1 | static double _hollow_cylinder_kernel(double q, double core_radius, double radius, |
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2 | double length, double dum); |
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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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7 | double form_volume(double radius, double core_radius, double length); |
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8 | |
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9 | double Iq(double q, double radius, double core_radius, double length, double sld, |
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10 | double solvent_sld); |
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11 | double Iqxy(double qx, double qy, double radius, double core_radius, double length, double sld, |
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12 | double solvent_sld, double theta, double phi); |
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13 | |
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14 | // From Igor library |
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15 | static double _hollow_cylinder_kernel(double q, double core_radius, double radius, |
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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 = sas_J1c(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 = sas_J1c(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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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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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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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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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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106 | |
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107 | double Iq(double q, double radius, double core_radius, double length, double sld, |
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108 | double solvent_sld) |
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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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114 | double norm,volume; //final calculation variables |
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115 | |
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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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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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133 | answer = hollow_cylinder_scaling(norm, delrho, volume); |
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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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139 | double solvent_sld, double theta, double phi) |
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140 | { |
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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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144 | } |
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