#include <iostream>
#include <fstream>
#include <math.h>
#include <stdlib.h>
#include <ctime>
using namespace std;
//**************************************************************
// 一维布朗运动
//
// 确定测量时间t，测量时间间隔dt，输出模式output_opt。点击运行。
// t取30分钟（即1800秒）左右
// 在t内进行100次以内的测量，即t/dt<=100
double t = 1800.;//s
double dt = 30.;//s
// 输出模式 1：观测时刻（秒），微粒坐标（微米），
// 观测时间间隔内微粒位移（微米）
// 输出模式 2：观测时刻微粒坐标（微米）
// 输出模式 3：观测时间间隔内微粒位移（微米）
int output_opt=1;
//**************************************************************
double temp = 293.;//K
double visc = 0.1;//cP=10^-3 Pa*s
double diam = 1.0;//micro meter=10^-6 m
double x0 = 0.;
double v0 = 0.;
int idg;//random seed
int main() {
srand((int)time(0));
int np = int(t / dt)+1;
double *x;
double tt;
void brown(double*,const int);
x = new double[np];
brown(x,np);
if(output_opt == 1){
cout << "时刻【秒】" << "\t" << "坐标【微米】" << "\t" << "位移【微米】" << endl;
cout << 0 << "\t" << "\t" << "\t" << x[0] << endl;
tt = dt;
for (int l = 1;l < np;l++) {
printf("%4.1f \t \t %5.6f \t %5.6f \n",tt,x[l],x[l]-x[l-1]);
tt = tt + dt;
}
}
else if(output_opt == 2){
for (int l = 0;l < np;l++) {
cout << x[l] << endl;
}
}
else if(output_opt == 3){
for (int l = 1;l < np;l++) {
cout << x[l]-x[l-1] << endl;
}
}
delete[] x;
return 0;
}
void brown(double *x,const int np){
const double kb = 1.380649;
const double masse = 1.0;//micro gram=10^-9 kg
double d = 0.1;//s
double kbT, A, stm, gamma;
double c1,c2;
int f,nt;
double *xx, *vv, *r;
double gaussnoise(int);
kbT = kb * temp / 100.;
A = 2.0 * kbT * 3.0 * 3.1415926 * visc * diam;
stm = sqrt(kbT / masse);
gamma = A / (2.0 * kbT);
c1 = 1. / (1. + gamma / masse * d);
c2 = d * sqrt(2. * gamma / masse / d);
f = int(dt / d);
if (f == 0) {
d = dt;
f = 1;
nt = np;
}
else {
d = dt / f;
nt = np * f;
}
xx = new double[nt];
vv = new double[nt];
r = new double[nt];
xx[0] = x0 / stm;
vv[0] = v0 / stm;
for (int j = 1;j < nt;j++) {
r[j] = gaussnoise(idg);
xx[j] = xx[j - 1] + d * vv[j - 1];
vv[j] = c1 * (vv[j - 1] + c2 * r[j]);
}
for (int j = 0;j < nt;j++) {
xx[j] = xx[j]*stm;
vv[j] = vv[j]*stm;
if (j == j / f * f) {
x[j/f] = xx[j];
}
}
delete[] xx;
delete[] vv;
delete[] r;
}
double gaussnoise(int idum1) {
int idum = idum1;
double gasdev;
int iset;
double fac, gset, rsq, v1, v2;
double U1, U2;
iset = 0;
gset = 0.0;
if (iset == 0) {
do {
U1 = (double)rand() / RAND_MAX;
U2 = (double)rand() / RAND_MAX;
v1 = 2. * U1 - 1;
v2 = 2. * U2 - 1;
rsq = v1 * v1 + v2 * v2;
} while (rsq >= 1 || rsq == 0);
fac = sqrt(-2. * log(rsq) / rsq);
gset = v1 * fac;
gasdev = v2 * fac;
iset = 1;
}
else {
gasdev = gset;
iset = 0;
}
return gasdev;
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