1 | double Iq(double q, double fp_case_num, |
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2 | double N[], double Phi[], double v[], double L[], double b[], |
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3 | double Kab, double Kac, double Kad, |
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4 | double Kbc, double Kbd, double Kcd |
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5 | ); |
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6 | |
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7 | double Iq(double q, double fp_case_num, |
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8 | double N[], // DEGREE OF POLYMERIZATION |
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9 | double Phi[], // VOL FRACTION |
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10 | double v[], // SPECIFIC VOLUME |
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11 | double L[], // SCATT. LENGTH |
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12 | double b[], // SEGMENT LENGTH |
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13 | double Kab, double Kac, double Kad, // CHI PARAM |
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14 | double Kbc, double Kbd, double Kcd |
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15 | ) |
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16 | { |
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17 | int icase = (int)(fp_case_num+0.5); |
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18 | |
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19 | double Nab,Nac,Nad,Nbc,Nbd,Ncd; |
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20 | double Phiab,Phiac,Phiad,Phibc,Phibd,Phicd; |
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21 | double vab,vac,vad,vbc,vbd,vcd; |
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22 | double m; |
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23 | double Xa,Xb,Xc,Xd; |
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24 | double Paa,S0aa,Pab,S0ab,Pac,S0ac,Pad,S0ad; |
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25 | double S0ba,Pbb,S0bb,Pbc,S0bc,Pbd,S0bd; |
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26 | double S0ca,S0cb,Pcc,S0cc,Pcd,S0cd; |
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27 | //double S0da,S0db,S0dc; |
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28 | double Pdd,S0dd; |
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29 | double Kaa,Kbb,Kcc; |
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30 | double Kba,Kca,Kcb; |
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31 | //double Kda,Kdb,Kdc,Kdd; |
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32 | double Zaa,Zab,Zac,Zba,Zbb,Zbc,Zca,Zcb,Zcc; |
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33 | double DenT,T11,T12,T13,T21,T22,T23,T31,T32,T33; |
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34 | double Y1,Y2,Y3,X11,X12,X13,X21,X22,X23,X31,X32,X33; |
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35 | double ZZ,DenQ1,DenQ2,DenQ3,DenQ,Q11,Q12,Q13,Q21,Q22,Q23,Q31,Q32,Q33; |
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36 | double N11,N12,N13,N21,N22,N23,N31,N32,N33; |
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37 | double M11,M12,M13,M21,M22,M23,M31,M32,M33; |
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38 | double S11,S12,S22,S23,S13,S33; |
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39 | //double S21,S31,S32,S44; |
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40 | //double S14,S24,S34,S41,S42,S43; |
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41 | double Lad,Lbd,Lcd,Nav,Intg; |
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42 | |
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43 | // Set values for non existent parameters (eg. no A or B in case 0 and 1 etc) |
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44 | //icase was shifted to N-1 from the original code |
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45 | if (icase <= 1){ |
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46 | Phi[0] = Phi[1] = 0.0000001; |
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47 | N[0] = N[1] = 1000.0; |
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48 | L[0] = L[1] = 1.e-12; |
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49 | v[0] = v[1] = 100.0; |
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50 | b[0] = b[1] = 5.0; |
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51 | Kab = Kac = Kad = Kbc = Kbd = -0.0004; |
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52 | } |
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53 | else if ((icase > 1) && (icase <= 4)){ |
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54 | Phi[0] = 0.0000001; |
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55 | N[0] = 1000.0; |
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56 | L[0] = 1.e-12; |
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57 | v[0] = 100.0; |
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58 | b[0] = 5.0; |
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59 | Kab = Kac = Kad = -0.0004; |
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60 | } |
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61 | |
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62 | // Set volume fraction of component D based on constraint that sum of vol frac =1 |
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63 | Phi[3]=1.0-Phi[0]-Phi[1]-Phi[2]; |
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64 | |
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65 | //set up values for cross terms in case of block copolymers (1,3,4,6,7,8,9) |
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66 | Nab=sqrt(N[0]*N[1]); |
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67 | Nac=sqrt(N[0]*N[2]); |
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68 | Nad=sqrt(N[0]*N[3]); |
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69 | Nbc=sqrt(N[1]*N[2]); |
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70 | Nbd=sqrt(N[1]*N[3]); |
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71 | Ncd=sqrt(N[2]*N[3]); |
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72 | |
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73 | vab=sqrt(v[0]*v[1]); |
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74 | vac=sqrt(v[0]*v[2]); |
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75 | vad=sqrt(v[0]*v[3]); |
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76 | vbc=sqrt(v[1]*v[2]); |
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77 | vbd=sqrt(v[1]*v[3]); |
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78 | vcd=sqrt(v[2]*v[3]); |
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79 | |
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80 | Phiab=sqrt(Phi[0]*Phi[1]); |
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81 | Phiac=sqrt(Phi[0]*Phi[2]); |
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82 | Phiad=sqrt(Phi[0]*Phi[3]); |
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83 | Phibc=sqrt(Phi[1]*Phi[2]); |
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84 | Phibd=sqrt(Phi[1]*Phi[3]); |
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85 | Phicd=sqrt(Phi[2]*Phi[3]); |
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86 | |
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87 | // Calculate Q^2 * Rg^2 for each homopolymer assuming random walk |
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88 | Xa=q*q*b[0]*b[0]*N[0]/6.0; |
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89 | Xb=q*q*b[1]*b[1]*N[1]/6.0; |
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90 | Xc=q*q*b[2]*b[2]*N[2]/6.0; |
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91 | Xd=q*q*b[3]*b[3]*N[3]/6.0; |
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92 | |
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93 | //calculate all partial structure factors Pij and normalize n^2 |
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94 | Paa=2.0*(exp(-Xa)-1.0+Xa)/(Xa*Xa); // free A chain form factor |
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95 | S0aa=N[0]*Phi[0]*v[0]*Paa; // Phi * Vp * P(Q)= I(Q0)/delRho^2 |
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96 | Pab=((1.0-exp(-Xa))/Xa)*((1.0-exp(-Xb))/Xb); //AB diblock (anchored Paa * anchored Pbb) partial form factor |
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97 | S0ab=(Phiab*vab*Nab)*Pab; |
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98 | Pac=((1.0-exp(-Xa))/Xa)*exp(-Xb)*((1.0-exp(-Xc))/Xc); //ABC triblock AC partial form factor |
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99 | S0ac=(Phiac*vac*Nac)*Pac; |
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100 | Pad=((1.0-exp(-Xa))/Xa)*exp(-Xb-Xc)*((1.0-exp(-Xd))/Xd); //ABCD four block |
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101 | S0ad=(Phiad*vad*Nad)*Pad; |
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102 | |
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103 | S0ba=S0ab; |
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104 | Pbb=2.0*(exp(-Xb)-1.0+Xb)/(Xb*Xb); // free B chain |
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105 | S0bb=N[1]*Phi[1]*v[1]*Pbb; |
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106 | Pbc=((1.0-exp(-Xb))/Xb)*((1.0-exp(-Xc))/Xc); // BC diblock |
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107 | S0bc=(Phibc*vbc*Nbc)*Pbc; |
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108 | Pbd=((1.0-exp(-Xb))/Xb)*exp(-Xc)*((1.0-exp(-Xd))/Xd); // BCD triblock |
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109 | S0bd=(Phibd*vbd*Nbd)*Pbd; |
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110 | |
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111 | S0ca=S0ac; |
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112 | S0cb=S0bc; |
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113 | Pcc=2.0*(exp(-Xc)-1.0+Xc)/(Xc*Xc); // Free C chain |
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114 | S0cc=N[2]*Phi[2]*v[2]*Pcc; |
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115 | Pcd=((1.0-exp(-Xc))/Xc)*((1.0-exp(-Xd))/Xd); // CD diblock |
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116 | S0cd=(Phicd*vcd*Ncd)*Pcd; |
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117 | |
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118 | //S0da=S0ad; |
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119 | //S0db=S0bd; |
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120 | //S0dc=S0cd; |
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121 | Pdd=2.0*(exp(-Xd)-1.0+Xd)/(Xd*Xd); // free D chain |
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122 | S0dd=N[3]*Phi[3]*v[3]*Pdd; |
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123 | |
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124 | // Reset all unused partial structure factors to 0 (depends on case) |
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125 | //icase was shifted to N-1 from the original code |
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126 | switch(icase){ |
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127 | case 0: |
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128 | S0aa=0.000001; |
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129 | S0ab=0.000002; |
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130 | S0ac=0.000003; |
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131 | S0ad=0.000004; |
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132 | S0bb=0.000005; |
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133 | S0bc=0.000006; |
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134 | S0bd=0.000007; |
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135 | S0cd=0.000008; |
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136 | break; |
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137 | case 1: |
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138 | S0aa=0.000001; |
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139 | S0ab=0.000002; |
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140 | S0ac=0.000003; |
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141 | S0ad=0.000004; |
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142 | S0bb=0.000005; |
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143 | S0bc=0.000006; |
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144 | S0bd=0.000007; |
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145 | break; |
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146 | case 2: |
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147 | S0aa=0.000001; |
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148 | S0ab=0.000002; |
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149 | S0ac=0.000003; |
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150 | S0ad=0.000004; |
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151 | S0bc=0.000005; |
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152 | S0bd=0.000006; |
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153 | S0cd=0.000007; |
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154 | break; |
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155 | case 3: |
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156 | S0aa=0.000001; |
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157 | S0ab=0.000002; |
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158 | S0ac=0.000003; |
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159 | S0ad=0.000004; |
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160 | S0bc=0.000005; |
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161 | S0bd=0.000006; |
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162 | break; |
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163 | case 4: |
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164 | S0aa=0.000001; |
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165 | S0ab=0.000002; |
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166 | S0ac=0.000003; |
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167 | S0ad=0.000004; |
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168 | break; |
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169 | case 5: |
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170 | S0ab=0.000001; |
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171 | S0ac=0.000002; |
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172 | S0ad=0.000003; |
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173 | S0bc=0.000004; |
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174 | S0bd=0.000005; |
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175 | S0cd=0.000006; |
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176 | break; |
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177 | case 6: |
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178 | S0ab=0.000001; |
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179 | S0ac=0.000002; |
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180 | S0ad=0.000003; |
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181 | S0bc=0.000004; |
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182 | S0bd=0.000005; |
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183 | break; |
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184 | case 7: |
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185 | S0ab=0.000001; |
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186 | S0ac=0.000002; |
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187 | S0ad=0.000003; |
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188 | break; |
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189 | case 8: |
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190 | S0ac=0.000001; |
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191 | S0ad=0.000002; |
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192 | S0bc=0.000003; |
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193 | S0bd=0.000004; |
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194 | break; |
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195 | default : //case 9: |
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196 | break; |
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197 | } |
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198 | S0ba=S0ab; |
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199 | S0ca=S0ac; |
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200 | S0cb=S0bc; |
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201 | //S0da=S0ad; |
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202 | //S0db=S0bd; |
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203 | //S0dc=S0cd; |
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204 | |
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205 | // self chi parameter is 0 ... of course |
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206 | Kaa=0.0; |
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207 | Kbb=0.0; |
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208 | Kcc=0.0; |
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209 | //Kdd=0.0; |
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210 | |
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211 | Kba=Kab; |
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212 | Kca=Kac; |
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213 | Kcb=Kbc; |
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214 | //Kda=Kad; |
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215 | //Kdb=Kbd; |
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216 | //Kdc=Kcd; |
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217 | |
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218 | Zaa=Kaa-Kad-Kad; |
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219 | Zab=Kab-Kad-Kbd; |
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220 | Zac=Kac-Kad-Kcd; |
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221 | Zba=Kba-Kbd-Kad; |
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222 | Zbb=Kbb-Kbd-Kbd; |
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223 | Zbc=Kbc-Kbd-Kcd; |
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224 | Zca=Kca-Kcd-Kad; |
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225 | Zcb=Kcb-Kcd-Kbd; |
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226 | Zcc=Kcc-Kcd-Kcd; |
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227 | |
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228 | DenT=(-(S0ac*S0bb*S0ca) + S0ab*S0bc*S0ca + S0ac*S0ba*S0cb - S0aa*S0bc*S0cb - S0ab*S0ba*S0cc + S0aa*S0bb*S0cc); |
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229 | |
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230 | T11= (-(S0bc*S0cb) + S0bb*S0cc)/DenT; |
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231 | T12= (S0ac*S0cb - S0ab*S0cc)/DenT; |
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232 | T13= (-(S0ac*S0bb) + S0ab*S0bc)/DenT; |
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233 | T21= (S0bc*S0ca - S0ba*S0cc)/DenT; |
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234 | T22= (-(S0ac*S0ca) + S0aa*S0cc)/DenT; |
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235 | T23= (S0ac*S0ba - S0aa*S0bc)/DenT; |
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236 | T31= (-(S0bb*S0ca) + S0ba*S0cb)/DenT; |
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237 | T32= (S0ab*S0ca - S0aa*S0cb)/DenT; |
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238 | T33= (-(S0ab*S0ba) + S0aa*S0bb)/DenT; |
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239 | |
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240 | Y1=T11*S0ad+T12*S0bd+T13*S0cd+1.0; |
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241 | Y2=T21*S0ad+T22*S0bd+T23*S0cd+1.0; |
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242 | Y3=T31*S0ad+T32*S0bd+T33*S0cd+1.0; |
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243 | |
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244 | X11=Y1*Y1; |
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245 | X12=Y1*Y2; |
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246 | X13=Y1*Y3; |
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247 | X21=Y2*Y1; |
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248 | X22=Y2*Y2; |
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249 | X23=Y2*Y3; |
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250 | X31=Y3*Y1; |
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251 | X32=Y3*Y2; |
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252 | X33=Y3*Y3; |
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253 | |
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254 | ZZ=S0ad*(T11*S0ad+T12*S0bd+T13*S0cd)+S0bd*(T21*S0ad+T22*S0bd+T23*S0cd)+S0cd*(T31*S0ad+T32*S0bd+T33*S0cd); |
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255 | |
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256 | // D is considered the matrix or background component so enters here |
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257 | m=1.0/(S0dd-ZZ); |
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258 | |
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259 | N11=m*X11+Zaa; |
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260 | N12=m*X12+Zab; |
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261 | N13=m*X13+Zac; |
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262 | N21=m*X21+Zba; |
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263 | N22=m*X22+Zbb; |
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264 | N23=m*X23+Zbc; |
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265 | N31=m*X31+Zca; |
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266 | N32=m*X32+Zcb; |
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267 | N33=m*X33+Zcc; |
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268 | |
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269 | M11= N11*S0aa + N12*S0ab + N13*S0ac; |
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270 | M12= N11*S0ab + N12*S0bb + N13*S0bc; |
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271 | M13= N11*S0ac + N12*S0bc + N13*S0cc; |
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272 | M21= N21*S0aa + N22*S0ab + N23*S0ac; |
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273 | M22= N21*S0ab + N22*S0bb + N23*S0bc; |
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274 | M23= N21*S0ac + N22*S0bc + N23*S0cc; |
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275 | M31= N31*S0aa + N32*S0ab + N33*S0ac; |
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276 | M32= N31*S0ab + N32*S0bb + N33*S0bc; |
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277 | M33= N31*S0ac + N32*S0bc + N33*S0cc; |
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278 | |
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279 | DenQ1=1.0+M11-M12*M21+M22+M11*M22-M13*M31-M13*M22*M31; |
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280 | DenQ2= M12*M23*M31+M13*M21*M32-M23*M32-M11*M23*M32+M33+M11*M33; |
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281 | DenQ3= -M12*M21*M33+M22*M33+M11*M22*M33; |
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282 | DenQ=DenQ1+DenQ2+DenQ3; |
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283 | |
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284 | Q11= (1.0 + M22-M23*M32 + M33 + M22*M33)/DenQ; |
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285 | Q12= (-M12 + M13*M32 - M12*M33)/DenQ; |
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286 | Q13= (-M13 - M13*M22 + M12*M23)/DenQ; |
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287 | Q21= (-M21 + M23*M31 - M21*M33)/DenQ; |
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288 | Q22= (1.0 + M11 - M13*M31 + M33 + M11*M33)/DenQ; |
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289 | Q23= (M13*M21 - M23 - M11*M23)/DenQ; |
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290 | Q31= (-M31 - M22*M31 + M21*M32)/DenQ; |
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291 | Q32= (M12*M31 - M32 - M11*M32)/DenQ; |
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292 | Q33= (1.0 + M11 - M12*M21 + M22 + M11*M22)/DenQ; |
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293 | |
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294 | S11= Q11*S0aa + Q21*S0ab + Q31*S0ac; |
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295 | S12= Q12*S0aa + Q22*S0ab + Q32*S0ac; |
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296 | S13= Q13*S0aa + Q23*S0ab + Q33*S0ac; |
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297 | S22= Q12*S0ba + Q22*S0bb + Q32*S0bc; |
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298 | S23= Q13*S0ba + Q23*S0bb + Q33*S0bc; |
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299 | S33= Q13*S0ca + Q23*S0cb + Q33*S0cc; |
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300 | //S21= Q11*S0ba + Q21*S0bb + Q31*S0bc; |
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301 | //S31= Q11*S0ca + Q21*S0cb + Q31*S0cc; |
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302 | //S32= Q12*S0ca + Q22*S0cb + Q32*S0cc; |
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303 | //S44=S11+S22+S33+2.0*S12+2.0*S13+2.0*S23; |
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304 | //S14=-S11-S12-S13; |
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305 | //S24=-S21-S22-S23; |
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306 | //S34=-S31-S32-S33; |
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307 | //S41=S14; |
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308 | //S42=S24; |
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309 | //S43=S34; |
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310 | |
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311 | //calculate contrast where L[i] is the scattering length of i and D is the matrix |
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312 | //Note that should multiply by Nav to get units of SLD which will become |
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313 | // Nav*2 in the next line (SLD^2) but then normalization in that line would |
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314 | //need to divide by Nav leaving only Nav or sqrt(Nav) before squaring. |
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315 | Nav=6.022045e+23; |
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316 | Lad=(L[0]/v[0]-L[3]/v[3])*sqrt(Nav); |
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317 | Lbd=(L[1]/v[1]-L[3]/v[3])*sqrt(Nav); |
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318 | Lcd=(L[2]/v[2]-L[3]/v[3])*sqrt(Nav); |
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319 | |
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320 | Intg=Lad*Lad*S11+Lbd*Lbd*S22+Lcd*Lcd*S33+2.0*Lad*Lbd*S12+2.0*Lbd*Lcd*S23+2.0*Lad*Lcd*S13; |
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321 | |
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322 | //rescale for units of Lij^2 (fm^2 to cm^2) |
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323 | Intg *= 1.0e-26; |
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324 | |
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325 | return Intg; |
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326 | |
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327 | |
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328 | /* Attempts at a new implementation --- supressed for now |
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329 | #if 1 // Sasview defaults |
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330 | if (icase <= 1) { |
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331 | N[0]=N[1]=1000.0; |
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332 | Phi[0]=Phi[1]=0.0000001; |
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333 | Kab=Kac=Kad=Kbc=Kbd=-0.0004; |
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334 | L[0]=L[1]=1.0e-12; |
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335 | v[0]=v[1]=100.0; |
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336 | b[0]=b[1]=5.0; |
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337 | } else if (icase <= 4) { |
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338 | Phi[0]=0.0000001; |
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339 | Kab=Kac=Kad=-0.0004; |
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340 | L[0]=1.0e-12; |
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341 | v[0]=100.0; |
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342 | b[0]=5.0; |
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343 | } |
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344 | #else |
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345 | if (icase <= 1) { |
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346 | N[0]=N[1]=0.0; |
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347 | Phi[0]=Phi[1]=0.0; |
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348 | Kab=Kac=Kad=Kbc=Kbd=0.0; |
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349 | L[0]=L[1]=L[3]; |
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350 | v[0]=v[1]=v[3]; |
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351 | b[0]=b[1]=0.0; |
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352 | } else if (icase <= 4) { |
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353 | N[0] = 0.0; |
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354 | Phi[0]=0.0; |
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355 | Kab=Kac=Kad=0.0; |
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356 | L[0]=L[3]; |
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357 | v[0]=v[3]; |
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358 | b[0]=0.0; |
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359 | } |
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360 | #endif |
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361 | |
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362 | const double Xa = q*q*b[0]*b[0]*N[0]/6.0; |
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363 | const double Xb = q*q*b[1]*b[1]*N[1]/6.0; |
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364 | const double Xc = q*q*b[2]*b[2]*N[2]/6.0; |
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365 | const double Xd = q*q*b[3]*b[3]*N[3]/6.0; |
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366 | |
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367 | // limit as Xa goes to 0 is 1 |
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368 | const double Pa = Xa==0 ? 1.0 : -expm1(-Xa)/Xa; |
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369 | const double Pb = Xb==0 ? 1.0 : -expm1(-Xb)/Xb; |
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370 | const double Pc = Xc==0 ? 1.0 : -expm1(-Xc)/Xc; |
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371 | const double Pd = Xd==0 ? 1.0 : -expm1(-Xd)/Xd; |
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372 | |
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373 | // limit as Xa goes to 0 is 1 |
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374 | const double Paa = Xa==0 ? 1.0 : 2.0*(1.0-Pa)/Xa; |
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375 | const double Pbb = Xb==0 ? 1.0 : 2.0*(1.0-Pb)/Xb; |
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376 | const double Pcc = Xc==0 ? 1.0 : 2.0*(1.0-Pc)/Xc; |
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377 | const double Pdd = Xd==0 ? 1.0 : 2.0*(1.0-Pd)/Xd; |
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378 | |
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379 | |
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380 | // Note: S0ij only defined for copolymers; otherwise set to zero |
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381 | // 0: C/D binary mixture |
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382 | // 1: C-D diblock copolymer |
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383 | // 2: B/C/D ternery mixture |
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384 | // 3: B/C-D binary mixture,1 homopolymer, 1 diblock copolymer |
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385 | // 4: B-C-D triblock copolymer |
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386 | // 5: A/B/C/D quaternary mixture |
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387 | // 6: A/B/C-D ternery mixture, 2 homopolymer, 1 diblock copolymer |
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388 | // 7: A/B-C-D binary mixture, 1 homopolymer, 1 triblock copolymer |
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389 | // 8: A-B/C-D binary mixture, 2 diblock copolymer |
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390 | // 9: A-B-C-D tetra-block copolymer |
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391 | #if 0 |
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392 | const double S0aa = icase<5 |
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393 | ? 1.0 : N[0]*Phi[0]*v[0]*Paa; |
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394 | const double S0bb = icase<2 |
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395 | ? 1.0 : N[1]*Phi[1]*v[1]*Pbb; |
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396 | const double S0cc = N[2]*Phi[2]*v[2]*Pcc; |
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397 | const double S0dd = N[3]*Phi[3]*v[3]*Pdd; |
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398 | const double S0ab = icase<8 |
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399 | ? 0.0 : sqrt(N[0]*v[0]*Phi[0]*N[1]*v[1]*Phi[1])*Pa*Pb; |
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400 | const double S0ac = icase<9 |
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401 | ? 0.0 : sqrt(N[0]*v[0]*Phi[0]*N[2]*v[2]*Phi[2])*Pa*Pc*exp(-Xb); |
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402 | const double S0ad = icase<9 |
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403 | ? 0.0 : sqrt(N[0]*v[0]*Phi[0]*N[3]*v[3]*Phi[3])*Pa*Pd*exp(-Xb-Xc); |
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404 | const double S0bc = (icase!=4 && icase!=7 && icase!= 9) |
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405 | ? 0.0 : sqrt(N[1]*v[1]*Phi[1]*N[2]*v[2]*Phi[2])*Pb*Pc; |
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406 | const double S0bd = (icase!=4 && icase!=7 && icase!= 9) |
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407 | ? 0.0 : sqrt(N[1]*v[1]*Phi[1]*N[3]*v[3]*Phi[3])*Pb*Pd*exp(-Xc); |
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408 | const double S0cd = (icase==0 || icase==2 || icase==5) |
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409 | ? 0.0 : sqrt(N[2]*v[2]*Phi[2]*N[3]*v[3]*Phi[3])*Pc*Pd; |
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410 | #else // sasview equivalent |
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411 | //printf("Xc=%g, S0cc=%g*%g*%g*%g\n",Xc,N[2],Phi[2],v[2],Pcc); |
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412 | double S0aa = N[0]*Phi[0]*v[0]*Paa; |
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413 | double S0bb = N[1]*Phi[1]*v[1]*Pbb; |
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414 | double S0cc = N[2]*Phi[2]*v[2]*Pcc; |
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415 | double S0dd = N[3]*Phi[3]*v[3]*Pdd; |
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416 | double S0ab = sqrt(N[0]*v[0]*Phi[0]*N[1]*v[1]*Phi[1])*Pa*Pb; |
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417 | double S0ac = sqrt(N[0]*v[0]*Phi[0]*N[2]*v[2]*Phi[2])*Pa*Pc*exp(-Xb); |
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418 | double S0ad = sqrt(N[0]*v[0]*Phi[0]*N[3]*v[3]*Phi[3])*Pa*Pd*exp(-Xb-Xc); |
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419 | double S0bc = sqrt(N[1]*v[1]*Phi[1]*N[2]*v[2]*Phi[2])*Pb*Pc; |
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420 | double S0bd = sqrt(N[1]*v[1]*Phi[1]*N[3]*v[3]*Phi[3])*Pb*Pd*exp(-Xc); |
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421 | double S0cd = sqrt(N[2]*v[2]*Phi[2]*N[3]*v[3]*Phi[3])*Pc*Pd; |
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422 | switch(icase){ |
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423 | case 0: |
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424 | S0aa=0.000001; |
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425 | S0ab=0.000002; |
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426 | S0ac=0.000003; |
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427 | S0ad=0.000004; |
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428 | S0bb=0.000005; |
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429 | S0bc=0.000006; |
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430 | S0bd=0.000007; |
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431 | S0cd=0.000008; |
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432 | break; |
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433 | case 1: |
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434 | S0aa=0.000001; |
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435 | S0ab=0.000002; |
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436 | S0ac=0.000003; |
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437 | S0ad=0.000004; |
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438 | S0bb=0.000005; |
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439 | S0bc=0.000006; |
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440 | S0bd=0.000007; |
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441 | break; |
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442 | case 2: |
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443 | S0aa=0.000001; |
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444 | S0ab=0.000002; |
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445 | S0ac=0.000003; |
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446 | S0ad=0.000004; |
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447 | S0bc=0.000005; |
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448 | S0bd=0.000006; |
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449 | S0cd=0.000007; |
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450 | break; |
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451 | case 3: |
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452 | S0aa=0.000001; |
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453 | S0ab=0.000002; |
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454 | S0ac=0.000003; |
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455 | S0ad=0.000004; |
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456 | S0bc=0.000005; |
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457 | S0bd=0.000006; |
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458 | break; |
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459 | case 4: |
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460 | S0aa=0.000001; |
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461 | S0ab=0.000002; |
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462 | S0ac=0.000003; |
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463 | S0ad=0.000004; |
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464 | break; |
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465 | case 5: |
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466 | S0ab=0.000001; |
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467 | S0ac=0.000002; |
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468 | S0ad=0.000003; |
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469 | S0bc=0.000004; |
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470 | S0bd=0.000005; |
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471 | S0cd=0.000006; |
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472 | break; |
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473 | case 6: |
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474 | S0ab=0.000001; |
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475 | S0ac=0.000002; |
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476 | S0ad=0.000003; |
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477 | S0bc=0.000004; |
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478 | S0bd=0.000005; |
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479 | break; |
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480 | case 7: |
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481 | S0ab=0.000001; |
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482 | S0ac=0.000002; |
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483 | S0ad=0.000003; |
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484 | break; |
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485 | case 8: |
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486 | S0ac=0.000001; |
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487 | S0ad=0.000002; |
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488 | S0bc=0.000003; |
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489 | S0bd=0.000004; |
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490 | break; |
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491 | default : //case 9: |
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492 | break; |
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493 | } |
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494 | #endif |
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495 | |
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496 | // eq 12a: \kappa_{ij}^F = \chi_{ij}^F - \chi_{i0}^F - \chi_{j0}^F |
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497 | const double Kaa = 0.0; |
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498 | const double Kbb = 0.0; |
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499 | const double Kcc = 0.0; |
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500 | //const double Kdd = 0.0; |
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501 | const double Zaa = Kaa - Kad - Kad; |
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502 | const double Zab = Kab - Kad - Kbd; |
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503 | const double Zac = Kac - Kad - Kcd; |
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504 | const double Zbb = Kbb - Kbd - Kbd; |
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505 | const double Zbc = Kbc - Kbd - Kcd; |
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506 | const double Zcc = Kcc - Kcd - Kcd; |
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507 | //printf("Za: %10.5g %10.5g %10.5g\n", Zaa, Zab, Zac); |
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508 | //printf("Zb: %10.5g %10.5g %10.5g\n", Zab, Zbb, Zbc); |
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509 | //printf("Zc: %10.5g %10.5g %10.5g\n", Zac, Zbc, Zcc); |
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510 | |
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511 | // T = inv(S0) |
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512 | const double DenT = (- S0ac*S0bb*S0ac + S0ab*S0bc*S0ac + S0ac*S0ab*S0bc |
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513 | - S0aa*S0bc*S0bc - S0ab*S0ab*S0cc + S0aa*S0bb*S0cc); |
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514 | const double T11 = (-S0bc*S0bc + S0bb*S0cc)/DenT; |
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515 | const double T12 = ( S0ac*S0bc - S0ab*S0cc)/DenT; |
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516 | const double T13 = (-S0ac*S0bb + S0ab*S0bc)/DenT; |
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517 | const double T22 = (-S0ac*S0ac + S0aa*S0cc)/DenT; |
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518 | const double T23 = ( S0ac*S0ab - S0aa*S0bc)/DenT; |
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519 | const double T33 = (-S0ab*S0ab + S0aa*S0bb)/DenT; |
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520 | |
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521 | //printf("T1: %10.5g %10.5g %10.5g\n", T11, T12, T13); |
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522 | //printf("T2: %10.5g %10.5g %10.5g\n", T12, T22, T23); |
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523 | //printf("T3: %10.5g %10.5g %10.5g\n", T13, T23, T33); |
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524 | |
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525 | // eq 18e: m = 1/(S0_{dd} - s0^T inv(S0) s0) |
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526 | const double ZZ = S0ad*(T11*S0ad + T12*S0bd + T13*S0cd) |
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527 | + S0bd*(T12*S0ad + T22*S0bd + T23*S0cd) |
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528 | + S0cd*(T13*S0ad + T23*S0bd + T33*S0cd); |
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529 | |
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530 | const double m=1.0/(S0dd-ZZ); |
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531 | |
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532 | // eq 18d: Y = inv(S0)s0 + e |
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533 | const double Y1 = T11*S0ad + T12*S0bd + T13*S0cd + 1.0; |
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534 | const double Y2 = T12*S0ad + T22*S0bd + T23*S0cd + 1.0; |
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535 | const double Y3 = T13*S0ad + T23*S0bd + T33*S0cd + 1.0; |
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536 | |
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537 | // N = mYY^T + \kappa^F |
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538 | const double N11 = m*Y1*Y1 + Zaa; |
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539 | const double N12 = m*Y1*Y2 + Zab; |
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540 | const double N13 = m*Y1*Y3 + Zac; |
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541 | const double N22 = m*Y2*Y2 + Zbb; |
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542 | const double N23 = m*Y2*Y3 + Zbc; |
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543 | const double N33 = m*Y3*Y3 + Zcc; |
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544 | |
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545 | //printf("N1: %10.5g %10.5g %10.5g\n", N11, N12, N13); |
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546 | //printf("N2: %10.5g %10.5g %10.5g\n", N12, N22, N23); |
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547 | //printf("N3: %10.5g %10.5g %10.5g\n", N13, N23, N33); |
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548 | //printf("S0a: %10.5g %10.5g %10.5g\n", S0aa, S0ab, S0ac); |
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549 | //printf("S0b: %10.5g %10.5g %10.5g\n", S0ab, S0bb, S0bc); |
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550 | //printf("S0c: %10.5g %10.5g %10.5g\n", S0ac, S0bc, S0cc); |
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551 | |
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552 | // M = I + S0 N |
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553 | const double Maa = N11*S0aa + N12*S0ab + N13*S0ac + 1.0; |
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554 | const double Mab = N11*S0ab + N12*S0bb + N13*S0bc; |
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555 | const double Mac = N11*S0ac + N12*S0bc + N13*S0cc; |
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556 | const double Mba = N12*S0aa + N22*S0ab + N23*S0ac; |
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557 | const double Mbb = N12*S0ab + N22*S0bb + N23*S0bc + 1.0; |
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558 | const double Mbc = N12*S0ac + N22*S0bc + N23*S0cc; |
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559 | const double Mca = N13*S0aa + N23*S0ab + N33*S0ac; |
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560 | const double Mcb = N13*S0ab + N23*S0bb + N33*S0bc; |
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561 | const double Mcc = N13*S0ac + N23*S0bc + N33*S0cc + 1.0; |
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562 | //printf("M1: %10.5g %10.5g %10.5g\n", Maa, Mab, Mac); |
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563 | //printf("M2: %10.5g %10.5g %10.5g\n", Mba, Mbb, Mbc); |
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564 | //printf("M3: %10.5g %10.5g %10.5g\n", Mca, Mcb, Mcc); |
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565 | |
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566 | // Q = inv(M) = inv(I + S0 N) |
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567 | const double DenQ = (+ Maa*Mbb*Mcc - Maa*Mbc*Mcb - Mab*Mba*Mcc |
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568 | + Mab*Mbc*Mca + Mac*Mba*Mcb - Mac*Mbb*Mca); |
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569 | |
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570 | const double Q11 = ( Mbb*Mcc - Mbc*Mcb)/DenQ; |
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571 | const double Q12 = (-Mab*Mcc + Mac*Mcb)/DenQ; |
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572 | const double Q13 = ( Mab*Mbc - Mac*Mbb)/DenQ; |
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573 | //const double Q21 = (-Mba*Mcc + Mbc*Mca)/DenQ; |
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574 | const double Q22 = ( Maa*Mcc - Mac*Mca)/DenQ; |
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575 | const double Q23 = (-Maa*Mbc + Mac*Mba)/DenQ; |
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576 | //const double Q31 = ( Mba*Mcb - Mbb*Mca)/DenQ; |
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577 | //const double Q32 = (-Maa*Mcb + Mab*Mca)/DenQ; |
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578 | const double Q33 = ( Maa*Mbb - Mab*Mba)/DenQ; |
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579 | |
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580 | //printf("Q1: %10.5g %10.5g %10.5g\n", Q11, Q12, Q13); |
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581 | //printf("Q2: %10.5g %10.5g %10.5g\n", Q21, Q22, Q23); |
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582 | //printf("Q3: %10.5g %10.5g %10.5g\n", Q31, Q32, Q33); |
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583 | // eq 18c: inv(S) = inv(S0) + mYY^T + \kappa^F |
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584 | // eq A1 in the appendix |
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585 | // To solve for S, use: |
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586 | // S = inv(inv(S^0) + N) inv(S^0) S^0 |
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587 | // = inv(S^0 inv(S^0) + N) S^0 |
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588 | // = inv(I + S^0 N) S^0 |
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589 | // = Q S^0 |
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590 | const double S11 = Q11*S0aa + Q12*S0ab + Q13*S0ac; |
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591 | const double S12 = Q12*S0aa + Q22*S0ab + Q23*S0ac; |
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592 | const double S13 = Q13*S0aa + Q23*S0ab + Q33*S0ac; |
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593 | const double S22 = Q12*S0ab + Q22*S0bb + Q23*S0bc; |
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594 | const double S23 = Q13*S0ab + Q23*S0bb + Q33*S0bc; |
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595 | const double S33 = Q13*S0ac + Q23*S0bc + Q33*S0cc; |
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596 | // If the full S is needed...it isn't since Ldd = (rho_d - rho_d) = 0 below |
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597 | //const double S14=-S11-S12-S13; |
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598 | //const double S24=-S12-S22-S23; |
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599 | //const double S34=-S13-S23-S33; |
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600 | //const double S44=S11+S22+S33 + 2.0*(S12+S13+S23); |
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601 | |
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602 | // eq 12 of Akcasu, 1990: I(q) = L^T S L |
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603 | // Note: eliminate cases without A and B polymers by setting Lij to 0 |
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604 | // Note: 1e-13 to convert from fm to cm for scattering length |
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605 | const double sqrt_Nav=sqrt(6.022045e+23) * 1.0e-13; |
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606 | const double Lad = icase<5 ? 0.0 : (L[0]/v[0] - L[3]/v[3])*sqrt_Nav; |
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607 | const double Lbd = icase<2 ? 0.0 : (L[1]/v[1] - L[3]/v[3])*sqrt_Nav; |
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608 | const double Lcd = (L[2]/v[2] - L[3]/v[3])*sqrt_Nav; |
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609 | |
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610 | const double result=Lad*Lad*S11 + Lbd*Lbd*S22 + Lcd*Lcd*S33 |
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611 | + 2.0*(Lad*Lbd*S12 + Lbd*Lcd*S23 + Lad*Lcd*S13); |
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612 | |
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613 | return result; |
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614 | */ |
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615 | } |
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