[2a0b2b1] | 1 | static double |
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[7e0b281] | 2 | sc_Zq(double qa, double qb, double qc, double dnn, double d_factor) |
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[9aac25d] | 3 | { |
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[f728001] | 4 | // Equations from Matsuoka 9-10-11, multiplied by |q| |
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[2a0b2b1] | 5 | const double a1 = qa; |
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| 6 | const double a2 = qb; |
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| 7 | const double a3 = qc; |
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| 8 | |
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[f728001] | 9 | // Matsuoka 13-14-15 |
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| 10 | // Z_k numerator: 1 - exp(a)^2 |
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| 11 | // Z_k denominator: 1 - 2 cos(d a_k) exp(a) + exp(2a) |
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| 12 | // Rewriting numerator |
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| 13 | // => -(exp(2a) - 1) |
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| 14 | // => -expm1(2a) |
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| 15 | // Rewriting denominator |
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| 16 | // => exp(a)^2 - 2 cos(d ak) exp(a) + 1) |
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| 17 | // => (exp(a) - 2 cos(d ak)) * exp(a) + 1 |
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[7e0b281] | 18 | const double arg = -0.5*square(dnn*d_factor)*(a1*a1 + a2*a2 + a3*a3); |
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| 19 | const double exp_arg = exp(arg); |
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| 20 | const double Zq = -cube(expm1(2.0*arg)) |
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[2a0b2b1] | 21 | / ( ((exp_arg - 2.0*cos(dnn*a1))*exp_arg + 1.0) |
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| 22 | * ((exp_arg - 2.0*cos(dnn*a2))*exp_arg + 1.0) |
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| 23 | * ((exp_arg - 2.0*cos(dnn*a3))*exp_arg + 1.0)); |
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| 24 | |
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[7e0b281] | 25 | return Zq; |
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[9aac25d] | 26 | } |
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| 27 | |
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[2a0b2b1] | 28 | // occupied volume fraction calculated from lattice symmetry and sphere radius |
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[9aac25d] | 29 | static double |
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[7e0b281] | 30 | sc_volume_fraction(double radius, double dnn) |
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[9aac25d] | 31 | { |
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[2a0b2b1] | 32 | return sphere_volume(radius/dnn); |
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[9aac25d] | 33 | } |
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| 34 | |
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| 35 | static double |
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[2a0b2b1] | 36 | form_volume(double radius) |
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[9aac25d] | 37 | { |
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[2a0b2b1] | 38 | return sphere_volume(radius); |
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[9aac25d] | 39 | } |
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| 40 | |
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| 41 | |
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[becded3] | 42 | static double |
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| 43 | Iq(double q, double dnn, |
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| 44 | double d_factor, double radius, |
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| 45 | double sld, double solvent_sld) |
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[2a0b2b1] | 46 | { |
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| 47 | // translate a point in [-1,1] to a point in [0, 2 pi] |
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| 48 | const double phi_m = M_PI_4; |
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| 49 | const double phi_b = M_PI_4; |
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| 50 | // translate a point in [-1,1] to a point in [0, pi] |
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| 51 | const double theta_m = M_PI_4; |
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| 52 | const double theta_b = M_PI_4; |
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| 53 | |
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| 54 | |
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| 55 | double outer_sum = 0.0; |
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[74768cb] | 56 | for(int i=0; i<GAUSS_N; i++) { |
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[2a0b2b1] | 57 | double inner_sum = 0.0; |
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[74768cb] | 58 | const double theta = GAUSS_Z[i]*theta_m + theta_b; |
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[2a0b2b1] | 59 | double sin_theta, cos_theta; |
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| 60 | SINCOS(theta, sin_theta, cos_theta); |
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| 61 | const double qc = q*cos_theta; |
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| 62 | const double qab = q*sin_theta; |
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[74768cb] | 63 | for(int j=0;j<GAUSS_N;j++) { |
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| 64 | const double phi = GAUSS_Z[j]*phi_m + phi_b; |
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[2a0b2b1] | 65 | double sin_phi, cos_phi; |
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| 66 | SINCOS(phi, sin_phi, cos_phi); |
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| 67 | const double qa = qab*cos_phi; |
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| 68 | const double qb = qab*sin_phi; |
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[7e0b281] | 69 | const double form = sc_Zq(qa, qb, qc, dnn, d_factor); |
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[74768cb] | 70 | inner_sum += GAUSS_W[j] * form; |
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[2a0b2b1] | 71 | } |
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| 72 | inner_sum *= phi_m; // sum(f(x)dx) = sum(f(x)) dx |
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[74768cb] | 73 | outer_sum += GAUSS_W[i] * inner_sum * sin_theta; |
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[2a0b2b1] | 74 | } |
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| 75 | outer_sum *= theta_m; |
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[7e0b281] | 76 | const double Zq = outer_sum/M_PI_2; |
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[2a0b2b1] | 77 | const double Pq = sphere_form(q, radius, sld, solvent_sld); |
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| 78 | |
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[7e0b281] | 79 | return sc_volume_fraction(radius, dnn) * Pq * Zq; |
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[9aac25d] | 80 | } |
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| 81 | |
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[2a0b2b1] | 82 | |
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[becded3] | 83 | static double |
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[108e70e] | 84 | Iqabc(double qa, double qb, double qc, |
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[2a0b2b1] | 85 | double dnn, double d_factor, double radius, |
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[becded3] | 86 | double sld, double solvent_sld) |
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[9aac25d] | 87 | { |
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[becded3] | 88 | const double q = sqrt(qa*qa + qb*qb + qc*qc); |
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[2a0b2b1] | 89 | const double Pq = sphere_form(q, radius, sld, solvent_sld); |
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[7e0b281] | 90 | const double Zq = sc_Zq(qa, qb, qc, dnn, d_factor); |
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| 91 | return sc_volume_fraction(radius, dnn) * Pq * Zq; |
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[2a0b2b1] | 92 | } |
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