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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3 | double b2a_ratio, double c2a_ratio, double thickness); |
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4 | |
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5 | double form_volume(double length_a, double b2a_ratio, double c2a_ratio, double thickness) |
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6 | { |
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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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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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13 | double vol_total = length_a * b_side * c_side; |
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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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21 | double length_a, |
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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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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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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 = M_PI_2; //theta integration limits |
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37 | double v2a = 0.0; |
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38 | double v2b = M_PI_2; //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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73 | double AP1 = (length_a*b_side*c_side) * termA1 * termB1 * termC1; |
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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 /= M_PI_2; |
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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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