# Changeset 63c6a08 in sasmodels

Ignore:
Timestamp:
Jul 27, 2016 3:54:44 PM (7 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:
3a45c2c, edf06e1
Parents:
ee5d14d
Message:

fix some latex problems

Location:
sasmodels/models
Files:
3 edited

### Legend:

Unmodified
 r42356c8 .. math:: \begin{eqnarray} I(q) = (1-x)f_1^2(q) S_{11}(q) + 2[x(1-x)]^{1/2} f_1(q)f_2(q)S_{12}(q) + x\,f_2^2(q)S_{22}(q) \end{eqnarray} where $S_{ij}$ are the partial structure factors and $f_i$ are the scattering .. math:: :nowrap: \begin{eqnarray} x &=& \frac{(\phi_2 / \phi)\alpha^3}{(1-(\phi_2/\phi) + (\phi_2/\phi) \begin{align} x &= \frac{(\phi_2 / \phi)\alpha^3}{(1-(\phi_2/\phi) + (\phi_2/\phi) \alpha^3)} \\ \phi &=& \phi_1 + \phi_2 = \text{total volume fraction} \\ \alpha &=& R_1/R_2 = \text{size ratio} \end{eqnarray} \phi &= \phi_1 + \phi_2 = \text{total volume fraction} \\ \alpha &= R_1/R_2 = \text{size ratio} \end{align} The 2D scattering intensity is the same as 1D, regardless of the orientation of
 r42356c8 .. math:: P(q) &= [f]^2 / V_\text{particle} P(q) = [f]^2 / V_\text{particle} where .. math:: f    &= f_\text{core} :nowrap: \begin{align*} f &= f_\text{core} + \left(\sum_{\text{shell}=1}^N f_\text{shell}\right) + f_\text{solvent} \end{align*} The shells are spherically symmetric with particle density $\rho(r)$ and .. math:: :nowrap: \begin{align*} f_\text{core} \rho_\text{solvent}\frac{\sin(qr)}{qr}\,r^2\,\mathrm{d}r &= -3\rho_\text{solvent}V(r_N)\frac{j_1(q r_N)}{q r_N} \end{align*} where the spherical bessel function $j_1$ is .. math:: :nowrap: \begin{align*} f_\text{shell} &= 4 \pi \int_{r_{\text{shell}-1}}^{r_\text{shell}} \left[ B\exp + 3CV(r_{\text{shell}}) \frac{j_1(\beta_\text{out})}{\beta_\text{out}} - 3CV(r_{\text{shell}-1}) \frac{j_1(\beta_\text{in})}{\beta_\text{in}} \end{align*} for .. math:: :nowrap: \begin{align*} f_\text{shell} &= +3\rho_\text{out}V(r_\text{shell}) \frac{j_1(qr_\text{out})}{qr_\text{out}} -3\rho_\text{in}V(r_{\text{shell}-1}) \frac{j_1(qr_\text{in})}{qr_\text{in}} \end{align*} For $A = 0$, the exponential function has no dependence on the radius (so that