[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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[ab2aea8] | 7 | double length_b = length_a * b2a_ratio; |
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| 8 | double length_c = length_a * c2a_ratio; |
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[a807206] | 9 | double a_core = length_a - 2.0*thickness; |
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[ab2aea8] | 10 | double b_core = length_b - 2.0*thickness; |
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| 11 | double c_core = length_c - 2.0*thickness; |
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[deb7ee0] | 12 | double vol_core = a_core * b_core * c_core; |
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[ab2aea8] | 13 | double vol_total = length_a * length_b * length_c; |
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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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[ab2aea8] | 28 | double length_b = length_a * b2a_ratio; |
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| 29 | double length_c = length_a * c2a_ratio; |
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[a807206] | 30 | double a_half = 0.5 * length_a; |
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[ab2aea8] | 31 | double b_half = 0.5 * length_b; |
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| 32 | double c_half = 0.5 * length_c; |
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| 33 | double vol_total = length_a * length_b * length_c; |
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| 34 | double vol_core = 8.0 * (a_half-thickness) * (b_half-thickness) * (c_half-thickness); |
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[deb7ee0] | 35 | |
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[ab2aea8] | 36 | //Integration limits to use in Gaussian quadrature |
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[deb7ee0] | 37 | double v1a = 0.0; |
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[3a48772] | 38 | double v1b = M_PI_2; //theta integration limits |
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[deb7ee0] | 39 | double v2a = 0.0; |
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[3a48772] | 40 | double v2b = M_PI_2; //phi integration limits |
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[deb7ee0] | 41 | |
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[ab2aea8] | 42 | double outer_sum = 0.0; |
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[deb7ee0] | 43 | |
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[ab2aea8] | 44 | for(int i=0; i<76; i++) { |
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[deb7ee0] | 45 | |
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[ab2aea8] | 46 | double theta = 0.5 * ( Gauss76Z[i]*(v1b-v1a) + v1a + v1b ); |
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[deb7ee0] | 47 | |
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[ab2aea8] | 48 | double termC1 = sinc(q * c_half * cos(theta)); |
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| 49 | double termC2 = sinc(q * (c_half-thickness)*cos(theta)); |
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[deb7ee0] | 50 | |
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[ab2aea8] | 51 | double inner_sum = 0.0; |
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[deb7ee0] | 52 | |
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[ab2aea8] | 53 | for(int j=0; j<76; j++) { |
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[deb7ee0] | 54 | |
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| 55 | double phi = 0.5 * ( Gauss76Z[j]*(v2b-v2a) + v2a + v2b ); |
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| 56 | |
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| 57 | // Amplitude AP from eqn. (13), rewritten to avoid round-off effects when arg=0 |
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| 58 | |
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[ab2aea8] | 59 | termA1 = sinc(q * a_half * sin(theta) * sin(phi)); |
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| 60 | termA2 = sinc(q * (a_half-thickness) * sin(theta) * sin(phi)); |
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[deb7ee0] | 61 | |
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[ab2aea8] | 62 | termB1 = sinc(q * b_half * sin(theta) * cos(phi)); |
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| 63 | termB2 = sinc(q * (b_half-thickness) * sin(theta) * cos(phi)); |
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[deb7ee0] | 64 | |
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[ab2aea8] | 65 | double AP1 = vol_total * termA1 * termB1 * termC1; |
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| 66 | double AP2 = vol_core * termA2 * termB2 * termC2; |
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[deb7ee0] | 67 | |
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[ab2aea8] | 68 | inner_sum += Gauss76Wt[j] * square(AP1-AP2); |
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[deb7ee0] | 69 | |
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[ab2aea8] | 70 | } |
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[deb7ee0] | 71 | |
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[ab2aea8] | 72 | inner_sum = 0.5 * (v2b-v2a) * inner_sum; |
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| 73 | outer_sum += Gauss76Wt[i] * inner_sum * sin(theta); |
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[deb7ee0] | 74 | |
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| 75 | } |
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| 76 | |
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[ab2aea8] | 77 | double answer = 0.5*(v1b-v1a)*outer_sum; |
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[deb7ee0] | 78 | |
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| 79 | // Normalize as in Eqn. (15) without the volume factor (as cancels with (V*DelRho)^2 normalization) |
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| 80 | // The factor 2 is due to the different theta integration limit (pi/2 instead of pi) |
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[3a48772] | 81 | answer /= M_PI_2; |
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[deb7ee0] | 82 | |
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| 83 | // Multiply by contrast^2. Factor corresponding to volume^2 cancels with previous normalization. |
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[ab2aea8] | 84 | answer *= square(sld-solvent_sld); |
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[deb7ee0] | 85 | |
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| 86 | // Convert from [1e-12 A-1] to [cm-1] |
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| 87 | answer *= 1.0e-4; |
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| 88 | |
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| 89 | return answer; |
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| 90 | |
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| 91 | } |
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