1 | static double |
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2 | stacked_disks_kernel( |
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3 | double qab, |
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4 | double qc, |
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5 | double halfheight, |
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6 | double thick_layer, |
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7 | double radius, |
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8 | int n_stacking, |
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9 | double sigma_dnn, |
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10 | double core_sld, |
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11 | double layer_sld, |
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12 | double solvent_sld, |
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13 | double d) |
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14 | |
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15 | { |
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16 | // q is the q-value for the calculation (1/A) |
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17 | // radius is the core radius of the cylinder (A) |
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18 | // *_sld are the respective SLD's |
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19 | // halfheight is the *Half* CORE-LENGTH of the cylinder = L (A) |
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20 | // zi is the dummy variable for the integration (x in Feigin's notation) |
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21 | |
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22 | const double besarg1 = radius*qab; |
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23 | //const double besarg2 = radius*qab; |
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24 | |
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25 | const double sinarg1 = halfheight*qc; |
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26 | const double sinarg2 = (halfheight+thick_layer)*qc; |
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27 | |
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28 | const double be1 = sas_2J1x_x(besarg1); |
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29 | //const double be2 = sas_2J1x_x(besarg2); |
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30 | const double be2 = be1; |
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31 | const double si1 = sas_sinx_x(sinarg1); |
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32 | const double si2 = sas_sinx_x(sinarg2); |
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33 | |
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34 | const double dr1 = core_sld - solvent_sld; |
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35 | const double dr2 = layer_sld - solvent_sld; |
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36 | const double area = M_PI*radius*radius; |
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37 | const double totald = 2.0*(thick_layer + halfheight); |
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38 | |
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39 | const double t1 = area * (2.0*halfheight) * dr1 * si1 * be1; |
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40 | const double t2 = area * dr2 * (totald*si2 - 2.0*halfheight*si1) * be2; |
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41 | |
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42 | double pq = square(t1 + t2); |
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43 | |
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44 | // loop for the structure factor S(q) |
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45 | double qd_cos_alpha = d*qc; |
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46 | //d*cos_alpha is the projection of d onto q (in other words the component |
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47 | //of d that is parallel to q. |
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48 | double debye_arg = -0.5*square(qd_cos_alpha*sigma_dnn); |
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49 | double sq=0.0; |
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50 | for (int kk=1; kk<n_stacking; kk++) { |
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51 | sq += (n_stacking-kk) * cos(qd_cos_alpha*kk) * exp(debye_arg*kk); |
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52 | } |
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53 | // end of loop for S(q) |
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54 | sq = 1.0 + 2.0*sq/n_stacking; |
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55 | |
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56 | return pq * sq * n_stacking; |
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57 | // volume normalization should be per disk not per stack but form_volume |
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58 | // is per stack so correct here for now. Could change form_volume but |
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59 | // if one ever wants to use P*S we need the ER based on the total volume |
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60 | } |
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61 | |
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62 | |
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63 | static double |
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64 | stacked_disks_1d( |
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65 | double q, |
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66 | double thick_core, |
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67 | double thick_layer, |
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68 | double radius, |
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69 | int n_stacking, |
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70 | double sigma_dnn, |
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71 | double core_sld, |
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72 | double layer_sld, |
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73 | double solvent_sld) |
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74 | { |
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75 | /* StackedDiscsX : calculates the form factor of a stacked "tactoid" of core shell disks |
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76 | like clay platelets that are not exfoliated |
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77 | */ |
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78 | double summ = 0.0; //initialize integral |
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79 | |
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80 | double d = 2.0*thick_layer+thick_core; |
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81 | double halfheight = 0.5*thick_core; |
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82 | |
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83 | for(int i=0; i<GAUSS_N; i++) { |
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84 | double zi = (GAUSS_Z[i] + 1.0)*M_PI_4; |
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85 | double sin_alpha, cos_alpha; // slots to hold sincos function output |
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86 | SINCOS(zi, sin_alpha, cos_alpha); |
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87 | double yyy = stacked_disks_kernel(q*sin_alpha, q*cos_alpha, |
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88 | halfheight, |
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89 | thick_layer, |
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90 | radius, |
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91 | n_stacking, |
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92 | sigma_dnn, |
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93 | core_sld, |
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94 | layer_sld, |
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95 | solvent_sld, |
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96 | d); |
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97 | summ += GAUSS_W[i] * yyy * sin_alpha; |
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98 | } |
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99 | |
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100 | double answer = M_PI_4*summ; |
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101 | |
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102 | //Convert to [cm-1] |
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103 | return 1.0e-4*answer; |
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104 | } |
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105 | |
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106 | static double |
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107 | form_volume( |
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108 | double thick_core, |
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109 | double thick_layer, |
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110 | double radius, |
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111 | double fp_n_stacking) |
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112 | { |
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113 | int n_stacking = (int)(fp_n_stacking + 0.5); |
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114 | double d = 2.0 * thick_layer + thick_core; |
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115 | return M_PI * radius * radius * d * n_stacking; |
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116 | } |
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117 | |
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118 | static double |
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119 | Iq( |
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120 | double q, |
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121 | double thick_core, |
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122 | double thick_layer, |
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123 | double radius, |
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124 | double fp_n_stacking, |
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125 | double sigma_dnn, |
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126 | double core_sld, |
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127 | double layer_sld, |
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128 | double solvent_sld) |
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129 | { |
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130 | int n_stacking = (int)(fp_n_stacking + 0.5); |
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131 | return stacked_disks_1d(q, |
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132 | thick_core, |
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133 | thick_layer, |
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134 | radius, |
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135 | n_stacking, |
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136 | sigma_dnn, |
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137 | core_sld, |
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138 | layer_sld, |
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139 | solvent_sld); |
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140 | } |
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141 | |
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142 | |
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143 | static double |
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144 | Iqac(double qab, double qc, |
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145 | double thick_core, |
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146 | double thick_layer, |
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147 | double radius, |
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148 | double fp_n_stacking, |
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149 | double sigma_dnn, |
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150 | double core_sld, |
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151 | double layer_sld, |
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152 | double solvent_sld) |
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153 | { |
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154 | int n_stacking = (int)(fp_n_stacking + 0.5); |
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155 | double d = 2.0 * thick_layer + thick_core; |
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156 | double halfheight = 0.5*thick_core; |
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157 | double answer = stacked_disks_kernel(qab, qc, |
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158 | halfheight, |
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159 | thick_layer, |
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160 | radius, |
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161 | n_stacking, |
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162 | sigma_dnn, |
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163 | core_sld, |
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164 | layer_sld, |
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165 | solvent_sld, |
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166 | d); |
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167 | |
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168 | //convert to [cm-1] |
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169 | answer *= 1.0e-4; |
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170 | |
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171 | return answer; |
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172 | } |
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173 | |
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