Added new codes

2018-05-17 22:24:48 -04:00
parent e7b42c6db5
commit f459b195f4
3 changed files with 151 additions and 2 deletions
@@ -0,0 +1,45 @@
+# Program to test the Metropolis algorithm with one particle at given temp in
+# one dimension
+#!/usr/bin/env python
+import numpy as np
+import matplotlib.mlab as mlab
+import matplotlib.pyplot as plt
+import random
+from math import sqrt, exp, log
+# initialize the rng with a seed
+random.seed()
+# Hard coding of input parameters
+MCcycles = 100000
+Temperature = 2.0
+beta = 1./Temperature
+InitialVelocity = -2.0
+CurrentVelocity = InitialVelocity
+Energy = 0.5*InitialVelocity*InitialVelocity
+VelocityRange = 10*sqrt(Temperature)
+VelocityStep = 2*VelocityRange/10.
+AverageEnergy = Energy
+AverageEnergy2 = Energy*Energy
+VelocityValues = np.zeros(MCcycles)
+# The Monte Carlo sampling with Metropolis starts here
+for i in range (1, MCcycles, 1):
+    TrialVelocity = CurrentVelocity + (2.0*random.random() - 1.0)*VelocityStep
+    EnergyChange = 0.5*(TrialVelocity*TrialVelocity -CurrentVelocity*CurrentVelocity);
+    if random.random() <= exp(-beta*EnergyChange):
+        CurrentVelocity = TrialVelocity
+        Energy += EnergyChange
+        VelocityValues[i] = CurrentVelocity
+    AverageEnergy += Energy
+    AverageEnergy2 += Energy*Energy
+#Final averages
+AverageEnergy = AverageEnergy/MCcycles
+AverageEnergy2 = AverageEnergy2/MCcycles
+Variance = AverageEnergy2 - AverageEnergy*AverageEnergy
+print(AverageEnergy, Variance)
+n, bins, patches = plt.hist(VelocityValues, 400, facecolor='green')
+
+plt.xlabel('$v$')
+plt.ylabel('Velocity distribution P(v)')
+plt.title(r'Velocity histogram at $k_BT=2$')
+plt.axis([-5, 5, 0, 600])
+plt.grid(True)
+plt.show()