1 | double form_volume(double radius, double num_pearls); |
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2 | |
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3 | double Iq(double q, |
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4 | double radius, |
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5 | double edge_sep, |
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6 | double num_pearls, |
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7 | double pearl_sld, |
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8 | double solvent_sld); |
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9 | |
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10 | double Iqxy(double qx, double qy, |
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11 | double radius, |
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12 | double edge_sep, |
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13 | double num_pearls, |
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14 | double pearl_sld, |
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15 | double solvent_sld); |
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16 | |
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17 | double linear_pearls_kernel(double q, |
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18 | double radius, |
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19 | double edge_sep, |
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20 | double num_pearls, |
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21 | double pearl_sld, |
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22 | double solvent_sld); |
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23 | |
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24 | |
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25 | double form_volume(double radius, double num_pearls) |
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26 | { |
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27 | // Pearl volume |
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28 | double pearl_vol = 4.0 /3.0 * M_PI * pow(radius, 3.0); |
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29 | // Return total volume |
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30 | return num_pearls * pearl_vol;; |
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31 | } |
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32 | |
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33 | // If used elsewhere - factor out to lib/ |
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34 | static |
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35 | double sinc(double x) |
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36 | { |
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37 | if (x==0.0){ |
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38 | return 1.0; |
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39 | } |
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40 | return sin(x)/x; |
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41 | } |
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42 | |
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43 | double linear_pearls_kernel(double q, |
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44 | double radius, |
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45 | double edge_sep, |
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46 | double num_pearls, |
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47 | double pearl_sld, |
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48 | double solvent_sld) |
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49 | { |
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50 | double n_contrib; |
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51 | //relative sld |
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52 | double contrast_pearl = pearl_sld - solvent_sld; |
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53 | //each volume |
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54 | double pearl_vol = 4.0 /3.0 * M_PI * pow(radius, 3.0); |
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55 | //total volume |
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56 | double tot_vol = num_pearls * pearl_vol; |
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57 | //mass |
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58 | double m_s = contrast_pearl * pearl_vol; |
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59 | //center to center distance between the neighboring pearls |
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60 | double separation = edge_sep + 2.0 * radius; |
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61 | |
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62 | double x=q*radius; |
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63 | |
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64 | // Try Taylor on x*xos(x) |
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65 | // double out_cos = x - pow(x,3)/2 + pow(x,5)/24 - pow(x,7)/720 + pow(x,9)/40320; |
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66 | // psi -= x*out_cos; |
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67 | |
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68 | //sine functions of a pearl |
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69 | double psi = sin(q * radius); |
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70 | psi -= x * cos(x); |
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71 | psi /= pow((q * radius), 3.0); |
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72 | |
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73 | // N pearls contribution |
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74 | int n_max = num_pearls - 1; |
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75 | n_contrib = num_pearls; |
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76 | for(int num=1; num<=n_max; num++) { |
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77 | n_contrib += (2.0*(num_pearls-num)*sinc(q*separation*num)); |
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78 | } |
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79 | // form factor for num_pearls |
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80 | double form_factor = n_contrib; |
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81 | form_factor *= pow((m_s*psi*3.0), 2.0); |
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82 | form_factor /= (tot_vol * 1.0e4); |
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83 | |
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84 | return form_factor; |
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85 | } |
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86 | |
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87 | double Iq(double q, |
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88 | double radius, |
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89 | double edge_sep, |
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90 | double num_pearls, |
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91 | double pearl_sld, |
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92 | double solvent_sld) |
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93 | { |
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94 | |
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95 | double result = linear_pearls_kernel(q, |
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96 | radius, |
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97 | edge_sep, |
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98 | num_pearls, |
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99 | pearl_sld, |
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100 | solvent_sld); |
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101 | |
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102 | return result; |
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103 | } |
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104 | |
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105 | double Iqxy(double qx, double qy, |
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106 | double radius, |
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107 | double edge_sep, |
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108 | double num_pearls, |
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109 | double pearl_sld, |
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110 | double solvent_sld) |
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111 | { |
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112 | double q; |
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113 | q = sqrt(qx*qx+qy*qy); |
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114 | |
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115 | double result = linear_pearls_kernel(q, |
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116 | radius, |
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117 | edge_sep, |
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118 | num_pearls, |
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119 | pearl_sld, |
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120 | solvent_sld); |
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121 | |
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122 | return result; |
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123 | } |
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