Changeset 29afc50 in sasmodels


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Timestamp:
Apr 4, 2018 7:03:51 AM (4 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:
1 edited

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  • doc/guide/pd/polydispersity.rst

    rf4ae8c4 r29afc50  
    2828sigmas $N_\sigma$ to include from the tails of the distribution, and the 
    2929number 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 $\sigma$. 
     30is set by the value of the model parameter. The meaning of a polydispersity  
     31parameter *PD* (not to be confused with a molecular weight distributions  
     32in polymer science) in a model depends on the type of parameter it is being  
     33applied too. 
     34 
     35The distribution width applied to *volume* (ie, shape-describing) parameters  
     36is relative to the center value such that $\sigma = \mathrm{PD} \cdot \bar x$.  
     37However, the distribution width applied to *orientation* (ie, angle-describing)  
     38parameters is just $\sigma = \mathrm{PD}$. 
    3539 
    3640$N_\sigma$ determines how far into the tails to evaluate the distribution, 
     
    6973or angular orientations, use the Gaussian or Boltzmann distributions. 
    7074 
     75If applying polydispersion to parameters describing angles, use the Uniform  
     76distribution. Beware of using distributions that are always positive (eg, the  
     77Lognormal) because angles can be negative! 
     78 
    7179The array distribution allows a user-defined distribution to be applied. 
    7280 
     
    215223The polydispersity in sasmodels is given by 
    216224 
    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 
     227The mean value of the distribution is given by $\bar x = \exp(\mu+ \sigma^2/2)$ 
     228and the peak value by $\max x = \exp(\mu - \sigma^2)$. 
    221229 
    222230The variance (the square of the standard deviation) of the *lognormal* 
     
    232240.. figure:: pd_lognormal.jpg 
    233241 
    234     Lognormal distribution. 
     242    Lognormal distribution for PD=0.1. 
    235243 
    236244For further information on the Lognormal distribution see: 
     
    334342| 2017-05-08 Paul Kienzle 
    335343| 2018-03-20 Steve King 
     344| 2018-04-04 Steve King 
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