Changeset bc69321 in sasmodels for doc/guide/fitting_sq.rst


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Timestamp:
Mar 30, 2019 8:26:12 AM (6 years ago)
Author:
smk78
Branches:
master, ticket_1156, ticket_822_more_unit_tests
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cddfef6
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77c91d0
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Updated Fitting P@S model help

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  • doc/guide/fitting_sq.rst

    r77c91d0 rbc69321  
    33.. Much of the following text was scraped from product.py 
    44 
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    66 
    77.. _Product Models: 
    … …  
    1414   This help document is under development 
    1515 
    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 
     20form factor. 
    1821 
    1922Many of the parameters in $P@S$ models take on specific meanings so that they 
    … …  
    2225* *scale*: 
    2326 
    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. 
    2532 
    2633* *volfraction*: 
    2734 
    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* 
    3039  *the shape.* SasView scales the user-specified volume fraction by the ratio 
    3140  form:shell computed from the average form volume and average shell volume 
    32   returned from the $P(q)$ calculation (the original *volfraction* is divided 
    33   by *shell_volume* to compute the number density, and then $P@S$ is scaled 
    34   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 $I(Q)$). 
    3544 
    3645* *radius_effective*: 
    3746 
    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 freely-rotating 
     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 half-length 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 
    4059  average of the effective radii computed for the polydisperse shape 
    4160  parameters. 
    … …  
    4362* *structure_factor_mode*: 
    4463 
    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.: 
    4870 
    49     $I = (scale / volume)$ x $P$ x $S + background$ 
     71    $I(Q)$ = $(scale$ / $volume)$ x $P(Q)$ x $S(Q)$ + $background$ 
    5072 
    51     or 1 for the beta correction: 
     73  If **structure_factor_mode = 1** then the $\beta(q)$ correction will be 
     74  used, i.e.: 
    5275 
    53     $I = (scale$ x $volfraction / volume)$ x $( <FF>$ + $<F>^2 (S-1) ) + background$ 
     76    $I(Q)$ = $(scale$ x $volfraction$ / $volume)$ x $( <F(Q)^2>$ + $<F(Q)>^2$ x $(S(Q)$ - $1) )$ + $background$ 
    5477 
    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 $(S(Q)$ - $1) )$ + $background$ 
    5683 
    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 
    5889  added. 
    5990 
    … …  
    6394.. [#] Kotlarchyk, M.; Chen, S.-H. *J. Chem. Phys.*, 1983, 79, 2461 
    6495 
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    6697 
    6798*Document History* 
    6899 
    69 | 2019-03-29 Paul Kienzle & Steve King 
     100| 2019-03-30 Paul Kienzle & Steve King 
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