# Changeset bc69321 in sasmodels

Ignore:
Timestamp:
Mar 30, 2019 8:26:12 AM (11 months ago)
Branches:
master, ticket_1156, ticket_822_more_unit_tests
Children:
cddfef6
Parents:
77c91d0
Message:

Updated Fitting P@S model help

Location:
doc/guide
Files:
2 edited

### Legend:

Unmodified
 r77c91d0 .. Much of the following text was scraped from product.py .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ .. _Product Models: This help document is under development *Product models*, $P@S$ models for short, multiply the structure factor $S(q)$ by the form factor $P(q)$, modulated by the *effective radius* of the form factor. .. figure:: p_and_s_buttons.png **Product models**, or $P@S$ models for short, multiply the structure factor $S(Q)$ by the form factor $P(Q)$, modulated by the **effective radius** of the form factor. Many of the parameters in $P@S$ models take on specific meanings so that they * *scale*: The *scale* for $P@S$ models should usually be set to 1.0. In simple $P(Q)$ models **scale** often represents the volume fraction of material. In $P@S$ models **scale** should be set to 1.0, as the $P@S$ model contains a **volfraction** parameter. * *volfraction*: For hollow shapes, *volfraction* represents the volume fraction of material but the $S(q)$ calculation needs the volume fraction *enclosed by* The volume fraction of material. For hollow shapes, **volfraction** still represents the volume fraction of material but the $S(Q)$ calculation needs the volume fraction *enclosed by* *the shape.* SasView scales the user-specified volume fraction by the ratio form:shell computed from the average form volume and average shell volume returned from the $P(q)$ calculation (the original *volfraction* is divided by *shell_volume* to compute the number density, and then $P@S$ is scaled by that to get the absolute scaling on the final $I(q)$). returned from the $P(Q)$ calculation (the original volfraction is divided by the shell volume to compute the number density, and then $P@S$ is scaled by that to get the absolute scaling on the final $I(Q)$). * *radius_effective*: If part of the $S(q)$ calculation, the value of *radius_effective* may be polydisperse. If it is calculated by $P(q)$, then it will be the weighted The radial distance determining the range of the $S(Q)$ interaction. This may, or may not, be the same as any "size" parameters describing the form of the shape. For example, in a system containing freely-rotating cylinders, the volume of space each cylinder requires to tumble will be much larger than the volume of the cylinder itself. Thus the effective radius will be larger than either the radius or half-length of the cylinder. It may be sensible to tie or constrain **radius_effective** to one or other of these "size" parameters. If just part of the $S(Q)$ calculation, the value of **radius_effective** may be polydisperse. If it is calculated by $P(Q)$, then it will be the weighted average of the effective radii computed for the polydisperse shape parameters. * *structure_factor_mode*: If the $P@S$ model supports the $\beta(q)$ *correction* [1] then *structure_factor_mode* will appear in the parameter table after the $S(q)$ parameters. This mode may be 0 for the local monodisperse approximation: If the $P@S$ model supports the $\beta(Q)$ *decoupling correction* [1] then **structure_factor_mode** will appear in the parameter table after the $S(Q)$ parameters. If **structure_factor_mode = 0** then the *local monodisperse approximation* will be used, i.e.: $I = (scale / volume)$ x $P$ x $S + background$ $I(Q)$ = $(scale$ / $volume)$ x $P(Q)$ x $S(Q)$ + $background$ or 1 for the beta correction: If **structure_factor_mode = 1** then the $\beta(q)$ correction will be used, i.e.: $I = (scale$ x $volfraction / volume)$ x $($ + $^2 (S-1) ) + background$ $I(Q)$ = $(scale$ x $volfraction$ / $volume)$ x $($ + $^2$ x $(S(Q)$ - $1) )$ + $background$ where $F$ where $P(Q)$ = $<|F(Q)|^2>$. This is equivalent to: $I(Q)$ = $(scale$ / $volume)$ x $P(Q)$ x $( 1$ + $\beta(Q)$ x $(S(Q)$ - $1) )$ + $background$ More options may appear here in future as more complicated operations are The $\beta(Q)$ decoupling approximation has the effect of damping the oscillations in the normal (local monodisperse) $S(Q)$. When $\beta(Q)$ = 1 the local monodisperse approximation is recovered. More mode options may appear in future as more complicated operations are added. .. [#] Kotlarchyk, M.; Chen, S.-H. *J. Chem. Phys.*, 1983, 79, 2461 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ *Document History* | 2019-03-29 Paul Kienzle & Steve King | 2019-03-30 Paul Kienzle & Steve King