1 | // NOTE that "length" here is the full height of the core! |
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2 | static double |
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3 | form_volume(double r_minor, |
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4 | double x_core, |
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5 | double thick_rim, |
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6 | double thick_face, |
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7 | double length) |
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8 | { |
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9 | return M_PI*(r_minor+thick_rim)*(r_minor*x_core+thick_rim)*(length+2.0*thick_face); |
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10 | } |
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11 | |
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12 | static double |
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13 | radius_from_volume(double r_minor, double x_core, double thick_rim, double thick_face, double length) |
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14 | { |
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15 | const double volume_bicelle = form_volume(r_minor, x_core, thick_rim,thick_face,length); |
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16 | return cbrt(volume_bicelle/M_4PI_3); |
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17 | } |
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18 | |
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19 | static double |
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20 | radius_from_diagonal(double r_minor, double x_core, double thick_rim, double thick_face, double length) |
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21 | { |
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22 | const double radius_max = (x_core < 1.0 ? r_minor : x_core*r_minor); |
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23 | const double radius_max_tot = radius_max + thick_rim; |
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24 | const double length_tot = length + 2.0*thick_face; |
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25 | return sqrt(radius_max_tot*radius_max_tot + 0.25*length_tot*length_tot); |
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26 | } |
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27 | |
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28 | static double |
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29 | effective_radius(int mode, double r_minor, double x_core, double thick_rim, double thick_face, double length) |
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30 | { |
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31 | switch (mode) { |
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32 | case 1: // equivalent sphere |
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33 | return radius_from_volume(r_minor, x_core, thick_rim, thick_face, length); |
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34 | case 2: // outer rim average radius |
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35 | return 0.5*r_minor*(1.0 + x_core) + thick_rim; |
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36 | case 3: // outer rim min radius |
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37 | return (x_core < 1.0 ? x_core*r_minor+thick_rim : r_minor+thick_rim); |
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38 | case 4: // outer max radius |
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39 | return (x_core > 1.0 ? x_core*r_minor+thick_rim : r_minor+thick_rim); |
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40 | case 5: // half outer thickness |
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41 | return 0.5*length + thick_face; |
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42 | case 6: // half diagonal |
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43 | return radius_from_diagonal(r_minor,x_core,thick_rim,thick_face,length); |
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44 | } |
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45 | } |
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46 | |
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47 | static void |
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48 | Fq(double q, |
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49 | double *F1, |
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50 | double *F2, |
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51 | double r_minor, |
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52 | double x_core, |
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53 | double thick_rim, |
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54 | double thick_face, |
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55 | double length, |
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56 | double sld_core, |
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57 | double sld_face, |
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58 | double sld_rim, |
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59 | double sld_solvent) |
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60 | { |
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61 | // core_shell_bicelle_elliptical, RKH Dec 2016, based on elliptical_cylinder and core_shell_bicelle |
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62 | // tested against limiting cases of cylinder, elliptical_cylinder, stacked_discs, and core_shell_bicelle |
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63 | const double halfheight = 0.5*length; |
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64 | const double r_major = r_minor * x_core; |
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65 | const double r2A = 0.5*(square(r_major) + square(r_minor)); |
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66 | const double r2B = 0.5*(square(r_major) - square(r_minor)); |
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67 | const double vol1 = M_PI*r_minor*r_major*(2.0*halfheight); |
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68 | const double vol2 = M_PI*(r_minor+thick_rim)*(r_major+thick_rim)*2.0*(halfheight+thick_face); |
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69 | const double vol3 = M_PI*r_minor*r_major*2.0*(halfheight+thick_face); |
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70 | const double dr1 = vol1*(sld_core-sld_face); |
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71 | const double dr2 = vol2*(sld_rim-sld_solvent); |
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72 | const double dr3 = vol3*(sld_face-sld_rim); |
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73 | |
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74 | //initialize integral |
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75 | double outer_total_F1 = 0.0; |
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76 | double outer_total_F2 = 0.0; |
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77 | for(int i=0;i<GAUSS_N;i++) { |
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78 | //setup inner integral over the ellipsoidal cross-section |
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79 | //const double cos_theta = ( GAUSS_Z[i]*(vb-va) + va + vb )/2.0; |
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80 | const double cos_theta = ( GAUSS_Z[i] + 1.0 )/2.0; |
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81 | const double sin_theta = sqrt(1.0 - cos_theta*cos_theta); |
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82 | const double qab = q*sin_theta; |
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83 | const double qc = q*cos_theta; |
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84 | const double si1 = sas_sinx_x(halfheight*qc); |
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85 | const double si2 = sas_sinx_x((halfheight+thick_face)*qc); |
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86 | double inner_total_F1 = 0; |
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87 | double inner_total_F2 = 0; |
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88 | for(int j=0;j<GAUSS_N;j++) { |
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89 | //76 gauss points for the inner integral (WAS 20 points,so this may make unecessarily slow, but playing safe) |
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90 | //const double beta = ( GAUSS_Z[j]*(vbj-vaj) + vaj + vbj )/2.0; |
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91 | const double beta = ( GAUSS_Z[j] +1.0)*M_PI_2; |
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92 | const double rr = sqrt(r2A - r2B*cos(beta)); |
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93 | const double be1 = sas_2J1x_x(rr*qab); |
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94 | const double be2 = sas_2J1x_x((rr+thick_rim)*qab); |
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95 | const double f = dr1*si1*be1 + dr2*si2*be2 + dr3*si2*be1; |
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96 | |
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97 | inner_total_F1 += GAUSS_W[j] * f; |
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98 | inner_total_F2 += GAUSS_W[j] * f * f; |
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99 | } |
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100 | //now calculate outer integral |
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101 | outer_total_F1 += GAUSS_W[i] * inner_total_F1; |
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102 | outer_total_F2 += GAUSS_W[i] * inner_total_F2; |
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103 | } |
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104 | // now complete change of integration variables (1-0)/(1-(-1))= 0.5 |
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105 | outer_total_F1 *= 0.25; |
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106 | outer_total_F2 *= 0.25; |
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107 | |
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108 | //convert from [1e-12 A-1] to [cm-1] |
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109 | *F1 = 1e-2*outer_total_F1; |
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110 | *F2 = 1e-4*outer_total_F2; |
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111 | } |
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112 | |
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113 | static double |
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114 | Iqabc(double qa, double qb, double qc, |
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115 | double r_minor, |
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116 | double x_core, |
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117 | double thick_rim, |
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118 | double thick_face, |
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119 | double length, |
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120 | double sld_core, |
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121 | double sld_face, |
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122 | double sld_rim, |
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123 | double sld_solvent) |
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124 | { |
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125 | const double dr1 = sld_core-sld_face; |
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126 | const double dr2 = sld_rim-sld_solvent; |
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127 | const double dr3 = sld_face-sld_rim; |
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128 | const double r_major = r_minor*x_core; |
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129 | const double halfheight = 0.5*length; |
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130 | const double vol1 = M_PI*r_minor*r_major*length; |
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131 | const double vol2 = M_PI*(r_minor+thick_rim)*(r_major+thick_rim)*2.0*(halfheight+thick_face); |
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132 | const double vol3 = M_PI*r_minor*r_major*2.0*(halfheight+thick_face); |
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133 | |
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134 | // Compute effective radius in rotated coordinates |
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135 | const double qr_hat = sqrt(square(r_major*qb) + square(r_minor*qa)); |
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136 | const double qrshell_hat = sqrt(square((r_major+thick_rim)*qb) |
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137 | + square((r_minor+thick_rim)*qa)); |
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138 | const double be1 = sas_2J1x_x( qr_hat ); |
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139 | const double be2 = sas_2J1x_x( qrshell_hat ); |
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140 | const double si1 = sas_sinx_x( halfheight*qc ); |
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141 | const double si2 = sas_sinx_x( (halfheight + thick_face)*qc ); |
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142 | const double fq = vol1*dr1*si1*be1 + vol2*dr2*si2*be2 + vol3*dr3*si2*be1; |
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143 | return 1.0e-4 * fq*fq; |
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144 | } |
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