1 | // NOTE that "length" here is the full height of the core! |
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2 | static double |
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3 | form_volume(double r_minor, |
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4 | double x_core, |
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5 | double thick_rim, |
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6 | double thick_face, |
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7 | double length) |
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8 | { |
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9 | return M_PI*(r_minor+thick_rim)*(r_minor*x_core+thick_rim)*(length+2.0*thick_face); |
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10 | } |
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11 | |
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12 | static double |
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13 | Iq(double q, |
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14 | double r_minor, |
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15 | double x_core, |
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16 | double thick_rim, |
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17 | double thick_face, |
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18 | double length, |
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19 | double rhoc, |
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20 | double rhoh, |
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21 | double rhor, |
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22 | double rhosolv) |
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23 | { |
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24 | double si1,si2,be1,be2; |
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25 | // core_shell_bicelle_elliptical, RKH Dec 2016, based on elliptical_cylinder and core_shell_bicelle |
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26 | // tested against limiting cases of cylinder, elliptical_cylinder, stacked_discs, and core_shell_bicelle |
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27 | // const double uplim = M_PI_4; |
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28 | const double halfheight = 0.5*length; |
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29 | //const double va = 0.0; |
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30 | //const double vb = 1.0; |
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31 | // inner integral limits |
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32 | //const double vaj=0.0; |
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33 | //const double vbj=M_PI; |
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34 | |
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35 | const double r_major = r_minor * x_core; |
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36 | const double r2A = 0.5*(square(r_major) + square(r_minor)); |
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37 | const double r2B = 0.5*(square(r_major) - square(r_minor)); |
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38 | const double dr1 = (rhoc-rhoh) *M_PI*r_minor*r_major*(2.0*halfheight);; |
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39 | const double dr2 = (rhor-rhosolv)*M_PI*(r_minor+thick_rim)*(r_major+thick_rim)*2.0*(halfheight+thick_face); |
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40 | const double dr3 = (rhoh-rhor) *M_PI*r_minor*r_major*2.0*(halfheight+thick_face); |
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41 | //const double vol1 = M_PI*r_minor*r_major*(2.0*halfheight); |
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42 | //const double vol2 = M_PI*(r_minor+thick_rim)*(r_major+thick_rim)*2.0*(halfheight+thick_face); |
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43 | //const double vol3 = M_PI*r_minor*r_major*2.0*(halfheight+thick_face); |
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44 | |
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45 | //initialize integral |
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46 | double outer_sum = 0.0; |
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47 | for(int i=0;i<76;i++) { |
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48 | //setup inner integral over the ellipsoidal cross-section |
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49 | // since we generate these lots of times, why not store them somewhere? |
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50 | //const double cos_alpha = ( Gauss76Z[i]*(vb-va) + va + vb )/2.0; |
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51 | const double cos_alpha = ( Gauss76Z[i] + 1.0 )/2.0; |
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52 | const double sin_alpha = sqrt(1.0 - cos_alpha*cos_alpha); |
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53 | double inner_sum=0; |
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54 | double sinarg1 = q*halfheight*cos_alpha; |
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55 | double sinarg2 = q*(halfheight+thick_face)*cos_alpha; |
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56 | si1 = sas_sinx_x(sinarg1); |
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57 | si2 = sas_sinx_x(sinarg2); |
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58 | for(int j=0;j<76;j++) { |
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59 | //76 gauss points for the inner integral (WAS 20 points,so this may make unecessarily slow, but playing safe) |
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60 | //const double beta = ( Gauss76Z[j]*(vbj-vaj) + vaj + vbj )/2.0; |
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61 | const double beta = ( Gauss76Z[j] +1.0)*M_PI_2; |
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62 | const double rr = sqrt(r2A - r2B*cos(beta)); |
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63 | double besarg1 = q*rr*sin_alpha; |
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64 | double besarg2 = q*(rr+thick_rim)*sin_alpha; |
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65 | be1 = sas_2J1x_x(besarg1); |
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66 | be2 = sas_2J1x_x(besarg2); |
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67 | inner_sum += Gauss76Wt[j] *square(dr1*si1*be1 + |
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68 | dr2*si2*be2 + |
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69 | dr3*si2*be1); |
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70 | } |
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71 | //now calculate outer integral |
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72 | outer_sum += Gauss76Wt[i] * inner_sum; |
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73 | } |
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74 | |
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75 | return outer_sum*2.5e-05; |
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76 | } |
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77 | |
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78 | static double |
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79 | Iqxy(double qx, double qy, |
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80 | double r_minor, |
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81 | double x_core, |
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82 | double thick_rim, |
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83 | double thick_face, |
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84 | double length, |
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85 | double rhoc, |
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86 | double rhoh, |
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87 | double rhor, |
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88 | double rhosolv, |
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89 | double theta, |
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90 | double phi, |
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91 | double psi) |
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92 | { |
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93 | // THIS NEEDS TESTING |
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94 | double q, xhat, yhat, zhat; |
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95 | ORIENT_ASYMMETRIC(qx, qy, theta, phi, psi, q, xhat, yhat, zhat); |
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96 | const double dr1 = rhoc-rhoh; |
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97 | const double dr2 = rhor-rhosolv; |
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98 | const double dr3 = rhoh-rhor; |
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99 | const double r_major = r_minor*x_core; |
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100 | const double halfheight = 0.5*length; |
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101 | const double vol1 = M_PI*r_minor*r_major*length; |
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102 | const double vol2 = M_PI*(r_minor+thick_rim)*(r_major+thick_rim)*2.0*(halfheight+thick_face); |
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103 | const double vol3 = M_PI*r_minor*r_major*2.0*(halfheight+thick_face); |
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104 | |
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105 | // Compute effective radius in rotated coordinates |
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106 | const double r_hat = sqrt(square(r_major*xhat) + square(r_minor*yhat)); |
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107 | const double rshell_hat = sqrt(square((r_major+thick_rim)*xhat) |
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108 | + square((r_minor+thick_rim)*yhat)); |
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109 | const double be1 = sas_2J1x_x( q*r_hat ); |
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110 | const double be2 = sas_2J1x_x( q*rshell_hat ); |
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111 | const double si1 = sas_sinx_x( q*halfheight*zhat ); |
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112 | const double si2 = sas_sinx_x( q*(halfheight + thick_face)*zhat ); |
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113 | const double Aq = square( vol1*dr1*si1*be1 + vol2*dr2*si2*be2 + vol3*dr3*si2*be1); |
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114 | return 1.0e-4 * Aq; |
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115 | } |
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116 | |
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