Sasview Function:Core Multi Shell
Implementation of “Core Multi Shell” fitting Function of SASVIEW. SASVIEW reference is here: http://marketplace.sasview.org/models/19/.
(1) $I(q)=\frac{\phi}{V(R_N)}F^2(q)\cdot10^{-4}$ $[cm^{-1}]$
(2) $F(q) = \sum_{i=0}^N V(R_{i})(\rho_{i+1}-\rho_i) \cdot \frac {3 \cdot j_1(qR_i)}{qR_i}$
(3) $V(R)=\frac{4 \cdot \pi}{3}R^3$
(4) $N=3$
| $i=0$ | $\rho_0=\rho_{core}$ | $R_0=R_{core}$ |
|---|---|---|
| $i=1$ | $\rho_1=\rho_{shell-No.-1}$ | $R_1=R_{core}+\Delta_1$ |
| $i=2$ | $\rho_2=\rho_{shell-No.-2}$ | $R_2=R_{core}+\Delta_1+\Delta_2$ |
| … | ||
| $i=N$ | $\rho_N=\rho_{shell-No.-N}$ | $R_N=R_{core}+\sum_{j=1}^N\Delta_j$ |
| $i=N+1$ | $\rho_{N+1}=\rho_{solvent}$ | — |
c-code of SASVIEW “core_multi_shell.c” is saved as the header file sasview-core_multi_shell.h.
Full function (with volume fraction and normalised to the volume) is also implemented as the header-file sasview-multicoreshell-3-shells.h. This implementation could be used as a sub-function of a more complicated function.
Finally, standard fif-function is created: sphere-core-3x-shell.fif.
Compilation:
- download 4 header files below and save them to your qtitisas-folder: ./qtisas/FitFunctions/IncludedFunctions/ folder
- download sphere-core-3x-shell.fif file and save it to ./qtisas/FitFunctions/ folder
- select “sphere-core-3x-shell” function in Fit.Compile interface and compile it.
| h-files: | sasview.h | Copy h-files to ./qtisas/FitFunctions/IncludedFunctions/ folder |
|---|---|---|
| sasview-sas_3j1x_x.h Spherical Bessel function: $\frac {3 \cdot j_1(x)}{x}$ |
||
| sasview-core_multi_shell.h | ||
| sasview-multicoreshell-3-shells.h | ||
| FIF-file: | sphere-core-3x-shell.fif | Copy fif-file to ./qtisas/FitFunctions/ folder |