| 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 linear_pearls_kernel(double q, |
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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 | |
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| 18 | double form_volume(double radius, double num_pearls) |
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| 19 | { |
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| 20 | // Pearl volume |
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| 21 | double pearl_vol = 4.0 /3.0 * M_PI * pow(radius, 3.0); |
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| 22 | // Return total volume |
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| 23 | return num_pearls * pearl_vol;; |
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| 24 | } |
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| 25 | |
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| 26 | double linear_pearls_kernel(double q, |
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| 27 | double radius, |
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| 28 | double edge_sep, |
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| 29 | double num_pearls, |
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| 30 | double pearl_sld, |
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| 31 | double solvent_sld) |
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| 32 | { |
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| 33 | double n_contrib; |
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| 34 | //relative sld |
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| 35 | double contrast_pearl = pearl_sld - solvent_sld; |
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| 36 | //each volume |
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| 37 | double pearl_vol = 4.0 /3.0 * M_PI * pow(radius, 3.0); |
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| 38 | //total volume |
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| 39 | double tot_vol = num_pearls * pearl_vol; |
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| 40 | //mass |
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| 41 | double m_s = contrast_pearl * pearl_vol; |
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| 42 | //center to center distance between the neighboring pearls |
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| 43 | double separation = edge_sep + 2.0 * radius; |
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| 44 | |
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| 45 | double x=q*radius; |
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| 46 | |
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| 47 | // Try Taylor on x*xos(x) |
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| 48 | // double out_cos = x - pow(x,3)/2 + pow(x,5)/24 - pow(x,7)/720 + pow(x,9)/40320; |
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| 49 | // psi -= x*out_cos; |
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| 50 | |
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| 51 | //sine functions of a pearl |
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| 52 | double psi = sin(q * radius); |
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| 53 | psi -= x * cos(x); |
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| 54 | psi /= pow((q * radius), 3.0); |
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| 55 | |
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| 56 | // N pearls contribution |
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| 57 | int n_max = num_pearls - 1; |
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| 58 | n_contrib = num_pearls; |
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| 59 | for(int num=1; num<=n_max; num++) { |
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| 60 | n_contrib += (2.0*(num_pearls-num)*sinc(q*separation*num)); |
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| 61 | } |
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| 62 | // form factor for num_pearls |
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| 63 | double form_factor = n_contrib; |
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| 64 | form_factor *= pow((m_s*psi*3.0), 2.0); |
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| 65 | form_factor /= (tot_vol * 1.0e4); |
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| 66 | |
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| 67 | return form_factor; |
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| 68 | } |
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| 69 | |
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| 70 | double Iq(double q, |
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| 71 | double radius, |
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| 72 | double edge_sep, |
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| 73 | double num_pearls, |
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| 74 | double pearl_sld, |
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| 75 | double solvent_sld) |
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| 76 | { |
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| 77 | |
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| 78 | double result = linear_pearls_kernel(q, |
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| 79 | radius, |
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| 80 | edge_sep, |
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| 81 | num_pearls, |
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| 82 | pearl_sld, |
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| 83 | solvent_sld); |
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| 84 | |
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| 85 | return result; |
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| 86 | } |
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