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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