source: sasmodels/sasmodels/models/core_shell_bicelle_elliptical_belt_rough.c @ 99658f6

core_shell_microgelsmagnetic_modelticket-1257-vesicle-productticket_1156ticket_1265_superballticket_822_more_unit_tests
Last change on this file since 99658f6 was 99658f6, checked in by grethevj, 13 months ago

updated ER functions including cylinder excluded volume, to match 4.x

  • Property mode set to 100644
File size: 7.1 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 +
10                 square(r_minor)*x_core*2.0*thick_face  );
11}
12
13static double
14radius_from_excluded_volume(double r_minor, double x_core, double thick_rim, double thick_face, double length)
15{
16    const double r_equiv     = sqrt((r_minor + thick_rim)*(r_minor*x_core + thick_rim));
17    const double length_tot  = length + 2.0*thick_face;
18    return 0.5*cbrt(0.75*r_equiv*(2.0*r_equiv*length_tot + (r_equiv + length_tot)*(M_PI*r_equiv + length_tot)));
19}
20
21static double
22radius_from_volume(double r_minor, double x_core, double thick_rim, double thick_face, double length)
23{
24    const double volume_bicelle = form_volume(r_minor, x_core, thick_rim,thick_face,length);
25    return cbrt(volume_bicelle/M_4PI_3);
26}
27
28static double
29radius_from_diagonal(double r_minor, double x_core, double thick_rim, double thick_face, double length)
30{
31    const double radius_max = (x_core < 1.0 ? r_minor : x_core*r_minor);
32    const double radius_max_tot = radius_max + thick_rim;
33    const double length_tot = length + 2.0*thick_face;
34    return sqrt(radius_max_tot*radius_max_tot + 0.25*length_tot*length_tot);
35}
36
37static double
38effective_radius(int mode, double r_minor, double x_core, double thick_rim, double thick_face, double length)
39{
40    switch (mode) {
41    default:
42    case 1: // equivalent cylinder excluded volume
43        return radius_from_excluded_volume(r_minor, x_core, thick_rim, thick_face, length);
44    case 2: // equivalent sphere
45        return radius_from_volume(r_minor, x_core, thick_rim, thick_face, length);
46    case 3: // outer rim average radius
47        return 0.5*r_minor*(1.0 + x_core) + thick_rim;
48    case 4: // outer rim min radius
49        return (x_core < 1.0 ? x_core*r_minor+thick_rim : r_minor+thick_rim);
50    case 5: // outer max radius
51        return (x_core > 1.0 ? x_core*r_minor+thick_rim : r_minor+thick_rim);
52    case 6: // half outer thickness
53        return 0.5*length + thick_face;
54    case 7: // half diagonal (this ignores the missing "corners", so may give unexpected answer if thick_face
55            //  or thick_rim is extremely large)
56        return radius_from_diagonal(r_minor,x_core,thick_rim,thick_face,length);
57    }
58}
59
60static void
61Fq(double q,
62        double *F1,
63        double *F2,
64        double r_minor,
65        double x_core,
66        double thick_rim,
67        double thick_face,
68        double length,
69        double rhoc,
70        double rhoh,
71        double rhor,
72        double rhosolv,
73        double sigma)
74{
75     // core_shell_bicelle_elliptical_belt, RKH 5th Oct 2017, core_shell_bicelle_elliptical
76     // tested briefly against limiting cases of cylinder, hollow cylinder & elliptical cylinder models
77     //    const double uplim = M_PI_4;
78    const double halfheight = 0.5*length;
79    //const double va = 0.0;
80    //const double vb = 1.0;
81    // inner integral limits
82    //const double vaj=0.0;
83    //const double vbj=M_PI;
84
85    const double r_major = r_minor * x_core;
86    const double r2A = 0.5*(square(r_major) + square(r_minor));
87    const double r2B = 0.5*(square(r_major) - square(r_minor));
88    const double vol1 = M_PI*r_minor*r_major*(2.0*halfheight);
89    const double vol2 = M_PI*(r_minor+thick_rim)*(r_major+thick_rim)*2.0*halfheight;
90    const double vol3 = M_PI*r_minor*r_major*2.0*(halfheight+thick_face);
91    // dr1,2,3 are now for Vcore, Vcore+rim, Vcore+face,
92    const double dr1 = vol1*(-rhor - rhoh + rhoc + rhosolv);
93    const double dr2 = vol2*(rhor-rhosolv);
94    const double dr3 = vol3*(rhoh-rhosolv);
95
96    //initialize integral
97    double outer_total_F1 = 0.0;
98    double outer_total_F2 = 0.0;
99    for(int i=0;i<GAUSS_N;i++) {
100        //setup inner integral over the ellipsoidal cross-section
101        // since we generate these lots of times, why not store them somewhere?
102        //const double cos_theta = ( GAUSS_Z[i]*(vb-va) + va + vb )/2.0;
103        const double cos_theta = ( GAUSS_Z[i] + 1.0 )/2.0;
104        const double sin_theta = sqrt(1.0 - cos_theta*cos_theta);
105        const double qab = q*sin_theta;
106        const double qc = q*cos_theta;
107        const double si1 = sas_sinx_x(halfheight*qc);
108        const double si2 = sas_sinx_x((halfheight+thick_face)*qc);
109        double inner_total_F1 = 0;
110        double inner_total_F2 = 0;
111        for(int j=0;j<GAUSS_N;j++) {
112            //76 gauss points for the inner integral (WAS 20 points,so this may make unecessarily slow, but playing safe)
113            //const double beta = ( GAUSS_Z[j]*(vbj-vaj) + vaj + vbj )/2.0;
114            const double beta = ( GAUSS_Z[j] +1.0)*M_PI_2;
115            const double rr = sqrt(r2A - r2B*cos(beta));
116            const double be1 = sas_2J1x_x(rr*qab);
117            const double be2 = sas_2J1x_x((rr+thick_rim)*qab);
118            const double f = dr1*si1*be1 + dr2*si1*be2 + dr3*si2*be1;
119
120            inner_total_F1 += GAUSS_W[j] * f;
121            inner_total_F2 += GAUSS_W[j] * f * f;
122        }
123        //now calculate outer integral
124        outer_total_F1 += GAUSS_W[i] * inner_total_F1;
125        outer_total_F2 += GAUSS_W[i] * inner_total_F2;
126    }
127    // now complete change of integration variables (1-0)/(1-(-1))= 0.5
128    outer_total_F1 *= 0.25;
129    outer_total_F2 *= 0.25;
130
131    //convert from [1e-12 A-1] to [cm-1]
132    *F1 = 1e-2*outer_total_F1*exp(-0.25*square(q*sigma));
133    *F2 = 1e-4*outer_total_F2*exp(-0.5*square(q*sigma));
134}
135
136static double
137Iqabc(double qa, double qb, double qc,
138          double r_minor,
139          double x_core,
140          double thick_rim,
141          double thick_face,
142          double length,
143          double rhoc,
144          double rhoh,
145          double rhor,
146          double rhosolv,
147          double sigma)
148{
149    // integrated 2d seems to match 1d reasonably well, except perhaps at very high Q
150    // Vol1,2,3 and dr1,2,3 are now for Vcore, Vcore+rim, Vcore+face,
151    const double dr1 = -rhor - rhoh + rhoc + rhosolv;
152    const double dr2 = rhor-rhosolv;
153    const double dr3 = rhoh-rhosolv;
154    const double r_major = r_minor*x_core;
155    const double halfheight = 0.5*length;
156    const double vol1 = M_PI*r_minor*r_major*length;
157    const double vol2 = M_PI*(r_minor+thick_rim)*(r_major+thick_rim)*2.0*halfheight;
158    const double vol3 = M_PI*r_minor*r_major*2.0*(halfheight+thick_face);
159
160    // Compute effective radius in rotated coordinates
161    const double qr_hat = sqrt(square(r_major*qb) + square(r_minor*qa));
162    // does this need to be changed for the "missing corners" where there there is no "belt" ?
163    const double qrshell_hat = sqrt(square((r_major+thick_rim)*qb)
164                                   + square((r_minor+thick_rim)*qa));
165    const double be1 = sas_2J1x_x( qr_hat );
166    const double be2 = sas_2J1x_x( qrshell_hat );
167    const double si1 = sas_sinx_x( halfheight*qc );
168    const double si2 = sas_sinx_x( (halfheight + thick_face)*qc );
169    const double fq = vol1*dr1*si1*be1 + vol2*dr2*si1*be2 +  vol3*dr3*si2*be1;
170    const double atten = exp(-0.5*(qa*qa + qb*qb + qc*qc)*(sigma*sigma));
171    return 1.0e-4 * fq*fq * atten;
172}
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