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 | Iq(double q, |
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31 | double core_sld, |
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32 | double arim_sld, |
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33 | double brim_sld, |
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34 | double crim_sld, |
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35 | double solvent_sld, |
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36 | double length_a, |
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37 | double length_b, |
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38 | double length_c, |
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39 | double thick_rim_a, |
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40 | double thick_rim_b, |
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41 | double thick_rim_c) |
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42 | { |
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43 | // Code converted from functions CSPPKernel and CSParallelepiped in libCylinder.c |
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44 | // Did not understand the code completely, it should be rechecked (Miguel Gonzalez) |
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45 | //Code is rewritten,the code is compliant with Diva Singhs thesis now (Dirk Honecker) |
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46 | |
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47 | const double mu = 0.5 * q * length_b; |
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48 | |
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49 | // Scale sides by B |
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50 | const double a_over_b = length_a / length_b; |
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51 | const double c_over_b = length_c / length_b; |
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52 | |
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53 | double tA_over_b = a_over_b + 2.0*thick_rim_a/length_b; |
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54 | double tB_over_b = 1+ 2.0*thick_rim_b/length_b; |
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55 | double tC_over_b = c_over_b + 2.0*thick_rim_c/length_b; |
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56 | |
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57 | double Vin = length_a * length_b * length_c; |
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58 | #if OVERLAPPING |
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59 | const double capA_area = length_b*length_c; |
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60 | const double capB_area = (length_a+2.*thick_rim_a)*length_c; |
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61 | const double capC_area = (length_a+2.*thick_rim_a)*(length_b+2.*thick_rim_b); |
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62 | #else |
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63 | const double capA_area = length_b*length_c; |
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64 | const double capB_area = length_a*length_c; |
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65 | const double capC_area = length_a*length_b; |
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66 | #endif |
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67 | const double Va = length_a * capA_area; |
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68 | const double Vb = length_b * capB_area; |
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69 | const double Vc = length_c * capC_area; |
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70 | const double Vat = Va + 2.0 * thick_rim_a * capA_area; |
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71 | const double Vbt = Vb + 2.0 * thick_rim_b * capB_area; |
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72 | const double Vct = Vc + 2.0 * thick_rim_c * capC_area; |
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73 | |
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74 | // Scale factors (note that drC is not used later) |
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75 | const double dr0 = (core_sld-solvent_sld); |
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76 | const double drA = (arim_sld-solvent_sld); |
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77 | const double drB = (brim_sld-solvent_sld); |
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78 | const double drC = (crim_sld-solvent_sld); |
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79 | |
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80 | // outer integral (with gauss points), integration limits = 0, 1 |
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81 | double outer_sum = 0; //initialize integral |
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82 | for( int i=0; i<76; i++) { |
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83 | double sigma = 0.5 * ( Gauss76Z[i] + 1.0 ); |
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84 | double mu_proj = mu * sqrt(1.0-sigma*sigma); |
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85 | |
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86 | // inner integral (with gauss points), integration limits = 0, pi/2 |
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87 | const double siC = sas_sinx_x(mu * sigma * c_over_b); |
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88 | const double siCt = sas_sinx_x(mu * sigma * tC_over_b); |
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89 | double inner_sum = 0.0; |
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90 | for(int j=0; j<76; j++) { |
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91 | const double uu = 0.5 * ( Gauss76Z[j] + 1.0 ); |
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92 | double sin_uu, cos_uu; |
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93 | SINCOS(M_PI_2*uu, sin_uu, cos_uu); |
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94 | const double siA = sas_sinx_x(mu_proj * sin_uu * a_over_b); |
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95 | const double siB = sas_sinx_x(mu_proj * cos_uu ); |
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96 | const double siAt = sas_sinx_x(mu_proj * sin_uu * tA_over_b); |
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97 | const double siBt = sas_sinx_x(mu_proj * cos_uu * tB_over_b); |
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98 | |
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99 | #if OVERLAPPING |
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100 | const double f = dr0*Vin*siA*siB*siC |
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101 | + drA*(Vat*siAt-Va*siA)*siB*siC |
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102 | + drB*siAt*(Vbt*siBt-Vb*siB)*siC |
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103 | + drC*siAt*siBt*(Vct*siCt-Vc*siC); |
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104 | #else |
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105 | const double f = dr0*Vin*siA*siB*siC |
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106 | + drA*(Vat*siAt-Va*siA)*siB*siC |
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107 | + drB*siA*(Vbt*siBt-Vb*siB)*siC |
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108 | + drC*siA*siB*(Vct*siCt-Vc*siC); |
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109 | #endif |
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110 | |
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111 | inner_sum += Gauss76Wt[j] * f * f; |
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112 | } |
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113 | inner_sum *= 0.5; |
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114 | // now sum up the outer integral |
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115 | outer_sum += Gauss76Wt[i] * inner_sum; |
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116 | } |
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117 | outer_sum *= 0.5; |
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118 | |
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119 | //convert from [1e-12 A-1] to [cm-1] |
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120 | return 1.0e-4 * outer_sum; |
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121 | } |
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122 | |
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123 | static double |
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124 | Iqxy(double qa, double qb, double qc, |
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125 | double core_sld, |
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126 | double arim_sld, |
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127 | double brim_sld, |
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128 | double crim_sld, |
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129 | double solvent_sld, |
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130 | double length_a, |
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131 | double length_b, |
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132 | double length_c, |
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133 | double thick_rim_a, |
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134 | double thick_rim_b, |
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135 | double thick_rim_c) |
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136 | { |
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137 | // cspkernel in csparallelepiped recoded here |
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138 | const double dr0 = core_sld-solvent_sld; |
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139 | const double drA = arim_sld-solvent_sld; |
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140 | const double drB = brim_sld-solvent_sld; |
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141 | const double drC = crim_sld-solvent_sld; |
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142 | |
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143 | double Vin = length_a * length_b * length_c; |
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144 | #if OVERLAPPING |
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145 | const double capA_area = length_b*length_c; |
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146 | const double capB_area = (length_a+2.*thick_rim_a)*length_c; |
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147 | const double capC_area = (length_a+2.*thick_rim_a)*(length_b+2.*thick_rim_b); |
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148 | #else |
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149 | const double capA_area = length_b*length_c; |
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150 | const double capB_area = length_a*length_c; |
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151 | const double capC_area = length_a*length_b; |
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152 | #endif |
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153 | const double Va = length_a * capA_area; |
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154 | const double Vb = length_b * capB_area; |
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155 | const double Vc = length_c * capC_area; |
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156 | const double Vat = Va + 2.0 * thick_rim_a * capA_area; |
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157 | const double Vbt = Vb + 2.0 * thick_rim_b * capB_area; |
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158 | const double Vct = Vc + 2.0 * thick_rim_c * capC_area; |
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159 | |
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160 | // The definitions of ta, tb, tc are not the same as in the 1D case because there is no |
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161 | // the scaling by B. |
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162 | const double tA = length_a + 2.0*thick_rim_a; |
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163 | const double tB = length_b + 2.0*thick_rim_b; |
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164 | const double tC = length_c + 2.0*thick_rim_c; |
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165 | const double siA = sas_sinx_x(0.5*length_a*qa); |
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166 | const double siB = sas_sinx_x(0.5*length_b*qb); |
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167 | const double siC = sas_sinx_x(0.5*length_c*qc); |
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168 | const double siAt = sas_sinx_x(0.5*tA*qa); |
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169 | const double siBt = sas_sinx_x(0.5*tB*qb); |
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170 | const double siCt = sas_sinx_x(0.5*tC*qc); |
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171 | |
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172 | #if OVERLAPPING |
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173 | const double f = dr0*Vin*siA*siB*siC |
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174 | + drA*(Vat*siAt-Va*siA)*siB*siC |
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175 | + drB*siAt*(Vbt*siBt-Vb*siB)*siC |
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176 | + drC*siAt*siBt*(Vct*siCt-Vc*siC); |
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177 | #else |
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178 | const double f = dr0*Vin*siA*siB*siC |
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179 | + drA*(Vat*siAt-Va*siA)*siB*siC |
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180 | + drB*siA*(Vbt*siBt-Vb*siB)*siC |
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181 | + drC*siA*siB*(Vct*siCt-Vc*siC); |
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182 | #endif |
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183 | |
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184 | return 1.0e-4 * f * f; |
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185 | } |
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