[aea2e2a] | 1 | double form_volume(double radius, double thickness, double length); |
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| 2 | double Iq(double q, double radius, double thickness, double length, double sld, |
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| 3 | double solvent_sld); |
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| 4 | double Iqxy(double qx, double qy, double radius, double thickness, double length, double sld, |
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| 5 | double solvent_sld, double theta, double phi); |
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| 6 | |
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| 7 | //#define INVALID(v) (v.radius_core >= v.radius) |
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| 8 | |
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| 9 | // From Igor library |
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[5bddd89] | 10 | static double |
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| 11 | _hollow_cylinder_scaling(double integrand, double delrho, double volume) |
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[aea2e2a] | 12 | { |
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[ed23abe] | 13 | return 1.0e-4 * square(volume * delrho) * integrand; |
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[aea2e2a] | 14 | } |
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| 15 | |
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| 16 | |
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[5bddd89] | 17 | static double |
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| 18 | _hollow_cylinder_kernel(double q, |
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| 19 | double radius, double thickness, double length, double sin_val, double cos_val) |
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[aea2e2a] | 20 | { |
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[5bddd89] | 21 | const double qs = q*sin_val; |
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[592343f] | 22 | const double lam1 = sas_2J1x_x((radius+thickness)*qs); |
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| 23 | const double lam2 = sas_2J1x_x(radius*qs); |
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[aea2e2a] | 24 | const double gamma_sq = square(radius/(radius+thickness)); |
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[592343f] | 25 | //Note: lim_{thickness -> 0} psi = sas_J0(radius*qs) |
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| 26 | //Note: lim_{radius -> 0} psi = sas_2J1x_x(thickness*qs) |
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[aea2e2a] | 27 | const double psi = (lam1 - gamma_sq*lam2)/(1.0 - gamma_sq); //SRK 10/19/00 |
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[1e7b0db0] | 28 | const double t2 = sas_sinx_x(0.5*q*length*cos_val); |
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[5bddd89] | 29 | return psi*t2; |
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[aea2e2a] | 30 | } |
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| 31 | |
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[5bddd89] | 32 | double |
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| 33 | form_volume(double radius, double thickness, double length) |
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[aea2e2a] | 34 | { |
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[ed23abe] | 35 | double v_shell = M_PI*length*(square(radius+thickness) - radius*radius); |
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| 36 | return v_shell; |
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[aea2e2a] | 37 | } |
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| 38 | |
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| 39 | |
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[5bddd89] | 40 | double |
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| 41 | Iq(double q, double radius, double thickness, double length, |
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[aea2e2a] | 42 | double sld, double solvent_sld) |
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| 43 | { |
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[5bddd89] | 44 | const double lower = 0.0; |
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| 45 | const double upper = 1.0; //limits of numerical integral |
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| 46 | |
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| 47 | double summ = 0.0; //initialize intergral |
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| 48 | for (int i=0;i<76;i++) { |
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| 49 | const double cos_val = 0.5*( Gauss76Z[i] * (upper-lower) + lower + upper ); |
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| 50 | const double sin_val = sqrt(1.0 - cos_val*cos_val); |
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| 51 | const double inter = _hollow_cylinder_kernel(q, radius, thickness, length, |
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| 52 | sin_val, cos_val); |
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[ed23abe] | 53 | summ += Gauss76Wt[i] * inter * inter; |
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[aea2e2a] | 54 | } |
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| 55 | |
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[5bddd89] | 56 | const double Aq = 0.5*summ*(upper-lower); |
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| 57 | const double volume = form_volume(radius, thickness, length); |
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| 58 | return _hollow_cylinder_scaling(Aq, solvent_sld - sld, volume); |
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| 59 | } |
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[aea2e2a] | 60 | |
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[5bddd89] | 61 | double |
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| 62 | Iqxy(double qx, double qy, |
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| 63 | double radius, double thickness, double length, |
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| 64 | double sld, double solvent_sld, double theta, double phi) |
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| 65 | { |
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| 66 | double q, sin_alpha, cos_alpha; |
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| 67 | ORIENT_SYMMETRIC(qx, qy, theta, phi, q, sin_alpha, cos_alpha); |
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| 68 | const double Aq = _hollow_cylinder_kernel(q, radius, thickness, length, |
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| 69 | sin_alpha, cos_alpha); |
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| 70 | |
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| 71 | const double vol = form_volume(radius, thickness, length); |
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[ed23abe] | 72 | return _hollow_cylinder_scaling(Aq*Aq, solvent_sld-sld, vol); |
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[aea2e2a] | 73 | } |
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| 74 | |
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