Changeset 7609046 in sasmodels for doc/guide/pd/polydispersity.rst
 Timestamp:
 Jul 19, 2018 12:47:44 PM (14 months ago)
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 master
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 f41027b
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 9ce5bcb (diff), 1d9998c (diff)
Note: this is a merge changeset, the changes displayed below correspond to the merge itself.
Use the (diff) links above to see all the changes relative to each parent.  gitauthor:
 Paul Kienzle <pkienzle@…> (07/19/18 12:47:44)
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 GitHub <noreply@…> (07/19/18 12:47:44)
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doc/guide/pd/polydispersity.rst
r9ce5bcb r7609046 20 20 P(q) = \text{scale} \langle F^* F \rangle / V + \text{background} 21 21 22 where $F$ is the scattering amplitude and $\langle\cdot\rangle$ denotes an 23 average over the size distribution. 22 where $F$ is the scattering amplitude and $\langle\cdot\rangle$ denotes an 23 average 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} 24 29 25 30 Each distribution is characterized by a center value $\bar x$ or … … 41 46 with larger values of $N_\sigma$ required for heavier tailed distributions. 42 47 The 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)$48 that $f(r  3\sigma_r)$ is tiny and therefore $f(r  3\sigma_r)f(r  3\sigma_r)$ 44 49 will not contribute much to the average may not hold when particles are large. 45 50 This, too, will require increasing $N_\sigma$. … … 63 68 These are all implemented as *numberaverage* distributions. 64 69 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 351353 <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). 65 79 66 80 Suggested Applications
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