Changeset 041bc75 in sasmodels

Timestamp:

Oct 11, 2016 9:06:38 AM (8 years ago)

Author:

richardh

Branches:

master, core_shell_microgels, costrafo411, magnetic_model, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests

Children:

483a022

Parents:

19e7ca7

Message:

better equations in multilayer_vesicle and typo sorted in core_shell_bicelle

Location:

sasmodels/models

Files:

• core_shell_bicelle.py (modified) (1 diff)
• multilayer_vesicle.py (modified) (1 diff)

sasmodels/models/core_shell_bicelle.py

@@ -40 +40 @@
 .. math::
 
-    I(Q,\alpha) = \frac{\text{scale}}{V} \cdot
+    I(Q,\alpha) = \frac{\text{scale}}{V_t} \cdot
         F(Q,\alpha)^2 + \text{background}
 

sasmodels/models/multilayer_vesicle.py

@@ -15 +15 @@
 
 See the :ref:`core-shell-sphere` model for more documentation.
+
+The 1D scattering intensity is calculated in the following way (Guinier, 1955)
+
+.. math::
+
+    P(q) = \frac{\text{scale.volfraction}}{V_t} F^2(q) + \text{background}
+
+where
+
+.. math::
+
+     F(q) = (\rho_{shell}-\rho_{solv}) \sum_{i=1}^{n\_pairs} \left[
+     3V(R_i)\frac{\sin(qR_i)-qR_i\cos(qR_i)}{(qR_i)^3} \\
+      - 3V(R_i+t_s)\frac{\sin(q(R_i+t_s))-q(R_i+t_s)\cos(q(R_i+t_s))}{(q(R_i+t_s))^3}
+     \right]
+
+
+where $R_i = r_c + (i-1)(t_s + t_w)$
+   
+where $V_t$ is the volume of the whole particle, $V(R)$ is the volume of a sphere
+of radius $R$, $r_c$ is the radius of the core, $\rho_{shell}$ is the scattering length 
+density of a shell, $\rho_{solv}$ is the scattering length density of the solvent.
+
 
 The 2D scattering intensity is the same as 1D, regardless of the orientation