mass_surface_fractal.py

    r232bb12 rca04add  
    2222.. math:: 
    2323 
    24     I(q) = scale \times P(q) + background 
    25  
     24    I(q) = scale \times P(q) + background \\ 
    2625    P(q) = \left\{ \left[ 1+(q^2a)\right]^{D_m/2} \times 
    2726                   \left[ 1+(q^2b)\right]^{(6-D_s-D_m)/2} 
    28            \right\}^{-1} 
    29  
    30     a = R_{g}^2/(3D_m/2) 
    31  
    32     b = r_{g}^2/[-3(D_s+D_m-6)/2] 
    33  
     27           \right\}^{-1} \\ 
     28    a = R_{g}^2/(3D_m/2) \\ 
     29    b = r_{g}^2/[-3(D_s+D_m-6)/2] \\ 
    3430    scale = scale\_factor \times NV^2 (\rho_{particle} - \rho_{solvent})^2 
    3531 

  • sasmodels/models/mono_gauss_coil.py

    r404ebbd rca04add  
    2424 
    2525     I_0 &= \phi_\text{poly} \cdot V 
    26             \cdot (\rho_\text{poly} - \rho_\text{solv})^2 
    27  
    28      P(q) &= 2 [\exp(-Z) + Z - 1] / Z^2 
    29  
    30      Z &= (q R_g)^2 
    31  
     26            \cdot (\rho_\text{poly} - \rho_\text{solv})^2 \\ 
     27     P(q) &= 2 [\exp(-Z) + Z - 1] / Z^2 \\ 
     28     Z &= (q R_g)^2 \\ 
    3229     V &= M / (N_A \delta) 
    3330 

  • sasmodels/models/onion.py

    rbccb40f rca04add  
    8181        \left[ B\exp 
    8282            \left(A (r - r_{\text{shell}-1}) / \Delta t_\text{shell} \right) + C 
    83         \right] \frac{\sin(qr)}{qr}\,r^2\,\mathrm{d}r 
    84  
     83        \right] \frac{\sin(qr)}{qr}\,r^2\,\mathrm{d}r \\ 
    8584    &= 3BV(r_\text{shell}) e^A h(\alpha_\text{out},\beta_\text{out}) 
    8685        - 3BV(r_{\text{shell}-1}) h(\alpha_\text{in},\beta_\text{in}) 
    … …  
    9594    \begin{align*} 
    9695    B&=\frac{\rho_\text{out} - \rho_\text{in}}{e^A-1} 
    97          &C &= \frac{\rho_\text{in}e^A - \rho_\text{out}}{e^A-1} \\ 
     96         & C &= \frac{\rho_\text{in}e^A - \rho_\text{out}}{e^A-1} \\ 
    9897    \alpha_\text{in} &= A\frac{r_{\text{shell}-1}}{\Delta t_\text{shell}} 
    99          &\alpha_\text{out} &= A\frac{r_\text{shell}}{\Delta t_\text{shell}} \\ 
     98         & \alpha_\text{out} &= A\frac{r_\text{shell}}{\Delta t_\text{shell}} \\ 
    10099    \beta_\text{in} &= qr_{\text{shell}-1} 
    101         &\beta_\text{out} &= qr_\text{shell} \\ 
     100        & \beta_\text{out} &= qr_\text{shell} \\ 
    102101    \end{align*} 
    103102 

  • sasmodels/models/parallelepiped.py

    r30b60d2 rca04add  
    6262        \left\{S\left[\frac{\mu}{2}\cos\left(\frac{\pi}{2}u\right)\right] 
    6363               S\left[\frac{\mu a}{2}\sin\left(\frac{\pi}{2}u\right)\right] 
    64                \right\}^2 du 
    65  
    66     S(x) &= \frac{\sin x}{x} 
    67  
     64               \right\}^2 du \\ 
     65    S(x) &= \frac{\sin x}{x} \\ 
    6866    \mu &= qB 
    6967 
    … …  
    133131.. math:: 
    134132 
    135     \cos\alpha &= \hat A \cdot \hat q, 
    136  
    137     \cos\beta  &= \hat B \cdot \hat q, 
    138  
     133    \cos\alpha &= \hat A \cdot \hat q, \\ 
     134    \cos\beta  &= \hat B \cdot \hat q, \\ 
    139135    \cos\gamma &= \hat C \cdot \hat q 
    140136 

  • sasmodels/models/poly_gauss_coil.py

    r404ebbd rca04add  
    2121.. math:: 
    2222 
    23      I_0 &= \phi_\text{poly} \cdot V \cdot (\rho_\text{poly}-\rho_\text{solv})^2 
    24  
    25      P(q) &= 2 [(1 + UZ)^{-1/U} + Z - 1] / [(1 + U) Z^2] 
    26  
    27      Z &= [(q R_g)^2] / (1 + 2U) 
    28  
    29      U &= (Mw / Mn) - 1 = \text{polydispersity ratio} - 1 
    30  
     23     I_0 &= \phi_\text{poly} \cdot V \cdot (\rho_\text{poly}-\rho_\text{solv})^2 \\ 
     24     P(q) &= 2 [(1 + UZ)^{-1/U} + Z - 1] / [(1 + U) Z^2] \\ 
     25     Z &= [(q R_g)^2] / (1 + 2U) \\ 
     26     U &= (Mw / Mn) - 1 = \text{polydispersity ratio} - 1 \\ 
    3127     V &= M / (N_A \delta) 
    3228 

  • sasmodels/models/polymer_micelle.py

    r404ebbd rca04add  
    2626 
    2727.. math:: 
    28     P(q) = N^2\beta^2_s\Phi(qR)^2+N\beta^2_cP_c(q)+2N^2\beta_s\beta_cS_{sc}s_c(q)+N(N-1)\beta_c^2S_{cc}(q) 
    29  
    30     \beta_s = v\_core(sld\_core - sld\_solvent) 
    31  
     28    P(q) = N^2\beta^2_s\Phi(qR)^2+N\beta^2_cP_c(q)+2N^2\beta_s\beta_cS_{sc}s_c(q)+N(N-1)\beta_c^2S_{cc}(q) \\ 
     29    \beta_s = v\_core(sld\_core - sld\_solvent) \\ 
    3230    \beta_c = v\_corona(sld\_corona - sld\_solvent) 
    3331 
    … …  
    4139.. math:: 
    4240 
    43    P_c(q) &= 2 [\exp(-Z) + Z - 1] / Z^2 
    44  
     41   P_c(q) &= 2 [\exp(-Z) + Z - 1] / Z^2 \\ 
    4542   Z &= (q R_g)^2 
    4643 
    … …  
    5047.. math:: 
    5148 
    52    S_{sc}(q)=\Phi(qR)\psi(Z)\frac{sin(q(R+d.R_g))}{q(R+d.R_g)} 
    53  
    54    S_{cc}(q)=\psi(Z)^2\left[\frac{sin(q(R+d.R_g))}{q(R+d.R_g)} \right ]^2 
    55  
     49   S_{sc}(q)=\Phi(qR)\psi(Z)\frac{sin(q(R+d.R_g))}{q(R+d.R_g)} \\ 
     50   S_{cc}(q)=\psi(Z)^2\left[\frac{sin(q(R+d.R_g))}{q(R+d.R_g)} \right ]^2 \\ 
    5651   \psi(Z)=\frac{[1-exp^{-Z}]}{Z} 
    5752 

  • sasmodels/models/spherical_sld.py

    r2ad5d30 rca04add  
    5151    3 \rho_\text{core} V(r_\text{core}) 
    5252    \Big[ \frac{\sin(qr_\text{core}) - qr_\text{core} \cos(qr_\text{core})} 
    53     {qr_\text{core}^3} \Big] 
    54  
     53    {qr_\text{core}^3} \Big] \\ 
    5554    f_{\text{inter}_i} &= 4 \pi \int_{\Delta t_{ \text{inter}_i } } 
    56     \rho_{ \text{inter}_i } \frac{\sin(qr)} {qr} r^2 dr 
    57  
     55    \rho_{ \text{inter}_i } \frac{\sin(qr)} {qr} r^2 dr \\ 
    5856    f_{\text{shell}_i} &= 4 \pi \int_{\Delta t_{ \text{inter}_i } } 
    5957    \rho_{ \text{flat}_i } \frac{\sin(qr)} {qr} r^2 dr = 
    … …  
    6664    -3 \rho_{ \text{flat}_i } V(r_{ \text{inter}_i }) 
    6765    \Big[ \frac{\sin(qr_{\text{inter}_i}) - qr_{\text{flat}_i} 
    68     \cos(qr_{\text{inter}_i}) } {qr_{\text{inter}_i}^3} \Big] 
    69  
     66    \cos(qr_{\text{inter}_i}) } {qr_{\text{inter}_i}^3} \Big] \\ 
    7067    f_\text{solvent} &= 4 \pi \int_{r_N}^{\infty} \rho_\text{solvent} 
    7168    \frac{\sin(qr)} {qr} r^2 dr = 
    … …  
    122119    4 \pi \sum_{j=1}^{n_\text{steps}} 
    123120    \int_{r_j}^{r_{j+1}} \rho_{ \text{inter}_i } (r_j) 
    124     \frac{\sin(qr)} {qr} r^2 dr 
    125  
    126     &\approx 4 \pi \sum_{j=1}^{n_\text{steps}} \Big[ 
     121    \frac{\sin(qr)} {qr} r^2 dr \\ 
     122    \approx 4 \pi \sum_{j=1}^{n_\text{steps}} \Big[ 
    127123    3 ( \rho_{ \text{inter}_i } ( r_{j+1} ) - \rho_{ \text{inter}_i } 
    128124    ( r_{j} ) V (r_j) 
    129125    \Big[ \frac {r_j^2 \beta_\text{out}^2 \sin(\beta_\text{out}) 
    130126    - (\beta_\text{out}^2-2) \cos(\beta_\text{out}) } 
    131     {\beta_\text{out}^4 } \Big] 
    132  
    133     &{} - 3 ( \rho_{ \text{inter}_i } ( r_{j+1} ) - \rho_{ \text{inter}_i } 
     127    {\beta_\text{out}^4 } \Big] \\ 
     128    {} - 3 ( \rho_{ \text{inter}_i } ( r_{j+1} ) - \rho_{ \text{inter}_i } 
    134129    ( r_{j} ) V ( r_{j-1} ) 
    135130    \Big[ \frac {r_{j-1}^2 \sin(\beta_\text{in}) 
    136131    - (\beta_\text{in}^2-2) \cos(\beta_\text{in}) } 
    137     {\beta_\text{in}^4 } \Big] 
    138  
    139     &{} + 3 \rho_{ \text{inter}_i } ( r_{j+1} )  V ( r_j ) 
     132    {\beta_\text{in}^4 } \Big] \\ 
     133    {} + 3 \rho_{ \text{inter}_i } ( r_{j+1} )  V ( r_j ) 
    140134    \Big[ \frac {\sin(\beta_\text{out}) - \cos(\beta_\text{out}) } 
    141135    {\beta_\text{out}^4 } \Big] 
    … …  
    152146    \begin{align*} 
    153147    V(a) &= \frac {4\pi}{3}a^3 && \\ 
    154     a_\text{in} &\sim \frac{r_j}{r_{j+1} -r_j} \text{, } &a_\text{out} 
    155     &\sim \frac{r_{j+1}}{r_{j+1} -r_j} \\ 
    156     \beta_\text{in} &= qr_j \text{, } &\beta_\text{out} &= qr_{j+1} 
     148    a_\text{in} \sim \frac{r_j}{r_{j+1} -r_j} \text{, } & a_\text{out} 
     149    \sim \frac{r_{j+1}}{r_{j+1} -r_j} \\ 
     150    \beta_\text{in} &= qr_j \text{, } & \beta_\text{out} &= qr_{j+1} 
    157151    \end{align*} 
    158152 
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