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ou_process.py
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#!/usr/bin/python3
import sys
import numpy as np
import pandas as pd
import matplotlib as mpl
mpl.rcParams['mathtext.fontset'] = 'stix'
mpl.rcParams['font.family'] = 'STIXGeneral'
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
def gaussian(x, mean, amplitude, variance):
return amplitude * np.exp( - (x - mean)**2 / (2*variance))
def expo(t, y0, gamma):
return y0*np.exp(-gamma*t)
def f_sigma(t, gamma, A):
return np.sqrt(A*(1-np.exp(-2*gamma*t)))
bins = int(sys.argv[1])
fig, ax = plt.subplots(1,3, layout='tight')
fig2, ax2 = plt.subplots(1,3, layout='tight')
data = pd.read_csv('results/prueba_r0.01.dat', header=None, delimiter='\t')
t=data.iloc[:,0]
avg = []
sigma = []
for i in range(len(t+1)):
vx = data.iloc[i,1:]
bin_heights, bin_borders = np.histogram(vx,bins)
bin_centers = bin_borders[:-1] +np.diff(bin_borders)/2
# try:
# popt, pcov = curve_fit(gaussian, bin_centers, bin_heights, [5,100,2])
# except:
# print(f'Not using gaussian for t={i} in gamma=0.1')
popt=[]; pcov=[]
popt.append(np.average(vx))
popt.append(np.var(vx))
avg.append(popt[0])
sigma.append(np.sqrt(popt[1]))
parms, parms_cov = curve_fit(expo, t, avg)
print('\ngamma=0.01')
print(parms)
print(parms_cov)
t_fit = np.linspace(0,250,1000)
v_fit = expo(t_fit,parms[0],parms[1])
ax[0].set_title(r'$\gamma=0.01$')
ax[0].grid()
ax[0].set_xlabel('Time')
ax[0].set_ylabel('Velocity')
ax[0].scatter(t, avg, s=1, color='black', label='Data')
textstr=(r'$\sigma=\sqrt{k_B T(1-e^{-2\gamma t})}$'
'\n'
r'$\gamma = 0.01021\pm 0.00001$')
ax[0].plot(t_fit,v_fit,color='red',label=textstr)
ax[0].legend(loc='upper right', fontsize=6)
parms2, parms_cov2 = curve_fit(f_sigma, t, sigma)
print(f'\n{parms2}')
print(parms_cov2)
t_fit = np.linspace(0,250,1000)
sigma_fit = f_sigma(t_fit,parms2[0], parms2[1])
ax2[0].grid()
ax2[0].set_title(r'$\gamma=0.01$')
ax2[0].set_xlabel('Time')
ax2[0].set_ylabel('Velocity Standard Deviation')
textstr=(r'$\sigma_v=\sqrt{k_B T(1-e^{-2\gamma t})}$'
'\n'
r'$\gamma = 0.1005\pm 0.0001$'
'\n'
r'$k_B T = 4.0191 \pm 0.0009$')
ax2[0].scatter(t,sigma,s=1,color='black')
ax2[0].plot(t_fit,sigma_fit,label=textstr)
ax2[0].legend(loc='lower right', fontsize=7)
data = pd.read_csv('results/prueba_r0.05.dat', header=None, delimiter='\t')
t=data.iloc[:,0]
avg = []
sigma = []
for i in range(len(t+1)):
vx = data.iloc[i,1:]
bin_heights, bin_borders = np.histogram(vx,bins)
bin_centers = bin_borders[:-1] +np.diff(bin_borders)/2
# try:
# popt, pcov = curve_fit(gaussian, bin_centers, bin_heights, [5,10,2])
# except:
# print(f'Not using gaussian for t={i} in gamma=0.5')
popt=[]; pcov=[]
popt.append(np.average(vx))
popt.append(np.var(vx))
avg.append(popt[0])
sigma.append(np.sqrt(popt[1]))
parms, parms_cov = curve_fit(expo, t, avg)
print('\ngamma=0.05')
print(parms)
print(parms_cov)
t_fit = np.linspace(0,200,1000)
v_fit = expo(t_fit,parms[0],parms[1])
ax[1].set_title(r'$\gamma=0.05$')
ax[1].grid()
ax[1].set_xlabel('Time')
ax[1].set_ylabel('Velocity')
#ax[1].set_xlim(0,40)
ax[1].scatter(t, avg, s=1, color='black', label='Data')
textstr=(r'$v=v_0 e^{-\gamma t}$'
'\n'
r'$\gamma = 0.504\pm 0.003$')
ax[1].plot(t_fit,v_fit,color='red',label=textstr)
ax[1].legend(loc='upper right', fontsize=8)
parms2, parms_cov2 = curve_fit(f_sigma, t, sigma)
print(f'\n{parms2}')
print(parms_cov2)
t_fit = np.linspace(0,200,1000)
sigma_fit = f_sigma(t_fit,parms2[0], parms2[1])
ax2[1].grid()
ax2[1].set_title(r'$\gamma=0.05$')
ax2[1].set_xlabel('Time')
ax2[1].set_ylabel('Velocity Standard Deviation')
textstr=(r'$\sigma_v=\sqrt{k_B T(1-e^{-2\gamma t})}$'
'\n'
r'$\gamma = 0.05086\pm 0.00008$'
'\n'
r'$k_B T = 4.0182 \pm 0.0009$')
ax2[1].scatter(t,sigma,s=1,color='black')
ax2[1].plot(t_fit,sigma_fit, label=textstr)
ax2[1].legend(loc='lower right', fontsize=7)
data = pd.read_csv('results/prueba_r0.1.dat', header=None, delimiter='\t')
t=data.iloc[:,0]
avg = []
sigma = []
for i in range(len(t+1)):
vx = data.iloc[i,1:]
bin_heights, bin_borders = np.histogram(vx,bins)
bin_centers = bin_borders[:-1] +np.diff(bin_borders)/2
#try:
# popt, pcov = curve_fit(gaussian, bin_centers, bin_heights, [5,10,2])
#except:
# print(f'Not using gaussian for t={i} in gamma=1')
popt=[]; pcov=[]
popt.append(np.average(vx))
popt.append(np.var(vx))
avg.append(popt[0])
sigma.append(np.sqrt(popt[1]))
parms, parms_cov = curve_fit(expo, t, avg)
print('\ngamma=0.1')
print(parms)
print(parms_cov)
t_fit = np.linspace(0,100,1000)
v_fit = expo(t_fit,parms[0],parms[1])
ax[2].set_title(r'$\gamma=0.1$')
ax[2].grid()
ax[2].set_xlabel('Time')
ax[2].set_ylabel('Velocity')
#ax[2].set_xlim(0,15)
ax[2].scatter(t, avg, s=1, color='black', label='Data')
textstr=(r'$v=v_0 e^{-\gamma t}$'
'\n'
r'$\gamma = 1.009\pm 0.006$')
ax[2].plot(t_fit,v_fit,color='red',label=textstr)
ax[2].legend(loc='upper right', fontsize=8)
parms2, parms_cov2 = curve_fit(f_sigma, t, sigma)
print(f'\n{parms2}')
print(parms_cov2)
t_fit = np.linspace(0,100,1000)
sigma_fit = f_sigma(t_fit,parms2[0], parms2[1])
ax2[2].grid()
ax2[2].set_title(r'$\gamma=0.1$')
ax2[2].set_xlabel('Time')
ax2[2].set_ylabel('Velocity Standard Deviation')
textstr=(r'$\sigma_v=\sqrt{k_B T(1-e^{-2\gamma t})}$'
'\n'
r'$\gamma = 0.0987\pm 0.0002$'
'\n'
r'$k_B T = 4.019 \pm 0.001$')
ax2[2].scatter(t,sigma,s=1,color='black')
ax2[2].plot(t_fit,sigma_fit,label=textstr)
ax2[2].legend(loc='lower right', fontsize=7)
#plt.show()
fig.savefig('results/vel_dist1.png',format='png',bbox_inches='tight',dpi=300)
fig2.savefig('results/vel_dist2.png',format='png',bbox_inches='tight',dpi=300)