[fcb33e4] | 1 | double form_volume(double radius, double x_core, double thick_rim, double thick_face, double length); |
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| 2 | double Iq(double q, |
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| 3 | double radius, |
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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 | double core_sld, |
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| 9 | double face_sld, |
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| 10 | double rim_sld, |
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| 11 | double solvent_sld); |
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| 12 | |
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| 13 | |
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| 14 | double Iqxy(double qx, double qy, |
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| 15 | double radius, |
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| 16 | double x_core, |
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| 17 | double thick_rim, |
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| 18 | double thick_face, |
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| 19 | double length, |
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| 20 | double core_sld, |
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| 21 | double face_sld, |
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| 22 | double rim_sld, |
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| 23 | double solvent_sld, |
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| 24 | double theta, |
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| 25 | double phi, |
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| 26 | double psi); |
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| 27 | |
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| 28 | // NOTE that "length" here is the full height of the core! |
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| 29 | double form_volume(double radius, double x_core, double thick_rim, double thick_face, double length) |
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| 30 | { |
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| 31 | return M_PI*(radius+thick_rim)*(radius*x_core+thick_rim)*(length+2.0*thick_face); |
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| 32 | } |
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| 33 | |
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| 34 | double |
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| 35 | Iq(double qq, |
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| 36 | double rad, |
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| 37 | double x_core, |
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| 38 | double radthick, |
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| 39 | double facthick, |
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| 40 | double length, |
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| 41 | double rhoc, |
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| 42 | double rhoh, |
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| 43 | double rhor, |
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| 44 | double rhosolv) |
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| 45 | { |
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| 46 | double si1,si2,be1,be2; |
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| 47 | // core_shell_bicelle_elliptical, RKH Dec 2016, based on elliptical_cylinder and core_shell_bicelle |
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| 48 | // tested against limiting cases of cylinder, elliptical_cylinder and core_shell_bicelle |
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| 49 | // const double uplim = M_PI_4; |
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| 50 | const double halfheight = 0.5*length; |
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| 51 | //const double va = 0.0; |
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| 52 | //const double vb = 1.0; |
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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 | |
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| 57 | const double radius_major = rad * x_core; |
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| 58 | const double rA = 0.5*(square(radius_major) + square(rad)); |
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| 59 | const double rB = 0.5*(square(radius_major) - square(rad)); |
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| 60 | const double dr1 = (rhoc-rhoh) *M_PI*rad*radius_major*(2.0*halfheight);; |
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| 61 | const double dr2 = (rhor-rhosolv)*M_PI*(rad+radthick)*(radius_major+radthick)*2.0*(halfheight+facthick); |
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| 62 | const double dr3 = (rhoh-rhor) *M_PI*rad*radius_major*2.0*(halfheight+facthick); |
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| 63 | //const double vol1 = M_PI*rad*radius_major*(2.0*halfheight); |
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| 64 | //const double vol2 = M_PI*(rad+radthick)*(radius_major+radthick)*2.0*(halfheight+facthick); |
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| 65 | //const double vol3 = M_PI*rad*radius_major*2.0*(halfheight+facthick); |
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| 66 | |
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| 67 | //initialize integral |
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| 68 | double outer_sum = 0.0; |
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| 69 | for(int i=0;i<76;i++) { |
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| 70 | //setup inner integral over the ellipsoidal cross-section |
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| 71 | // since we generate these lots of times, why not store them somewhere? |
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| 72 | //const double cos_alpha = ( Gauss76Z[i]*(vb-va) + va + vb )/2.0; |
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| 73 | const double cos_alpha = ( Gauss76Z[i] + 1.0 )/2.0; |
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| 74 | const double sin_alpha = sqrt(1.0 - cos_alpha*cos_alpha); |
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| 75 | double inner_sum=0; |
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| 76 | double sinarg1 = qq*halfheight*cos_alpha; |
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| 77 | double sinarg2 = qq*(halfheight+facthick)*cos_alpha; |
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[1e7b0db0] | 78 | si1 = sas_sinx_x(sinarg1); |
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| 79 | si2 = sas_sinx_x(sinarg2); |
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[fcb33e4] | 80 | for(int j=0;j<76;j++) { |
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| 81 | //76 gauss points for the inner integral (WAS 20 points,so this may make unecessarily slow, but playing safe) |
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| 82 | //const double beta = ( Gauss76Z[j]*(vbj-vaj) + vaj + vbj )/2.0; |
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| 83 | const double beta = ( Gauss76Z[j] +1.0)*M_PI_2; |
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| 84 | const double rr = sqrt(rA - rB*cos(beta)); |
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| 85 | double besarg1 = qq*rr*sin_alpha; |
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| 86 | double besarg2 = qq*(rr+radthick)*sin_alpha; |
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[592343f] | 87 | be1 = sas_2J1x_x(besarg1); |
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| 88 | be2 = sas_2J1x_x(besarg2); |
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[fcb33e4] | 89 | inner_sum += Gauss76Wt[j] *square(dr1*si1*be1 + |
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| 90 | dr2*si2*be2 + |
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| 91 | dr3*si2*be1); |
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| 92 | } |
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| 93 | //now calculate outer integral |
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| 94 | outer_sum += Gauss76Wt[i] * inner_sum; |
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| 95 | } |
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| 96 | |
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| 97 | return outer_sum*2.5e-05; |
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| 98 | } |
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| 99 | |
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| 100 | double |
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| 101 | Iqxy(double qx, double qy, |
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| 102 | double rad, |
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| 103 | double x_core, |
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| 104 | double radthick, |
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| 105 | double facthick, |
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| 106 | double length, |
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| 107 | double rhoc, |
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| 108 | double rhoh, |
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| 109 | double rhor, |
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| 110 | double rhosolv, |
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| 111 | double theta, |
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| 112 | double phi, |
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| 113 | double psi) |
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| 114 | { |
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| 115 | // THIS NEEDS TESTING |
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| 116 | double qq, cos_val, cos_mu, cos_nu; |
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| 117 | ORIENT_ASYMMETRIC(qx, qy, theta, phi, psi, qq, cos_val, cos_mu, cos_nu); |
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| 118 | const double dr1 = rhoc-rhoh; |
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| 119 | const double dr2 = rhor-rhosolv; |
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| 120 | const double dr3 = rhoh-rhor; |
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| 121 | const double radius_major = rad*x_core; |
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| 122 | const double halfheight = 0.5*length; |
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| 123 | const double vol1 = M_PI*rad*radius_major*length; |
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| 124 | const double vol2 = M_PI*(rad+radthick)*(radius_major+radthick)*2.0*(halfheight+facthick); |
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| 125 | const double vol3 = M_PI*rad*radius_major*2.0*(halfheight+facthick); |
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| 126 | |
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| 127 | // Compute: r = sqrt((radius_major*cos_nu)^2 + (radius_minor*cos_mu)^2) |
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| 128 | // Given: radius_major = r_ratio * radius_minor |
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| 129 | // ASSUME the sin_alpha is included in the separate integration over orientation of rod angle |
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| 130 | const double r = rad*sqrt(square(x_core*cos_nu) + cos_mu*cos_mu); |
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[592343f] | 131 | const double be1 = sas_2J1x_x( qq*r ); |
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| 132 | const double be2 = sas_2J1x_x( qq*(r + radthick ) ); |
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[1e7b0db0] | 133 | const double si1 = sas_sinx_x( qq*halfheight*cos_val ); |
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| 134 | const double si2 = sas_sinx_x( qq*(halfheight + facthick)*cos_val ); |
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[fcb33e4] | 135 | const double Aq = square( vol1*dr1*si1*be1 + vol2*dr2*si2*be2 + vol3*dr3*si2*be1); |
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| 136 | //const double vol = form_volume(radius_minor, r_ratio, length); |
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| 137 | return 1.0e-4 * Aq; |
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| 138 | } |
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| 139 | |
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