def gibbsDist():
fig, ax = plt.subplots(1, 1)
mean, var, skew, kurt = maxwell.stats(moments='mvsk')
x = np.linspace(maxwell.ppf(0.01), maxwell.ppf(0.99), 100)
ax.plot(x, maxwell.pdf(x), 'r-', lw=5, alpha=0.6, label='maxwell pdf')
ax.legend(loc='best', frameon=False)
plt.show()
def set_initial_speeds(self) -> np.ndarray:
""" Function for sampling initial speeds for the atoms
from the maxwell-boltzman distribution. Here this is achieved
by means of the 'Inverse CDF sampling' method where sampling
N points from a given PDF is similar to evaluating its inverse CDF
on N uniformly distributed points (in Uniform(0,1)).
Returns:
--------
speeds: np.ndarray of shape (nr_particles,) containing floats
"""
PARENT_SAMPLE_SIZE = 1000000
u = np.random.uniform(low=0, high=1, size=PARENT_SAMPLE_SIZE)
scale_factor = np.sqrt(consts.k * self.temperature /
(self.mass)) # sqrt(kT/m)
speeds = maxwell.ppf(q=u,
scale=scale_factor) # ppf is inverse cdf in scipy
return speeds[:self.nr_particles]
def gen_velocities(v_0, v_Esc, v_E, num_object):
"""
Generates a list of velocities
"""
cdf_v_Esc = maxwell.cdf(v_Esc, scale=v_0 / np.sqrt(2))
velocity_r = maxwell.ppf(np.random.rand(num_object) * cdf_v_Esc,
scale=v_0 / np.sqrt(2)) # kpc/yr
velocity_theta = np.arccos(1 - 2 * np.random.rand(num_object))
velocity_phi = 2 * np.pi * np.random.rand(num_object)
velocity = np.zeros((3, num_object))
velocity[0] = velocity_r * np.sin(velocity_theta) * np.cos(velocity_phi)
velocity[1] = velocity_r * np.sin(velocity_theta) * np.sin(velocity_phi)
velocity[2] = velocity_r * np.cos(velocity_theta)
return velocity.T # (N, 3)
# for a particle
# In[8]:
temp = 400
kb = 1.380649e-23
# In[9]:
mean, var, skew, kurt = maxwell.stats(moments ='mvsk')
fig, ax = plt.subplots(1, 1)
x = np.linspace(maxwell.ppf(0.01),maxwell.ppf(0.99), 100)
ax.plot(x, maxwell.pdf(x), 'r-', lw=4, alpha=0.6, label='maxwell pdf')
plt.title('1D Maxwell-Boltzmann Distribution')
plt.xlabel('Speed (m/s)') # fix this
plt.ylabel('Probability Density (s/m)')
# In[10]:
m = 2*kb*temp/(np.pi*float(mean)**2)
print('At STP, \nmass of particle = %s kg' % (m))
# In[11]:
def hobbs_vdist2(x):
return maxwell.ppf(x)*265./10.
from scipy.stats import maxwell
import matplotlib.pyplot as plt
fig, ax = plt.subplots(1, 1)
# Calculate a few first moments:
mean, var, skew, kurt = maxwell.stats(moments='mvsk')
# Display the probability density function (``pdf``):
x = np.linspace(maxwell.ppf(0.01),
maxwell.ppf(0.99), 100)
ax.plot(x, maxwell.pdf(x),
'r-', lw=5, alpha=0.6, label='maxwell pdf')
# Alternatively, the distribution object can be called (as a function)
# to fix the shape, location and scale parameters. This returns a "frozen"
# RV object holding the given parameters fixed.
# Freeze the distribution and display the frozen ``pdf``:
rv = maxwell()
ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
# Check accuracy of ``cdf`` and ``ppf``:
vals = maxwell.ppf([0.001, 0.5, 0.999])
np.allclose([0.001, 0.5, 0.999], maxwell.cdf(vals))
# True
# Generate random numbers:
v = []
for i in range(n):
# Posición inicial
pos = (rd.uniform(-1,1)*L/2,rd.uniform(-1,1)*L/2,rd.uniform(-1,1)*L/2)
# Velocidad inicial
cos_theta = rd.uniform(-1,1)
phi = rd.uniform(0,2*np.pi)
theta = np.arccos(cos_theta)
f_inv_cdf = rd.uniform(0,1)
x = maxwell.ppf(f_inv_cdf)
v = x/escala
v_x = v*np.sin(theta)*np.cos(phi)
v_y = v*np.sin(theta)*np.sin(phi)
v_z = v*np.cos(theta)
bola = vs.sphere(pos=np.array(pos),radius=r,color=(0,0,1),v=np.array([v_x,v_y,v_z]))
bolas.append(bola)
# Funciones a utilizar
def centro_de_masas(bola1,bola2):
def get_v_maxwell(m, T):
"""Draw velocity from Maxwell-Boltzmann distribution with mean 0."""
s = np.sqrt(T / m)
x_rand = np.random.random(1)
return maxwell.ppf(x_rand, loc=0., scale=s)
