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I created script which draw plot of Lennard Jones potential for two particles. Now i want to create 2D simulation for 10 particles with verlet alghoritm but I have no idea how to create that. My problem is implementation of verlet alghoritm and calculating forces. I implemented boundaries and drawing of particles but I do not know how to calculate force properly using verlet alghoritm so I cant implement moving properly.Someone have solution of that problem? Any advices would be useful.

Below I present my code for plot.

Code (Python):import numpy as np

import matplotlib.pyplot as plt

sigma = 1

e = 1

r = np.zeros([1001])

v = np.zeros([1001])

t = np.zeros([1001])

a = np.zeros([1001])

dt = 0.01

r[0] = 1

def LJ(r):

return -24*e*((2/r*(sigma/r)**12)-1/r*(sigma/r)**6)

def verlet():

for i in range(0,1000):

a[i] = -LJ(r[i])

r[i+1] = r[i] + dt*v[i]+0.5*dt**2*a[i]

a[i+1] = -LJ(r[i+1])

v[i+1] = v[i] + 0.5*dt*(a[i]+a[i+1])

t[i+1] = t[i]+dt

verlet()

plt.plot(r,a)

plt.axis([1, 2, -2.5, 2.5 ])

plt.show()

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# Verlet alghoritm and Lennard Jones simulation in Python

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