Changeset a5a12ca in sasmodels for doc/guide/pd/polydispersity.rst


Ignore:
Timestamp:
Oct 28, 2017 4:02:56 AM (5 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

File:
1 edited

Legend:

Unmodified
Added
Removed
  • doc/guide/pd/polydispersity.rst

    r1f058ea ra5a12ca  
    4040calculations are generally more robust with more data points or more angles. 
    4141 
    42 The following five distribution functions are provided: 
     42The following six distribution functions are provided: 
    4343 
    4444*  *Rectangular Distribution* 
     
    4747*  *Schulz Distribution* 
    4848*  *Array Distribution* 
     49*  *Boltzmann Distribution* 
    4950 
    5051These are all implemented as *number-average* distributions. 
     
    181182^^^^^^^^^^^^^^^^^^ 
    182183 
    183 This user-definable distribution should be given as as a simple ASCII text 
     184This user-definable distribution should be given as a simple ASCII text 
    184185file where the array is defined by two columns of numbers: $x$ and $f(x)$. 
    185186The $f(x)$ will be normalized to 1 during the computation. 
     
    200201given for the model will have no affect, and will be ignored when computing 
    201202the average.  This means that any parameter with an array distribution will 
    202 not be fittable. 
     203not be fitable. 
     204 
     205.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ 
     206 
     207Boltzmann Distribution 
     208^^^^^^^^^^^^^^^^^^^^^^ 
     209 
     210The Boltzmann Distribution is defined as 
     211 
     212.. math:: 
     213 
     214    f(x) = \frac{1}{\text{Norm}} 
     215           \exp\left(-\frac{ | x - \bar x | }{\sigma}\right) 
     216 
     217where $\bar x$ is the mean of the distribution and *Norm* is a normalization 
     218factor which is determined during the numerical calculation. 
     219The width is defined as 
     220 
     221.. math:: \sigma=\frac{k T}{E} 
     222 
     223which is the inverse Boltzmann factor, 
     224where $k$ is the Boltzmann constant, $T$ the temperature in Kelvin and $E$ a 
     225characteristic energy per particle. 
     226 
     227.. figure:: pd_boltzmann.jpg 
     228 
     229    Boltzmann distribution. 
    203230 
    204231.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ 
Note: See TracChangeset for help on using the changeset viewer.