[66ebdd6] | 1 | static double _hollow_cylinder_kernel(double q, double core_radius, double radius, |
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[84e6942] | 2 | double length, double dum); |
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[66ebdd6] | 3 | static double hollow_cylinder_analytical_2D_scaled(double q, double q_x, double q_y, double radius, double core_radius, double length, double sld, |
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| 4 | double solvent_sld, double theta, double phi); |
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| 5 | static double hollow_cylinder_scaling(double integrand, double delrho, double volume); |
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| 6 | |
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[84e6942] | 7 | double form_volume(double radius, double core_radius, double length); |
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[66ebdd6] | 8 | |
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[84e6942] | 9 | double Iq(double q, double radius, double core_radius, double length, double sld, |
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[6cf1cb3] | 10 | double solvent_sld); |
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[84e6942] | 11 | double Iqxy(double qx, double qy, double radius, double core_radius, double length, double sld, |
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[6cf1cb3] | 12 | double solvent_sld, double theta, double phi); |
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[84e6942] | 13 | |
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| 14 | // From Igor library |
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[66ebdd6] | 15 | static double _hollow_cylinder_kernel(double q, double core_radius, double radius, |
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[84e6942] | 16 | double length, double dum) |
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| 17 | { |
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| 18 | double gamma,arg1,arg2,lam1,lam2,psi,sinarg,t2,retval; //local variables |
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| 19 | |
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| 20 | gamma = core_radius/radius; |
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| 21 | arg1 = q*radius*sqrt(1.0-dum*dum); //1=shell (outer radius) |
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| 22 | arg2 = q*core_radius*sqrt(1.0-dum*dum); //2=core (inner radius) |
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| 23 | if (arg1 == 0.0){ |
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| 24 | lam1 = 1.0; |
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| 25 | }else{ |
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| 26 | lam1 = 2.0*J1(arg1)/arg1; |
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| 27 | } |
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| 28 | if (arg2 == 0.0){ |
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| 29 | lam2 = 1.0; |
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| 30 | }else{ |
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| 31 | lam2 = 2.0*J1(arg2)/arg2; |
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| 32 | } |
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| 33 | //Todo: Need to check psi behavior as gamma goes to 1. |
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| 34 | psi = (lam1 - gamma*gamma*lam2)/(1.0-gamma*gamma); //SRK 10/19/00 |
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| 35 | sinarg = q*length*dum/2.0; |
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| 36 | if (sinarg == 0.0){ |
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| 37 | t2 = 1.0; |
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| 38 | }else{ |
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| 39 | t2 = sin(sinarg)/sinarg; |
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| 40 | } |
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| 41 | |
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| 42 | retval = psi*psi*t2*t2; |
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| 43 | |
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| 44 | return(retval); |
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| 45 | } |
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[66ebdd6] | 46 | static double hollow_cylinder_analytical_2D_scaled(double q, double q_x, double q_y, double radius, double core_radius, double length, double sld, |
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| 47 | double solvent_sld, double theta, double phi) { |
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| 48 | double cyl_x, cyl_y; //, cyl_z |
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| 49 | //double q_z; |
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| 50 | double vol, cos_val, delrho; |
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| 51 | double answer; |
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| 52 | //convert angle degree to radian |
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| 53 | double pi = 4.0*atan(1.0); |
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| 54 | theta = theta * pi/180.0; |
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| 55 | phi = phi * pi/180.0; |
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| 56 | delrho = solvent_sld - sld; |
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| 57 | |
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| 58 | // Cylinder orientation |
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| 59 | cyl_x = cos(theta) * cos(phi); |
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| 60 | cyl_y = sin(theta); |
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| 61 | //cyl_z = -cos(theta) * sin(phi); |
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| 62 | |
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| 63 | // q vector |
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| 64 | //q_z = 0; |
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| 65 | |
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| 66 | // Compute the angle btw vector q and the |
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| 67 | // axis of the cylinder |
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| 68 | cos_val = cyl_x*q_x + cyl_y*q_y;// + cyl_z*q_z; |
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| 69 | |
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| 70 | // The following test should always pass |
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| 71 | if (fabs(cos_val)>1.0) { |
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[07e72e6] | 72 | //printf("core_shell_cylinder_analytical_2D: Unexpected error: cos(alpha)=%g\n", cos_val); |
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| 73 | return NAN; |
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[66ebdd6] | 74 | } |
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| 75 | |
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| 76 | answer = _hollow_cylinder_kernel(q, core_radius, radius, length, cos_val); |
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| 77 | |
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| 78 | vol = form_volume(radius, core_radius, length); |
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| 79 | answer = hollow_cylinder_scaling(answer, delrho, vol); |
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| 80 | |
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| 81 | return answer; |
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| 82 | } |
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| 83 | static double hollow_cylinder_scaling(double integrand, double delrho, double volume) |
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| 84 | { |
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| 85 | double answer; |
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| 86 | // Multiply by contrast^2 |
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| 87 | answer = integrand*delrho*delrho; |
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| 88 | |
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| 89 | //normalize by cylinder volume |
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| 90 | answer *= volume*volume; |
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| 91 | |
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| 92 | //convert to [cm-1] |
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| 93 | answer *= 1.0e-4; |
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| 94 | |
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| 95 | return answer; |
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| 96 | } |
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| 97 | |
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[84e6942] | 98 | |
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| 99 | double form_volume(double radius, double core_radius, double length) |
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| 100 | { |
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| 101 | double pi = 4.0*atan(1.0); |
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| 102 | double v_shell = pi*length*(radius*radius-core_radius*core_radius); |
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| 103 | return(v_shell); |
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| 104 | } |
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| 105 | |
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[66ebdd6] | 106 | |
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[84e6942] | 107 | double Iq(double q, double radius, double core_radius, double length, double sld, |
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[6cf1cb3] | 108 | double solvent_sld) |
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[84e6942] | 109 | { |
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| 110 | int i; |
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| 111 | int nord=76; //order of integration |
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| 112 | double lower,upper,zi, inter; //upper and lower integration limits |
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| 113 | double summ,answer,delrho; //running tally of integration |
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[66ebdd6] | 114 | double norm,volume; //final calculation variables |
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[84e6942] | 115 | |
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[0420af7] | 116 | if (core_radius >= radius || radius >= length) { |
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| 117 | return NAN; |
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| 118 | } |
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| 119 | |
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[84e6942] | 120 | delrho = solvent_sld - sld; |
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| 121 | lower = 0.0; |
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| 122 | upper = 1.0; //limits of numerical integral |
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| 123 | |
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| 124 | summ = 0.0; //initialize intergral |
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| 125 | for(i=0;i<nord;i++) { |
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| 126 | zi = ( Gauss76Z[i] * (upper-lower) + lower + upper )/2.0; |
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| 127 | inter = Gauss76Wt[i] * _hollow_cylinder_kernel(q, core_radius, radius, length, zi); |
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| 128 | summ += inter; |
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| 129 | } |
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| 130 | |
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| 131 | norm = summ*(upper-lower)/2.0; |
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| 132 | volume = form_volume(radius, core_radius, length); |
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[66ebdd6] | 133 | answer = hollow_cylinder_scaling(norm, delrho, volume); |
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[84e6942] | 134 | |
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| 135 | return(answer); |
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| 136 | } |
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| 137 | |
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| 138 | double Iqxy(double qx, double qy, double radius, double core_radius, double length, double sld, |
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[6cf1cb3] | 139 | double solvent_sld, double theta, double phi) |
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[84e6942] | 140 | { |
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[66ebdd6] | 141 | double q; |
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| 142 | q = sqrt(qx*qx+qy*qy); |
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| 143 | return hollow_cylinder_analytical_2D_scaled(q, qx/q, qy/q, radius, core_radius, length, sld, solvent_sld, theta, phi); |
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[0420af7] | 144 | } |
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