Solution of exercise 1

exercise_1_final.py

import random
import pylab as plt

npart = 100
nsteps = 10000
dt = 0.001

X = [random.random() for i in range(npart)]
Y = [2*(random.random() - 0.5) for i in range(npart)]
dX = [2*(random.random() - 0.5) for i in range(npart)]
dY = [2*(random.random() - 0.5) for i in range(npart)]

# make nsteps steps
for n in range(nsteps):
  # loop over each particle
  for i in range(npart):
    # if the particle is exiting the box in the x-direction
    if abs(X[i] + dt*dX[i])>1:
      dX[i] = -dX[i]
    if abs(Y[i] + dt*dY[i])>1:
      dY[i] = -dY[i]

    # make the actual step
    X[i] = X[i]+dt*dX[i]
    Y[i] = Y[i]+dt*dY[i]

# plot final positions
plt.clf()
plt.plot(X,Y,'bo')
plt.axis((-1,1,-1,1))
plt.savefig('final_positions.png')