Changeset 7609046 in sasmodels for doc/guide/pd/polydispersity.rst


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Timestamp:
Jul 19, 2018 12:47:44 PM (14 months ago)
Author:
GitHub <noreply@…>
Branches:
master
Children:
f41027b
Parents:
9ce5bcb (diff), 1d9998c (diff)
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git-author:
Paul Kienzle <pkienzle@…> (07/19/18 12:47:44)
git-committer:
GitHub <noreply@…> (07/19/18 12:47:44)
Message:

Merge branch 'master' into ticket-608-user-defined-weights

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  • doc/guide/pd/polydispersity.rst

    r9ce5bcb r7609046  
    2020  P(q) = \text{scale} \langle F^* F \rangle / V + \text{background} 
    2121 
    22 where $F$ is the scattering amplitude and $\langle\cdot\rangle$ denotes an 
    23 average over the size distribution. 
     22where $F$ is the scattering amplitude and $\langle\cdot\rangle$ denotes an  
     23average over the size distribution $f(x; \bar x, \sigma)$, giving 
     24 
     25.. math:: 
     26 
     27  P(q) = \frac{\text{scale}}{V} \int_\mathbb{R}  
     28  f(x; \bar x, \sigma) F^2(q, x)\, dx + \text{background} 
    2429 
    2530Each distribution is characterized by a center value $\bar x$ or 
     
    4146with larger values of $N_\sigma$ required for heavier tailed distributions. 
    4247The scattering in general falls rapidly with $qr$ so the usual assumption 
    43 that $G(r - 3\sigma_r)$ is tiny and therefore $f(r - 3\sigma_r)G(r - 3\sigma_r)$ 
     48that $f(r - 3\sigma_r)$ is tiny and therefore $f(r - 3\sigma_r)f(r - 3\sigma_r)$ 
    4449will not contribute much to the average may not hold when particles are large. 
    4550This, too, will require increasing $N_\sigma$. 
     
    6368These are all implemented as *number-average* distributions. 
    6469 
     70 
     71.. note:: In 2009 IUPAC decided to introduce the new term 'dispersity' to replace  
     72           the term 'polydispersity' (see `Pure Appl. Chem., (2009), 81(2),  
     73           351-353 <http://media.iupac.org/publications/pac/2009/pdf/8102x0351.pdf>`_  
     74           in order to make the terminology describing distributions of properties  
     75           unambiguous. Throughout the SasView documentation we continue to use the  
     76           term polydispersity because one of the consequences of the IUPAC change is  
     77           that orientational polydispersity would not meet their new criteria (which  
     78           requires dispersity to be dimensionless). 
    6579 
    6680Suggested Applications 
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