1 | /** |
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2 | * spheresld model |
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3 | */ |
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4 | #include <math.h> |
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5 | #include "pearlnecklace.h" |
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6 | #include "libmultifunc/libfunc.h" |
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7 | #include <stdio.h> |
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8 | #include <stdlib.h> |
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9 | |
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10 | |
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11 | double pearl_necklace_kernel(double dp[], double q) { |
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12 | // fit parameters |
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13 | double scale = dp[0]; |
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14 | double radius = dp[1]; |
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15 | double edge_separation = dp[2]; |
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16 | double thick_string = dp[3]; |
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17 | double num_pearls = dp[4]; |
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18 | double sld_pearl = dp[5]; |
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19 | double sld_string = dp[6]; |
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20 | double sld_solv = dp[7]; |
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21 | double background = dp[8]; |
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22 | |
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23 | //relative slds |
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24 | double contrast_pearl = sld_pearl - sld_solv; |
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25 | double contrast_string = sld_string - sld_solv; |
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26 | |
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27 | // number of string segments |
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28 | double num_strings = num_pearls - 1.0; |
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29 | |
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30 | //Pi |
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31 | double pi = 4.0*atan(1.0); |
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32 | |
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33 | // each volumes |
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34 | double string_vol = edge_separation * pi * pow((thick_string / 2.0), 2); |
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35 | double pearl_vol = 4.0 /3.0 * pi * pow(radius, 3); |
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36 | |
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37 | //total volume |
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38 | double tot_vol; |
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39 | tot_vol = num_strings * string_vol; |
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40 | tot_vol += num_pearls * pearl_vol; |
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41 | |
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42 | //each masses |
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43 | double m_r= contrast_string * string_vol; |
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44 | double m_s= contrast_pearl * pearl_vol; |
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45 | |
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46 | //sine functions of a pearl |
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47 | double psi; |
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48 | psi = sin(q*radius); |
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49 | psi -= q * radius * cos(q * radius); |
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50 | psi /= pow((q * radius), 3); |
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51 | psi *= 3.0; |
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52 | |
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53 | // Note take only 20 terms in Si series: 10 terms may be enough though. |
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54 | double gamma; |
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55 | gamma = Si(q* edge_separation, 6); |
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56 | gamma /= (q* edge_separation); |
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57 | double beta; |
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58 | beta = Si(q * (edge_separation + radius), 6); |
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59 | beta -= Si(q * radius, 6); |
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60 | beta /= (q* edge_separation); |
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61 | |
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62 | //form factors |
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63 | double sss; //pearls |
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64 | double srr; //strings |
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65 | double srs; //cross |
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66 | // center to center distance between the neighboring pearls |
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67 | double A_s = edge_separation + 2.0 * radius; |
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68 | |
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69 | // form factor for num_pearls |
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70 | sss = 1.0 - pow(sin_x(q*A_s), (int)num_pearls ); |
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71 | sss /= pow((1.0-sin_x(q*A_s)), 2); |
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72 | sss *= sin_x(q*A_s); |
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73 | sss -= num_pearls/2.0; |
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74 | sss += num_pearls/(1.0-sin_x(q*A_s)); |
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75 | sss *= 2.0 * pow((m_s*psi), 2); |
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76 | |
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77 | // form factor for num_strings (like thin rods) |
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78 | double srr_1; |
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79 | srr_1 = -pow(sin_x(q*edge_separation/2.0), 2); |
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80 | //printf ("sss %g, %g, %g\n",sss, srr_1, gamma); |
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81 | srr_1 += 2.0 * gamma; |
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82 | srr_1 *= num_strings; |
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83 | double srr_2; |
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84 | srr_2 = 2.0/(1.0-sin_x(q*A_s)); |
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85 | srr_2 *= num_strings; |
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86 | srr_2 *= pow(beta, 2); |
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87 | double srr_3; |
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88 | srr_3 = 1.0 - pow(sin_x(q*A_s), (int)num_strings); |
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89 | srr_3 /= pow((1.0-sin_x(q*A_s)), 2); |
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90 | srr_3 *= pow(beta, 2); |
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91 | srr_3 *= -2.0; |
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92 | |
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93 | // total srr |
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94 | srr = srr_1 + srr_2 + srr_3; |
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95 | srr *= pow(m_r, 2); |
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96 | |
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97 | // form factor for correlations |
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98 | srs = -1.0; |
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99 | srs -= pow(sin_x(q*A_s), (int)num_strings); |
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100 | srs /= pow((1.0-sin_x(q*A_s)), 2); |
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101 | srs *= sin_x(q*A_s); |
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102 | srs += (num_strings/(1.0-sin_x(q*A_s))); |
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103 | srs *= 4.0; |
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104 | srs *= (m_r * m_s * beta * psi); |
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105 | |
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106 | double form_factor; |
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107 | form_factor = sss + srr + srs; |
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108 | form_factor /= (tot_vol * 1.0e-8); // norm by volume and A^-1 to cm^-1 |
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109 | |
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110 | // scale and background |
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111 | form_factor *= scale; |
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112 | form_factor += background; |
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113 | |
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114 | return (form_factor); |
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115 | } |
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116 | |
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117 | /** |
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118 | * Function to evaluate pearlnecklace function |
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119 | * @param pars: parameters of pearlnecklace |
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120 | * @param q: q-value |
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121 | * @return: function value |
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122 | */ |
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123 | |
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124 | double pearl_necklace_analytical_1D(PeralNecklaceParameters *pars, double q) { |
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125 | double dp[9]; |
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126 | |
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127 | dp[0] = pars->scale; |
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128 | dp[1] = pars->radius; |
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129 | dp[2] = pars->edge_separation; |
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130 | dp[3] = pars->thick_string; |
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131 | dp[4] = pars->num_pearls; |
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132 | dp[5] = pars->sld_pearl; |
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133 | dp[6] = pars->sld_string; |
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134 | dp[7] = pars->sld_solv; |
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135 | dp[8] = pars->background; |
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136 | |
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137 | return pearl_necklace_kernel(dp, q); |
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138 | } |
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139 | |
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140 | /** |
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141 | * Function to evaluate pearl_necklace function |
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142 | * @param pars: parameters of PeralNecklace |
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143 | * @param q: q-value |
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144 | * @return: function value |
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145 | */ |
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146 | double pearl_necklace_analytical_2D(PeralNecklaceParameters *pars, double q, double phi) { |
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147 | return pearl_necklace_analytical_1D(pars,q); |
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148 | } |
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149 | |
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150 | double pearl_necklace_analytical_2DXY(PeralNecklaceParameters *pars, double qx, double qy){ |
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151 | return pearl_necklace_analytical_1D(pars,sqrt(qx*qx+qy*qy)); |
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152 | } |
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153 | |
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