Changeset 29afc50 in sasmodels
 Timestamp:
 Apr 4, 2018 7:03:51 AM (4 years ago)
 Branches:
 master, core_shell_microgels, magnetic_model, ticket1257vesicleproduct, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests
 Children:
 05df1de, d712a0f
 Parents:
 c462169
 File:

 1 edited
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doc/guide/pd/polydispersity.rst
rf4ae8c4 r29afc50 28 28 sigmas $N_\sigma$ to include from the tails of the distribution, and the 29 29 number of points used to compute the average. The center of the distribution 30 is set by the value of the model parameter. 31 32 Volume parameters have polydispersity *PD* (not to be confused with a 33 molecular weight distributions in polymer science), but orientation parameters 34 use angular distributions of width $\sigma$. 30 is set by the value of the model parameter. The meaning of a polydispersity 31 parameter *PD* (not to be confused with a molecular weight distributions 32 in polymer science) in a model depends on the type of parameter it is being 33 applied too. 34 35 The distribution width applied to *volume* (ie, shapedescribing) parameters 36 is relative to the center value such that $\sigma = \mathrm{PD} \cdot \bar x$. 37 However, the distribution width applied to *orientation* (ie, angledescribing) 38 parameters is just $\sigma = \mathrm{PD}$. 35 39 36 40 $N_\sigma$ determines how far into the tails to evaluate the distribution, … … 69 73 or angular orientations, use the Gaussian or Boltzmann distributions. 70 74 75 If applying polydispersion to parameters describing angles, use the Uniform 76 distribution. Beware of using distributions that are always positive (eg, the 77 Lognormal) because angles can be negative! 78 71 79 The array distribution allows a userdefined distribution to be applied. 72 80 … … 215 223 The polydispersity in sasmodels is given by 216 224 217 .. math:: \text{PD} = p = \sigma/ x_\text{med}218 219 The mean value of the distribution is given by $\bar x = \exp(\mu+ p^2/2)$220 and the peak value by $\max x = \exp(\mu  p^2)$.225 .. math:: \text{PD} = \sigma = p / x_\text{med} 226 227 The mean value of the distribution is given by $\bar x = \exp(\mu+ \sigma^2/2)$ 228 and the peak value by $\max x = \exp(\mu  \sigma^2)$. 221 229 222 230 The variance (the square of the standard deviation) of the *lognormal* … … 232 240 .. figure:: pd_lognormal.jpg 233 241 234 Lognormal distribution .242 Lognormal distribution for PD=0.1. 235 243 236 244 For further information on the Lognormal distribution see: … … 334 342  20170508 Paul Kienzle 335 343  20180320 Steve King 344  20180404 Steve King
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