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

Ignore:
Timestamp:
Apr 4, 2018 7:03:51 AM (4 years ago)
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:
1 edited

### Legend:

Unmodified
 rf4ae8c4 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, 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. 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* .. figure:: pd_lognormal.jpg Lognormal distribution. Lognormal distribution for PD=0.1. For further information on the Lognormal distribution see: | 2017-05-08 Paul Kienzle | 2018-03-20 Steve King | 2018-04-04 Steve King