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

Timestamp:

Jul 19, 2018 10:47:44 AM (6 years ago)

Author:

GitHub <noreply@…>

Branches:

master

Children:

f41027b

Parents:

9ce5bcb (diff), 1d9998c (diff)
Note: this is a merge changeset, the changes displayed below correspond to the merge itself.
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git-author:

Paul Kienzle <pkienzle@…> (07/19/18 10:47:44)

git-committer:

GitHub <noreply@…> (07/19/18 10:47:44)

Message:

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

File:

• doc/guide/pd/polydispersity.rst (modified) (3 diffs)

doc/guide/pd/polydispersity.rst

@@ -20 +20 @@
   P(q) = \text{scale} \langle F^* F \rangle / V + \text{background}
 
-where $F$ is the scattering amplitude and $\langle\cdot\rangle$ denotes an
-average over the size distribution.
+where $F$ is the scattering amplitude and $\langle\cdot\rangle$ denotes an 
+average over the size distribution $f(x; \bar x, \sigma)$, giving
+
+.. math::
+
+  P(q) = \frac{\text{scale}}{V} \int_\mathbb{R} 
+  f(x; \bar x, \sigma) F^2(q, x)\, dx + \text{background}
 
 Each distribution is characterized by a center value $\bar x$ or
@@ -41 +46 @@
 with larger values of $N_\sigma$ required for heavier tailed distributions.
 The scattering in general falls rapidly with $qr$ so the usual assumption
-that $G(r - 3\sigma_r)$ is tiny and therefore $f(r - 3\sigma_r)G(r - 3\sigma_r)$
+that $f(r - 3\sigma_r)$ is tiny and therefore $f(r - 3\sigma_r)f(r - 3\sigma_r)$
 will not contribute much to the average may not hold when particles are large.
 This, too, will require increasing $N_\sigma$.
@@ -63 +68 @@
 These are all implemented as *number-average* distributions.
 
+
+.. note:: In 2009 IUPAC decided to introduce the new term 'dispersity' to replace 
+           the term 'polydispersity' (see `Pure Appl. Chem., (2009), 81(2), 
+           351-353 <http://media.iupac.org/publications/pac/2009/pdf/8102x0351.pdf>`_ 
+           in order to make the terminology describing distributions of properties 
+           unambiguous. Throughout the SasView documentation we continue to use the 
+           term polydispersity because one of the consequences of the IUPAC change is 
+           that orientational polydispersity would not meet their new criteria (which 
+           requires dispersity to be dimensionless).
 
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