Changeset 40a87fa in sasmodels for sasmodels/models/guinier_porod.py

Timestamp:

Aug 8, 2016 11:24:11 AM (8 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:

2472141

Parents:

2d65d51

Message:

lint and latex cleanup

File:

• sasmodels/models/guinier_porod.py (modified) (4 diffs)

sasmodels/models/guinier_porod.py

@@ -1 @@
-# pylint: disable=line-too-long
 r"""
 Calculates the scattering for a generalized Guinier/power law object.
@@ -13 +12 @@
 
 .. math::
-    I(q) = \frac{G}{Q^s} \ \exp{\left[ \frac{-Q^2R_g^2}{3-s} \right]} \textrm{ for } Q \leq Q_1
-    \\
-    I(q) = D / Q^m \textrm{ for } Q \geq Q_1
+
+    I(q) = \begin{cases}
+    \frac{G}{Q^s}\ \exp{\left[\frac{-Q^2R_g^2}{3-s} \right]} & Q \leq Q_1 \\
+    D / Q^m  & Q \geq Q_1
+    \end{cases}
 
 This is based on the generalized Guinier law for such elongated objects
-(see the Glatter reference below). For 3D globular objects (such as spheres), $s = 0$
-and one recovers the standard Guinier formula.
-For 2D symmetry (such as for rods) $s = 1$,
-and for 1D symmetry (such as for lamellae or platelets) $s = 2$.
-A dimensionality parameter ($3-s$) is thus defined, and is 3 for spherical objects,
-2 for rods, and 1 for plates.
+(see the Glatter reference below). For 3D globular objects (such as spheres),
+$s = 0$ and one recovers the standard Guinier formula. For 2D symmetry
+(such as for rods) $s = 1$, and for 1D symmetry (such as for lamellae or
+platelets) $s = 2$. A dimensionality parameter ($3-s$) is thus defined,
+and is 3 for spherical objects, 2 for rods, and 1 for plates.
 
-Enforcing the continuity of the Guinier and Porod functions and their derivatives yields
+Enforcing the continuity of the Guinier and Porod functions and their
+derivatives yields
 
 .. math::
+
     Q_1 = \frac{1}{R_g} \sqrt{(m-s)(3-s)/2}
 
@@ -33 +35 @@
 
 .. math::
-    D = G \ \exp{ \left[ \frac{-Q_1^2 R_g^2}{3-s} \right]} \ Q_1^{m-s}
-      = \frac{G}{R_g^{m-s}} \ \exp{\left[  -\frac{m-s}{2} \right]} \left( \frac{(m-s)(3-s)}{2} \right)^{\frac{m-s}{2}}
+
+    D &= G \ \exp{ \left[ \frac{-Q_1^2 R_g^2}{3-s} \right]} \ Q_1^{m-s}
+
+      &= \frac{G}{R_g^{m-s}} \ \exp \left[ -\frac{m-s}{2} \right]
+          \left( \frac{(m-s)(3-s)}{2} \right)^{\frac{m-s}{2}}
 
 
-Note that the radius-of-gyration for a sphere of radius R is given by $R_g = R \sqrt(3/5)$.
-
-For a cylinder of radius $R$ and length $L$,    $R_g^2 = \frac{L^2}{12} + \frac{R^2}{2}$
-
-from which the cross-sectional radius-of-gyration for a randomly oriented thin 
-cylinder is $R_g = R / \sqrt(2)$.
-
-and the cross-sectional radius-of-gyration of a randomly oriented lamella
-of thickness $T$ is given by $R_g = T / \sqrt(12)$.
+Note that the radius of gyration for a sphere of radius $R$ is given
+by $R_g = R \sqrt{3/5}$. For a cylinder of radius $R$ and length $L$,
+$R_g^2 = \frac{L^2}{12} + \frac{R^2}{2}$ from which the cross-sectional
+radius of gyration for a randomly oriented thin cylinder is $R_g = R/\sqrt{2}$
+and the cross-sectional radius of gyration of a randomly oriented lamella
+of thickness $T$ is given by $R_g = T / \sqrt{12}$.
 
 For 2D data: The 2D scattering intensity is calculated in the same way as 1D,
@@ -57 +59 @@
 ---------
 
-A Guinier, G Fournet, Small-Angle Scattering of X-Rays, John Wiley and Sons, New York, (1955)
+A Guinier, G Fournet, *Small-Angle Scattering of X-Rays*,
+John Wiley and Sons, New York, (1955)
 
-O Glatter, O Kratky, Small-Angle X-Ray Scattering, Academic Press (1982)
+O Glatter, O Kratky, *Small-Angle X-Ray Scattering*, Academic Press (1982)
 Check out Chapter 4 on Data Treatment, pages 155-156.
 """