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 sld_core, |
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20 | double sld_face, |
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21 | double sld_rim, |
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22 | double sld_solvent) |
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23 | { |
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24 | // core_shell_bicelle_elliptical, RKH Dec 2016, based on elliptical_cylinder and core_shell_bicelle |
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25 | // tested against limiting cases of cylinder, elliptical_cylinder, stacked_discs, and core_shell_bicelle |
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26 | const double halfheight = 0.5*length; |
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27 | const double r_major = r_minor * x_core; |
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28 | const double r2A = 0.5*(square(r_major) + square(r_minor)); |
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29 | const double r2B = 0.5*(square(r_major) - square(r_minor)); |
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30 | const double vol1 = M_PI*r_minor*r_major*(2.0*halfheight); |
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31 | const double vol2 = M_PI*(r_minor+thick_rim)*(r_major+thick_rim)*2.0*(halfheight+thick_face); |
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32 | const double vol3 = M_PI*r_minor*r_major*2.0*(halfheight+thick_face); |
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33 | const double dr1 = vol1*(sld_core-sld_face); |
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34 | const double dr2 = vol2*(sld_rim-sld_solvent); |
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35 | const double dr3 = vol3*(sld_face-sld_rim); |
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36 | |
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37 | //initialize integral |
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38 | double outer_sum = 0.0; |
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39 | for(int i=0;i<76;i++) { |
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40 | //setup inner integral over the ellipsoidal cross-section |
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41 | //const double va = 0.0; |
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42 | //const double vb = 1.0; |
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43 | //const double cos_theta = ( Gauss76Z[i]*(vb-va) + va + vb )/2.0; |
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44 | const double cos_theta = ( Gauss76Z[i] + 1.0 )/2.0; |
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45 | const double sin_theta = sqrt(1.0 - cos_theta*cos_theta); |
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46 | const double qab = q*sin_theta; |
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47 | const double qc = q*cos_theta; |
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48 | const double si1 = sas_sinx_x(halfheight*qc); |
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49 | const double si2 = sas_sinx_x((halfheight+thick_face)*qc); |
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50 | double inner_sum=0.0; |
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51 | for(int j=0;j<76;j++) { |
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52 | //76 gauss points for the inner integral (WAS 20 points,so this may make unecessarily slow, but playing safe) |
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53 | // inner integral limits |
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54 | //const double vaj=0.0; |
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55 | //const double vbj=M_PI; |
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56 | //const double phi = ( Gauss76Z[j]*(vbj-vaj) + vaj + vbj )/2.0; |
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57 | const double phi = ( Gauss76Z[j] +1.0)*M_PI_2; |
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58 | const double rr = sqrt(r2A - r2B*cos(phi)); |
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59 | const double be1 = sas_2J1x_x(rr*qab); |
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60 | const double be2 = sas_2J1x_x((rr+thick_rim)*qab); |
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61 | const double fq = dr1*si1*be1 + dr2*si2*be2 + dr3*si2*be1; |
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62 | |
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63 | inner_sum += Gauss76Wt[j] * fq * fq; |
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64 | } |
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65 | //now calculate outer integral |
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66 | outer_sum += Gauss76Wt[i] * inner_sum; |
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67 | } |
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68 | |
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69 | return outer_sum*2.5e-05; |
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70 | } |
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71 | |
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72 | static double |
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73 | Iqxy(double qa, double qb, double qc, |
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74 | double r_minor, |
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75 | double x_core, |
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76 | double thick_rim, |
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77 | double thick_face, |
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78 | double length, |
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79 | double sld_core, |
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80 | double sld_face, |
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81 | double sld_rim, |
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82 | double sld_solvent) |
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83 | { |
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84 | const double dr1 = sld_core-sld_face; |
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85 | const double dr2 = sld_rim-sld_solvent; |
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86 | const double dr3 = sld_face-sld_rim; |
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87 | const double r_major = r_minor*x_core; |
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88 | const double halfheight = 0.5*length; |
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89 | const double vol1 = M_PI*r_minor*r_major*length; |
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90 | const double vol2 = M_PI*(r_minor+thick_rim)*(r_major+thick_rim)*2.0*(halfheight+thick_face); |
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91 | const double vol3 = M_PI*r_minor*r_major*2.0*(halfheight+thick_face); |
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92 | |
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93 | // Compute effective radius in rotated coordinates |
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94 | const double qr_hat = sqrt(square(r_major*qa) + square(r_minor*qb)); |
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95 | const double qrshell_hat = sqrt(square((r_major+thick_rim)*qa) |
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96 | + square((r_minor+thick_rim)*qb)); |
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97 | const double be1 = sas_2J1x_x( qr_hat ); |
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98 | const double be2 = sas_2J1x_x( qrshell_hat ); |
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99 | const double si1 = sas_sinx_x( halfheight*qc ); |
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100 | const double si2 = sas_sinx_x( (halfheight + thick_face)*qc ); |
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101 | const double fq = vol1*dr1*si1*be1 + vol2*dr2*si2*be2 + vol3*dr3*si2*be1; |
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102 | return 1.0e-4 * fq*fq; |
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103 | } |
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