[cf404cb] | 1 | double _pearl_necklace_kernel(double q, double radius, double edge_separation, |
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| 2 | double thick_string, double num_pearls, double sld_pearl, |
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| 3 | double sld_string, double sld_solv); |
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| 4 | double form_volume(double radius, double edge_separation, |
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| 5 | double string_thickness, double number_of_pearls); |
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| 6 | double sinc(double x); |
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| 7 | |
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| 8 | double Iq(double q, double radius, double edge_separation, |
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| 9 | double string_thickness, double number_of_pearls, double sld, |
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| 10 | double string_sld, double solvent_sld); |
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| 11 | double Iqxy(double qx, double qy, double radius, double edge_separation, |
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| 12 | double string_thickness, double number_of_pearls, double sld, |
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| 13 | double string_sld, double solvent_sld); |
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| 14 | |
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| 15 | double ER(double radius, double edge_separation, |
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| 16 | double string_thickness, double number_of_pearls); |
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| 17 | double VR(double radius, double edge_separation, |
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| 18 | double string_thickness, double number_of_pearls); |
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| 19 | |
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| 20 | // From Igor library |
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| 21 | double _pearl_necklace_kernel(double q, double radius, double edge_separation, double thick_string, |
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| 22 | double num_pearls, double sld_pearl, double sld_string, double sld_solv) |
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| 23 | { |
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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 | //total volume |
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| 28 | double pi = 4.0*atan(1.0); |
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| 29 | double tot_vol = form_volume(radius, edge_separation, thick_string, num_pearls); |
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| 30 | double string_vol = edge_separation * pi * pow((thick_string / 2.0), 2); |
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| 31 | double pearl_vol = 4.0 /3.0 * pi * pow(radius, 3); |
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| 32 | double num_strings = num_pearls - 1; |
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| 33 | //each mass |
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| 34 | double m_r= contrast_string * string_vol; |
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| 35 | double m_s= contrast_pearl * pearl_vol; |
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| 36 | double psi, gamma, beta; |
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| 37 | //form factors |
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| 38 | double sss; //pearls |
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| 39 | double srr; //strings |
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| 40 | double srs; //cross |
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| 41 | double A_s, srr_1, srr_2, srr_3; |
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| 42 | double form_factor; |
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| 43 | |
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| 44 | //sine functions of a pearl |
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| 45 | psi = sin(q*radius); |
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| 46 | psi -= q * radius * cos(q * radius); |
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| 47 | psi /= pow((q * radius), 3); |
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| 48 | psi *= 3.0; |
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| 49 | |
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| 50 | // Note take only 20 terms in Si series: 10 terms may be enough though. |
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| 51 | gamma = Si(q* edge_separation); |
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| 52 | gamma /= (q* edge_separation); |
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| 53 | beta = Si(q * (edge_separation + radius)); |
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| 54 | beta -= Si(q * radius); |
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| 55 | beta /= (q* edge_separation); |
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| 56 | |
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| 57 | // center to center distance between the neighboring pearls |
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| 58 | A_s = edge_separation + 2.0 * radius; |
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| 59 | |
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| 60 | // form factor for num_pearls |
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| 61 | sss = 1.0 - pow(sinc(q*A_s), num_pearls ); |
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| 62 | sss /= pow((1.0-sinc(q*A_s)), 2); |
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| 63 | sss *= -sinc(q*A_s); |
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| 64 | sss -= num_pearls/2.0; |
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| 65 | sss += num_pearls/(1.0-sinc(q*A_s)); |
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| 66 | sss *= 2.0 * pow((m_s*psi), 2); |
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| 67 | |
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| 68 | // form factor for num_strings (like thin rods) |
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| 69 | srr_1 = -pow(sinc(q*edge_separation/2.0), 2); |
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| 70 | |
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| 71 | srr_1 += 2.0 * gamma; |
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| 72 | srr_1 *= num_strings; |
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| 73 | srr_2 = 2.0/(1.0-sinc(q*A_s)); |
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| 74 | srr_2 *= num_strings * pow(beta, 2); |
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| 75 | srr_3 = 1.0 - pow(sinc(q*A_s), num_strings); |
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| 76 | srr_3 /= pow((1.0-sinc(q*A_s)), 2); |
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| 77 | srr_3 *= -2.0 * pow(beta, 2); |
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| 78 | |
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| 79 | // total srr |
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| 80 | srr = srr_1 + srr_2 + srr_3; |
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| 81 | srr *= pow(m_r, 2); |
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| 82 | |
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| 83 | // form factor for correlations |
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| 84 | srs = 1.0; |
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| 85 | srs -= pow(sinc(q*A_s), num_strings); |
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| 86 | srs /= pow((1.0-sinc(q*A_s)), 2); |
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| 87 | srs *= -sinc(q*A_s); |
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| 88 | srs += (num_strings/(1.0-sinc(q*A_s))); |
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| 89 | srs *= 4.0 * (m_r * m_s * beta * psi); |
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| 90 | |
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| 91 | form_factor = sss + srr + srs; |
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| 92 | form_factor /= (tot_vol * 1.0e4); // norm by volume and A^-1 to cm^-1 |
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| 93 | |
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| 94 | return (form_factor); |
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| 95 | } |
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| 96 | |
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| 97 | double form_volume(double radius, double edge_separation, |
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| 98 | double string_thickness, double number_of_pearls) |
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| 99 | { |
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| 100 | double total_vol; |
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| 101 | |
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| 102 | double pi = 4.0*atan(1.0); |
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| 103 | double number_of_strings = number_of_pearls - 1.0; |
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| 104 | |
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| 105 | double string_vol = edge_separation * pi * pow((string_thickness / 2.0), 2); |
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| 106 | double pearl_vol = 4.0 /3.0 * pi * pow(radius, 3); |
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| 107 | |
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| 108 | total_vol = number_of_strings * string_vol; |
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| 109 | total_vol += number_of_pearls * pearl_vol; |
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| 110 | |
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| 111 | return(total_vol); |
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| 112 | } |
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| 113 | |
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| 114 | double sinc(double x) |
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| 115 | { |
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| 116 | double num = sin(x); |
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| 117 | double denom = x; |
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| 118 | return num/denom; |
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| 119 | } |
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| 120 | |
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| 121 | |
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| 122 | double Iq(double q, double radius, double edge_separation, |
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| 123 | double string_thickness, double number_of_pearls, double sld, |
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| 124 | double string_sld, double solvent_sld) |
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| 125 | { |
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| 126 | double value = 0.0; |
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| 127 | double tot_vol = 0.0; |
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| 128 | |
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| 129 | value = _pearl_necklace_kernel(q, radius, edge_separation, string_thickness, |
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| 130 | number_of_pearls, sld, string_sld, solvent_sld); |
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| 131 | tot_vol = form_volume(radius, edge_separation, string_thickness, number_of_pearls); |
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| 132 | |
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| 133 | return value*tot_vol; |
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| 134 | } |
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| 135 | |
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| 136 | double Iqxy(double qx, double qy, double radius, double edge_separation, |
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| 137 | double string_thickness, double number_of_pearls, double sld, |
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| 138 | double string_sld, double solvent_sld) |
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| 139 | { |
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| 140 | double q = sqrt(qx*qx + qy*qy); |
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| 141 | return(Iq(q, radius, edge_separation, string_thickness, number_of_pearls, |
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| 142 | sld, string_sld, solvent_sld)); |
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| 143 | } |
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| 144 | |
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| 145 | |
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| 146 | double ER(double radius, double edge_separation, |
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| 147 | double string_thickness, double number_of_pearls) |
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| 148 | { |
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| 149 | double tot_vol = form_volume(radius, edge_separation, string_thickness, number_of_pearls); |
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| 150 | double pi = 4.0*atan(1.0); |
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| 151 | |
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| 152 | double rad_out = pow((3.0*tot_vol/4.0/pi), 0.33333); |
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| 153 | |
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| 154 | return rad_out; |
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| 155 | } |
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| 156 | double VR(double radius, double edge_separation, |
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| 157 | double string_thickness, double number_of_pearls) |
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| 158 | { |
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| 159 | return 1.0; |
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| 160 | } |
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