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md.cc
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md.cc
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#include <stdlib.h>
#include <stdio.h>
#include <time.h>
#include <math.h>
#include <string.h>
#include <iostream>
#include <omp.h>
using namespace std;
//parameters
#define L 50 //lattice length
#define dx 10 //lattice spacing
#define Lx (L/dx) //renormalised length
#define N (Lx*Lx*Lx) // 125 particles (Lx*Lx*Lx) //total number of particles
#define NSTEP 5000000 //total number of time steps
//constants
double const vmax = 2.7; //T_LJ = 2.4
double const dt = 0.001;
double const rcut = 3.0;
double const rcut2 = rcut*rcut;
double const halfdtdt = 0.5*dt*dt;
double const halfdt = 0.5*dt;
//variables
double x[N];
double y[N];
double z[N];
double vx[N];
double vy[N];
double vz[N];
double fx[N];
double fy[N];
double fz[N];
double fx0[N];
double fy0[N];
double fz0[N];
double xi[N];
double yi[N];
double zi[N];
double T; //reduced temperature
double D; //diffusion constant
int i, j;
double r6, r12;
// file output
FILE *file[10];
const char *dirs[] = { "./data/x.dat" , "./data/y.dat","./data/z.dat" ,"./data/vx.dat","./data/vy.dat","./data/vz.dat","./data/fx.dat","./data/fy.dat","./data/fz.dat", "./data/temperature_diffusion-coefficient.dat" };
const char *headers[] = { "#X(t) Coordinates\n#Time(t)\t","#Y(t) Coordinates\n#Time(t)\t","#Z(t) Coordinates\n#Time(t)\t","#X(t) Velocities\n#Time(t)\t","#Y(t) Velocities\n#Time(t)\t","#Z(t) Velocities\n#Time(t)\t","#X(t) Forces\n#Time(t)\t","#Y(t) Forces\n#Time(t)\t","#Z(t) Forces\n#Time(t)\t", "#Time(t)\tTemperature (t)\tDiffusion coefficient (t)" };
//functions
void initialize_force_positions_velocities();
void update_force_positions_velocities(int *);
void lennard_jones_force();
void temperature(double *);
void diffusion_coefficient(double *, double *, double *, int *);
void file_write(int *, double *, double *);
void file_start();
void file_end();
// main program
int main(int argc, char *argv[])
{
double v2, rms, time_spent, r20, T, D=0; int k=0; // double r2, v2, r20, rms, time_spent;
srand48(time(0)); // time-based seed for random initial particle velocities
// Open files
printf("Preparing output files...\n");
for(int fi=0; fi<10; fi++ ){
file[fi] = fopen(dirs[fi],"w");
}
file_start();
//
// INITIATE: particle positions & velocities & forces //
//
printf("Initiating particle's coordinates and velocities...\n");
initialize_force_positions_velocities();
file_write(&k, &T, &D);
////////////////////////
// Main Loop (t + dt) //
////////////////////////
printf("Simulating particle's dynamics...\n");
for(int k=1; k<NSTEP; k++){
if(k%2000==0){
printf("\t %f percent\n",((double)k/NSTEP)*100.0); // progress
}
//
// Update: particle positions, velocities & forces
//
update_force_positions_velocities( &k );
//
// Macroscopic Properties: (i) temperature, (ii) diffusion
//
temperature( &T );
diffusion_coefficient( &D, &rms, &r20, &k );
if (k%1000==0){
file_write( &k, &T, &D ); // write every 1000 time-steps
}
}
//
// Finish
//
file_end();
k=NSTEP;
srand48(time(0)); // time-based seed for random initial particle velocities
printf("Temperature: %f\tr2=%f\trms=%f\tDiffusion: %f\n", T, r20/N, sqrt(rms), D);
return 0;
}
///////////////
// FUNCTIONS //
///////////////
void initialize_force_positions_velocities()
{
/* (i) Position initialisation*/
int l;
for(int i = 0; i < Lx; i++){
for(int j = 0; j < Lx; j++){
for(int k = 0; k < Lx; k++){
l = (i*Lx*Lx + j*Lx + k);
x[l] = i*dx;
y[l] = j*dx;
z[l] = k*dx;
}
}
}
/* (ii) Velocity initialisation*/
double vxcm, vycm, vzcm = 0.;
for(int i = 0; i < N; i++){
vx[i] = vmax*(2.*drand48()-1.); // <V2a>=Kb*T/m
vy[i] = vmax*(2.*drand48()-1.);
vz[i] = vmax*(2.*drand48()-1.);
vxcm += vx[i]; // summing velocities (for subtracting center of mass V)
vycm += vy[i];
vzcm += vz[i];
}
/* (iii) Subtract center of mass velocities*/
vxcm /= N; // averaging velocities (for subtracting center of mass V)
vycm /= N;
vzcm /= N;
for(int i = 0; i < N; i++){
vx[i] -= vxcm;
vy[i] -= vycm;
vz[i] -= vzcm;
}
/* (v) Force initialization */
lennard_jones_force();
/* (vi) Temperature initialization */
temperature(&T);
}
void lennard_jones_force() //total force
{
double r2, xmin, ymin, zmin, diff, f;
for(int i = 0; i<N; i++){
fx[i] = 0;
fy[i] = 0;
fz[i] = 0;
}
# pragma omp parallel \
shared ( fx,fy,fz, x,y,z, vx,vy,vz ) \
private ( i, j, xmin,ymin,zmin, r2, r6, r12, f )
# pragma omp for
//Pairwise forces, particles i vs. j
for(int i = 0; i<N; i++){
for(int j = i+1; j<N; j++){
// Periodic Boundary Conditions
xmin = ((x[i]-x[j]) - L*round((x[i]-x[j])/L));
ymin = ((y[i]-y[j]) - L*round((y[i]-y[j])/L));
zmin = ((z[i]-z[j]) - L*round((z[i]-z[j])/L));
// Sq. distance, i vs j
r2 = xmin*xmin + ymin*ymin + zmin*zmin;
// Ignore i,j particles's forces > rcut2 distance
if(r2 < rcut2){
// r6 = r2*r2*r2;
// r12 = r6*r6;
f = (48./pow(r2,8) - 24./pow(r2,4)); //LJ-potential
fx[i] += f*xmin;
fy[i] += f*ymin;
fz[i] += f*zmin;
fx[j] -= f*xmin;
fy[j] -= f*ymin;
fz[j] -= f*zmin;
}
}
}
}
void update_force_positions_velocities(int *k) //one time step move dt
{
// UPDATE PARTICLES': Positions (x,y,z), then velocities (vx,vy,vz) according to forces
// MOVE_R: update particle positions
for(int i = 0; i < N; i++){
x[i] += dt*vx[i] + halfdtdt*fx[i]; //updated positions
y[i] += dt*vy[i] + halfdtdt*fy[i];
z[i] += dt*vz[i] + halfdtdt*fz[i];
fx0[i] = fx[i]; // fx0, fy0, fz0 store forces at f(t)
fy0[i] = fy[i];
fz0[i] = fz[i];
}
// FORCE: update forces
lennard_jones_force(); // fx, fy and fz stores forces for f(t+1)
// MOVE_V: update particle velocities
for(int i = 0; i < N; i++){
vx[i] += halfdt*(fx0[i] + fx[i]); //updated velocities
vy[i] += halfdt*(fy0[i] + fy[i]);
vz[i] += halfdt*(fz0[i] + fz[i]);
}
// positions at t0 = k = 1000 stored for diffusion coefficient
if(*k==1000){
for(int i = 0; i < N; i++){
xi[i]=x[i]; yi[i]=y[i]; zi[i]=z[i];
}
}
}
void temperature(double *T)
{
// Temperatures calculated over all molecules
double v2 = 0.;
for(int i=0; i<N; i++){
v2 += (vx[i]*vx[i]) + (vy[i]*vy[i]) + (vz[i]*vz[i]);
}
*T = v2/(3*N);
}
void diffusion_coefficient(double *D, double *rms, double *r20, int *k)
{
// Diffusion coefficients calculated over all molecules
double r2 = 0;
*r20 = 0;
for(int i = 0; i < N; i++){
r2 += x[i]*x[i] + y[i]*y[i] + z[i]*z[i];
*r20 += xi[i]*xi[i] + yi[i]*yi[i] + zi[i]*zi[i];
}
*rms = (r2 - *r20)/N;
*D = *rms/(6.*(*k)*dt);
}
void file_start(){
// Files to store datarows (t), 1 particle per ith column
for(int fi=0; fi<9; fi++ )
{
fprintf(file[fi],"%s",headers[fi]);
for (int i = 0; i < N; i++){
fprintf(file[fi], "Molecule %i\t", i);
}
fprintf(file[fi], "\n");
}
// temperature
int fi = 9;
fprintf(file[fi], "%s\n", headers[fi]); // time
}
void file_write(int *k, double *T, double *D){
// @test: to save time
// Writing datarows (t), 1 particle per ith column
double *data[] = {x,y,z,vx,vy,vz,fx,fy,fz};
for(int fi=0; fi<9; fi++ ){
fprintf(file[fi], "%f\t", *k*dt); // time
for (int i = 0; i<N; i++){ // for each molecule
fprintf(file[fi], "%f\t", data[fi][i]);
}
fprintf(file[fi], "\n");
}
// temperature, diffusion coefficient
int fi = 9;
fprintf(file[fi], "%f\t%f\t%f\n", *k*dt, *T, *D); // time
}
void file_end(){
// close output files
for(int fi=0; fi<10; fi++ ){
fclose(file[fi]);
}
}