Core Shell Bicelle Elliptical Belt Rough - core_shell_bicelle_elliptical_belt_rough.c
// NOTE that "length" here is the full height of the core!
static double
form_volume(double r_minor,
double x_core,
double thick_rim,
double thick_face,
double length)
{
return M_PI*( (r_minor + thick_rim)*(r_minor*x_core + thick_rim)* length +
square(r_minor)*x_core*2.0*thick_face );
}
static double
radius_from_excluded_volume(double r_minor, double x_core, double thick_rim, double thick_face, double length)
{
const double r_equiv = sqrt((r_minor + thick_rim)*(r_minor*x_core + thick_rim));
const double length_tot = length + 2.0*thick_face;
return 0.5*cbrt(0.75*r_equiv*(2.0*r_equiv*length_tot + (r_equiv + length_tot)*(M_PI*r_equiv + length_tot)));
}
static double
radius_from_volume(double r_minor, double x_core, double thick_rim, double thick_face, double length)
{
const double volume_bicelle = form_volume(r_minor, x_core, thick_rim,thick_face,length);
return cbrt(volume_bicelle/M_4PI_3);
}
static double
radius_from_diagonal(double r_minor, double x_core, double thick_rim, double thick_face, double length)
{
const double radius_max = (x_core < 1.0 ? r_minor : x_core*r_minor);
const double radius_max_tot = radius_max + thick_rim;
const double length_tot = length + 2.0*thick_face;
return sqrt(radius_max_tot*radius_max_tot + 0.25*length_tot*length_tot);
}
static double
radius_effective(int mode, double r_minor, double x_core, double thick_rim, double thick_face, double length)
{
switch (mode) {
default:
case 1: // equivalent cylinder excluded volume
return radius_from_excluded_volume(r_minor, x_core, thick_rim, thick_face, length);
case 2: // equivalent sphere
return radius_from_volume(r_minor, x_core, thick_rim, thick_face, length);
case 3: // outer rim average radius
return 0.5*r_minor*(1.0 + x_core) + thick_rim;
case 4: // outer rim min radius
return (x_core < 1.0 ? x_core*r_minor+thick_rim : r_minor+thick_rim);
case 5: // outer max radius
return (x_core > 1.0 ? x_core*r_minor+thick_rim : r_minor+thick_rim);
case 6: // half outer thickness
return 0.5*length + thick_face;
case 7: // half diagonal (this ignores the missing "corners", so may give unexpected answer if thick_face
// or thick_rim is extremely large)
return radius_from_diagonal(r_minor,x_core,thick_rim,thick_face,length);
}
}
static void
Fq(double q,
double *F1,
double *F2,
double r_minor,
double x_core,
double thick_rim,
double thick_face,
double length,
double rhoc,
double rhoh,
double rhor,
double rhosolv,
double sigma)
{
// core_shell_bicelle_elliptical_belt, RKH 5th Oct 2017, core_shell_bicelle_elliptical
// tested briefly against limiting cases of cylinder, hollow cylinder & elliptical cylinder models
// const double uplim = M_PI_4;
const double halfheight = 0.5*length;
//const double va = 0.0;
//const double vb = 1.0;
// inner integral limits
//const double vaj=0.0;
//const double vbj=M_PI;
const double r_major = r_minor * x_core;
const double r2A = 0.5*(square(r_major) + square(r_minor));
const double r2B = 0.5*(square(r_major) - square(r_minor));
const double vol1 = M_PI*r_minor*r_major*(2.0*halfheight);
const double vol2 = M_PI*(r_minor+thick_rim)*(r_major+thick_rim)*2.0*halfheight;
const double vol3 = M_PI*r_minor*r_major*2.0*(halfheight+thick_face);
// dr1,2,3 are now for Vcore, Vcore+rim, Vcore+face,
const double dr1 = vol1*(-rhor - rhoh + rhoc + rhosolv);
const double dr2 = vol2*(rhor-rhosolv);
const double dr3 = vol3*(rhoh-rhosolv);
//initialize integral
double outer_total_F1 = 0.0;
double outer_total_F2 = 0.0;
for(int i=0;i<GAUSS_N;i++) {
//setup inner integral over the ellipsoidal cross-section
// since we generate these lots of times, why not store them somewhere?
//const double cos_theta = ( GAUSS_Z[i]*(vb-va) + va + vb )/2.0;
const double cos_theta = ( GAUSS_Z[i] + 1.0 )/2.0;
const double sin_theta = sqrt(1.0 - cos_theta*cos_theta);
const double qab = q*sin_theta;
const double qc = q*cos_theta;
const double si1 = sas_sinx_x(halfheight*qc);
const double si2 = sas_sinx_x((halfheight+thick_face)*qc);
double inner_total_F1 = 0;
double inner_total_F2 = 0;
for(int j=0;j<GAUSS_N;j++) {
//76 gauss points for the inner integral (WAS 20 points,so this may make unecessarily slow, but playing safe)
//const double beta = ( GAUSS_Z[j]*(vbj-vaj) + vaj + vbj )/2.0;
const double beta = ( GAUSS_Z[j] +1.0)*M_PI_2;
const double rr = sqrt(r2A - r2B*cos(beta));
const double be1 = sas_2J1x_x(rr*qab);
const double be2 = sas_2J1x_x((rr+thick_rim)*qab);
const double f = dr1*si1*be1 + dr2*si1*be2 + dr3*si2*be1;
inner_total_F1 += GAUSS_W[j] * f;
inner_total_F2 += GAUSS_W[j] * f * f;
}
//now calculate outer integral
outer_total_F1 += GAUSS_W[i] * inner_total_F1;
outer_total_F2 += GAUSS_W[i] * inner_total_F2;
}
// now complete change of integration variables (1-0)/(1-(-1))= 0.5
outer_total_F1 *= 0.25;
outer_total_F2 *= 0.25;
//convert from [1e-12 A-1] to [cm-1]
*F1 = 1e-2*outer_total_F1*exp(-0.25*square(q*sigma));
*F2 = 1e-4*outer_total_F2*exp(-0.5*square(q*sigma));
}
static double
Iqabc(double qa, double qb, double qc,
double r_minor,
double x_core,
double thick_rim,
double thick_face,
double length,
double rhoc,
double rhoh,
double rhor,
double rhosolv,
double sigma)
{
// integrated 2d seems to match 1d reasonably well, except perhaps at very high Q
// Vol1,2,3 and dr1,2,3 are now for Vcore, Vcore+rim, Vcore+face,
const double dr1 = -rhor - rhoh + rhoc + rhosolv;
const double dr2 = rhor-rhosolv;
const double dr3 = rhoh-rhosolv;
const double r_major = r_minor*x_core;
const double halfheight = 0.5*length;
const double vol1 = M_PI*r_minor*r_major*length;
const double vol2 = M_PI*(r_minor+thick_rim)*(r_major+thick_rim)*2.0*halfheight;
const double vol3 = M_PI*r_minor*r_major*2.0*(halfheight+thick_face);
// Compute effective radius in rotated coordinates
const double qr_hat = sqrt(square(r_major*qb) + square(r_minor*qa));
// does this need to be changed for the "missing corners" where there there is no "belt" ?
const double qrshell_hat = sqrt(square((r_major+thick_rim)*qb)
+ square((r_minor+thick_rim)*qa));
const double be1 = sas_2J1x_x( qr_hat );
const double be2 = sas_2J1x_x( qrshell_hat );
const double si1 = sas_sinx_x( halfheight*qc );
const double si2 = sas_sinx_x( (halfheight + thick_face)*qc );
const double fq = vol1*dr1*si1*be1 + vol2*dr2*si1*be2 + vol3*dr3*si2*be1;
const double atten = exp(-0.5*(qa*qa + qb*qb + qc*qc)*(sigma*sigma));
return 1.0e-4 * fq*fq * atten;
}
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