1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
|
double form_volume(double radius);
double Iq(double q,
double radius,
double fractal_dim_surf,
double cutoff_length);
static double _surface_fractal_kernel(double q,
double radius,
double fractal_dim_surf,
double cutoff_length)
{
// calculate P(q)
const double pq = square(sas_3j1x_x(q*radius));
// calculate S(q)
// Note: lim q->0 S(q) = -gamma(mmo) cutoff_length^mmo (mmo cutoff_length)
// however, the surface fractal formula is invalid outside the range
const double mmo = 5.0 - fractal_dim_surf;
const double sq = sas_gamma(mmo) * pow(cutoff_length, mmo)
* pow(1.0 + square(q*cutoff_length), -0.5*mmo)
* sin(-mmo * atan(q*cutoff_length)) / q;
// Empirically determined that the results are valid within this range.
// Above 1/r, the form starts to oscillate; below
//const double result = (q > 5./(3-fractal_dim_surf)/cutoff_length) && q < 1./radius
// ? pq * sq : 0.);
double result = pq * sq;
// exclude negative results
return result > 0. ? result : 0.;
}
double form_volume(double radius)
{
return M_4PI_3*cube(radius);
}
double Iq(double q,
double radius,
double fractal_dim_surf,
double cutoff_length
)
{
return _surface_fractal_kernel(q, radius, fractal_dim_surf, cutoff_length);
}
|
