1 | double form_volume(double radius, double edge_sep, |
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2 | double thick_string, double fp_num_pearls); |
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3 | double Iq(double q, double radius, double edge_sep, |
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4 | double thick_string, double fp_num_pearls, double sld, |
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5 | double string_sld, double solvent_sld); |
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6 | |
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7 | #define INVALID(v) (v.thick_string >= v.radius || v.num_pearls <= 0) |
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8 | |
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9 | // From Igor library |
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10 | static double |
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11 | pearl_necklace_kernel(double q, double radius, double edge_sep, double thick_string, |
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12 | int num_pearls, double sld_pearl, double sld_string, double sld_solv) |
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13 | { |
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14 | // number of string segments |
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15 | const int num_strings = num_pearls - 1; |
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16 | |
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17 | //each masses: contrast * volume |
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18 | const double contrast_pearl = sld_pearl - sld_solv; |
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19 | const double contrast_string = sld_string - sld_solv; |
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20 | const double string_vol = edge_sep * M_PI_4 * thick_string * thick_string; |
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21 | const double pearl_vol = M_4PI_3 * radius * radius * radius; |
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22 | const double m_string = contrast_string * string_vol; |
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23 | const double m_pearl = contrast_pearl * pearl_vol; |
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24 | |
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25 | // center to center distance between the neighboring pearls |
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26 | const double A_s = edge_sep + 2.0 * radius; |
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27 | |
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28 | //sine functions of a pearl |
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29 | // Note: lim_(q->0) Si(q*a)/(q*b) = a/b |
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30 | // So therefore: |
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31 | // beta = q==0. ? 1.0 : (Si(q*(A_s-radius)) - Si(q*radius))/q_edge; |
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32 | // gamma = q==0. ? 1.0 : Si(q_edge)/q_edge; |
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33 | // But there is a 1/(1-sinc) term below which blows up so don't bother |
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34 | const double q_edge = q * edge_sep; |
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35 | const double beta = (sas_Si(q*(A_s-radius)) - sas_Si(q*radius)) / q_edge; |
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36 | const double gamma = sas_Si(q_edge) / q_edge; |
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37 | const double psi = sas_3j1x_x(q*radius); |
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38 | |
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39 | // Precomputed sinc terms |
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40 | const double si = sas_sinx_x(q*A_s); |
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41 | const double omsi = 1.0 - si; |
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42 | const double pow_si = pown(si, num_pearls); |
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43 | |
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44 | // form factor for num_pearls |
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45 | const double sss = 2.0*square(m_pearl*psi) * ( |
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46 | - si * (1.0 - pow_si) / (omsi*omsi) |
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47 | + num_pearls / omsi |
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48 | - 0.5 * num_pearls |
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49 | ); |
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50 | |
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51 | // form factor for num_strings (like thin rods) |
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52 | const double srr = m_string * m_string * ( |
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53 | - 2.0 * (1.0 - pow_si/si)*beta*beta / (omsi*omsi) |
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54 | + 2.0 * num_strings*beta*beta / omsi |
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55 | + num_strings * (2.0*gamma - square(sas_sinx_x(q_edge/2.0))) |
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56 | ); |
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57 | |
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58 | // form factor for correlations |
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59 | const double srs = 4.0 * m_string * m_pearl * beta * psi * ( |
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60 | - si * (1.0 - pow_si/si) / (omsi*omsi) |
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61 | + num_strings / omsi |
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62 | ); |
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63 | |
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64 | const double form = sss + srr + srs; |
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65 | |
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66 | return 1.0e-4 * form; |
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67 | } |
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68 | |
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69 | double form_volume(double radius, double edge_sep, double thick_string, double fp_num_pearls) |
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70 | { |
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71 | const int num_pearls = (int)(fp_num_pearls + 0.5); //Force integer number of pearls |
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72 | const int num_strings = num_pearls - 1; |
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73 | const double string_vol = edge_sep * M_PI_4 * thick_string * thick_string; |
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74 | const double pearl_vol = M_4PI_3 * radius * radius * radius; |
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75 | const double volume = num_strings*string_vol + num_pearls*pearl_vol; |
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76 | |
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77 | return volume; |
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78 | } |
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79 | |
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80 | static double |
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81 | radius_from_volume(double radius, double edge_sep, double thick_string, double fp_num_pearls) |
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82 | { |
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83 | const double vol_tot = form_volume(radius, edge_sep, thick_string, fp_num_pearls); |
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84 | return cbrt(vol_tot/M_4PI_3); |
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85 | } |
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86 | |
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87 | static double |
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88 | effective_radius(int mode, double radius, double edge_sep, double thick_string, double fp_num_pearls) |
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89 | { |
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90 | switch (mode) { |
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91 | default: |
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92 | case 1: |
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93 | return radius_from_volume(radius, edge_sep, thick_string, fp_num_pearls); |
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94 | } |
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95 | } |
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96 | |
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97 | double Iq(double q, double radius, double edge_sep, |
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98 | double thick_string, double fp_num_pearls, double sld, |
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99 | double string_sld, double solvent_sld) |
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100 | { |
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101 | const int num_pearls = (int)(fp_num_pearls + 0.5); //Force integer number of pearls |
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102 | const double form = pearl_necklace_kernel(q, radius, edge_sep, |
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103 | thick_string, num_pearls, sld, string_sld, solvent_sld); |
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104 | |
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105 | return form; |
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106 | } |
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