Changeset a5a12ca in sasmodels for doc/guide

Timestamp:

Oct 28, 2017 2:02:56 AM (7 years ago)

Author:

dirk

Branches:

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

Children:

75e4319

Parents:

6db17bd

Message:

implementation of Boltzmann distribution refs #1018

Location:

doc/guide/pd

Files:

• pd_boltzmann.jpg (added)
• polydispersity.rst (modified) (4 diffs)

doc/guide/pd/polydispersity.rst

@@ -40 +40 @@
 calculations are generally more robust with more data points or more angles.
 
-The following five distribution functions are provided:
+The following six distribution functions are provided:
 
 *  *Rectangular Distribution*
@@ -47 +47 @@
 *  *Schulz Distribution*
 *  *Array Distribution*
+*  *Boltzmann Distribution*
 
 These are all implemented as *number-average* distributions.
@@ -181 +182 @@
 ^^^^^^^^^^^^^^^^^^
 
-This user-definable distribution should be given as as a simple ASCII text
+This user-definable distribution should be given as a simple ASCII text
 file where the array is defined by two columns of numbers: $x$ and $f(x)$.
 The $f(x)$ will be normalized to 1 during the computation.
@@ -200 +201 @@
 given for the model will have no affect, and will be ignored when computing
 the average.  This means that any parameter with an array distribution will
-not be fittable.
+not be fitable.
+
+.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
+
+Boltzmann Distribution
+^^^^^^^^^^^^^^^^^^^^^^
+
+The Boltzmann Distribution is defined as
+
+.. math::
+
+    f(x) = \frac{1}{\text{Norm}}
+           \exp\left(-\frac{ | x - \bar x | }{\sigma}\right)
+
+where $\bar x$ is the mean of the distribution and *Norm* is a normalization
+factor which is determined during the numerical calculation.
+The width is defined as
+
+.. math:: \sigma=\frac{k T}{E}
+
+which is the inverse Boltzmann factor,
+where $k$ is the Boltzmann constant, $T$ the temperature in Kelvin and $E$ a
+characteristic energy per particle.
+
+.. figure:: pd_boltzmann.jpg
+
+    Boltzmann distribution.
 
 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ