vrorv.py

#!/usr/bin/env python

"""
These are the Langevin integrators
"""

import numpy as np
import math
vt = 1 #initial velocity
deltat = 4 #timestep
m = 1 #mass
fofxt = np.array([1, 1, 1]) #force

vtonefourth = vt + ((deltat / 2) * (1 / m) * fofxt); #first Langevin integrator

print ("Vt 1/4 is", vtonefourth)


xt = np.array([1, 1, 1])  #initial position

xthalf = xt + ((deltat / 2) * vtonefourth); #second Langevin integrator

print ("Xt 1/2 is", xthalf)

gamma = (1) / (500 * deltat)
gammat = (-1 * gamma * deltat)
e = math.exp(gammat) #base e
y = (2 * gammat)
e2 = math.exp(y)
z = (1) - (e2)
x = math.sqrt(z)
kB = 1.38064852 ** (-23)
zeta = np.random.randn()
#zeta = 3
T = 0.9 
vtthreefourths = (e * vtonefourth) + (z * (math.sqrt(T)) * zeta) #third Langevin integrator

print ("Vt 3.4 is", vtthreefourths)

x1 = xthalf + (deltat / 2) * (vtthreefourths)

print ("x1 is", x1)


fofxt1 = np.array([2, 2, 2])

v1 = vtthreefourths + ((deltat / 2) * (1 / m) * fofxt1) #fifth Langevin integrator

print ("v1 is", v1)