Changeset 19dcb933 in sasmodels for sasmodels/models/core_shell_cylinder.py

Timestamp:

Sep 3, 2014 3:16:10 AM (10 years ago)

Author:

Paul Kienzle <pkienzle@…>

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:

1c7ffdc

Parents:

87985ca

Message:

build docs for models

File:

• sasmodels/models/core_shell_cylinder.py (modified) (8 diffs)

sasmodels/models/core_shell_cylinder.py

@@ -12 +12 @@
 .. math::
 
-    P(q,\alpha) = \frac{\text{scale}}{V_s} f^2(q) + \text{background}
+    P(Q,\alpha) = {\text{scale} \over V_s} F^2(Q) + \text{background}
 
 where
@@ -18 +18 @@
 .. math::
 
-    f(q) = (\rho_c - \rho_s) V_c \
-           \frac{\sin( Q L/2 \cos \alpha)}{Q L/2 \cos \alpha} \
-           \frac{2 J_1 (Q R \sin \alpha)}{Q R \sin \alpha}
-           + (\rho_s - \rho_\text{solv}) V_s \
-           \frac{\sin( Q (L/2+T) \cos \alpha)}{Q (L/2+T) \cos \alpha}
-           \frac{2 J_1 (Q (R+T) \sin \alpha)}{Q (R+T) \sin \alpha}
+    F(Q) = &\ (\rho_c - \rho_s) V_c
+           {\sin \left( Q \tfrac12 L\cos\alpha \right)
+               \over Q \tfrac12 L\cos\alpha }
+           {2 J_1 \left( QR\sin\alpha \right)
+               \over QR\sin\alpha } \\
+         &\ + (\rho_s - \rho_\text{solv}) V_s
+           {\sin \left( Q \left(\tfrac12 L+T\right) \cos\alpha \right)
+               \over Q \left(\tfrac12 L +T \right) \cos\alpha }
+           { 2 J_1 \left( Q(R+T)\sin\alpha \right)
+               \over Q(R+T)\sin\alpha }
 
 and
@@ -29 +33 @@
 .. math::
 
-    V_s = \pi (R + T)^2 \dot (L + 2T)
-
+    V_s = \pi (R + T)^2 (L + 2T)
 
 and $\alpha$ is the angle between the axis of the cylinder and $\vec q$,
@@ -42 +45 @@
 shell is given by $L+2T$. $J1$ is the first order Bessel function.
 
-.. figure:: img/image069.JPG
+.. _core-shell-cylinder-geometry:
+
+.. figure:: img/core_shell_cylinder_geometry.jpg
 
     Core shell cylinder schematic.
@@ -49 +54 @@
 define the axis of the cylinder using two angles $\theta$ and $\phi$. As
 for the case of the cylinder, those angles are defined in
-Figure :num:`figure #cylinder-orientation`.
+:num:`figure #cylinder-orientation`.
 
 NB: The 2nd virial coefficient of the cylinder is calculated based on
 the radius and 2 length values, and used as the effective radius for
-$S(Q)$ when $P(Q) \dot S(Q)$ is applied.
+$S(Q)$ when $P(Q) \cdot S(Q)$ is applied.
 
 The $\theta$ and $\phi$ parameters are not used for the 1D output. Our
@@ -64 +69 @@
 Validation of our code was done by comparing the output of the 1D model to
 the output of the software provided by the NIST (Kline, 2006).
-Figure :num:`figure #core-shell-cylinder-comparison-1d` shows a comparison
+:num:`Figure #core-shell-cylinder-1d` shows a comparison
 of the 1D output of our model and the output of the NIST software.
 
-.. _core-shell-cylinder-comparison-1d:
+.. _core-shell-cylinder-1d:
 
-.. figure:: img/image070.JPG
+.. figure:: img/core_shell_cylinder_1d.jpg
 
     Comparison of the SasView scattering intensity for a core-shell cylinder
     with the output of the NIST SANS analysis software. The parameters were
-    set to: *scale=1.0 |Ang|*, *radius=20 |Ang|*, *thickness=10 |Ang|*,
-    *length=400 |Ang|*, *core_sld=1e-6 |Ang^-2|*, *shell_sld=4e-6 |Ang^-2|*,
-    *solvent_sld=1e-6 |Ang^-2|*, and *background=0.01 |cm^-1|*.
+    set to: *scale* = 1.0 |Ang|, *radius* = 20 |Ang|, *thickness* = 10 |Ang|,
+    *length* =400 |Ang|, *core_sld* =1e-6 |Ang^-2|, *shell_sld* = 4e-6 |Ang^-2|,
+    *solvent_sld* = 1e-6 |Ang^-2|, and *background* = 0.01 |cm^-1|.
 
 Averaging over a distribution of orientation is done by evaluating the
@@ -81 +86 @@
 implementation of the intensity for fully oriented cylinders, we can
 compare the result of averaging our 2D output using a uniform
-distribution $p(\theta,\phi)* = 1.0$.
-Figure :num:`figure #core-shell-cylinder-comparison-2d` shows the result
+distribution $p(\theta,\phi) = 1.0$.
+:num:`Figure #core-shell-cylinder-2d` shows the result
 of such a cross-check.
 
-.. _core-shell-cylinder-comparison-2d:
+.. _core-shell-cylinder-2d:
 
-.. figure:: img/image071.JPG
+.. figure:: img/core_shell_cylinder_2d.jpg
 
     Comparison of the intensity for uniformly distributed core-shell
     cylinders calculated from our 2D model and the intensity from the
-    NIST SANS analysis software. The parameters used were: *scale*=1.0*,
-    *radius=20 |Ang|*, *thickness=10 |Ang|*, *length*=400 |Ang|*,
-    *core_sld=1e-6 |Ang^-2|*, *shell_sld=4e-6 |Ang^-2|*,
-    *solvent_sld=1e-6 |Ang^-2|*, and *background=0.0 |cm^-1|*.
+    NIST SANS analysis software. The parameters used were: *scale* = 1.0,
+    *radius* = 20 |Ang|, *thickness* = 10 |Ang|, *length* = 400 |Ang|,
+    *core_sld* = 1e-6 |Ang^-2|, *shell_sld* = 4e-6 |Ang^-2|,
+    *solvent_sld* = 1e-6 |Ang^-2|, and *background* = 0.0 |cm^-1|.
 
 2013/11/26 - Description reviewed by Heenan, R.
@@ -101 +106 @@
 from numpy import pi, inf
 
-name = "cylinder"
+name = "core_shell_cylinder"
 title = "Right circular cylinder with a core-shell scattering length density profile."
 description = """