| 1 | /** |
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| 2 | * pearl necklace 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 | //each masses |
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| 40 | double m_r= contrast_string * string_vol; |
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| 41 | double m_s= contrast_pearl * pearl_vol; |
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| 42 | double psi; |
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| 43 | double gamma; |
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| 44 | double beta; |
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| 45 | //form factors |
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| 46 | double sss; //pearls |
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| 47 | double srr; //strings |
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| 48 | double srs; //cross |
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| 49 | double A_s; |
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| 50 | double srr_1; |
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| 51 | double srr_2; |
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| 52 | double srr_3; |
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| 53 | double form_factor; |
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| 54 | |
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| 55 | tot_vol = num_strings * string_vol; |
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| 56 | tot_vol += num_pearls * pearl_vol; |
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| 57 | |
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| 58 | //sine functions of a pearl |
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| 59 | psi = sin(q*radius); |
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| 60 | psi -= q * radius * cos(q * radius); |
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| 61 | psi /= pow((q * radius), 3); |
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| 62 | psi *= 3.0; |
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| 63 | |
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| 64 | // Note take only 20 terms in Si series: 10 terms may be enough though. |
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| 65 | gamma = Si(q* edge_separation); |
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| 66 | gamma /= (q* edge_separation); |
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| 67 | beta = Si(q * (edge_separation + radius)); |
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| 68 | beta -= Si(q * radius); |
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| 69 | beta /= (q* edge_separation); |
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| 70 | |
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| 71 | // center to center distance between the neighboring pearls |
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| 72 | A_s = edge_separation + 2.0 * radius; |
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| 73 | |
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| 74 | // form factor for num_pearls |
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| 75 | sss = 1.0 - pow(sinc(q*A_s), num_pearls ); |
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| 76 | sss /= pow((1.0-sinc(q*A_s)), 2); |
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| 77 | sss *= -sinc(q*A_s); |
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| 78 | sss -= num_pearls/2.0; |
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| 79 | sss += num_pearls/(1.0-sinc(q*A_s)); |
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| 80 | sss *= 2.0 * pow((m_s*psi), 2); |
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| 81 | |
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| 82 | // form factor for num_strings (like thin rods) |
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| 83 | srr_1 = -pow(sinc(q*edge_separation/2.0), 2); |
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| 84 | |
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| 85 | srr_1 += 2.0 * gamma; |
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| 86 | srr_1 *= num_strings; |
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| 87 | srr_2 = 2.0/(1.0-sinc(q*A_s)); |
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| 88 | srr_2 *= num_strings; |
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| 89 | srr_2 *= pow(beta, 2); |
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| 90 | srr_3 = 1.0 - pow(sinc(q*A_s), num_strings); |
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| 91 | srr_3 /= pow((1.0-sinc(q*A_s)), 2); |
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| 92 | srr_3 *= pow(beta, 2); |
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| 93 | srr_3 *= -2.0; |
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| 94 | |
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| 95 | // total srr |
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| 96 | srr = srr_1 + srr_2 + srr_3; |
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| 97 | srr *= pow(m_r, 2); |
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| 98 | |
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| 99 | // form factor for correlations |
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| 100 | srs = 1.0; |
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| 101 | srs -= pow(sinc(q*A_s), num_strings); |
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| 102 | srs /= pow((1.0-sinc(q*A_s)), 2); |
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| 103 | srs *= -sinc(q*A_s); |
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| 104 | srs += (num_strings/(1.0-sinc(q*A_s))); |
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| 105 | srs *= 4.0; |
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| 106 | srs *= (m_r * m_s * beta * psi); |
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| 107 | |
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| 108 | form_factor = sss + srr + srs; |
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| 109 | form_factor /= (tot_vol * 1.0e-8); // norm by volume and A^-1 to cm^-1 |
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| 110 | |
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| 111 | // scale and background |
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| 112 | form_factor *= scale; |
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| 113 | form_factor += background; |
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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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