Changeset bc69321 in sasmodels
 Timestamp:
 Mar 30, 2019 8:26:12 AM (11 months ago)
 Branches:
 master, ticket_1156, ticket_822_more_unit_tests
 Children:
 cddfef6
 Parents:
 77c91d0
 Location:
 doc/guide
 Files:

 2 edited
Legend:
 Unmodified
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 Removed

doc/guide/fitting_sq.rst
r77c91d0 rbc69321 3 3 .. Much of the following text was scraped from product.py 4 4 5 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ Z5 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ 6 6 7 7 .. _Product Models: … … 14 14 This help document is under development 15 15 16 *Product models*, $P@S$ models for short, multiply the structure factor $S(q)$ by 17 the form factor $P(q)$, modulated by the *effective radius* of the form factor. 16 .. figure:: p_and_s_buttons.png 17 18 **Product models**, or $P@S$ models for short, multiply the structure factor 19 $S(Q)$ by the form factor $P(Q)$, modulated by the **effective radius** of the 20 form factor. 18 21 19 22 Many of the parameters in $P@S$ models take on specific meanings so that they … … 22 25 * *scale*: 23 26 24 The *scale* for $P@S$ models should usually be set to 1.0. 27 In simple $P(Q)$ models **scale** often represents the volume fraction of 28 material. 29 30 In $P@S$ models **scale** should be set to 1.0, as the $P@S$ model contains a 31 **volfraction** parameter. 25 32 26 33 * *volfraction*: 27 34 28 For hollow shapes, *volfraction* represents the volume fraction of 29 material but the $S(q)$ calculation needs the volume fraction *enclosed by* 35 The volume fraction of material. 36 37 For hollow shapes, **volfraction** still represents the volume fraction of 38 material but the $S(Q)$ calculation needs the volume fraction *enclosed by* 30 39 *the shape.* SasView scales the userspecified volume fraction by the ratio 31 40 form:shell computed from the average form volume and average shell volume 32 returned from the $P( q)$ calculation (the original *volfraction*is divided33 by *shell_volume*to compute the number density, and then $P@S$ is scaled34 by that to get the absolute scaling on the final $I( q)$).41 returned from the $P(Q)$ calculation (the original volfraction is divided 42 by the shell volume to compute the number density, and then $P@S$ is scaled 43 by that to get the absolute scaling on the final $I(Q)$). 35 44 36 45 * *radius_effective*: 37 46 38 If part of the $S(q)$ calculation, the value of *radius_effective* may be 39 polydisperse. If it is calculated by $P(q)$, then it will be the weighted 47 The radial distance determining the range of the $S(Q)$ interaction. 48 49 This may, or may not, be the same as any "size" parameters describing the 50 form of the shape. For example, in a system containing freelyrotating 51 cylinders, the volume of space each cylinder requires to tumble will be 52 much larger than the volume of the cylinder itself. Thus the effective 53 radius will be larger than either the radius or halflength of the 54 cylinder. It may be sensible to tie or constrain **radius_effective** to one 55 or other of these "size" parameters. 56 57 If just part of the $S(Q)$ calculation, the value of **radius_effective** may 58 be polydisperse. If it is calculated by $P(Q)$, then it will be the weighted 40 59 average of the effective radii computed for the polydisperse shape 41 60 parameters. … … 43 62 * *structure_factor_mode*: 44 63 45 If the $P@S$ model supports the $\beta(q)$ *correction* [1] then 46 *structure_factor_mode* will appear in the parameter table after the $S(q)$ 47 parameters. This mode may be 0 for the local monodisperse approximation: 64 If the $P@S$ model supports the $\beta(Q)$ *decoupling correction* [1] then 65 **structure_factor_mode** will appear in the parameter table after the $S(Q)$ 66 parameters. 67 68 If **structure_factor_mode = 0** then the *local monodisperse approximation* 69 will be used, i.e.: 48 70 49 $I = (scale / volume)$ x $P$ x $S +background$71 $I(Q)$ = $(scale$ / $volume)$ x $P(Q)$ x $S(Q)$ + $background$ 50 72 51 or 1 for the beta correction: 73 If **structure_factor_mode = 1** then the $\beta(q)$ correction will be 74 used, i.e.: 52 75 53 $I = (scale$ x $volfraction / volume)$ x $( <FF>$ + $<F>^2 (S1) ) +background$76 $I(Q)$ = $(scale$ x $volfraction$ / $volume)$ x $( <F(Q)^2>$ + $<F(Q)>^2$ x $(S(Q)$  $1) )$ + $background$ 54 77 55 where $F$ 78 where $P(Q)$ = $<F(Q)^2>$. 79 80 This is equivalent to: 81 82 $I(Q)$ = $(scale$ / $volume)$ x $P(Q)$ x $( 1$ + $\beta(Q)$ x $(S(Q)$  $1) )$ + $background$ 56 83 57 More options may appear here in future as more complicated operations are 84 The $\beta(Q)$ decoupling approximation has the effect of damping the 85 oscillations in the normal (local monodisperse) $S(Q)$. When $\beta(Q)$ = 1 86 the local monodisperse approximation is recovered. 87 88 More mode options may appear in future as more complicated operations are 58 89 added. 59 90 … … 63 94 .. [#] Kotlarchyk, M.; Chen, S.H. *J. Chem. Phys.*, 1983, 79, 2461 64 95 65 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ Z96 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ 66 97 67 98 *Document History* 68 99 69  201903 29Paul Kienzle & Steve King100  20190330 Paul Kienzle & Steve King 
doc/guide/index.rst
rda5536f rbc69321 12 12 pd/polydispersity.rst 13 13 resolution.rst 14 plugin.rst 15 fitting_sq.rst 14 16 magnetism/magnetism.rst 15 17 orientation/orientation.rst 16 18 sesans/sans_to_sesans.rst 17 19 sesans/sesans_fitting.rst 18 plugin.rst19 20 scripting.rst 20 21 refs.rst
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