[2a0b2b1] | 1 | static double |
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| 2 | form_volume(double radius_polar, double radius_equatorial) |
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[ce27e21] | 3 | { |
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[a807206] | 4 | return M_4PI_3*radius_polar*radius_equatorial*radius_equatorial; |
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[ce27e21] | 5 | } |
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| 6 | |
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[6e7ba14] | 7 | static double |
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| 8 | radius_from_volume(double radius_polar, double radius_equatorial) |
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| 9 | { |
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| 10 | return cbrt(radius_polar*radius_equatorial*radius_equatorial); |
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| 11 | } |
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| 12 | |
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| 13 | static double |
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| 14 | radius_from_curvature(double radius_polar, double radius_equatorial) |
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| 15 | { |
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| 16 | // Trivial cases |
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| 17 | if (radius_polar == radius_equatorial) return radius_polar; |
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| 18 | if (radius_polar * radius_equatorial == 0.) return 0.; |
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| 19 | |
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| 20 | // see equation (26) in A.Isihara, J.Chem.Phys. 18(1950)1446-1449 |
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[d277229] | 21 | const double ratio = (radius_polar < radius_equatorial |
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[6e7ba14] | 22 | ? radius_polar / radius_equatorial |
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| 23 | : radius_equatorial / radius_polar); |
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| 24 | const double e1 = sqrt(1.0 - ratio*ratio); |
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| 25 | const double b1 = 1.0 + asin(e1) / (e1 * ratio); |
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| 26 | const double bL = (1.0 + e1) / (1.0 - e1); |
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| 27 | const double b2 = 1.0 + 0.5 * ratio * ratio / e1 * log(bL); |
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| 28 | const double delta = 0.75 * b1 * b2; |
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| 29 | const double ddd = 2.0 * (delta + 1.0) * radius_polar * radius_equatorial * radius_equatorial; |
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| 30 | return 0.5 * cbrt(ddd); |
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| 31 | } |
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| 32 | |
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| 33 | static double |
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| 34 | effective_radius(int mode, double radius_polar, double radius_equatorial) |
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| 35 | { |
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[ee60aa7] | 36 | switch (mode) { |
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[d42dd4a] | 37 | default: |
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[ee60aa7] | 38 | case 1: // equivalent sphere |
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[6e7ba14] | 39 | return radius_from_volume(radius_polar, radius_equatorial); |
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[ee60aa7] | 40 | case 2: // average curvature |
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[d277229] | 41 | return radius_from_curvature(radius_polar, radius_equatorial); |
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[ee60aa7] | 42 | case 3: // min radius |
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[6e7ba14] | 43 | return (radius_polar < radius_equatorial ? radius_polar : radius_equatorial); |
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[ee60aa7] | 44 | case 4: // max radius |
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[6e7ba14] | 45 | return (radius_polar > radius_equatorial ? radius_polar : radius_equatorial); |
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| 46 | } |
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| 47 | } |
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| 48 | |
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| 49 | |
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[01c8d9e] | 50 | static void |
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| 51 | Fq(double q, |
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| 52 | double *F1, |
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| 53 | double *F2, |
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| 54 | double sld, |
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| 55 | double sld_solvent, |
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| 56 | double radius_polar, |
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| 57 | double radius_equatorial) |
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| 58 | { |
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| 59 | // Using ratio v = Rp/Re, we can implement the form given in Guinier (1955) |
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| 60 | // i(h) = int_0^pi/2 Phi^2(h a sqrt(cos^2 + v^2 sin^2) cos dT |
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| 61 | // = int_0^pi/2 Phi^2(h a sqrt((1-sin^2) + v^2 sin^2) cos dT |
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| 62 | // = int_0^pi/2 Phi^2(h a sqrt(1 + sin^2(v^2-1)) cos dT |
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| 63 | // u-substitution of |
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| 64 | // u = sin, du = cos dT |
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| 65 | // i(h) = int_0^1 Phi^2(h a sqrt(1 + u^2(v^2-1)) du |
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| 66 | const double v_square_minus_one = square(radius_polar/radius_equatorial) - 1.0; |
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| 67 | // translate a point in [-1,1] to a point in [0, 1] |
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| 68 | // const double u = GAUSS_Z[i]*(upper-lower)/2 + (upper+lower)/2; |
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| 69 | const double zm = 0.5; |
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| 70 | const double zb = 0.5; |
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| 71 | double total_F2 = 0.0; |
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| 72 | double total_F1 = 0.0; |
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| 73 | for (int i=0;i<GAUSS_N;i++) { |
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| 74 | const double u = GAUSS_Z[i]*zm + zb; |
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| 75 | const double r = radius_equatorial*sqrt(1.0 + u*u*v_square_minus_one); |
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| 76 | const double f = sas_3j1x_x(q*r); |
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| 77 | total_F2 += GAUSS_W[i] * f * f; |
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| 78 | total_F1 += GAUSS_W[i] * f; |
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| 79 | } |
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| 80 | // translate dx in [-1,1] to dx in [lower,upper] |
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[71b751d] | 81 | total_F1 *= zm; |
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| 82 | total_F2 *= zm; |
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[01c8d9e] | 83 | const double s = (sld - sld_solvent) * form_volume(radius_polar, radius_equatorial); |
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[71b751d] | 84 | *F1 = 1e-2 * s * total_F1; |
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| 85 | *F2 = 1e-4 * s * s * total_F2; |
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[ce27e21] | 86 | } |
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| 87 | |
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[2a0b2b1] | 88 | static double |
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[108e70e] | 89 | Iqac(double qab, double qc, |
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[994d77f] | 90 | double sld, |
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[a807206] | 91 | double sld_solvent, |
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| 92 | double radius_polar, |
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[becded3] | 93 | double radius_equatorial) |
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[ce27e21] | 94 | { |
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[2a0b2b1] | 95 | const double qr = sqrt(square(radius_equatorial*qab) + square(radius_polar*qc)); |
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| 96 | const double f = sas_3j1x_x(qr); |
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[a807206] | 97 | const double s = (sld - sld_solvent) * form_volume(radius_polar, radius_equatorial); |
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[ce27e21] | 98 | |
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[3b571ae] | 99 | return 1.0e-4 * square(f * s); |
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[ce27e21] | 100 | } |
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