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static double
shell_volume(double radius, double thickness)
{
return M_4PI_3 * (cube(radius+thickness) - cube(radius));
}
static double
form_volume(double radius, double thickness)
{
return M_4PI_3 * cube(radius+thickness);
}
static double
radius_effective(int mode, double radius, double thickness)
{
// case 1: outer radius
return radius + thickness;
}
static void
Fq(double q,
double *F1,
double *F2,
double sld,
double sld_solvent,
double volfraction,
double radius,
double thickness)
/*
scattering from a unilamellar vesicle.
same functional form as the core-shell sphere, but more intuitive for
a vesicle
*/
{
double vol,contrast,f;
// core first, then add in shell
contrast = sld_solvent-sld;
vol = M_4PI_3*cube(radius);
f = vol * sas_3j1x_x(q*radius) * contrast;
//now the shell. No volume normalization as this is done by the caller
contrast = sld-sld_solvent;
vol = M_4PI_3*cube(radius+thickness);
f += vol * sas_3j1x_x(q*(radius+thickness)) * contrast;
//rescale to [cm-1].
// With volume fraction as part of the model in the dilute limit need
// to return F2 = Vf <fq^2>. In order for beta approx. to work correctly
// need F1^2/F2 equal to <fq>^2 / <fq^2>. By returning F1 = sqrt(Vf) <fq>
// and F2 = Vf <fq^2> both conditions are satisfied.
// Since Vf is the volume fraction of vesicles of all radii, it is
// constant when averaging F1 and F2 over radii and so pops out of the
// polydispersity loop, so it is safe to apply it inside the model
// (albeit conceptually ugly).
*F1 = 1e-2 * sqrt(volfraction) * f;
*F2 = 1.0e-4 * volfraction * f * f;
}
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