1 | |
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2 | // Converted from Igor function gfn4, using the same pattern as ellipsoid |
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3 | // for evaluating the parts of the integral. |
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4 | // FUNCTION gfn4: CONTAINS F(Q,A,B,MU)**2 AS GIVEN |
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5 | // BY (53) & (58-59) IN CHEN AND |
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6 | // KOTLARCHYK REFERENCE |
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7 | // |
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8 | // <OBLATE ELLIPSOID> |
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9 | static double |
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10 | _cs_ellipsoid_kernel(double qab, double qc, |
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11 | double equat_core, double polar_core, |
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12 | double equat_shell, double polar_shell, |
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13 | double sld_core_shell, double sld_shell_solvent) |
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14 | { |
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15 | const double qr_core = sqrt(square(equat_core*qab) + square(polar_core*qc)); |
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16 | const double si_core = sas_3j1x_x(qr_core); |
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17 | const double volume_core = M_4PI_3*equat_core*equat_core*polar_core; |
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18 | const double fq_core = si_core*volume_core*sld_core_shell; |
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19 | |
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20 | const double qr_shell = sqrt(square(equat_shell*qab) + square(polar_shell*qc)); |
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21 | const double si_shell = sas_3j1x_x(qr_shell); |
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22 | const double volume_shell = M_4PI_3*equat_shell*equat_shell*polar_shell; |
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23 | const double fq_shell = si_shell*volume_shell*sld_shell_solvent; |
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24 | |
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25 | return fq_core + fq_shell; |
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26 | } |
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27 | |
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28 | static double |
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29 | form_volume(double radius_equat_core, |
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30 | double x_core, |
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31 | double thick_shell, |
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32 | double x_polar_shell) |
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33 | { |
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34 | const double equat_shell = radius_equat_core + thick_shell; |
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35 | const double polar_shell = radius_equat_core*x_core + thick_shell*x_polar_shell; |
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36 | double vol = M_4PI_3*equat_shell*equat_shell*polar_shell; |
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37 | return vol; |
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38 | } |
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39 | |
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40 | static double |
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41 | Iq(double q, |
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42 | double radius_equat_core, |
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43 | double x_core, |
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44 | double thick_shell, |
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45 | double x_polar_shell, |
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46 | double core_sld, |
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47 | double shell_sld, |
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48 | double solvent_sld) |
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49 | { |
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50 | const double sld_core_shell = core_sld - shell_sld; |
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51 | const double sld_shell_solvent = shell_sld - solvent_sld; |
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52 | |
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53 | const double polar_core = radius_equat_core*x_core; |
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54 | const double equat_shell = radius_equat_core + thick_shell; |
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55 | const double polar_shell = radius_equat_core*x_core + thick_shell*x_polar_shell; |
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56 | |
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57 | // translate from [-1, 1] => [0, 1] |
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58 | const double m = 0.5; |
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59 | const double b = 0.5; |
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60 | double total = 0.0; //initialize intergral |
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61 | for(int i=0;i<76;i++) { |
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62 | const double cos_theta = Gauss76Z[i]*m + b; |
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63 | const double sin_theta = sqrt(1.0 - cos_theta*cos_theta); |
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64 | double fq = _cs_ellipsoid_kernel(q*sin_theta, q*cos_theta, |
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65 | radius_equat_core, polar_core, |
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66 | equat_shell, polar_shell, |
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67 | sld_core_shell, sld_shell_solvent); |
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68 | total += Gauss76Wt[i] * fq * fq; |
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69 | } |
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70 | total *= m; |
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71 | |
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72 | // convert to [cm-1] |
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73 | return 1.0e-4 * total; |
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74 | } |
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75 | |
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76 | static double |
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77 | Iqxy(double qab, double qc, |
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78 | double radius_equat_core, |
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79 | double x_core, |
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80 | double thick_shell, |
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81 | double x_polar_shell, |
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82 | double core_sld, |
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83 | double shell_sld, |
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84 | double solvent_sld) |
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85 | { |
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86 | const double sld_core_shell = core_sld - shell_sld; |
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87 | const double sld_shell_solvent = shell_sld - solvent_sld; |
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88 | |
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89 | const double polar_core = radius_equat_core*x_core; |
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90 | const double equat_shell = radius_equat_core + thick_shell; |
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91 | const double polar_shell = radius_equat_core*x_core + thick_shell*x_polar_shell; |
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92 | |
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93 | double fq = _cs_ellipsoid_kernel(qab, qc, |
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94 | radius_equat_core, polar_core, |
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95 | equat_shell, polar_shell, |
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96 | sld_core_shell, sld_shell_solvent); |
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97 | |
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98 | //convert to [cm-1] |
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99 | return 1.0e-4 * fq * fq; |
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100 | } |
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