[fcb33e4] | 1 | // NOTE that "length" here is the full height of the core! |
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[44e8a93] | 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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[fcb33e4] | 8 | { |
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[44e8a93] | 9 | return M_PI*(r_minor+thick_rim)*(r_minor*x_core+thick_rim)*(length+2.0*thick_face); |
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[fcb33e4] | 10 | } |
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| 11 | |
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[44e8a93] | 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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[2a0b2b1] | 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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[fcb33e4] | 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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[dedcf34] | 25 | // tested against limiting cases of cylinder, elliptical_cylinder, stacked_discs, and core_shell_bicelle |
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[fcb33e4] | 26 | const double halfheight = 0.5*length; |
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[44e8a93] | 27 | const double r_major = r_minor * x_core; |
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[dedcf34] | 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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[2a0b2b1] | 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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[fcb33e4] | 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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[2a0b2b1] | 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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[fcb33e4] | 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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[2a0b2b1] | 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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[fcb33e4] | 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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[44e8a93] | 72 | static double |
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[fcb33e4] | 73 | Iqxy(double qx, double qy, |
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[44e8a93] | 74 | double r_minor, |
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[fcb33e4] | 75 | double x_core, |
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[44e8a93] | 76 | double thick_rim, |
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| 77 | double thick_face, |
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[fcb33e4] | 78 | double length, |
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[2a0b2b1] | 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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[fcb33e4] | 83 | double theta, |
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| 84 | double phi, |
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| 85 | double psi) |
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| 86 | { |
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[f4f85b3] | 87 | double q, xhat, yhat, zhat; |
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| 88 | ORIENT_ASYMMETRIC(qx, qy, theta, phi, psi, q, xhat, yhat, zhat); |
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[2a0b2b1] | 89 | const double qa = q*xhat; |
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| 90 | const double qb = q*yhat; |
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| 91 | const double qc = q*zhat; |
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| 92 | |
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| 93 | const double dr1 = sld_core-sld_face; |
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| 94 | const double dr2 = sld_rim-sld_solvent; |
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| 95 | const double dr3 = sld_face-sld_rim; |
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[44e8a93] | 96 | const double r_major = r_minor*x_core; |
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[fcb33e4] | 97 | const double halfheight = 0.5*length; |
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[44e8a93] | 98 | const double vol1 = M_PI*r_minor*r_major*length; |
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| 99 | const double vol2 = M_PI*(r_minor+thick_rim)*(r_major+thick_rim)*2.0*(halfheight+thick_face); |
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| 100 | const double vol3 = M_PI*r_minor*r_major*2.0*(halfheight+thick_face); |
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[fcb33e4] | 101 | |
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[44e8a93] | 102 | // Compute effective radius in rotated coordinates |
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[2a0b2b1] | 103 | const double qr_hat = sqrt(square(r_major*qa) + square(r_minor*qb)); |
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| 104 | const double qrshell_hat = sqrt(square((r_major+thick_rim)*qa) |
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| 105 | + square((r_minor+thick_rim)*qb)); |
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| 106 | const double be1 = sas_2J1x_x( qr_hat ); |
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| 107 | const double be2 = sas_2J1x_x( qrshell_hat ); |
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| 108 | const double si1 = sas_sinx_x( halfheight*qc ); |
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| 109 | const double si2 = sas_sinx_x( (halfheight + thick_face)*qc ); |
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| 110 | const double fq = vol1*dr1*si1*be1 + vol2*dr2*si2*be2 + vol3*dr3*si2*be1; |
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| 111 | return 1.0e-4 * fq*fq; |
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[fcb33e4] | 112 | } |
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