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SPT2.c
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#include "stdio.h"
#include "math.h"
#include "stdlib.h"
#define OHS 0
#define HS 1
double rho_0, rho_1, rho_2; // rho_0 is the density of the matrix, rho_1 and rho_2 are the densities of fluid.
double sigma_0, sigma_1, sigma_2; // sigma_0 is the diameter of the matrix, sigma_1 and sigma_2 are the diameters os fluid.
double xi_m1, xi_m2, xi_m3;
double xi_f1, xi_f2, xi_f3;
double x1, x2;
double P1(double sigma, int flag);
double a_alpha(double sigma, int flag);
double b_alpha(double sigma, int flag);
double c_alpha(double sigma, int flag);
double e_alpha(double sigma, int flag);
double Pressure_SPT2a(int flag);
double Pressure_SPT2(int flag);
double miu_SPT2a (double sigma, double rho, int flag);
double miu_SPT2b (double sigma, double rho, int flag);
double miu_SPT2b1 (double sigma, double rho, int flag);
double miu_SPT2c (double sigma, double rho, int flag);
double miu_SPT2d (double sigma, double rho, int flag);
double miu_SPT2 (double sigma, double rho, int flag);
int main (int argc, char **argv){
FILE * fp;
int flag; // flag = 0 is OHS matrix, flag = 1 is HS matrix.
double rho; // rho = rho_1 + rho_2.
double miu1_GCMC, miu2_GCMC;
/*
if((fp=fopen(argv[1],"wt"))==NULL){
printf("cannot open %s\n",argv[1]);
exit(1);
}
*/
printf("0 is OHS, 1 is HS:\n");
scanf("%d",&flag);
printf("the density of matrix: \n");
scanf("%lf",&rho_0);
printf("the total density of fluid : \n");
scanf("%lf",&rho);
printf("the concentration of species 1: \n");
scanf("%lf",&x1);
printf("the DIAMETER of matrix:\n");
scanf("%lf",&sigma_0);
printf("the DIAMETER of compoment 1:\n");
scanf("%lf",&sigma_1);
printf("the DIAMETER of compoment 2:\n");
scanf("%lf",&sigma_2);
rho_1 = rho * x1;
rho_2 = rho - rho_1;
x2 = 1-x1;
xi_f1 = M_PI*(x1 * sigma_1 + x2 * sigma_2)*rho/6.0;
xi_f2 = M_PI*(x1 * sigma_1 * sigma_1 + x2 * sigma_2 * sigma_2)*rho/6.0;
xi_f3 = M_PI*(x1 * sigma_1 * sigma_1 * sigma_1 + x2 * sigma_2 * sigma_2 * sigma_2)*rho/6.0;
xi_m1 = M_PI*rho_0*sigma_0/6.0;
xi_m2 = M_PI*rho_0*sigma_0*sigma_0/6.0;
xi_m3 = M_PI*rho_0*sigma_0*sigma_0*sigma_0/6.0;
/*
printf("component 1: spt2a: %lf ( %lf ) \t spt2b: %lf (%lf) \t spt2c: %lf (%lf) \t spt2d: %lf (%lf) \t spt2: %lf (%lf)\t \n", miu_SPT2a(sigma_1, rho_1, flag), miu_SPT2a(sigma_1, rho_1, flag)-miu1_GCMC,\
miu_SPT2b(sigma_1, rho_1, flag), miu_SPT2b(sigma_1, rho_1, flag)-miu1_GCMC,\
miu_SPT2c(sigma_1, rho_1, flag), miu_SPT2c(sigma_1, rho_1, flag)-miu1_GCMC,\
miu_SPT2d(sigma_1, rho_1, flag), miu_SPT2d(sigma_1, rho_1, flag)-miu1_GCMC,\
miu_SPT2(sigma_1, rho_1, flag), miu_SPT2(sigma_1, rho_1, flag)-miu1_GCMC);
printf("component 2: spt2a: %lf ( %lf ) \t spt2b: %lf (%lf) \t spt2c: %lf (%lf) \t spt2d: %lf (%lf) \t spt2: %lf (%lf)\t \n", miu_SPT2a(sigma_2, rho_2, flag), miu_SPT2a(sigma_2, rho_2, flag)-miu2_GCMC,\
miu_SPT2b(sigma_2, rho_2, flag), miu_SPT2b(sigma_2, rho_2, flag)-miu2_GCMC,\
miu_SPT2c(sigma_2, rho_2, flag), miu_SPT2c(sigma_2, rho_2, flag)-miu2_GCMC,\
miu_SPT2d(sigma_2, rho_2, flag), miu_SPT2d(sigma_2, rho_2, flag)-miu2_GCMC,\
miu_SPT2(sigma_2, rho_2, flag), miu_SPT2(sigma_2, rho_2, flag)-miu2_GCMC);
*/
printf("component 1:\n spt2a: %lf \n spt2b: %lf \n spt2b1: %lf \n spt2c: %lf \n spt2d: %lf \n spt2: %lf \n",
miu_SPT2a(sigma_1, rho_1, flag),\
miu_SPT2b(sigma_1, rho_1, flag),\
miu_SPT2b1(sigma_1, rho_1, flag),\
miu_SPT2c(sigma_1, rho_1, flag),\
miu_SPT2d(sigma_1, rho_1, flag),\
miu_SPT2(sigma_1, rho_1, flag));
printf("component 2:\n spt2a: %lf \n spt2b: %lf \n spt2b1: %lf \n spt2c: %lf \n spt2d: %lf \n spt2: %lf \n",
miu_SPT2a(sigma_2, rho_2, flag),\
miu_SPT2b(sigma_2, rho_2, flag),\
miu_SPT2b1(sigma_2, rho_2, flag),\
miu_SPT2c(sigma_2, rho_2, flag),\
miu_SPT2d(sigma_2, rho_2, flag),\
miu_SPT2(sigma_2, rho_2, flag));
return 0;
}
// The probability of inserting a scaled particle into an empty matrix
double P1(double sigma, int flag) {
double P0;
double t0;
P0 =rho_0 * (1.0+xi_m3+xi_m3*xi_m3)/pow(1.0-xi_m3,3.0);
if(flag == HS) {
t0 = -log(1.0-xi_m3)+3.0*xi_m2/(1.0-xi_m3)*sigma+(3.0*xi_m1/(1.0-xi_m3)+9.0/2.0*xi_m2*xi_m2/pow(1.0-xi_m3,2.0))*sigma*sigma+M_PI*sigma*sigma*sigma*P0/6.0;
}else if(flag == OHS){
t0 = xi_m3*(1 + sigma / sigma_0)*(1 + sigma / sigma_0)*(1 + sigma / sigma_0);
}
return(exp(-1.0*t0));
}
double a_alpha(double sigma, int flag){
double x;
double R;
double D1, D2;
R = 0.5 * sigma;
if(flag == OHS){
D1 = -3.0 * xi_m3 / (sigma_0 / 2);
D2 = -6.0 * xi_m3 / (sigma_0 / 2) / (sigma_0 / 2);
} else if(flag == HS) {
D1 = -6.0 * xi_m2 / (1.0 - xi_m3);
D2 = -24.0 * xi_m1 / (1.0 - xi_m3) - 36.0 * xi_m2 * xi_m2 / (1.0 - xi_m3) / (1.0 - xi_m3);
}
x = 6.0 * xi_f2 * R / xi_f3 + 12 * xi_f1 * R * R / xi_f3 - (1.0 + 6.0 * xi_f2 * R / xi_f3) * R * D1 + 0.5 * ((R * D1 * R * D1) - R * R * D2);
return x;
}
double b_alpha(double sigma, int flag){
double x;
double R;
double D1, D2;
R = 0.5 * sigma;
if(flag == OHS){
D1 = -3.0 * xi_m3 / (sigma_0 / 2);
D2 = -6.0 * xi_m3 / (sigma_0 / 2) / (sigma_0 / 2);
} else if(flag == HS) {
D1 = -6.0 * xi_m2 / (1.0 - xi_m3);
D2 = -24.0 * xi_m1 / (1.0 - xi_m3) - 36.0 * xi_m2 * xi_m2 / (1.0 - xi_m3) / (1.0 - xi_m3);
}
x = 0.5 * (R * D1 - 6.0 * xi_f2 * R / xi_f3) * (R * D1 - 6.0 * xi_f2 * R / xi_f3);
return x;
}
double c_alpha(double sigma, int flag){
double x;
double R;
double D1, D2;
R = 0.5 * sigma;
if(flag == OHS){
D1 = -3.0 * xi_m3 / (sigma_0 / 2);
D2 = -6.0 * xi_m3 / (sigma_0 / 2) / (sigma_0 / 2);
} else if(flag == HS) {
D1 = -6.0 * xi_m2 / (1.0 - xi_m3);
D2 = -24.0 * xi_m1 / (1.0 - xi_m3) - 36.0 * xi_m2 * xi_m2 / (1.0 - xi_m3) / (1.0 - xi_m3);
}
x = -6.0 * R *R * D1 * xi_f2 / xi_f3 + 0.5 * R * R *D1 * D1;
return x;
}
double e_alpha(double sigma, int flag){
double x;
double R;
double D1, D2;
R = 0.5 * sigma;
if(flag == OHS){
D1 = -3.0 * xi_m3 / (sigma_0 / 2);
D2 = -6.0 * xi_m3 / (sigma_0 / 2) / (sigma_0 / 2);
} else if(flag == HS) {
D1 = -6.0 * xi_m2 / (1.0 - xi_m3);
D2 = -24.0 * xi_m1 / (1.0 - xi_m3) - 36.0 * xi_m2 * xi_m2 / (1.0 - xi_m3) / (1.0 - xi_m3);
}
x = R * D1 + 0.5 * R * R * D2;
return x;
}
double Pressure_SPT2a(int flag){
double x;
double phi_0;
double A, B;
if(flag == OHS){
phi_0 = P1(0.0, OHS);
A = x1 * a_alpha(sigma_1,OHS) + x2 * a_alpha(sigma_2, OHS);
B = x1 * b_alpha(sigma_1,OHS) + x2 * b_alpha(sigma_2, OHS);
} else if(flag == HS){
phi_0 = P1(0.0, HS);
A = x1 * a_alpha(sigma_1,HS) + x2 * a_alpha(sigma_2, HS);
B = x1 * b_alpha(sigma_1,HS) + x2 * b_alpha(sigma_2, HS);
}
x = 1.0 / (1.0 - xi_f3 / phi_0) + 0.5 * A * (xi_f3 / phi_0)/(1.0 - xi_f3 / phi_0)/(1.0 - xi_f3 / phi_0) + 2.0 * B * (xi_f3 / phi_0) * (xi_f3 / phi_0) /(1.0 - xi_f3 / phi_0)/(1.0 - xi_f3 / phi_0)/ (1.0 - xi_f3 / phi_0)/3.0;
x = (rho_1 + rho_2) * x;
return x;
}
double Pressure_SPT2(int flag){
double phi_0, phi;
double A, B;
double y;
double t1, t2, t3, t4;
if(flag == OHS){
phi_0 = P1(0.0, OHS);
A = x1 * a_alpha(sigma_1,OHS) + x2 * a_alpha(sigma_2, OHS);
B = x1 * b_alpha(sigma_1,OHS) + x2 * b_alpha(sigma_2, OHS);
} else if(flag == HS){
phi_0 = P1(0.0, HS);
A = x1 * a_alpha(sigma_1,HS) + x2 * a_alpha(sigma_2, HS);
B = x1 * b_alpha(sigma_1,HS) + x2 * b_alpha(sigma_2, HS);
}
y = M_PI * sigma_1 * sigma_1 * sigma_1 * rho_1 / 6.0 / P1(sigma_1, flag) + M_PI * sigma_2 * sigma_2 * sigma_2 * rho_2 / 6.0 / P1(sigma_2, flag) ;
phi = xi_f3 / y;
t1 = -1.0 * phi * log(1.0 - xi_f3 / phi) / xi_f3;
t2 = ((1.0 + A) * phi / (phi - phi_0)) * (phi * log(1.0 - xi_f3 / phi) / xi_f3 - phi_0 * log(1.0 - xi_f3 / phi_0) / xi_f3);
t3 = ((A + 2.0 * B) * phi / (phi - phi_0)) * (1.0 / (1.0 - xi_f3 / phi_0) + phi_0 * log(1.0 - xi_f3 / phi_0) / xi_f3 - (phi / (phi - phi_0)) * (phi * log(1.0 - xi_f3 / phi) / xi_f3 - phi_0 * log(1.0 - xi_f3 / phi_0) / xi_f3));
t4 = (2.0 * B * phi / (phi - phi_0)) * ((xi_f3/phi_0)/2.0/(1.0 - xi_f3 / phi_0)/(1.0 - xi_f3 / phi_0) - 1.0 / (1.0 - xi_f3 / phi_0) - (phi / (phi - phi_0))*(1.0 / (1.0 - xi_f3 / phi_0) + phi_0 * log(1.0 - xi_f3 / phi_0) / xi_f3) + (phi / (phi - phi_0))*(phi / (phi - phi_0))*(phi * log(1.0 - xi_f3 / phi) / xi_f3 - phi_0 * log(1.0 - xi_f3 / phi_0) / xi_f3));
return (t1+t2+t3+t4);
}
double miu_SPT2a (double sigma, double rho, int flag){
double x;
double phi_0;
double C, E;
double D1, D2;
double R = 0.5 * sigma;
if(flag == OHS){
phi_0 = P1(0.0, OHS);
C = x1 * c_alpha(sigma_1,OHS) + x2 * c_alpha(sigma_2, OHS);
E = x1 * e_alpha(sigma_1,OHS) + x2 * e_alpha(sigma_2, OHS);
D1 = -3.0 * xi_m3 / (sigma_0 / 2);
D2 = -6.0 * xi_m3 / (sigma_0 / 2) / (sigma_0 / 2);
} else if(flag == HS){
phi_0 = P1(0.0, HS);
C = x1 * c_alpha(sigma_1,HS) + x2 * c_alpha(sigma_2, HS);
E = x1 * e_alpha(sigma_1,HS) + x2 * e_alpha(sigma_2, HS);
D1 = -6.0 * xi_m2 / (1.0 - xi_m3);
D2 = -24.0 * xi_m1 / (1.0 - xi_m3) - 36.0 * xi_m2 * xi_m2 / (1.0 - xi_m3) / (1.0 - xi_m3);
}
x = log(rho) - log(P1(sigma, flag)) - log(1.0 - xi_f3/phi_0) + a_alpha(sigma, flag) * (xi_f3 / phi_0)/(1.0 - xi_f3 / phi_0) + b_alpha(sigma, flag)* (xi_f3 / phi_0) * (xi_f3 / phi_0) /(1.0 - xi_f3 / phi_0)/(1.0 - xi_f3 / phi_0) \
+ 4.0 * M_PI * R * R * R * Pressure_SPT2a(flag) / 3.0 / phi_0 \
+ (4.0 * M_PI * R * R * R * (rho_1 + rho_2) * (C - E) / 3.0 / xi_f3 - c_alpha(sigma,flag) + e_alpha(sigma,flag)) * (xi_f3 / phi_0)/(1.0 - xi_f3 / phi_0)/2.0 \
+ (4.0 * M_PI * R * R * R * (rho_1 + rho_2) * C / 3.0 / xi_f3 - c_alpha(sigma,flag)) * 2.0 * (xi_f3 / phi_0) * (xi_f3 / phi_0) /(1.0 - xi_f3 / phi_0)/(1.0 - xi_f3 / phi_0)/3.0 \
+ (sigma * sigma * sigma / (xi_f3 / phi_0) - sigma * sigma / (xi_f2 /phi_0)) * ((xi_f3 / phi_0)/(1.0 - xi_f3 / phi_0)/2.0 + (xi_f3 / phi_0) * (xi_f3 / phi_0) /(1.0 - xi_f3 / phi_0)/(1.0 - xi_f3 / phi_0)/3.0) * 3.0 * D1 * (xi_f2 / phi_0) * (xi_f2 / phi_0) / 2.0 / (xi_f3 / phi_0);
return x;
}
double miu_SPT2b (double sigma, double rho, int flag){
double x;
double phi_0, phi;
double y;
double R = 0.5 * sigma;
if(flag == OHS){
phi_0 = P1(0.0, OHS);
} else if(flag == HS){
phi_0 = P1(0.0, HS);
}
y = M_PI * sigma_1 * sigma_1 * sigma_1 * rho_1 / 6.0 / P1(sigma_1, flag) + M_PI * sigma_2 * sigma_2 * sigma_2 * rho_2 / 6.0 / P1(sigma_2, flag) ;
phi = xi_f3 / y;
x = miu_SPT2a(sigma,rho,flag) - log(1 - xi_f3/phi) + log(1- xi_f3/phi_0) + (4.0 * M_PI * R * R * R * (rho_1 + rho_2) / 3.0 / xi_f3 - 1.0) \
* (-1.0 * phi * log(1.0 - xi_f3 / phi) / xi_f3 + phi_0 * log(1.0 - xi_f3 / phi_0) / xi_f3 ) \
- (phi * log(1.0 - xi_f3 / phi) / xi_f3 + 1.0) * (phi / P1(sigma,flag) - 1.0) * 4.0 * M_PI * R * R * R * (rho_1 + rho_2) / 3.0 / xi_f3;
return x;
}
double miu_SPT2b1 (double sigma, double rho, int flag){
double x;
double phi_0, phi;
double y;
double R = 0.5 * sigma;
if(flag == OHS){
phi_0 = P1(0.0, OHS);
} else if(flag == HS){
phi_0 = P1(0.0, HS);
}
y = M_PI * sigma_1 * sigma_1 * sigma_1 * rho_1 / 6.0 / P1(sigma_1, flag) + M_PI * sigma_2 * sigma_2 * sigma_2 * rho_2 / 6.0 / P1(sigma_2, flag) ;
phi = xi_f3 / y;
x = miu_SPT2a(sigma,rho,flag) + (phi/phi_0 - 1.0) * (phi_0 * log(1.0 - xi_f3 / phi_0) / xi_f3 + 1.0) \
- (4.0 * M_PI * R * R * R * (rho_1 + rho_2) / 3.0 / xi_f3) * (phi/phi_0 - 1.0) * (phi_0 * log(1.0 - xi_f3 / phi_0) / xi_f3 + 1.0/(1.0 - xi_f3 / phi_0)) \
+ (4.0 * M_PI * R * R * R * (rho_1 + rho_2) / 3.0 / xi_f3) * (phi/phi_0)*(1.0-phi/P1(sigma,flag))*(phi_0 * log(1.0 - xi_f3 / phi_0) / xi_f3 + 1.0);
return x;
}
double miu_SPT2c (double sigma, double rho, int flag){
double x;
double phi_0, phi;
double y;
double R = 0.5 * sigma;
double A, D1;
if(flag == OHS){
phi_0 = P1(0.0, OHS);
A = x1 * a_alpha(sigma_1,OHS) + x2 * a_alpha(sigma_2, OHS);
D1 = -3.0 * xi_m3 / (sigma_0 / 2);
} else if(flag == HS){
phi_0 = P1(0.0, HS);
A = x1 * a_alpha(sigma_1,HS) + x2 * a_alpha(sigma_2, HS);
D1 = -6.0 * xi_m2 / (1.0 - xi_m3);
}
y = M_PI * sigma_1 * sigma_1 * sigma_1 * rho_1 / 6.0 / P1(sigma_1, flag) + M_PI * sigma_2 * sigma_2 * sigma_2 * rho_2 / 6.0 / P1(sigma_2, flag) ;
phi = xi_f3 / y;
x = miu_SPT2b(sigma,rho,flag) + (1 + a_alpha(sigma,flag) + 3.0 * xi_f1 * xi_f2 * (sigma / xi_f1 + sigma * sigma / xi_f2 - 2.0 * sigma * sigma * sigma / xi_f3) / xi_f3 + 3 * D1 * xi_f2 * xi_f2 * (sigma * sigma * sigma / xi_f3 - sigma * sigma / xi_f2) / xi_f3 / 2 ) \
* (1.0 + phi_0 * log(1.0 - xi_f3 / phi_0) / xi_f3 + (phi/(phi-phi_0)) * ((1 - phi / xi_f3) * log(1.0 - xi_f3 / phi) - (1.0 - phi_0 / xi_f3) * log(1.0 - xi_f3 / phi_0))) \
+ (4.0 * M_PI * R * R * R * (rho_1 + rho_2) / 3.0 / xi_f3) * ((1.0 + A) * (-1.0 * phi_0 * log(1.0 - xi_f3 / phi_0) / xi_f3 - 1.0 / (1.0 - xi_f3 / phi_0) + phi * (phi * log(1.0 - xi_f3 / phi) / xi_f3 - phi_0 * log(1.0 - xi_f3 / phi_0) / xi_f3) / (phi - phi_0))) \
+ (1.0 + A) * (4.0 * M_PI * R * R * R * (rho_1 + rho_2)/ 3.0 / xi_f3) * (phi / P1(sigma_1, flag) -1.0) * (phi / (phi - phi_0)) * (1.0 + phi * log(1.0 - xi_f3 / phi) / xi_f3 + (phi_0 / (phi - phi_0)) * ((1.0 - phi/xi_f3)*log(1.0 - xi_f3 / phi) - (1.0 - phi_0 / xi_f3) * log(1.0 - xi_f3 / phi_0)));
return x;
}
double miu_SPT2d (double sigma, double rho, int flag){
double x;
double phi_0, phi;
double y;
double R = 0.5 * sigma;
double A, B, D1;
double t1, t2, t3, t4;
if(flag == OHS){
phi_0 = P1(0.0, OHS);
A = x1 * a_alpha(sigma_1,OHS) + x2 * a_alpha(sigma_2, OHS);
B = x1 * b_alpha(sigma_1,OHS) + x2 * b_alpha(sigma_2, OHS);
D1 = -3.0 * xi_m3 / (sigma_0 / 2);
} else if(flag == HS){
phi_0 = P1(0.0, HS);
A = x1 * a_alpha(sigma_1,HS) + x2 * a_alpha(sigma_2, HS);
B = x1 * b_alpha(sigma_1,HS) + x2 * b_alpha(sigma_2, HS);
D1 = -6.0 * xi_m2 / (1.0 - xi_m3);
}
y = M_PI * sigma_1 * sigma_1 * sigma_1 * rho_1 / 6.0 / P1(sigma_1, flag) + M_PI * sigma_2 * sigma_2 * sigma_2 * rho_2 / 6.0 / P1(sigma_2, flag) ;
phi = xi_f3 / y;
t1 = a_alpha(sigma,flag) + 2.0 * b_alpha(sigma,flag) + (3.0 * xi_f1 * xi_f2 / xi_f3 ) * (sigma / xi_f1 + sigma * sigma / xi_f2 - 2.0 * sigma * sigma * sigma / xi_f3)\
+ (9.0 * xi_f2 * xi_f2 / 2.0 / xi_f3) * (D1 - 4.0 * xi_f2 / xi_f3) * (sigma * sigma * sigma / xi_f3 - sigma * sigma / xi_f2);
t2 = (1.0 + phi/(phi - phi_0)) * (phi_0 * log(1.0 - xi_f3 / phi_0) / xi_f3 + 1.0) + xi_f3 / phi_0 / 2.0 / (1.0 - xi_f3 / phi_0) + (phi/(phi - phi_0)) * (phi/(phi - phi_0)) \
* ((1.0 - phi / xi_f3) * log(1.0 - xi_f3 / phi) - (1.0 - phi_0 / xi_f3) * log(1.0 - xi_f3 / phi_0));
t3 = (A + 2.0 * B) * (4.0 * M_PI * R * R * R * (rho_1 + rho_2) / 3.0 / xi_f3) * (phi / P1(sigma, flag) - 1.0) * (phi/(phi - phi_0)) * ((phi_0/(phi - phi_0)) * (phi_0 * log(1.0 - xi_f3 / phi_0) / xi_f3 + 1.0) \
+ (phi/(phi - phi_0)) * (phi * log(1.0 - xi_f3 / phi) / xi_f3 + 1.0) + (2.0 * phi_0 * phi / (phi - phi_0) / (phi - phi_0)) * ((1.0 - phi / xi_f3) * log(1.0 - xi_f3 / phi) - (1.0 - phi_0 / xi_f3) * log(1.0 - xi_f3 / phi_0)));
t4 = (4.0 * M_PI * R * R * R * (rho_1 + rho_2) / 3.0 / xi_f3) * (A + 2.0 * B) * ((1.0 + phi/(phi - phi_0)) * (phi_0 * log(1.0 - xi_f3 / phi_0) / xi_f3 + 1.0 / (1.0 - xi_f3 / phi_0)) \
- (xi_f3 / phi_0 / 2.0 / (1.0 - xi_f3 / phi_0) / (1.0 - xi_f3 / phi_0)) - (phi/(phi - phi_0)) * (phi/(phi - phi_0)) * ((phi / xi_f3) * log(1.0 - xi_f3 / phi) - (phi_0 / xi_f3) * log(1.0 - xi_f3 / phi_0)));
x = miu_SPT2c(sigma,rho,flag) - t1 * t2 + t3 + t4;
return x;
}
double miu_SPT2 (double sigma, double rho, int flag) {
double x;
double phi_0, phi;
double y;
double R = 0.5 * sigma;
double A, B, D1;
double t1, t2, t3, t4;
if(flag == OHS){
phi_0 = P1(0.0, OHS);
A = x1 * a_alpha(sigma_1,OHS) + x2 * a_alpha(sigma_2, OHS);
B = x1 * b_alpha(sigma_1,OHS) + x2 * b_alpha(sigma_2, OHS);
D1 = -3.0 * xi_m3 / (sigma_0 / 2);
} else if(flag == HS){
phi_0 = P1(0.0, HS);
A = x1 * a_alpha(sigma_1,HS) + x2 * a_alpha(sigma_2, HS);
B = x1 * b_alpha(sigma_1,HS) + x2 * b_alpha(sigma_2, HS);
D1 = -6.0 * xi_m2 / (1.0 - xi_m3);
}
y = M_PI * sigma_1 * sigma_1 * sigma_1 * rho_1 / 6.0 / P1(sigma_1, flag) + M_PI * sigma_2 * sigma_2 * sigma_2 * rho_2 / 6.0 / P1(sigma_2, flag) ;
phi = xi_f3 / y;
t1 = 2.0 * b_alpha(sigma,flag) + (3.0 * xi_f2 * xi_f2 / xi_f3) * (D1 - 6.0 * xi_f2 / xi_f3) * (sigma * sigma * sigma / xi_f3 - sigma * sigma / xi_f2);
t2 = (1.0 + phi/(phi - phi_0) + (phi/(phi - phi_0)) * (phi/(phi - phi_0))) * ((phi_0 / xi_f3) * log(1.0 - xi_f3 / phi_0) + 1.0) \
+ (1 + phi/(phi - phi_0)) * (xi_f3 / phi_0 / 2.0 / (1.0 - xi_f3 / phi_0)) \
- (xi_f3 / phi_0 / (1.0 - xi_f3 / phi_0)) * (xi_f3 / phi_0 / (1.0 - xi_f3 / phi_0)) / 6.0 \
+ ((phi/(phi - phi_0)) * (phi/(phi - phi_0)) * (phi/(phi - phi_0))) * ((1.0 - phi / xi_f3) * log(1.0 - xi_f3 / phi) - (1.0 - phi_0 / xi_f3) * log(1.0 - xi_f3 / phi_0));
t3 = 2.0 * B * (4.0 * M_PI * R * R * R * (rho_1 + rho_2) / 3.0 / xi_f3) * (phi / P1(sigma,flag) - 1.0) * (phi/(phi - phi_0)) \
* ( (phi_0/(phi - phi_0)) * ( 1.0 + 2.0 * phi / (phi - phi_0) ) * ( phi_0 * log(1.0 - xi_f3 / phi_0) / xi_f3 + 1.0) + (phi/(phi - phi_0)) * (phi/(phi - phi_0)) * ( phi * log(1.0 - xi_f3 / phi) / xi_f3 + 1.0 ) \
+ ( phi_0/(phi - phi_0) ) * ( xi_f3 / phi_0 / 2.0 / ( 1.0 - xi_f3/phi_0) ) + ( 3.0 * phi_0 * phi * phi / (phi - phi_0) / (phi - phi_0) / (phi - phi_0) ) * ( (1.0 - phi / xi_f3) * log(1.0 - xi_f3 / phi) - (1.0 - phi_0 / xi_f3) * log(1.0 - xi_f3 / phi_0) ));
t4 = ( 4.0 * M_PI * R * R * R * (rho_1 + rho_2) / 3.0 / xi_f3 ) \
* 2.0 * B * ( -1.0 * (1.0 + (phi / (phi - phi_0)) + (phi / (phi - phi_0)) * (phi / (phi - phi_0)) ) \
* (phi_0 * log(1.0 - xi_f3 / phi_0) / xi_f3 + 1.0 / ( 1.0 - xi_f3 / phi_0) ) \
+ (1.0 + phi / (phi - phi_0)) * (xi_f3 / phi_0) / 2.0 / (1.0 - xi_f3 / phi_0) / (1.0 - xi_f3 / phi_0) \
- (xi_f3/phi_0)*(xi_f3/phi_0)/3.0/(1.0 - xi_f3 / phi_0)/(1.0 - xi_f3 / phi_0)/(1.0 - xi_f3 / phi_0)\
+ ((phi/(phi - phi_0)) * (phi/(phi - phi_0)) * (phi/(phi - phi_0))) * ((phi / xi_f3) * log(1.0 - xi_f3 / phi) - (phi_0 / xi_f3) * log(1.0 - xi_f3 / phi_0) )) ;
x = miu_SPT2d(sigma,rho,flag) + t1 * t2 + t3 + t4;
return x;
}