1 | static double |
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2 | sc_Zq(double qa, double qb, double qc, double dnn, double d_factor) |
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3 | { |
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4 | // Equations from Matsuoka 9-10-11, multiplied by |q| |
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5 | const double a1 = qa; |
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6 | const double a2 = qb; |
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7 | const double a3 = qc; |
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8 | |
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9 | // Matsuoka 13-14-15 |
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10 | // Z_k numerator: 1 - exp(a)^2 |
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11 | // Z_k denominator: 1 - 2 cos(d a_k) exp(a) + exp(2a) |
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12 | // Rewriting numerator |
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13 | // => -(exp(2a) - 1) |
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14 | // => -expm1(2a) |
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15 | // Rewriting denominator |
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16 | // => exp(a)^2 - 2 cos(d ak) exp(a) + 1) |
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17 | // => (exp(a) - 2 cos(d ak)) * exp(a) + 1 |
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18 | const double arg = -0.5*square(dnn*d_factor)*(a1*a1 + a2*a2 + a3*a3); |
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19 | const double exp_arg = exp(arg); |
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20 | const double Zq = -cube(expm1(2.0*arg)) |
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21 | / ( ((exp_arg - 2.0*cos(dnn*a1))*exp_arg + 1.0) |
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22 | * ((exp_arg - 2.0*cos(dnn*a2))*exp_arg + 1.0) |
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23 | * ((exp_arg - 2.0*cos(dnn*a3))*exp_arg + 1.0)); |
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24 | |
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25 | return Zq; |
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26 | } |
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27 | |
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28 | // occupied volume fraction calculated from lattice symmetry and sphere radius |
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29 | static double |
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30 | sc_volume_fraction(double radius, double dnn) |
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31 | { |
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32 | return sphere_volume(radius/dnn); |
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33 | } |
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34 | |
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35 | static double |
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36 | form_volume(double radius) |
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37 | { |
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38 | return sphere_volume(radius); |
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39 | } |
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40 | |
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41 | |
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42 | static double |
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43 | Iq(double q, double dnn, |
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44 | double d_factor, double radius, |
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45 | double sld, double solvent_sld) |
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46 | { |
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47 | // translate a point in [-1,1] to a point in [0, 2 pi] |
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48 | const double phi_m = M_PI_4; |
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49 | const double phi_b = M_PI_4; |
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50 | // translate a point in [-1,1] to a point in [0, pi] |
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51 | const double theta_m = M_PI_4; |
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52 | const double theta_b = M_PI_4; |
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53 | |
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54 | |
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55 | double outer_sum = 0.0; |
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56 | for(int i=0; i<GAUSS_N; i++) { |
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57 | double inner_sum = 0.0; |
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58 | const double theta = GAUSS_Z[i]*theta_m + theta_b; |
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59 | double sin_theta, cos_theta; |
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60 | SINCOS(theta, sin_theta, cos_theta); |
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61 | const double qc = q*cos_theta; |
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62 | const double qab = q*sin_theta; |
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63 | for(int j=0;j<GAUSS_N;j++) { |
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64 | const double phi = GAUSS_Z[j]*phi_m + phi_b; |
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65 | double sin_phi, cos_phi; |
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66 | SINCOS(phi, sin_phi, cos_phi); |
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67 | const double qa = qab*cos_phi; |
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68 | const double qb = qab*sin_phi; |
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69 | const double form = sc_Zq(qa, qb, qc, dnn, d_factor); |
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70 | inner_sum += GAUSS_W[j] * form; |
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71 | } |
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72 | inner_sum *= phi_m; // sum(f(x)dx) = sum(f(x)) dx |
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73 | outer_sum += GAUSS_W[i] * inner_sum * sin_theta; |
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74 | } |
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75 | outer_sum *= theta_m; |
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76 | const double Zq = outer_sum/M_PI_2; |
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77 | const double Pq = sphere_form(q, radius, sld, solvent_sld); |
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78 | |
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79 | return sc_volume_fraction(radius, dnn) * Pq * Zq; |
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80 | } |
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81 | |
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82 | static double |
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83 | Iqabc(double qa, double qb, double qc, |
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84 | double dnn, double d_factor, double radius, |
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85 | double sld, double solvent_sld) |
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86 | { |
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87 | const double q = sqrt(qa*qa + qb*qb + qc*qc); |
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88 | const double Pq = sphere_form(q, radius, sld, solvent_sld); |
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89 | const double Zq = sc_Zq(qa, qb, qc, dnn, d_factor); |
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90 | return sc_volume_fraction(radius, dnn) * Pq * Zq; |
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91 | } |
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