Changeset 29afc50 in sasmodels for doc/guide/pd/polydispersity.rst

Timestamp:

Apr 4, 2018 7:03:51 AM (7 years ago)

Author:

smk78

Branches:

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

Children:

05df1de, d712a0f

Parents:

c462169

Message:

More tweaks to polydispersity.rst

File:

• doc/guide/pd/polydispersity.rst (modified) (5 diffs)

doc/guide/pd/polydispersity.rst

@@ -28 +28 @@
 sigmas $N_\sigma$ to include from the tails of the distribution, and the
 number of points used to compute the average. The center of the distribution
-is set by the value of the model parameter.
-
-Volume parameters have polydispersity *PD* (not to be confused with a
-molecular weight distributions in polymer science), but orientation parameters
-use angular distributions of width $\sigma$.
+is set by the value of the model parameter. The meaning of a polydispersity 
+parameter *PD* (not to be confused with a molecular weight distributions 
+in polymer science) in a model depends on the type of parameter it is being 
+applied too.
+
+The distribution width applied to *volume* (ie, shape-describing) parameters 
+is relative to the center value such that $\sigma = \mathrm{PD} \cdot \bar x$. 
+However, the distribution width applied to *orientation* (ie, angle-describing) 
+parameters is just $\sigma = \mathrm{PD}$.
 
 $N_\sigma$ determines how far into the tails to evaluate the distribution,
@@ -69 +73 @@
 or angular orientations, use the Gaussian or Boltzmann distributions.
 
+If applying polydispersion to parameters describing angles, use the Uniform 
+distribution. Beware of using distributions that are always positive (eg, the 
+Lognormal) because angles can be negative!
+
 The array distribution allows a user-defined distribution to be applied.
 
@@ -215 +223 @@
 The polydispersity in sasmodels is given by
 
-.. math:: \text{PD} = p = \sigma / x_\text{med}
-
-The mean value of the distribution is given by $\bar x = \exp(\mu+ p^2/2)$
-and the peak value by $\max x = \exp(\mu - p^2)$.
+.. math:: \text{PD} = \sigma = p / x_\text{med}
+
+The mean value of the distribution is given by $\bar x = \exp(\mu+ \sigma^2/2)$
+and the peak value by $\max x = \exp(\mu - \sigma^2)$.
 
 The variance (the square of the standard deviation) of the *lognormal*
@@ -232 +240 @@
 .. figure:: pd_lognormal.jpg
 
-    Lognormal distribution.
+    Lognormal distribution for PD=0.1.
 
 For further information on the Lognormal distribution see:
@@ -334 +342 @@
 | 2017-05-08 Paul Kienzle
 | 2018-03-20 Steve King
+| 2018-04-04 Steve King