Changeset 45330ed in sasmodels

Timestamp:

Mar 20, 2016 12:09:06 PM (9 years ago)

Author:

richardh

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:

4416868

Parents:

b9f4c26

Message:

improved docs

Location:

sasmodels/models

Files:

• guinier.py (modified) (2 diffs)
• guinier_porod.py (modified) (1 diff)

sasmodels/models/guinier.py

@@ -5 +5 @@
 This model fits the Guinier function
 
-.. math:: q_1=\frac{1}{R_g}\sqrt{\frac{(m-s)(3-s)}{2}}
+.. math:: I(q) = scale \exp{\left[ \frac{-Q^2R_g^2}{3} \right]}
 
 to the data directly without any need for linearisation
-(*cf*. $\ln I(q)$ vs $q^2$\ ).
+(*cf*. the usual plot of $\ln I(q)$ vs $q^2$\ ). Note that you may have to 
+restrict the data range to include small q only, where the Guinier approximation
+actually applies. See also the guinier_porod model.
 
 For 2D data the scattering intensity is calculated in the same way as 1D,
@@ -27 +29 @@
 title = ""
 description = """
- I(q) = scale exp ( - rg^2 q^2 / 3.0 )
+ I(q) = scale.exp ( - rg^2 q^2 / 3.0 )
  
     List of default parameters:

sasmodels/models/guinier_porod.py

@@ -39 +39 @@
 Note that the radius-of-gyration for a sphere of radius R is given by $R_g = R \sqrt(3/5)$.
 
-The cross-sectional radius-of-gyration for a randomly oriented cylinder
-of radius R is given by $R_g = R / \sqrt(2)$.
+For a cylinder of radius $R$ and length $L$,    $R_g^2 = \frac{L^2}{12} + \frac{R^2}{2}$
 
-The cross-sectional radius-of-gyration of a randomly oriented lamella
+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 $R_g = T / \sqrt(12)$.