MEAN SQUARED DISPLACEMENT-1D RANDOM WALK

## Routine random walk(rw) for simulating
## one-dimensional random walk
## and calculating the mean squared displacement.
x2ave=[]; ## Initial array of the squared
## displacement at initial time(meters).
Nrw=3000; ## Number of walkers (Dimensionless).
beg=1000; ## Minimum step number ( // ).
inc=1000; ## Step number increment ( // ).
Nstepsmax=10000; ## Maximum step number ( // ).
dt=1; ## Time increment(second).
##Entering the nested loops.
for Nsteps=beg:inc:Nstepsmax; ## The loop through the number
Nsteps ## of steps each in walk.
x2=0; ## Initial squared location of all of the
## walkers at all steps.
for m=1:Nrw ## The loop through the desired
## number of walkers.
r=rand_disc_rev(Nsteps,0.5); ## Calling the rw generator
## function which will give column vector
## of each elements are either 1 or -1.
x2+=sum(r)^2; ## Total displacement squared whose
## elements stems from the vector r.
endfor
x2ave=[x2ave;x2/Nrw]; ## Accumulation of the squared displacements
endfor ## at the step Nsteps into the array x2ave(Nsteps).
## Exiting the nested loops. Continuing by constructing polynomials.
hold off
plot(dt*[beg:inc:Nstepsmax],x2ave,'b*;RawData;') ## Plot of the raw data
## of mean squared displament vs. step
## number or here the time.
[p,s]=polyfit(dt*[beg:inc:Nstepsmax]',x2ave,1); ## Calculate the coefficients
## p and the quality of measure s
## of the 'imaginary' polinomial, x2ave(Nsteps).
pval=polyval(p,dt*[beg:inc:Nstepsmax]); ## The values of the fit polynomial
## in the time interval dt*[beg,Nstepsmax].
hold on
plot(dt*[beg:inc:Nstepsmax],pval,'r-;Fit;') ## Plot of fit data of x2ave vs time.
hold off