Changes in / [9644b5a:dd4f5ed] in sasmodels


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  • deploy.sh

    r9d1e3e4 r2ba5ba5  
    1 if [[ $encrypted_cb04388797b6_iv ]] 
     1if [ "$encrypted_cb04388797b6_iv" ] 
    22then 
    33    eval "$(ssh-agent -s)" 

  • sasmodels/models/fractal_core_shell.py

    r8f04da4 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 

  • sasmodels/models/star_polymer.py

    r30b60d2 r5da1ac8  
    3636   Star polymers in solutions tend to have strong interparticle and osmotic 
    3737   effects. Thus the Benoit equation may not work well for many real cases. 
    38    At small $q$ the Guinier term and hence $I(q=0)$ is the same as for $f$ arms 
    39    of radius of gyration $R_g$, as described for the :ref:`mono-gauss-coil` 
    40    model. A newer model for star polymer incorporating excluded volume has been 
    41    developed by Li et al in arXiv:1404.6269 [physics.chem-ph]. 
     38   A newer model for star polymer incorporating excluded volume has been 
     39   developed by Li et al in arXiv:1404.6269 [physics.chem-ph].  Also, at small 
     40   $q$ the scattering, i.e. the Guinier term, is not sensitive to the number of 
     41   arms, and hence 'scale' here is simply $I(q=0)$ as described for the 
     42   :ref:`mono-gauss-coil` model, using volume fraction $\phi$ and volume V 
     43   for the whole star polymer. 
    4244 
    4345References 
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