[a807206] | 1 | double form_volume(double length_a, double b2a_ratio, double c2a_ratio, double thickness); |
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| 2 | double Iq(double q, double sld, double solvent_sld, double length_a, |
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[deb7ee0] | 3 | double b2a_ratio, double c2a_ratio, double thickness); |
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| 4 | |
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[a807206] | 5 | double form_volume(double length_a, double b2a_ratio, double c2a_ratio, double thickness) |
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[deb7ee0] | 6 | { |
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[a807206] | 7 | double b_side = length_a * b2a_ratio; |
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| 8 | double c_side = length_a * c2a_ratio; |
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| 9 | double a_core = length_a - 2.0*thickness; |
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[deb7ee0] | 10 | double b_core = b_side - 2.0*thickness; |
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| 11 | double c_core = c_side - 2.0*thickness; |
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| 12 | double vol_core = a_core * b_core * c_core; |
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[a807206] | 13 | double vol_total = length_a * b_side * c_side; |
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[deb7ee0] | 14 | double vol_shell = vol_total - vol_core; |
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| 15 | return vol_shell; |
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| 16 | } |
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| 17 | |
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| 18 | double Iq(double q, |
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| 19 | double sld, |
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| 20 | double solvent_sld, |
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[a807206] | 21 | double length_a, |
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[deb7ee0] | 22 | double b2a_ratio, |
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| 23 | double c2a_ratio, |
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| 24 | double thickness) |
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| 25 | { |
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| 26 | double termA1, termA2, termB1, termB2, termC1, termC2; |
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| 27 | |
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[a807206] | 28 | double b_side = length_a * b2a_ratio; |
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| 29 | double c_side = length_a * c2a_ratio; |
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| 30 | double a_half = 0.5 * length_a; |
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[deb7ee0] | 31 | double b_half = 0.5 * b_side; |
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| 32 | double c_half = 0.5 * c_side; |
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| 33 | |
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| 34 | //Integration limits to use in Gaussian quadrature |
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| 35 | double v1a = 0.0; |
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| 36 | double v1b = 0.5 * M_PI; //theta integration limits |
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| 37 | double v2a = 0.0; |
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| 38 | double v2b = 0.5 * M_PI; //phi integration limits |
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| 39 | |
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| 40 | //Order of integration |
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| 41 | int nordi=76; |
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| 42 | int nordj=76; |
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| 43 | |
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| 44 | double sumi = 0.0; |
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| 45 | |
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| 46 | for(int i=0; i<nordi; i++) { |
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| 47 | |
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| 48 | double theta = 0.5 * ( Gauss76Z[i]*(v1b-v1a) + v1a + v1b ); |
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| 49 | |
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| 50 | double arg = q * c_half * cos(theta); |
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| 51 | if (fabs(arg) > 1.e-16) {termC1 = sin(arg)/arg;} else {termC1 = 1.0;} |
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| 52 | arg = q * (c_half-thickness)*cos(theta); |
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| 53 | if (fabs(arg) > 1.e-16) {termC2 = sin(arg)/arg;} else {termC2 = 1.0;} |
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| 54 | |
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| 55 | double sumj = 0.0; |
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| 56 | |
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| 57 | for(int j=0; j<nordj; j++) { |
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| 58 | |
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| 59 | double phi = 0.5 * ( Gauss76Z[j]*(v2b-v2a) + v2a + v2b ); |
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| 60 | |
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| 61 | // Amplitude AP from eqn. (13), rewritten to avoid round-off effects when arg=0 |
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| 62 | |
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| 63 | arg = q * a_half * sin(theta) * sin(phi); |
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| 64 | if (fabs(arg) > 1.e-16) {termA1 = sin(arg)/arg;} else {termA1 = 1.0;} |
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| 65 | arg = q * (a_half-thickness) * sin(theta) * sin(phi); |
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| 66 | if (fabs(arg) > 1.e-16) {termA2 = sin(arg)/arg;} else {termA2 = 1.0;} |
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| 67 | |
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| 68 | arg = q * b_half * sin(theta) * cos(phi); |
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| 69 | if (fabs(arg) > 1.e-16) {termB1 = sin(arg)/arg;} else {termB1 = 1.0;} |
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| 70 | arg = q * (b_half-thickness) * sin(theta) * cos(phi); |
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| 71 | if (fabs(arg) > 1.e-16) {termB2 = sin(arg)/arg;} else {termB2 = 1.0;} |
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| 72 | |
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[a807206] | 73 | double AP1 = (length_a*b_side*c_side) * termA1 * termB1 * termC1; |
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[deb7ee0] | 74 | double AP2 = 8.0 * (a_half-thickness) * (b_half-thickness) * (c_half-thickness) * termA2 * termB2 * termC2; |
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| 75 | double AP = AP1 - AP2; |
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| 76 | |
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| 77 | sumj += Gauss76Wt[j] * (AP*AP); |
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| 78 | |
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| 79 | } |
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| 80 | |
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| 81 | sumj = 0.5 * (v2b-v2a) * sumj; |
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| 82 | sumi += Gauss76Wt[i] * sumj * sin(theta); |
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| 83 | |
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| 84 | } |
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| 85 | |
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| 86 | double answer = 0.5*(v1b-v1a)*sumi; |
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| 87 | |
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| 88 | // Normalize as in Eqn. (15) without the volume factor (as cancels with (V*DelRho)^2 normalization) |
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| 89 | // The factor 2 is due to the different theta integration limit (pi/2 instead of pi) |
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| 90 | answer *= (2.0/M_PI); |
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| 91 | |
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| 92 | // Multiply by contrast^2. Factor corresponding to volume^2 cancels with previous normalization. |
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| 93 | answer *= (sld-solvent_sld)*(sld-solvent_sld); |
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| 94 | |
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| 95 | // Convert from [1e-12 A-1] to [cm-1] |
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| 96 | answer *= 1.0e-4; |
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| 97 | |
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| 98 | return answer; |
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| 99 | |
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| 100 | } |
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