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Effective_Interaction
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#include <iostream>
#include <cmath>
#include <stdlib.h>
#include <fstream>
extern int Baxtor(double* ueff, double* sk, double * p_prs, double* r, int M, int N_sig, double beta, double rho, double dr, double mix, double Pe, bool Lable_HI);
using namespace std;
int Potential(double* r,const int M,const double sigma, double epsi, double* u,double* du, double *ddu)
{
int i;
ofstream fout;
fout.open("data/potential.dat");
//For Lenard-Jones
for(i=0;i<M;i++){
u[i] = 4.0*epsi*(pow(sigma/r[i],12)-pow(sigma/r[i],6));
du[i] = 4.0*epsi*(-12.0*pow(sigma/r[i],13)/sigma+6.0*pow(sigma/r[i],7)/sigma);
ddu[i]= 4.0*epsi*(156.0*pow(sigma/r[i],14)/sigma/sigma-42.0*pow(sigma/r[i],8)/sigma/sigma);
fout<<r[i]<<" "<<u[i]<<endl;
}
//For r^-12 potential
/*for(i=0;i<M;i++){
u[i] = pow(sigma/r[i],12);
du[i] = -12.0*pow(sigma/r[i],13)/sigma;
ddu[i]=156.0*pow(sigma/r[i],14)/sigma/sigma;
fout<<r[i]<<" "<<u[i]<<endl;
}*/
//For WCA potential
/*double core = 4;
double cut = pow(2.0, 1.0/6.0) * sigma;
i=0;
while(r[i] < cut){
u[i] = 4.0*core*(pow(sigma/r[i],12)-pow(sigma/r[i],6)) + 4.0*(epsi-core)*(pow(sigma/cut,12)-pow(sigma/cut,6));
du[i] = 4.0*core*(-12.0*pow(sigma/r[i],13)/sigma+6.0*pow(sigma/r[i],7)/sigma);
ddu[i]= 4.0*core*(156.0*pow(sigma/r[i],14)/sigma/sigma-42.0*pow(sigma/r[i],8)/sigma/sigma);
fout<<r[i]<<" "<<u[i]<<endl;
i++;
}
while(i<M){
u[i] = 4.0*epsi*(pow(sigma/r[i],12)-pow(sigma/r[i],6));
du[i] = 4.0*epsi*(-12.0*pow(sigma/r[i],13)/sigma+6.0*pow(sigma/r[i],7)/sigma);
ddu[i]= 4.0*epsi*(156.0*pow(sigma/r[i],14)/sigma/sigma-42.0*pow(sigma/r[i],8)/sigma/sigma);
fout<<r[i]<<" "<<u[i]<<endl;
i++;
}*/
fout.close();
return 0;
}
int Effective_Potential(int M, double delta_r, double beta, double* du, double* ddu,
double tau_p, double v0, double Dt, double* u_eff)
{
int i;
double Pe=v0/Dt, Da = v0*v0*tau_p/3.0;
double* Di = new double [M];
for(i=0;i<M;i++){
Di[i] = Dt + Da / (1.0 + tau_p * Dt * beta * ddu[i]);
}
double* dDi = new double [M];
for(i=1;i<M;i++) dDi[i] = (Di[i]-Di[i-1])/delta_r;
dDi[0] = 2.0*dDi[1]-dDi[2];
double* Feff = new double [M];
for(i=0;i<M;i++){
Feff[i] = (-Dt*du[i]-dDi[i]/beta) / Di[i];
}
char fn[30];
sprintf(fn, "data/eff_pot_%3.0f.dat", Pe);
ofstream fout;
fout.open(fn);
u_eff[M-1] = 0.0;
for(i=M-2;i>=0;i--){
u_eff[i]=u_eff[i+1] + delta_r * Feff[i];
}
for (i=0;i<M;i++)
fout<<delta_r*i+delta_r/2<<" "<<u_eff[i]<<endl;
delete [] Di;
delete [] dDi;
delete [] Feff;
fout.close();
return 0;
}
int Effective_Potential_HI(int M, int N_sig, double sigma, double delta_r, double beta, double* du, double* ddu,
double* r, double tau_p, double v0, double Dt, double* u_eff)
{
int i;
double Pe=v0/Dt, radius = sigma/2.0; //adjustable
double* lmn = new double [M];
double* Di = new double [M];
for(i=0;i<N_sig;i++){
lmn[i] = Dt * (1.0-3.0*r[i]/(16.0*radius));
}
for(i=N_sig;i<M;i++){
lmn[i] = Dt*(3.0*radius*r[i]*r[i]-2.0*pow(radius,3))/(2.0*pow(r[i],3));
}
double Da = v0*v0*tau_p/3.0;
double* dDi = new double [M];
for(i=0;i<M;i++){
Di[i] = Dt + Da / (1.0 + tau_p * Dt * beta * (Dt-lmn[i]) *ddu[i]);
}
for(i=1;i<M;i++) dDi[i] = (Di[i]-Di[i-1])/delta_r;
dDi[0] = 2.0*dDi[1]-dDi[2];
double* Feff = new double [M];
for(i=0;i<M;i++){
Feff[i] = -du[i]*(Dt-lmn[i])/(Di[i]-lmn[i]) - dDi[i]/(beta*(Di[i]-lmn[i]));
}
char fn[30];
sprintf(fn, "data/eff_pot_%3.0f_HI.dat", Pe);
ofstream fout;
fout.open(fn);
u_eff[M-1] = 0.0;
for(i=M-2;i>=0;i--){
u_eff[i]=u_eff[i+1] + delta_r * Feff[i];
}
for (i=0;i<M;i++)
fout<<delta_r*i+delta_r/2<<" "<<u_eff[i]<<endl;
delete [] lmn;
delete [] dDi;
delete [] Di;
delete [] Feff;
fout.close();
return 0;
}
int evolution() {
const int N_total = 2000;
const int N_sig = 200; /*number in a diameter*/
double sigma = 1.0; /*diameter*/
double beta = 1.0;
double epsi = 1.0; /*LJ potential*/
double delta_r = sigma/N_sig; /**/
double Dt = 1.0/beta; /*translational diffusion*/
double tau = 0.01; /*dimensionless persistent time*/
double tau_p = tau * sigma * sigma / Dt; /*time dimension*/
double mix = 0.90; /*mixing parameter*/ /*the Pe bigger, the mix larger*/
double Pe = 0.0; /*Pelect number*/
double Rho = 0.1; /*number density*/
double v0 = Pe*Dt/sigma;
double *p_prs, prs1, prs2;
double r[N_total], sk[N_total];
double u[N_total];
double du[N_total], ddu[N_total], u_eff[N_total], u_eff_HI[N_total] ;
int i;
for(i=0;i<N_total;i++){
r[i]=delta_r/2.0 + delta_r*i;
}
Potential(r, N_total, sigma, epsi, u, du, ddu);
/*Effective_Potential(N_total, delta_r, beta, du, ddu, tau_p, v0, Dt, u_eff);
Baxtor(u_eff, sk, p_prs r, N_total, N_sig, beta, Rho, delta_r, mix, Pe, 0);
Effective_Potential_HI(N_total, N_sig, sigma, delta_r, beta, du, ddu, r, tau_p, v0, Dt, u_eff_HI);
Baxtor(u_eff_HI, sk, p_prs r, N_total, N_sig, beta, Rho, delta_r, mix, Pe, 1); */
//Pressure
char fn[30];
sprintf(fn, "data/presure.dat");
ofstream fout;
fout.open(fn);
double range[10] = {0, 5, 10, 20, 40, 80}; //{0, 5, 10, 20, 40, 80};
for (i=0; i<10; i++) {
if (i>1 && range[i]<1.0e-9)
break;
Effective_Potential(N_total, delta_r, beta, du, ddu, tau_p, range[i], Dt, u_eff);
p_prs = &prs1;
Baxtor(u_eff, sk, p_prs, r, N_total, N_sig, beta, Rho, delta_r, mix, range[i], 0);
p_prs = &prs2;
Effective_Potential_HI(N_total, N_sig, sigma, delta_r, beta, du, ddu, r, tau_p, range[i], Dt, u_eff_HI);
Baxtor(u_eff_HI, sk, p_prs, r, N_total, N_sig, beta, Rho, delta_r, mix, range[i], 1);
fout<< range[i] <<" "<< prs1 << " "<< prs2 <<endl;
printf("%d \n", i);
}
/*double Pe_upper=60, Pe_lower=40;
do {
Pe = (Pe_upper + Pe_lower)/2.0;
v0 = Pe * Dt/sigma;
Effective_Potential(N_total, delta_r, beta, du, ddu, tau_p, v0, Dt, u_eff);
Baxtor(u_eff, sk, p_prs, r, N_total, N_sig, beta, Rho, delta_r, mix, Pe, 0);
if (sk[1]<0.0) { //divergence criteria
Pe_upper = Pe;
continue;
}
Pe_lower = Pe;
} while (Pe_upper - Pe_lower>1.0);
Pe_upper=60;
Pe_lower=40;
do {
Pe = (Pe_upper + Pe_lower)/2.0;
v0 = Pe * Dt/sigma;
Effective_Potential_HI(N_total, N_sig, sigma, delta_r, beta, du, ddu, r, tau_p, v0, Dt, u_eff_HI);
Baxtor(u_eff_HI, sk, p_prs, r, N_total, N_sig, beta, Rho, delta_r, mix, Pe, 1);
if (sk[1]<0.0) { //divergence criteria
Pe_upper = Pe;
continue;
}
Pe_lower = Pe;
} while (Pe_upper - Pe_lower>1.0);*/
fout.close();
return 0;
}