Changeset d18f8a8 in sasmodels
- Timestamp:
- Dec 1, 2015 10:30:30 AM (9 years ago)
- Branches:
- master, core_shell_microgels, costrafo411, magnetic_model, release_v0.94, release_v0.95, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests
- Children:
- e88bb78
- Parents:
- eb69cce
- Location:
- sasmodels/models
- Files:
-
- 5 edited
-
hollow_cylinder.py (modified) (2 diffs)
-
lamellarCaille.py (modified) (1 diff)
-
lamellarCailleHG.py (modified) (1 diff)
-
lamellarPC.py (modified) (4 diffs)
-
stickyhardsphere.py (modified) (1 diff)
Legend:
- Unmodified
- Added
- Removed
-
sasmodels/models/hollow_cylinder.py
reb69cce rd18f8a8 19 19 .. math:: 20 20 21 %\begin{align*} % isn't working with pdflatex22 \begin{array}{rl}23 21 P(q) &= (\text{scale})V_\text{shell}\Delta\rho^2 24 22 \int_0^{1}\Psi^2 … … 31 29 \gamma &= R_\text{core} / R_\text{shell} \\ 32 30 V_\text{shell} &= \pi \left(R_\text{shell}^2 - R_\text{core}^2 \right)L \\ 33 J_1(x) &= (\sin(x)-x\cdot \cos(x)) / x^2 \\ 34 \end{array} 31 J_1(x) &= (\sin(x)-x\cdot \cos(x)) / x^2 35 32 36 33 where *scale* is a scale factor and $J_1$ is the 1st order -
sasmodels/models/lamellarCaille.py
reb69cce rd18f8a8 30 30 31 31 .. math:: 32 :nowrap: 32 33 33 %\begin{align*} % isn't working with pdflatex 34 \begin{array}{rll} 34 \begin{align*} 35 35 \alpha(n) &= \frac{\eta_{cp}}{4\pi^2} \left(\ln(\pi n)+\gamma_E\right) 36 & \\36 && \\ 37 37 \gamma_E &= 0.5772156649 38 & \text{Euler's constant} \\38 && \text{Euler's constant} \\ 39 39 \eta_{cp} &= \frac{q_o^2k_B T}{8\pi\sqrt{K\overline{B}}} 40 & \text{Caille constant} \\ 41 & 42 \end{array} 40 && \text{Caille constant} 41 \end{align*} 43 42 44 43 Here $d$ = (repeat) spacing, $\delta$ = bilayer thickness, -
sasmodels/models/lamellarCailleHG.py
reb69cce rd18f8a8 30 30 31 31 .. math:: 32 :nowrap: 32 33 33 %\begin{align*} % isn't working with pdflatex 34 \begin{array}{rll} 34 \begin{align*} 35 35 \alpha(n) &= \frac{\eta_{cp}}{4\pi^2} \left(\ln(\pi n)+\gamma_E\right) 36 & \\36 && \\ 37 37 \gamma_E &= 0.5772156649 38 & \text{Euler's constant} \\38 && \text{Euler's constant} \\ 39 39 \eta_{cp} &= \frac{q_o^2k_B T}{8\pi\sqrt{K\overline{B}}} 40 & \text{Caille constant} \\ 41 & 42 \end{array} 40 && \text{Caille constant} 41 \end{align*} 43 42 44 43 -
sasmodels/models/lamellarPC.py
reb69cce rd18f8a8 23 23 24 24 - *spacing* is the average distance between adjacent layers 25 $\l eft<D\right>$, and25 $\langle D \rangle$, and 26 26 27 27 - *spacing_polydisp* is the relative standard deviation of the Gaussian 28 layer distance distribution $\sigma_D / \l eft<D\right>$.28 layer distance distribution $\sigma_D / \langle D \rangle$. 29 29 30 30 … … 49 49 50 50 51 Z_N(q) = \frac{1 - w^2}{1 + w^2 - 2w \cos(q \l eft<D\right>)}51 Z_N(q) = \frac{1 - w^2}{1 + w^2 - 2w \cos(q \langle D \rangle)} 52 52 + x_N S_N + (1 - x_N) S_{N+1} 53 53 … … 56 56 .. math:: 57 57 58 S_N(q) = \frac{a_N}{N}[1 + w^2 - 2 w \cos(q \l eft<D\right>)]^258 S_N(q) = \frac{a_N}{N}[1 + w^2 - 2 w \cos(q \langle D \rangle)]^2 59 59 60 60 and … … 62 62 .. math:: 63 63 64 \begin{array}{rcl} 65 a_N &=& 4w^2 - 2(w^3 + w) \cos(q \left<D\right>) 66 - 4w^{N+2}\cos(Nq \left<D\right>) \\ 67 &&{} + 2 w^{N+3}\cos[(N-1)q \left<D\right>] 68 + 2w^{N+1}\cos[(N+1)q \left<D\right>] 69 \end{array} 64 a_N &= 4w^2 - 2(w^3 + w) \cos(q \langle D \rangle) \\ 65 &\quad - 4w^{N+2}\cos(Nq \langle D \rangle) 66 + 2 w^{N+3}\cos[(N-1)q \langle D \rangle] 67 + 2w^{N+1}\cos[(N+1)q \langle D \rangle] 70 68 71 69 for the layer spacing distribution $w = \exp(-\sigma_D^2 q^2/2)$. -
sasmodels/models/stickyhardsphere.py
reb69cce rd18f8a8 18 18 .. math:: 19 19 20 %\begin{align*} % isn't working with pdflatex21 \begin{array}{rl}22 20 \tau &= \frac{1}{12\epsilon} \exp(u_o / kT) \\ 23 \epsilon &= \Delta / (\sigma + \Delta) \\ 24 \end{array} 21 \epsilon &= \Delta / (\sigma + \Delta) 25 22 26 23 where the interaction potential is
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