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import numpy as np
import scipy.stats as stats
import scipy.constants as const
from scipy.optimize import minimize
import matplotlib
import matplotlib.pyplot as plt
from boltzgas import HardSphereSetup, HardSphereSimulation
from boltzgas.initial_condition import grid_of_random_velocity_particles
grid_width = 30
radius = 0.002
char_u = 1120
position, velocity = grid_of_random_velocity_particles(grid_width, radius, char_u)
velocity[:,:] = 0
velocity[0,0] = 10.75*char_u
velocity[0,1] = -.25*char_u
config = HardSphereSetup(radius, char_u, position, velocity)
gas = HardSphereSimulation(config)
gas.setup()
m_nitrogen = 0.028 / const.N_A
def plot(step, velocities):
velocities = np.array([np.linalg.norm(v) for v in velocities])
maxwellian = stats.maxwell.fit(velocities)
print("T = %.0f K; u_mean = %.0f [m/s]; energy = %.05f" % ((maxwellian[1]**2 / const.k * m_nitrogen, stats.maxwell.mean(*maxwellian), np.sum([x**2 for x in velocities]))))
plt.figure()
plt.ylim(0, 0.003)
plt.ylabel('Probability')
plt.xlim(0, 1.2*char_u)
plt.xlabel('Velocity magnitude [m/s]')
plt.hist(velocities, bins=50, density=True, alpha=0.5, label='Simulated velocities')
xs = np.linspace(0, 1.2*char_u, 100)
plt.plot(xs, stats.maxwell.pdf(xs, *maxwellian), label='Maxwell-Boltzmann distribution')
plt.legend(loc='upper right')
plt.savefig("result/%04d.png" % step)
plt.close()
def simulate(n_steps, section):
for i in range(0, int(n_steps / section)):
print("Plot step %d." % (i * section))
velocities = gas.get_velocities()
for j in range(0,section):
gas.evolve()
plot(i, velocities)
simulate(100000, 1000)
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