1 | // Set OVERLAPPING to 1 in order to fill in the edges of the box, with |
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2 | // c endcaps and b overlapping a. With the proper choice of parameters, |
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3 | // (setting rim slds to sld, core sld to solvent, rim thickness to thickness |
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4 | // and subtracting 2*thickness from length, this should match the hollow |
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5 | // rectangular prism.) Set it to 0 for the documented behaviour. |
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6 | #define OVERLAPPING 0 |
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7 | static double |
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8 | form_volume(double length_a, double length_b, double length_c, |
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9 | double thick_rim_a, double thick_rim_b, double thick_rim_c) |
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10 | { |
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11 | return |
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12 | #if OVERLAPPING |
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13 | // Hollow rectangular prism only includes the volume of the shell |
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14 | // so uncomment the next line when comparing. Solid rectangular |
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15 | // prism, or parallelepiped want filled cores, so comment when |
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16 | // comparing. |
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17 | //-length_a * length_b * length_c + |
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18 | (length_a + 2.0*thick_rim_a) * |
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19 | (length_b + 2.0*thick_rim_b) * |
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20 | (length_c + 2.0*thick_rim_c); |
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21 | #else |
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22 | length_a * length_b * length_c + |
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23 | 2.0 * thick_rim_a * length_b * length_c + |
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24 | 2.0 * length_a * thick_rim_b * length_c + |
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25 | 2.0 * length_a * length_b * thick_rim_c; |
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26 | #endif |
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27 | } |
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28 | |
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29 | static double |
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30 | radius_from_excluded_volume(double length_a, double length_b, double length_c, |
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31 | double thick_rim_a, double thick_rim_b, double thick_rim_c) |
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32 | { |
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33 | double r_equiv, length; |
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34 | double lengths[3] = {length_a+thick_rim_a, length_b+thick_rim_b, length_c+thick_rim_c}; |
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35 | double lengthmax = fmax(lengths[0],fmax(lengths[1],lengths[2])); |
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36 | double length_1 = lengthmax; |
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37 | double length_2 = lengthmax; |
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38 | double length_3 = lengthmax; |
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39 | |
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40 | for(int ilen=0; ilen<3; ilen++) { |
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41 | if (lengths[ilen] < length_1) { |
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42 | length_2 = length_1; |
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43 | length_1 = lengths[ilen]; |
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44 | } else { |
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45 | if (lengths[ilen] < length_2) { |
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46 | length_2 = lengths[ilen]; |
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47 | } |
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48 | } |
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49 | } |
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50 | if(length_2-length_1 > length_3-length_2) { |
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51 | r_equiv = sqrt(length_2*length_3/M_PI); |
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52 | length = length_1; |
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53 | } else { |
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54 | r_equiv = sqrt(length_1*length_2/M_PI); |
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55 | length = length_3; |
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56 | } |
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57 | |
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58 | return 0.5*cbrt(0.75*r_equiv*(2.0*r_equiv*length + (r_equiv + length)*(M_PI*r_equiv + length))); |
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59 | } |
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60 | |
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61 | static double |
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62 | radius_from_volume(double length_a, double length_b, double length_c, |
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63 | double thick_rim_a, double thick_rim_b, double thick_rim_c) |
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64 | { |
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65 | const double volume = form_volume(length_a, length_b, length_c, thick_rim_a, thick_rim_b, thick_rim_c); |
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66 | return cbrt(volume/M_4PI_3); |
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67 | } |
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68 | |
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69 | static double |
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70 | radius_from_crosssection(double length_a, double length_b, double thick_rim_a, double thick_rim_b) |
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71 | { |
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72 | const double area_xsec_paral = length_a*length_b + 2.0*thick_rim_a*length_b + 2.0*thick_rim_b*length_a; |
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73 | return sqrt(area_xsec_paral/M_PI); |
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74 | } |
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75 | |
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76 | static double |
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77 | effective_radius(int mode, double length_a, double length_b, double length_c, |
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78 | double thick_rim_a, double thick_rim_b, double thick_rim_c) |
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79 | { |
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80 | switch (mode) { |
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81 | default: |
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82 | case 1: // equivalent cylinder excluded volume |
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83 | return radius_from_excluded_volume(length_a, length_b, length_c, thick_rim_a, thick_rim_b, thick_rim_c); |
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84 | case 2: // equivalent volume sphere |
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85 | return radius_from_volume(length_a, length_b, length_c, thick_rim_a, thick_rim_b, thick_rim_c); |
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86 | case 3: // half outer length a |
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87 | return 0.5 * length_a + thick_rim_a; |
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88 | case 4: // half outer length b |
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89 | return 0.5 * length_b + thick_rim_b; |
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90 | case 5: // half outer length c |
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91 | return 0.5 * length_c + thick_rim_c; |
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92 | case 6: // equivalent circular cross-section |
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93 | return radius_from_crosssection(length_a, length_b, thick_rim_a, thick_rim_b); |
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94 | case 7: // half outer ab diagonal |
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95 | return 0.5*sqrt(square(length_a+ 2.0*thick_rim_a) + square(length_b+ 2.0*thick_rim_b)); |
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96 | case 8: // half outer diagonal |
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97 | return 0.5*sqrt(square(length_a+ 2.0*thick_rim_a) + square(length_b+ 2.0*thick_rim_b) + square(length_c+ 2.0*thick_rim_c)); |
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98 | } |
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99 | } |
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100 | |
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101 | static void |
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102 | Fq(double q, |
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103 | double *F1, |
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104 | double *F2, |
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105 | double core_sld, |
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106 | double arim_sld, |
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107 | double brim_sld, |
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108 | double crim_sld, |
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109 | double solvent_sld, |
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110 | double length_a, |
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111 | double length_b, |
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112 | double length_c, |
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113 | double thick_rim_a, |
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114 | double thick_rim_b, |
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115 | double thick_rim_c) |
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116 | { |
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117 | // Code converted from functions CSPPKernel and CSParallelepiped in libCylinder.c |
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118 | // Did not understand the code completely, it should be rechecked (Miguel Gonzalez) |
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119 | // Code is rewritten, the code is compliant with Diva Singh's thesis now (Dirk Honecker) |
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120 | // Code rewritten; cross checked against hollow rectangular prism and realspace (PAK) |
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121 | |
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122 | const double half_q = 0.5*q; |
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123 | |
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124 | const double tA = length_a + 2.0*thick_rim_a; |
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125 | const double tB = length_b + 2.0*thick_rim_b; |
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126 | const double tC = length_c + 2.0*thick_rim_c; |
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127 | |
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128 | // Scale factors |
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129 | const double dr0 = (core_sld-solvent_sld); |
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130 | const double drA = (arim_sld-solvent_sld); |
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131 | const double drB = (brim_sld-solvent_sld); |
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132 | const double drC = (crim_sld-solvent_sld); |
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133 | |
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134 | // outer integral (with gauss points), integration limits = 0, 1 |
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135 | // substitute d_cos_alpha for sin_alpha d_alpha |
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136 | double outer_sum_F1 = 0; //initialize integral |
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137 | double outer_sum_F2 = 0; //initialize integral |
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138 | for( int i=0; i<GAUSS_N; i++) { |
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139 | const double cos_alpha = 0.5 * ( GAUSS_Z[i] + 1.0 ); |
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140 | const double mu = half_q * sqrt(1.0-cos_alpha*cos_alpha); |
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141 | const double siC = length_c * sas_sinx_x(length_c * cos_alpha * half_q); |
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142 | const double siCt = tC * sas_sinx_x(tC * cos_alpha * half_q); |
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143 | |
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144 | // inner integral (with gauss points), integration limits = 0, 1 |
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145 | // substitute beta = PI/2 u (so 2/PI * d_(PI/2 * beta) = d_beta) |
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146 | double inner_sum_F1 = 0.0; |
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147 | double inner_sum_F2 = 0.0; |
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148 | for(int j=0; j<GAUSS_N; j++) { |
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149 | const double u = 0.5 * ( GAUSS_Z[j] + 1.0 ); |
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150 | double sin_beta, cos_beta; |
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151 | SINCOS(M_PI_2*u, sin_beta, cos_beta); |
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152 | const double siA = length_a * sas_sinx_x(length_a * mu * sin_beta); |
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153 | const double siB = length_b * sas_sinx_x(length_b * mu * cos_beta); |
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154 | const double siAt = tA * sas_sinx_x(tA * mu * sin_beta); |
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155 | const double siBt = tB * sas_sinx_x(tB * mu * cos_beta); |
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156 | |
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157 | #if OVERLAPPING |
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158 | const double f = dr0*siA*siB*siC |
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159 | + drA*(siAt-siA)*siB*siC |
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160 | + drB*siAt*(siBt-siB)*siC |
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161 | + drC*siAt*siBt*(siCt-siC); |
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162 | #else |
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163 | const double f = dr0*siA*siB*siC |
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164 | + drA*(siAt-siA)*siB*siC |
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165 | + drB*siA*(siBt-siB)*siC |
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166 | + drC*siA*siB*(siCt-siC); |
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167 | #endif |
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168 | |
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169 | inner_sum_F1 += GAUSS_W[j] * f; |
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170 | inner_sum_F2 += GAUSS_W[j] * f * f; |
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171 | } |
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172 | // now complete change of inner integration variable (1-0)/(1-(-1))= 0.5 |
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173 | // and sum up the outer integral |
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174 | outer_sum_F1 += GAUSS_W[i] * inner_sum_F1 * 0.5; |
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175 | outer_sum_F2 += GAUSS_W[i] * inner_sum_F2 * 0.5; |
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176 | } |
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177 | // now complete change of outer integration variable (1-0)/(1-(-1))= 0.5 |
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178 | outer_sum_F1 *= 0.5; |
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179 | outer_sum_F2 *= 0.5; |
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180 | |
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181 | //convert from [1e-12 A-1] to [cm-1] |
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182 | *F1 = 1.0e-2 * outer_sum_F1; |
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183 | *F2 = 1.0e-4 * outer_sum_F2; |
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184 | } |
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185 | |
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186 | static double |
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187 | Iqabc(double qa, double qb, double qc, |
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188 | double core_sld, |
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189 | double arim_sld, |
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190 | double brim_sld, |
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191 | double crim_sld, |
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192 | double solvent_sld, |
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193 | double length_a, |
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194 | double length_b, |
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195 | double length_c, |
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196 | double thick_rim_a, |
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197 | double thick_rim_b, |
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198 | double thick_rim_c) |
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199 | { |
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200 | // cspkernel in csparallelepiped recoded here |
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201 | const double dr0 = core_sld-solvent_sld; |
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202 | const double drA = arim_sld-solvent_sld; |
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203 | const double drB = brim_sld-solvent_sld; |
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204 | const double drC = crim_sld-solvent_sld; |
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205 | |
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206 | const double tA = length_a + 2.0*thick_rim_a; |
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207 | const double tB = length_b + 2.0*thick_rim_b; |
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208 | const double tC = length_c + 2.0*thick_rim_c; |
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209 | const double siA = length_a*sas_sinx_x(0.5*length_a*qa); |
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210 | const double siB = length_b*sas_sinx_x(0.5*length_b*qb); |
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211 | const double siC = length_c*sas_sinx_x(0.5*length_c*qc); |
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212 | const double siAt = tA*sas_sinx_x(0.5*tA*qa); |
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213 | const double siBt = tB*sas_sinx_x(0.5*tB*qb); |
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214 | const double siCt = tC*sas_sinx_x(0.5*tC*qc); |
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215 | |
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216 | #if OVERLAPPING |
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217 | const double f = dr0*siA*siB*siC |
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218 | + drA*(siAt-siA)*siB*siC |
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219 | + drB*siAt*(siBt-siB)*siC |
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220 | + drC*siAt*siBt*(siCt-siC); |
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221 | #else |
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222 | const double f = dr0*siA*siB*siC |
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223 | + drA*(siAt-siA)*siB*siC |
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224 | + drB*siA*(siBt-siB)*siC |
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225 | + drC*siA*siB*(siCt-siC); |
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226 | #endif |
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227 | |
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228 | return 1.0e-4 * f * f; |
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229 | } |
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