1 | double form_volume(double radius_bell, double radius, double length); |
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2 | double Iq(double q, double sld, double solvent_sld, |
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3 | double radius_bell, double radius, double length); |
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4 | double Iqxy(double qx, double qy, double sld, double solvent_sld, |
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5 | double radius_bell, double radius, double length, |
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6 | double theta, double phi); |
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7 | |
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8 | #define INVALID(v) (v.radius_bell < v.radius) |
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9 | |
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10 | //barbell kernel - same as dumbell |
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11 | static double |
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12 | _bell_kernel(double q, double h, double radius_bell, |
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13 | double half_length, double sin_alpha, double cos_alpha) |
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14 | { |
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15 | // translate a point in [-1,1] to a point in [lower,upper] |
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16 | const double upper = 1.0; |
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17 | const double lower = h/radius_bell; |
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18 | const double zm = 0.5*(upper-lower); |
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19 | const double zb = 0.5*(upper+lower); |
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20 | |
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21 | // cos term in integral is: |
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22 | // cos (q (R t - h + L/2) cos(alpha)) |
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23 | // so turn it into: |
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24 | // cos (m t + b) |
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25 | // where: |
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26 | // m = q R cos(alpha) |
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27 | // b = q(L/2-h) cos(alpha) |
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28 | const double m = q*radius_bell*cos_alpha; // cos argument slope |
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29 | const double b = q*(half_length-h)*cos_alpha; // cos argument intercept |
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30 | const double qrst = q*radius_bell*sin_alpha; // Q*R*sin(theta) |
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31 | double total = 0.0; |
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32 | for (int i = 0; i < 76; i++){ |
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33 | const double t = Gauss76Z[i]*zm + zb; |
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34 | const double radical = 1.0 - t*t; |
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35 | const double bj = sas_J1c(qrst*sqrt(radical)); |
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36 | const double Fq = cos(m*t + b) * radical * bj; |
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37 | total += Gauss76Wt[i] * Fq; |
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38 | } |
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39 | // translate dx in [-1,1] to dx in [lower,upper] |
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40 | const double integral = total*zm; |
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41 | const double bell_Fq = 2*M_PI*cube(radius_bell)*integral; |
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42 | return bell_Fq; |
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43 | } |
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44 | |
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45 | double form_volume(double radius_bell, |
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46 | double radius, |
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47 | double length) |
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48 | { |
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49 | |
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50 | // bell radius should never be less than radius when this is called |
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51 | const double hdist = sqrt(square(radius_bell) - square(radius)); |
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52 | const double p1 = 2.0/3.0*cube(radius_bell); |
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53 | const double p2 = square(radius_bell)*hdist; |
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54 | const double p3 = cube(hdist)/3.0; |
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55 | |
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56 | return M_PI*square(radius)*length + 2.0*M_PI*(p1+p2-p3); |
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57 | } |
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58 | |
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59 | double Iq(double q, double sld, double solvent_sld, |
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60 | double radius_bell, double radius, double length) |
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61 | { |
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62 | const double h = -sqrt(radius_bell*radius_bell - radius*radius); |
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63 | const double half_length = 0.5*length; |
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64 | |
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65 | // translate a point in [-1,1] to a point in [0, pi/2] |
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66 | const double zm = M_PI_4; |
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67 | const double zb = M_PI_4; |
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68 | double total = 0.0; |
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69 | for (int i = 0; i < 76; i++){ |
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70 | const double alpha= Gauss76Z[i]*zm + zb; |
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71 | double sin_alpha, cos_alpha; // slots to hold sincos function output |
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72 | SINCOS(alpha, sin_alpha, cos_alpha); |
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73 | |
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74 | const double bell_Fq = _bell_kernel(q, h, radius_bell, half_length, sin_alpha, cos_alpha); |
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75 | const double bj = sas_J1c(q*radius*sin_alpha); |
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76 | const double si = sinc(q*half_length*cos_alpha); |
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77 | const double cyl_Fq = M_PI*radius*radius*length*bj*si; |
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78 | const double Aq = bell_Fq + cyl_Fq; |
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79 | total += Gauss76Wt[i] * Aq * Aq * sin_alpha; |
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80 | } |
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81 | // translate dx in [-1,1] to dx in [lower,upper] |
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82 | const double form = total*zm; |
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83 | |
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84 | //Contrast |
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85 | const double s = (sld - solvent_sld); |
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86 | return 1.0e-4 * s * s * form; |
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87 | } |
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88 | |
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89 | |
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90 | double Iqxy(double qx, double qy, |
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91 | double sld, double solvent_sld, |
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92 | double radius_bell, double radius, double length, |
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93 | double theta, double phi) |
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94 | { |
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95 | // Compute angle alpha between q and the cylinder axis |
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96 | double sn, cn; // slots to hold sincos function output |
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97 | SINCOS(phi*M_PI_180, sn, cn); |
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98 | const double q = sqrt(qx*qx + qy*qy); |
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99 | const double cos_val = (q==0. ? 1.0 : (cn*qx + sn*qy)*sin(theta*M_PI_180)/q); |
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100 | const double alpha = acos(cos_val); // rod angle relative to q |
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101 | |
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102 | const double h = -sqrt(square(radius_bell) - square(radius)); |
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103 | const double half_length = 0.5*length; |
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104 | |
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105 | double sin_alpha, cos_alpha; // slots to hold sincos function output |
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106 | SINCOS(alpha, sin_alpha, cos_alpha); |
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107 | const double bell_Fq = _bell_kernel(q, h, radius_bell, half_length, sin_alpha, cos_alpha); |
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108 | const double bj = sas_J1c(q*radius*sin_alpha); |
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109 | const double si = sinc(q*half_length*cos_alpha); |
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110 | const double cyl_Fq = M_PI*radius*radius*length*bj*si; |
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111 | const double Aq = cyl_Fq + bell_Fq; |
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112 | |
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113 | // Multiply by contrast^2 and convert to cm-1 |
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114 | const double s = (sld - solvent_sld); |
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115 | return 1.0e-4 * square(s * Aq); |
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116 | } |
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