source: sasmodels/sasmodels/models/core_shell_bicelle_elliptical.c @ 82592da

core_shell_microgelsmagnetic_modelticket-1257-vesicle-productticket_1156ticket_1265_superballticket_822_more_unit_tests
Last change on this file since 82592da was 82592da, checked in by richardh, 7 years ago

swapped 2d qa with qb in three elliptical particles, edits to orientation doc

  • Property mode set to 100644
File size: 4.0 KB
Line 
1// NOTE that "length" here is the full height of the core!
2static double
3form_volume(double r_minor,
4    double x_core,
5    double thick_rim,
6    double thick_face,
7    double length)
8{
9    return M_PI*(r_minor+thick_rim)*(r_minor*x_core+thick_rim)*(length+2.0*thick_face);
10}
11
12static double
13Iq(double q,
14    double r_minor,
15    double x_core,
16    double thick_rim,
17    double thick_face,
18    double length,
19    double sld_core,
20    double sld_face,
21    double sld_rim,
22    double sld_solvent)
23{
24     // core_shell_bicelle_elliptical, RKH Dec 2016, based on elliptical_cylinder and core_shell_bicelle
25     // tested against limiting cases of cylinder, elliptical_cylinder, stacked_discs, and core_shell_bicelle
26    const double halfheight = 0.5*length;
27    const double r_major = r_minor * x_core;
28    const double r2A = 0.5*(square(r_major) + square(r_minor));
29    const double r2B = 0.5*(square(r_major) - square(r_minor));
30    const double vol1 = M_PI*r_minor*r_major*(2.0*halfheight);
31    const double vol2 = M_PI*(r_minor+thick_rim)*(r_major+thick_rim)*2.0*(halfheight+thick_face);
32    const double vol3 = M_PI*r_minor*r_major*2.0*(halfheight+thick_face);
33    const double dr1 = vol1*(sld_core-sld_face);
34    const double dr2 = vol2*(sld_rim-sld_solvent);
35    const double dr3 = vol3*(sld_face-sld_rim);
36
37    //initialize integral
38    double outer_sum = 0.0;
39    for(int i=0;i<76;i++) {
40        //setup inner integral over the ellipsoidal cross-section
41        //const double va = 0.0;
42        //const double vb = 1.0;
43        //const double cos_theta = ( Gauss76Z[i]*(vb-va) + va + vb )/2.0;
44        const double cos_theta = ( Gauss76Z[i] + 1.0 )/2.0;
45        const double sin_theta = sqrt(1.0 - cos_theta*cos_theta);
46        const double qab = q*sin_theta;
47        const double qc = q*cos_theta;
48        const double si1 = sas_sinx_x(halfheight*qc);
49        const double si2 = sas_sinx_x((halfheight+thick_face)*qc);
50        double inner_sum=0.0;
51        for(int j=0;j<76;j++) {
52            //76 gauss points for the inner integral (WAS 20 points,so this may make unecessarily slow, but playing safe)
53            // inner integral limits
54            //const double vaj=0.0;
55            //const double vbj=M_PI;
56            //const double phi = ( Gauss76Z[j]*(vbj-vaj) + vaj + vbj )/2.0;
57            const double phi = ( Gauss76Z[j] +1.0)*M_PI_2;
58            const double rr = sqrt(r2A - r2B*cos(phi));
59            const double be1 = sas_2J1x_x(rr*qab);
60            const double be2 = sas_2J1x_x((rr+thick_rim)*qab);
61            const double fq = dr1*si1*be1 + dr2*si2*be2 + dr3*si2*be1;
62
63            inner_sum += Gauss76Wt[j] * fq * fq;
64        }
65        //now calculate outer integral
66        outer_sum += Gauss76Wt[i] * inner_sum;
67    }
68
69    return outer_sum*2.5e-05;
70}
71
72static double
73Iqxy(double qa, double qb, double qc,
74    double r_minor,
75    double x_core,
76    double thick_rim,
77    double thick_face,
78    double length,
79    double sld_core,
80    double sld_face,
81    double sld_rim,
82    double sld_solvent)
83{
84    const double dr1 = sld_core-sld_face;
85    const double dr2 = sld_rim-sld_solvent;
86    const double dr3 = sld_face-sld_rim;
87    const double r_major = r_minor*x_core;
88    const double halfheight = 0.5*length;
89    const double vol1 = M_PI*r_minor*r_major*length;
90    const double vol2 = M_PI*(r_minor+thick_rim)*(r_major+thick_rim)*2.0*(halfheight+thick_face);
91    const double vol3 = M_PI*r_minor*r_major*2.0*(halfheight+thick_face);
92
93    // Compute effective radius in rotated coordinates
94    const double qr_hat = sqrt(square(r_major*qb) + square(r_minor*qa));
95    const double qrshell_hat = sqrt(square((r_major+thick_rim)*qb)
96                                   + square((r_minor+thick_rim)*qa));
97    const double be1 = sas_2J1x_x( qr_hat );
98    const double be2 = sas_2J1x_x( qrshell_hat );
99    const double si1 = sas_sinx_x( halfheight*qc );
100    const double si2 = sas_sinx_x( (halfheight + thick_face)*qc );
101    const double fq = vol1*dr1*si1*be1 + vol2*dr2*si2*be2 +  vol3*dr3*si2*be1;
102    return 1.0e-4 * fq*fq;
103}
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