[82c299f] | 1 | double Iq(double q, double case_num, |
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[d2bb604] | 2 | double N[], double Phi[], double v[], double L[], double b[], |
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[82c299f] | 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 case_num, |
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[d2bb604] | 8 | double N[], double Phi[], double v[], double L[], double b[], |
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[82c299f] | 9 | double Kab, double Kac, double Kad, |
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| 10 | double Kbc, double Kbd, double Kcd |
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| 11 | ) { |
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| 12 | int icase = (int)case_num; |
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| 13 | |
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| 14 | #if 0 // Sasview defaults |
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| 15 | if (icase <= 1) { |
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[d2bb604] | 16 | N[0]=N[1]=1000.0; |
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| 17 | Phi[0]=Phi[1]=0.0000001; |
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[82c299f] | 18 | Kab=Kac=Kad=Kbc=Kbd=-0.0004; |
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[d2bb604] | 19 | L[0]=L[1]=1e-12; |
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| 20 | v[0]=v[1]=100.0; |
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| 21 | b[0]=b[1]=5.0; |
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[82c299f] | 22 | } else if (icase <= 4) { |
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[d2bb604] | 23 | Phi[0]=0.0000001; |
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[82c299f] | 24 | Kab=Kac=Kad=-0.0004; |
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[d2bb604] | 25 | L[0]=1e-12; |
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| 26 | v[0]=100.0; |
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| 27 | b[0]=5.0; |
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[82c299f] | 28 | } |
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| 29 | #else |
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| 30 | if (icase <= 1) { |
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[d2bb604] | 31 | N[0]=N[1]=0.0; |
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| 32 | Phi[0]=Phi[1]=0.0; |
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[82c299f] | 33 | Kab=Kac=Kad=Kbc=Kbd=0.0; |
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[d2bb604] | 34 | L[0]=L[1]=L[3]; |
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| 35 | v[0]=v[1]=v[3]; |
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| 36 | b[0]=b[1]=0.0; |
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[82c299f] | 37 | } else if (icase <= 4) { |
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[d2bb604] | 38 | N[0] = 0.0; |
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| 39 | Phi[0]=0.0; |
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[82c299f] | 40 | Kab=Kac=Kad=0.0; |
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[d2bb604] | 41 | L[0]=L[3]; |
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| 42 | v[0]=v[3]; |
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| 43 | b[0]=0.0; |
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[82c299f] | 44 | } |
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| 45 | #endif |
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| 46 | |
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[d2bb604] | 47 | const double Xa = q*q*b[0]*b[0]*N[0]/6.0; |
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| 48 | const double Xb = q*q*b[1]*b[1]*N[1]/6.0; |
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| 49 | const double Xc = q*q*b[2]*b[2]*N[2]/6.0; |
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| 50 | const double Xd = q*q*b[3]*b[3]*N[3]/6.0; |
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[82c299f] | 51 | |
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| 52 | // limit as Xa goes to 0 is 1 |
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| 53 | const double Pa = Xa==0 ? 1.0 : -expm1(-Xa)/Xa; |
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| 54 | const double Pb = Xb==0 ? 1.0 : -expm1(-Xb)/Xb; |
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| 55 | const double Pc = Xc==0 ? 1.0 : -expm1(-Xc)/Xc; |
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| 56 | const double Pd = Xd==0 ? 1.0 : -expm1(-Xd)/Xd; |
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| 57 | |
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| 58 | // limit as Xa goes to 0 is 1 |
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| 59 | const double Paa = Xa==0 ? 1.0 : 2.0*(1.0-Pa)/Xa; |
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| 60 | const double Pbb = Xb==0 ? 1.0 : 2.0*(1.0-Pb)/Xb; |
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| 61 | const double Pcc = Xc==0 ? 1.0 : 2.0*(1.0-Pc)/Xc; |
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| 62 | const double Pdd = Xd==0 ? 1.0 : 2.0*(1.0-Pd)/Xd; |
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| 63 | |
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| 64 | |
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| 65 | // Note: S0ij only defined for copolymers; otherwise set to zero |
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| 66 | // 0: C/D binary mixture |
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| 67 | // 1: C-D diblock copolymer |
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| 68 | // 2: B/C/D ternery mixture |
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| 69 | // 3: B/C-D binary mixture,1 homopolymer, 1 diblock copolymer |
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| 70 | // 4: B-C-D triblock copolymer |
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| 71 | // 5: A/B/C/D quaternary mixture |
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| 72 | // 6: A/B/C-D ternery mixture, 2 homopolymer, 1 diblock copolymer |
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| 73 | // 7: A/B-C-D binary mixture, 1 homopolymer, 1 triblock copolymer |
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| 74 | // 8: A-B/C-D binary mixture, 2 diblock copolymer |
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| 75 | // 9: A-B-C-D tetra-block copolymer |
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| 76 | #if 0 |
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| 77 | const double S0aa = icase<5 |
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[d2bb604] | 78 | ? 1.0 : N[0]*Phi[0]*v[0]*Paa; |
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[82c299f] | 79 | const double S0bb = icase<2 |
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[d2bb604] | 80 | ? 1.0 : N[1]*Phi[1]*v[1]*Pbb; |
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| 81 | const double S0cc = N[2]*Phi[2]*v[2]*Pcc; |
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| 82 | const double S0dd = N[3]*Phi[3]*v[3]*Pdd; |
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[82c299f] | 83 | const double S0ab = icase<8 |
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[d2bb604] | 84 | ? 0.0 : sqrt(N[0]*v[0]*Phi[0]*N[1]*v[1]*Phi[1])*Pa*Pb; |
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[82c299f] | 85 | const double S0ac = icase<9 |
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[d2bb604] | 86 | ? 0.0 : sqrt(N[0]*v[0]*Phi[0]*N[2]*v[2]*Phi[2])*Pa*Pc*exp(-Xb); |
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[82c299f] | 87 | const double S0ad = icase<9 |
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[d2bb604] | 88 | ? 0.0 : sqrt(N[0]*v[0]*Phi[0]*N[3]*v[3]*Phi[3])*Pa*Pd*exp(-Xb-Xc); |
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[82c299f] | 89 | const double S0bc = (icase!=4 && icase!=7 && icase!= 9) |
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[d2bb604] | 90 | ? 0.0 : sqrt(N[1]*v[1]*Phi[1]*N[2]*v[2]*Phi[2])*Pb*Pc; |
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[82c299f] | 91 | const double S0bd = (icase!=4 && icase!=7 && icase!= 9) |
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[d2bb604] | 92 | ? 0.0 : sqrt(N[1]*v[1]*Phi[1]*N[3]*v[3]*Phi[3])*Pb*Pd*exp(-Xc); |
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[82c299f] | 93 | const double S0cd = (icase==0 || icase==2 || icase==5) |
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[d2bb604] | 94 | ? 0.0 : sqrt(N[2]*v[2]*Phi[2]*N[3]*v[3]*Phi[3])*Pc*Pd; |
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[82c299f] | 95 | #else // sasview equivalent |
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[d2bb604] | 96 | //printf("Xc=%g, S0cc=%g*%g*%g*%g\n",Xc,N[2],Phi[2],v[2],Pcc); |
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| 97 | double S0aa = N[0]*Phi[0]*v[0]*Paa; |
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| 98 | double S0bb = N[1]*Phi[1]*v[1]*Pbb; |
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| 99 | double S0cc = N[2]*Phi[2]*v[2]*Pcc; |
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| 100 | double S0dd = N[3]*Phi[3]*v[3]*Pdd; |
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| 101 | double S0ab = sqrt(N[0]*v[0]*Phi[0]*N[1]*v[1]*Phi[1])*Pa*Pb; |
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| 102 | double S0ac = sqrt(N[0]*v[0]*Phi[0]*N[2]*v[2]*Phi[2])*Pa*Pc*exp(-Xb); |
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| 103 | double S0ad = sqrt(N[0]*v[0]*Phi[0]*N[3]*v[3]*Phi[3])*Pa*Pd*exp(-Xb-Xc); |
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| 104 | double S0bc = sqrt(N[1]*v[1]*Phi[1]*N[2]*v[2]*Phi[2])*Pb*Pc; |
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| 105 | double S0bd = sqrt(N[1]*v[1]*Phi[1]*N[3]*v[3]*Phi[3])*Pb*Pd*exp(-Xc); |
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| 106 | double S0cd = sqrt(N[2]*v[2]*Phi[2]*N[3]*v[3]*Phi[3])*Pc*Pd; |
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[82c299f] | 107 | switch(icase){ |
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| 108 | case 0: |
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| 109 | S0aa=0.000001; |
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| 110 | S0ab=0.000002; |
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| 111 | S0ac=0.000003; |
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| 112 | S0ad=0.000004; |
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| 113 | S0bb=0.000005; |
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| 114 | S0bc=0.000006; |
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| 115 | S0bd=0.000007; |
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| 116 | S0cd=0.000008; |
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| 117 | break; |
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| 118 | case 1: |
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| 119 | S0aa=0.000001; |
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| 120 | S0ab=0.000002; |
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| 121 | S0ac=0.000003; |
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| 122 | S0ad=0.000004; |
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| 123 | S0bb=0.000005; |
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| 124 | S0bc=0.000006; |
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| 125 | S0bd=0.000007; |
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| 126 | break; |
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| 127 | case 2: |
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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 | S0bc=0.000005; |
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| 133 | S0bd=0.000006; |
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| 134 | S0cd=0.000007; |
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| 135 | break; |
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| 136 | case 3: |
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| 137 | S0aa=0.000001; |
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| 138 | S0ab=0.000002; |
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| 139 | S0ac=0.000003; |
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| 140 | S0ad=0.000004; |
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| 141 | S0bc=0.000005; |
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| 142 | S0bd=0.000006; |
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| 143 | break; |
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| 144 | case 4: |
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| 145 | S0aa=0.000001; |
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| 146 | S0ab=0.000002; |
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| 147 | S0ac=0.000003; |
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| 148 | S0ad=0.000004; |
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| 149 | break; |
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| 150 | case 5: |
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| 151 | S0ab=0.000001; |
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| 152 | S0ac=0.000002; |
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| 153 | S0ad=0.000003; |
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| 154 | S0bc=0.000004; |
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| 155 | S0bd=0.000005; |
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| 156 | S0cd=0.000006; |
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| 157 | break; |
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| 158 | case 6: |
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| 159 | S0ab=0.000001; |
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| 160 | S0ac=0.000002; |
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| 161 | S0ad=0.000003; |
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| 162 | S0bc=0.000004; |
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| 163 | S0bd=0.000005; |
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| 164 | break; |
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| 165 | case 7: |
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| 166 | S0ab=0.000001; |
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| 167 | S0ac=0.000002; |
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| 168 | S0ad=0.000003; |
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| 169 | break; |
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| 170 | case 8: |
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| 171 | S0ac=0.000001; |
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| 172 | S0ad=0.000002; |
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| 173 | S0bc=0.000003; |
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| 174 | S0bd=0.000004; |
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| 175 | break; |
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| 176 | default : //case 9: |
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| 177 | break; |
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| 178 | } |
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| 179 | #endif |
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| 180 | |
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| 181 | // eq 12a: \kappa_{ij}^F = \chi_{ij}^F - \chi_{i0}^F - \chi_{j0}^F |
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| 182 | const double Kaa = 0.0; |
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| 183 | const double Kbb = 0.0; |
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| 184 | const double Kcc = 0.0; |
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[13ed84c] | 185 | //const double Kdd = 0.0; |
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[82c299f] | 186 | const double Zaa = Kaa - Kad - Kad; |
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| 187 | const double Zab = Kab - Kad - Kbd; |
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| 188 | const double Zac = Kac - Kad - Kcd; |
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| 189 | const double Zbb = Kbb - Kbd - Kbd; |
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| 190 | const double Zbc = Kbc - Kbd - Kcd; |
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| 191 | const double Zcc = Kcc - Kcd - Kcd; |
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| 192 | //printf("Za: %10.5g %10.5g %10.5g\n", Zaa, Zab, Zac); |
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| 193 | //printf("Zb: %10.5g %10.5g %10.5g\n", Zab, Zbb, Zbc); |
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| 194 | //printf("Zc: %10.5g %10.5g %10.5g\n", Zac, Zbc, Zcc); |
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| 195 | |
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| 196 | // T = inv(S0) |
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| 197 | const double DenT = (- S0ac*S0bb*S0ac + S0ab*S0bc*S0ac + S0ac*S0ab*S0bc |
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| 198 | - S0aa*S0bc*S0bc - S0ab*S0ab*S0cc + S0aa*S0bb*S0cc); |
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| 199 | const double T11 = (-S0bc*S0bc + S0bb*S0cc)/DenT; |
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| 200 | const double T12 = ( S0ac*S0bc - S0ab*S0cc)/DenT; |
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| 201 | const double T13 = (-S0ac*S0bb + S0ab*S0bc)/DenT; |
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| 202 | const double T22 = (-S0ac*S0ac + S0aa*S0cc)/DenT; |
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| 203 | const double T23 = ( S0ac*S0ab - S0aa*S0bc)/DenT; |
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| 204 | const double T33 = (-S0ab*S0ab + S0aa*S0bb)/DenT; |
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| 205 | |
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| 206 | //printf("T1: %10.5g %10.5g %10.5g\n", T11, T12, T13); |
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| 207 | //printf("T2: %10.5g %10.5g %10.5g\n", T12, T22, T23); |
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| 208 | //printf("T3: %10.5g %10.5g %10.5g\n", T13, T23, T33); |
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| 209 | |
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| 210 | // eq 18e: m = 1/(S0_{dd} - s0^T inv(S0) s0) |
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| 211 | const double ZZ = S0ad*(T11*S0ad + T12*S0bd + T13*S0cd) |
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| 212 | + S0bd*(T12*S0ad + T22*S0bd + T23*S0cd) |
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| 213 | + S0cd*(T13*S0ad + T23*S0bd + T33*S0cd); |
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| 214 | |
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| 215 | const double m=1.0/(S0dd-ZZ); |
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| 216 | |
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| 217 | // eq 18d: Y = inv(S0)s0 + e |
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| 218 | const double Y1 = T11*S0ad + T12*S0bd + T13*S0cd + 1.0; |
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| 219 | const double Y2 = T12*S0ad + T22*S0bd + T23*S0cd + 1.0; |
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| 220 | const double Y3 = T13*S0ad + T23*S0bd + T33*S0cd + 1.0; |
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| 221 | |
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| 222 | // N = mYY^T + \kappa^F |
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| 223 | const double N11 = m*Y1*Y1 + Zaa; |
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| 224 | const double N12 = m*Y1*Y2 + Zab; |
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| 225 | const double N13 = m*Y1*Y3 + Zac; |
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| 226 | const double N22 = m*Y2*Y2 + Zbb; |
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| 227 | const double N23 = m*Y2*Y3 + Zbc; |
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| 228 | const double N33 = m*Y3*Y3 + Zcc; |
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| 229 | |
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| 230 | //printf("N1: %10.5g %10.5g %10.5g\n", N11, N12, N13); |
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| 231 | //printf("N2: %10.5g %10.5g %10.5g\n", N12, N22, N23); |
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| 232 | //printf("N3: %10.5g %10.5g %10.5g\n", N13, N23, N33); |
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| 233 | //printf("S0a: %10.5g %10.5g %10.5g\n", S0aa, S0ab, S0ac); |
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| 234 | //printf("S0b: %10.5g %10.5g %10.5g\n", S0ab, S0bb, S0bc); |
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| 235 | //printf("S0c: %10.5g %10.5g %10.5g\n", S0ac, S0bc, S0cc); |
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| 236 | |
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| 237 | // M = I + S0 N |
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| 238 | const double Maa = N11*S0aa + N12*S0ab + N13*S0ac + 1.0; |
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| 239 | const double Mab = N11*S0ab + N12*S0bb + N13*S0bc; |
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| 240 | const double Mac = N11*S0ac + N12*S0bc + N13*S0cc; |
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| 241 | const double Mba = N12*S0aa + N22*S0ab + N23*S0ac; |
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| 242 | const double Mbb = N12*S0ab + N22*S0bb + N23*S0bc + 1.0; |
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| 243 | const double Mbc = N12*S0ac + N22*S0bc + N23*S0cc; |
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| 244 | const double Mca = N13*S0aa + N23*S0ab + N33*S0ac; |
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| 245 | const double Mcb = N13*S0ab + N23*S0bb + N33*S0bc; |
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| 246 | const double Mcc = N13*S0ac + N23*S0bc + N33*S0cc + 1.0; |
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| 247 | //printf("M1: %10.5g %10.5g %10.5g\n", Maa, Mab, Mac); |
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| 248 | //printf("M2: %10.5g %10.5g %10.5g\n", Mba, Mbb, Mbc); |
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| 249 | //printf("M3: %10.5g %10.5g %10.5g\n", Mca, Mcb, Mcc); |
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| 250 | |
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| 251 | // Q = inv(M) = inv(I + S0 N) |
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| 252 | const double DenQ = (+ Maa*Mbb*Mcc - Maa*Mbc*Mcb - Mab*Mba*Mcc |
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| 253 | + Mab*Mbc*Mca + Mac*Mba*Mcb - Mac*Mbb*Mca); |
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| 254 | |
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| 255 | const double Q11 = ( Mbb*Mcc - Mbc*Mcb)/DenQ; |
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| 256 | const double Q12 = (-Mab*Mcc + Mac*Mcb)/DenQ; |
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| 257 | const double Q13 = ( Mab*Mbc - Mac*Mbb)/DenQ; |
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[13ed84c] | 258 | //const double Q21 = (-Mba*Mcc + Mbc*Mca)/DenQ; |
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[82c299f] | 259 | const double Q22 = ( Maa*Mcc - Mac*Mca)/DenQ; |
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| 260 | const double Q23 = (-Maa*Mbc + Mac*Mba)/DenQ; |
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[13ed84c] | 261 | //const double Q31 = ( Mba*Mcb - Mbb*Mca)/DenQ; |
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| 262 | //const double Q32 = (-Maa*Mcb + Mab*Mca)/DenQ; |
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[82c299f] | 263 | const double Q33 = ( Maa*Mbb - Mab*Mba)/DenQ; |
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| 264 | |
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| 265 | //printf("Q1: %10.5g %10.5g %10.5g\n", Q11, Q12, Q13); |
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| 266 | //printf("Q2: %10.5g %10.5g %10.5g\n", Q21, Q22, Q23); |
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| 267 | //printf("Q3: %10.5g %10.5g %10.5g\n", Q31, Q32, Q33); |
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| 268 | // eq 18c: inv(S) = inv(S0) + mYY^T + \kappa^F |
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| 269 | // eq A1 in the appendix |
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| 270 | // To solve for S, use: |
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| 271 | // S = inv(inv(S^0) + N) inv(S^0) S^0 |
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| 272 | // = inv(S^0 inv(S^0) + N) S^0 |
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| 273 | // = inv(I + S^0 N) S^0 |
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| 274 | // = Q S^0 |
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| 275 | const double S11 = Q11*S0aa + Q12*S0ab + Q13*S0ac; |
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| 276 | const double S12 = Q12*S0aa + Q22*S0ab + Q23*S0ac; |
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| 277 | const double S13 = Q13*S0aa + Q23*S0ab + Q33*S0ac; |
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| 278 | const double S22 = Q12*S0ab + Q22*S0bb + Q23*S0bc; |
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| 279 | const double S23 = Q13*S0ab + Q23*S0bb + Q33*S0bc; |
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| 280 | const double S33 = Q13*S0ac + Q23*S0bc + Q33*S0cc; |
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| 281 | // If the full S is needed...it isn't since Ldd = (rho_d - rho_d) = 0 below |
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| 282 | //const double S14=-S11-S12-S13; |
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| 283 | //const double S24=-S12-S22-S23; |
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| 284 | //const double S34=-S13-S23-S33; |
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| 285 | //const double S44=S11+S22+S33 + 2.0*(S12+S13+S23); |
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| 286 | |
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| 287 | // eq 12 of Akcasu, 1990: I(q) = L^T S L |
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| 288 | // Note: eliminate cases without A and B polymers by setting Lij to 0 |
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| 289 | // Note: 1e-13 to convert from fm to cm for scattering length |
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| 290 | const double sqrt_Nav=sqrt(6.022045e+23) * 1.0e-13; |
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[d2bb604] | 291 | const double Lad = icase<5 ? 0.0 : (L[0]/v[0] - L[3]/v[3])*sqrt_Nav; |
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| 292 | const double Lbd = icase<2 ? 0.0 : (L[1]/v[1] - L[3]/v[3])*sqrt_Nav; |
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| 293 | const double Lcd = (L[2]/v[2] - L[3]/v[3])*sqrt_Nav; |
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[82c299f] | 294 | |
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| 295 | const double result=Lad*Lad*S11 + Lbd*Lbd*S22 + Lcd*Lcd*S33 |
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| 296 | + 2.0*(Lad*Lbd*S12 + Lbd*Lcd*S23 + Lad*Lcd*S13); |
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| 297 | |
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| 298 | return result; |
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| 299 | |
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| 300 | } |
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