Mean Square Displacement in 1D Random Walk
by Maciej Matyka
I realized that calculating MSD (mean square displacement) may be a little tricky for students and beginners. Have a look here, this may help to demistify it a little bit. It is a C++ implementation based on simple 1D random walk.
Reference: https://en.wikipedia.org/wiki/Mean_squared_displacement
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Results:
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| Exeplary trajectory of particle in 1D |
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| MSD calculated with the code in this post. |
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/**
* Mean Square Displacement
* Definition: https://en.wikipedia.org/wiki/Mean_squared_displacement
* Implementation by Maciej Matyka
* 14-03-2018 http://panoramix.ift.uni.wroc.pl/~maq/eng/
**/
#include <iostream>
#include <cstdlib>
#include <ctime>
using namespace std;
int main(void)
{
srand(time(NULL));
float x0=0, y0=0;
float x=x0,y=y0;
float xn = 0; // position at step n
int STEPS = 100000;
float averagex =0;
float msd = 0;
for(int N=0; N<1000; N++)
{
averagex =0;
msd = 0;
for(int s=0; s<STEPS;s++)
{
x=x0;
for(int t=0; t<N; t++)
{
float dx = rand()/float(RAND_MAX); // 1d random walk
if(dx>0.5) dx=1; else dx=-1;
x = x+dx;
}
averagex = averagex + x;
msd = msd + (x-x0)*(x-x0);
}
averagex/=(float)STEPS;
msd/=(float)STEPS;
cout << N << "\t" << averagex << "\t" << msd << endl;
}
}
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