Changeset d712a0f in sasmodels


Ignore:
Timestamp:
Apr 5, 2018 4:06:06 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:
1cdfd47
Parents:
29afc50
Message:

Further tweaks to polydispersity.rst

File:
1 edited

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  • doc/guide/pd/polydispersity.rst

    r29afc50 rd712a0f  
    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 $N_\sigma$. 
     
    6368 
    6469Additional distributions are under consideration. 
     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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