source: sasmodels/sasmodels/models/barbell.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, 10 months ago

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

  • Property mode set to 100644
File size: 4.9 KB
Line 
1#define INVALID(v) (v.radius_bell < v.radius)
2
3//barbell kernel - same as dumbell
4static double
5_bell_kernel(double qab, double qc, double h, double radius_bell,
6             double half_length)
7{
8    // translate a point in [-1,1] to a point in [lower,upper]
9    const double upper = 1.0;
10    const double lower = h/radius_bell;
11    const double zm = 0.5*(upper-lower);
12    const double zb = 0.5*(upper+lower);
13
14    // cos term in integral is:
15    //    cos (q (R t - h + L/2) cos(alpha))
16    // so turn it into:
17    //    cos (m t + b)
18    // where:
19    //    m = q R cos(alpha)
20    //    b = q(L/2-h) cos(alpha)
21    const double m = radius_bell*qc; // cos argument slope
22    const double b = (half_length-h)*qc; // cos argument intercept
23    const double qab_r = radius_bell*qab; // Q*R*sin(theta)
24    double total = 0.0;
25    for (int i = 0; i < GAUSS_N; i++){
26        const double t = GAUSS_Z[i]*zm + zb;
27        const double radical = 1.0 - t*t;
28        const double bj = sas_2J1x_x(qab_r*sqrt(radical));
29        const double Fq = cos(m*t + b) * radical * bj;
30        total += GAUSS_W[i] * Fq;
31    }
32    // translate dx in [-1,1] to dx in [lower,upper]
33    const double integral = total*zm;
34    const double bell_fq = 2.0*M_PI*cube(radius_bell)*integral;
35    return bell_fq;
36}
37
38static double
39_fq(double qab, double qc, double h,
40    double radius_bell, double radius, double half_length)
41{
42    const double bell_fq = _bell_kernel(qab, qc, h, radius_bell, half_length);
43    const double bj = sas_2J1x_x(radius*qab);
44    const double si = sas_sinx_x(half_length*qc);
45    const double cyl_fq = 2.0*M_PI*radius*radius*half_length*bj*si;
46    const double Aq = bell_fq + cyl_fq;
47    return Aq;
48}
49
50static double
51form_volume(double radius_bell,
52    double radius,
53    double length)
54{
55    // bell radius should never be less than radius when this is called
56    const double hdist = sqrt(square(radius_bell) - square(radius));
57    const double p1 = 2.0/3.0*cube(radius_bell);
58    const double p2 = square(radius_bell)*hdist;
59    const double p3 = cube(hdist)/3.0;
60
61    return M_PI*square(radius)*length + 2.0*M_PI*(p1+p2-p3);
62}
63
64static double
65radius_from_excluded_volume(double radius_bell, double radius, double length)
66{
67    const double hdist = sqrt(square(radius_bell) - square(radius));
68    const double length_tot = length + 2.0*(hdist+ radius);
69    return 0.5*cbrt(0.75*radius_bell*(2.0*radius_bell*length_tot + (radius_bell + length_tot)*(M_PI*radius_bell + length_tot)));
70}
71
72static double
73radius_from_volume(double radius_bell, double radius, double length)
74{
75    const double vol_barbell = form_volume(radius_bell,radius,length);
76    return cbrt(vol_barbell/M_4PI_3);
77}
78
79static double
80radius_from_totallength(double radius_bell, double radius, double length)
81{
82    const double hdist = sqrt(square(radius_bell) - square(radius));
83    return 0.5*length + hdist + radius_bell;
84}
85
86static double
87effective_radius(int mode, double radius_bell, double radius, double length)
88{
89    switch (mode) {
90    default:
91    case 1: // equivalent cylinder excluded volume
92        return radius_from_excluded_volume(radius_bell, radius , length);
93    case 2: // equivalent volume sphere
94        return radius_from_volume(radius_bell, radius , length);
95    case 3: // radius
96        return radius;
97    case 4: // half length
98        return 0.5*length;
99    case 5: // half total length
100        return radius_from_totallength(radius_bell,radius,length);
101    }
102}
103
104static void
105Fq(double q,double *F1, double *F2, double sld, double solvent_sld,
106    double radius_bell, double radius, double length)
107{
108    const double h = -sqrt(radius_bell*radius_bell - radius*radius);
109    const double half_length = 0.5*length;
110
111    // translate a point in [-1,1] to a point in [0, pi/2]
112    const double zm = M_PI_4;
113    const double zb = M_PI_4;
114    double total_F1 = 0.0;
115    double total_F2 = 0.0;
116    for (int i = 0; i < GAUSS_N; i++){
117        const double alpha= GAUSS_Z[i]*zm + zb;
118        double sin_alpha, cos_alpha; // slots to hold sincos function output
119        SINCOS(alpha, sin_alpha, cos_alpha);
120        const double Aq = _fq(q*sin_alpha, q*cos_alpha, h, radius_bell, radius, half_length);
121        total_F1 += GAUSS_W[i] * Aq * sin_alpha;
122        total_F2 += GAUSS_W[i] * Aq * Aq * sin_alpha;
123    }
124    // translate dx in [-1,1] to dx in [lower,upper]
125    const double form_avg = total_F1*zm;
126    const double form_squared_avg = total_F2*zm;
127
128    //Contrast
129    const double s = (sld - solvent_sld);
130    *F1 = 1.0e-2 * s * form_avg;
131    *F2 = 1.0e-4 * s * s * form_squared_avg;
132}
133
134static double
135Iqac(double qab, double qc,
136    double sld, double solvent_sld,
137    double radius_bell, double radius, double length)
138{
139    const double h = -sqrt(square(radius_bell) - square(radius));
140    const double Aq = _fq(qab, qc, h, radius_bell, radius, 0.5*length);
141
142    // Multiply by contrast^2 and convert to cm-1
143    const double s = (sld - solvent_sld);
144    return 1.0e-4 * square(s * Aq);
145}
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