[9aa4881] | 1 | // vd = volume * delta_rho |
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[2a0b2b1] | 2 | // besarg = q * R * sin(theta) |
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| 3 | // siarg = q * L/2 * cos(theta) |
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| 4 | static double _cyl(double vd, double besarg, double siarg) |
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[5d4777d] | 5 | { |
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[592343f] | 6 | return vd * sas_sinx_x(siarg) * sas_2J1x_x(besarg); |
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[5d4777d] | 7 | } |
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| 8 | |
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[2a0b2b1] | 9 | static double |
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| 10 | form_volume(double radius, double thickness, double length) |
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[5d4777d] | 11 | { |
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[2a0b2b1] | 12 | return M_PI*square(radius+thickness)*(length+2.0*thickness); |
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[5d4777d] | 13 | } |
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| 14 | |
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[d277229] | 15 | static double |
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[99658f6] | 16 | radius_from_excluded_volume(double radius, double thickness, double length) |
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| 17 | { |
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| 18 | const double radius_tot = radius + thickness; |
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| 19 | const double length_tot = length + 2.0*thickness; |
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| 20 | return 0.5*cbrt(0.75*radius_tot*(2.0*radius_tot*length_tot + (radius_tot + length_tot)*(M_PI*radius_tot + length_tot))); |
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| 21 | } |
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| 22 | |
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| 23 | static double |
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[d277229] | 24 | radius_from_volume(double radius, double thickness, double length) |
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| 25 | { |
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| 26 | const double volume_outer_cyl = form_volume(radius,thickness,length); |
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[6d5601c] | 27 | return cbrt(volume_outer_cyl/M_4PI_3); |
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[d277229] | 28 | } |
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| 29 | |
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| 30 | static double |
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| 31 | radius_from_diagonal(double radius, double thickness, double length) |
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| 32 | { |
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| 33 | const double radius_outer = radius + thickness; |
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[a94046f] | 34 | const double length_outer = length + 2.0*thickness; |
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[d277229] | 35 | return sqrt(radius_outer*radius_outer + 0.25*length_outer*length_outer); |
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| 36 | } |
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| 37 | |
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| 38 | static double |
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[a34b811] | 39 | radius_effective(int mode, double radius, double thickness, double length) |
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[d277229] | 40 | { |
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[ee60aa7] | 41 | switch (mode) { |
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[d42dd4a] | 42 | default: |
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[99658f6] | 43 | case 1: //cylinder excluded volume |
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| 44 | return radius_from_excluded_volume(radius, thickness, length); |
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| 45 | case 2: // equivalent volume sphere |
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[d277229] | 46 | return radius_from_volume(radius, thickness, length); |
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[99658f6] | 47 | case 3: // outer radius |
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[d277229] | 48 | return radius + thickness; |
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[99658f6] | 49 | case 4: // half outer length |
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[d277229] | 50 | return 0.5*length + thickness; |
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[99658f6] | 51 | case 5: // half min outer length |
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[d277229] | 52 | return (radius < 0.5*length ? radius + thickness : 0.5*length + thickness); |
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[99658f6] | 53 | case 6: // half max outer length |
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[d277229] | 54 | return (radius > 0.5*length ? radius + thickness : 0.5*length + thickness); |
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[99658f6] | 55 | case 7: // half outer diagonal |
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[d277229] | 56 | return radius_from_diagonal(radius,thickness,length); |
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| 57 | } |
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| 58 | } |
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| 59 | |
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[71b751d] | 60 | static void |
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| 61 | Fq(double q, |
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| 62 | double *F1, |
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| 63 | double *F2, |
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[994d77f] | 64 | double core_sld, |
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| 65 | double shell_sld, |
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| 66 | double solvent_sld, |
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| 67 | double radius, |
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| 68 | double thickness, |
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| 69 | double length) |
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[5d4777d] | 70 | { |
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| 71 | // precalculate constants |
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[2a0b2b1] | 72 | const double core_r = radius; |
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| 73 | const double core_h = 0.5*length; |
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[9aa4881] | 74 | const double core_vd = form_volume(radius,0,length) * (core_sld-shell_sld); |
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[2a0b2b1] | 75 | const double shell_r = (radius + thickness); |
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| 76 | const double shell_h = (0.5*length + thickness); |
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[9aa4881] | 77 | const double shell_vd = form_volume(radius,thickness,length) * (shell_sld-solvent_sld); |
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[71b751d] | 78 | double total_F1 = 0.0; |
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| 79 | double total_F2 = 0.0; |
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[74768cb] | 80 | for (int i=0; i<GAUSS_N ;i++) { |
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[2a0b2b1] | 81 | // translate a point in [-1,1] to a point in [0, pi/2] |
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[74768cb] | 82 | //const double theta = ( GAUSS_Z[i]*(upper-lower) + upper + lower )/2.0; |
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[2a0b2b1] | 83 | double sin_theta, cos_theta; |
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[74768cb] | 84 | const double theta = GAUSS_Z[i]*M_PI_4 + M_PI_4; |
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[2a0b2b1] | 85 | SINCOS(theta, sin_theta, cos_theta); |
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| 86 | const double qab = q*sin_theta; |
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| 87 | const double qc = q*cos_theta; |
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| 88 | const double fq = _cyl(core_vd, core_r*qab, core_h*qc) |
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| 89 | + _cyl(shell_vd, shell_r*qab, shell_h*qc); |
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[71b751d] | 90 | total_F1 += GAUSS_W[i] * fq * sin_theta; |
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| 91 | total_F2 += GAUSS_W[i] * fq * fq * sin_theta; |
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[5d4777d] | 92 | } |
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| 93 | // translate dx in [-1,1] to dx in [lower,upper] |
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[994d77f] | 94 | //const double form = (upper-lower)/2.0*total; |
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[71b751d] | 95 | *F1 = 1.0e-2 * total_F1 * M_PI_4; |
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| 96 | *F2 = 1.0e-4 * total_F2 * M_PI_4; |
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[5d4777d] | 97 | } |
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| 98 | |
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[d86f0fc] | 99 | static double |
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| 100 | Iqac(double qab, double qc, |
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[994d77f] | 101 | double core_sld, |
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| 102 | double shell_sld, |
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| 103 | double solvent_sld, |
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| 104 | double radius, |
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| 105 | double thickness, |
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[becded3] | 106 | double length) |
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[5d4777d] | 107 | { |
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[2a0b2b1] | 108 | const double core_r = radius; |
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| 109 | const double core_h = 0.5*length; |
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[9aa4881] | 110 | const double core_vd = form_volume(radius,0,length) * (core_sld-shell_sld); |
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[2a0b2b1] | 111 | const double shell_r = (radius + thickness); |
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| 112 | const double shell_h = (0.5*length + thickness); |
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[9aa4881] | 113 | const double shell_vd = form_volume(radius,thickness,length) * (shell_sld-solvent_sld); |
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[5d4777d] | 114 | |
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[2a0b2b1] | 115 | const double fq = _cyl(core_vd, core_r*qab, core_h*qc) |
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| 116 | + _cyl(shell_vd, shell_r*qab, shell_h*qc); |
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[994d77f] | 117 | return 1.0e-4 * fq * fq; |
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[5d4777d] | 118 | } |
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