[a807206] | 1 | double form_volume(double radius, double edge_sep, |
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[d2deac2] | 2 | double thick_string, double fp_num_pearls); |
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[a807206] | 3 | double Iq(double q, double radius, double edge_sep, |
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[d2deac2] | 4 | double thick_string, double fp_num_pearls, double sld, |
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[2126131] | 5 | double string_sld, double solvent_sld); |
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[cf404cb] | 6 | |
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[a807206] | 7 | #define INVALID(v) (v.thick_string >= v.radius || v.num_pearls <= 0) |
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[2f5c6d4] | 8 | |
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[cf404cb] | 9 | // From Igor library |
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[2126131] | 10 | static double |
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[d2deac2] | 11 | pearl_necklace_kernel(double q, double radius, double edge_sep, double thick_string, |
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| 12 | int num_pearls, double sld_pearl, double sld_string, double sld_solv) |
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[cf404cb] | 13 | { |
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[2126131] | 14 | // number of string segments |
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[3f853beb] | 15 | const int num_strings = num_pearls - 1; |
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[2126131] | 16 | |
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| 17 | //each masses: contrast * volume |
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| 18 | const double contrast_pearl = sld_pearl - sld_solv; |
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| 19 | const double contrast_string = sld_string - sld_solv; |
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| 20 | const double string_vol = edge_sep * M_PI_4 * thick_string * thick_string; |
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| 21 | const double pearl_vol = M_4PI_3 * radius * radius * radius; |
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| 22 | const double m_string = contrast_string * string_vol; |
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| 23 | const double m_pearl = contrast_pearl * pearl_vol; |
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| 24 | |
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| 25 | // center to center distance between the neighboring pearls |
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| 26 | const double A_s = edge_sep + 2.0 * radius; |
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| 27 | |
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| 28 | //sine functions of a pearl |
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| 29 | // Note: lim_(q->0) Si(q*a)/(q*b) = a/b |
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| 30 | // So therefore: |
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| 31 | // beta = q==0. ? 1.0 : (Si(q*(A_s-radius)) - Si(q*radius))/q_edge; |
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| 32 | // gamma = q==0. ? 1.0 : Si(q_edge)/q_edge; |
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| 33 | // But there is a 1/(1-sinc) term below which blows up so don't bother |
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| 34 | const double q_edge = q * edge_sep; |
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[4b541ac] | 35 | const double beta = (sas_Si(q*(A_s-radius)) - sas_Si(q*radius)) / q_edge; |
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| 36 | const double gamma = sas_Si(q_edge) / q_edge; |
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[925ad6e] | 37 | const double psi = sas_3j1x_x(q*radius); |
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[2126131] | 38 | |
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| 39 | // Precomputed sinc terms |
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[1e7b0db0] | 40 | const double si = sas_sinx_x(q*A_s); |
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[2126131] | 41 | const double omsi = 1.0 - si; |
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| 42 | const double pow_si = pow(si, num_pearls); |
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| 43 | |
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| 44 | // form factor for num_pearls |
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| 45 | const double sss = 2.0*square(m_pearl*psi) * ( |
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| 46 | - si * (1.0 - pow_si) / (omsi*omsi) |
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| 47 | + num_pearls / omsi |
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| 48 | - 0.5 * num_pearls |
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| 49 | ); |
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| 50 | |
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| 51 | // form factor for num_strings (like thin rods) |
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| 52 | const double srr = m_string * m_string * ( |
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| 53 | - 2.0 * (1.0 - pow_si/si)*beta*beta / (omsi*omsi) |
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| 54 | + 2.0 * num_strings*beta*beta / omsi |
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[1e7b0db0] | 55 | + num_strings * (2.0*gamma - square(sas_sinx_x(q_edge/2.0))) |
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[2126131] | 56 | ); |
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| 57 | |
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| 58 | // form factor for correlations |
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| 59 | const double srs = 4.0 * m_string * m_pearl * beta * psi * ( |
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| 60 | - si * (1.0 - pow_si/si) / (omsi*omsi) |
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| 61 | + num_strings / omsi |
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| 62 | ); |
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| 63 | |
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| 64 | const double form = sss + srr + srs; |
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| 65 | |
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| 66 | return 1.0e-4 * form; |
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[cf404cb] | 67 | } |
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| 68 | |
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[a807206] | 69 | double form_volume(double radius, double edge_sep, |
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[d2deac2] | 70 | double thick_string, double fp_num_pearls) |
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[cf404cb] | 71 | { |
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[d2deac2] | 72 | const int num_pearls = (int)(fp_num_pearls + 0.5); //Force integer number of pearls |
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| 73 | const int num_strings = num_pearls - 1; |
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[2126131] | 74 | const double string_vol = edge_sep * M_PI_4 * thick_string * thick_string; |
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| 75 | const double pearl_vol = M_4PI_3 * radius * radius * radius; |
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| 76 | const double volume = num_strings*string_vol + num_pearls*pearl_vol; |
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[cf404cb] | 77 | |
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[2126131] | 78 | return volume; |
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[cf404cb] | 79 | } |
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| 80 | |
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[a807206] | 81 | double Iq(double q, double radius, double edge_sep, |
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[d2deac2] | 82 | double thick_string, double fp_num_pearls, double sld, |
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[2126131] | 83 | double string_sld, double solvent_sld) |
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[cf404cb] | 84 | { |
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[d2deac2] | 85 | const int num_pearls = (int)(fp_num_pearls + 0.5); //Force integer number of pearls |
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| 86 | const double form = pearl_necklace_kernel(q, radius, edge_sep, |
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[2126131] | 87 | thick_string, num_pearls, sld, string_sld, solvent_sld); |
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[cf404cb] | 88 | |
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[2126131] | 89 | return form; |
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[cf404cb] | 90 | } |
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