polydisperse_spheres

Overlapping spheres with a distribution of sizes

import inspect

import matplotlib.pyplot as plt
import numpy as np
import scipy.stats as spst

import porespy as ps

np.random.seed(10)
inspect.signature(ps.generators.polydisperse_spheres)

<Signature (shape: List, porosity: float, dist, nbins: int = 5, r_min: int = 5, seed=None)>

shape

Images can be 2D or 3D.

shape = [150, 150]
porosity = 0.5
dist = spst.norm(loc=10, scale=5)
im = ps.generators.polydisperse_spheres(shape=shape, porosity=porosity, dist=dist)

fig, ax = plt.subplots(1, 1, figsize=[6, 6])
ax.imshow(im, interpolation='none', origin='lower')
ax.axis(False);

porosity

Porosity controls how many spheres are added. The algorithms for determining the number of spheres to add is not very sophisticated, so the actual porosity is not perfect.

fig, ax = plt.subplots(1, 2, figsize=[12, 6])

porosity = 0.75
im1 = ps.generators.polydisperse_spheres(shape=shape, porosity=porosity, dist=dist)
ax[0].imshow(im1, interpolation='none', origin='lower')
ax[0].set_title(f'porosity = {im1.sum()/im1.size}')
ax[0].axis(False)

porosity = 0.5
im2 = ps.generators.polydisperse_spheres(shape=shape, porosity=porosity, dist=dist)
ax[1].imshow(im2, interpolation='none', origin='lower')
ax[1].set_title(f'porosity = {im2.sum()/im2.size}')
ax[1].axis(False);

dist

The statistical distribution from which sphere diameter should be drawn. This should be a handle to an initialized scipy.stats object:

fig, ax = plt.subplots(1, 2, figsize=[12, 6])

dist = spst.norm(loc=10, scale=5)
im1 = ps.generators.polydisperse_spheres(shape=shape, porosity=porosity, dist=dist)
ax[0].imshow(im1, interpolation='none', origin='lower')
ax[0].set_title(f'distribution = {dist.kwds}')
ax[0].axis(False)

dist = spst.norm(loc=5, scale=2)
im2 = ps.generators.polydisperse_spheres(shape=shape, porosity=porosity, dist=dist)
ax[1].imshow(im2, interpolation='none', origin='lower')
ax[1].set_title(f'distribution = {dist.kwds}')
ax[1].axis(False);

nbins

Spheres must be generated with discrete sizes, so this controls how many unique sizes are used. The default is 5.

fig, ax = plt.subplots(1, 2, figsize=[12, 6])

dist = spst.norm(loc=10, scale=5)
nbins = 3
im1 = ps.generators.polydisperse_spheres(shape=shape, porosity=porosity, dist=dist, nbins=nbins)
ax[0].imshow(im1, interpolation='none', origin='lower')
ax[0].set_title(f'nbins = {nbins}')
ax[0].axis(False)

nbins = 10
im2 = ps.generators.polydisperse_spheres(shape=shape, porosity=porosity, dist=dist, nbins=nbins)
ax[1].imshow(im2, interpolation='none', origin='lower')
ax[1].set_title(f'nbins = {nbins}')
ax[1].axis(False);

r_min

The smallest sphere to generate, essentially limiting the size of the smallest bin. The default is 5.

fig, ax = plt.subplots(1, 2, figsize=[12, 6])

dist = spst.norm(loc=10, scale=5)
r_min = 5
im1 = ps.generators.polydisperse_spheres(shape=shape, porosity=porosity, dist=dist, r_min=r_min)
ax[0].imshow(im1, interpolation='none', origin='lower')
ax[0].set_title(f'r_min = {r_min}')
ax[0].axis(False)

r_min = 2
im2 = ps.generators.polydisperse_spheres(shape=shape, porosity=porosity, dist=dist, r_min=r_min)
ax[1].imshow(im2, interpolation='none', origin='lower')
ax[1].set_title(f'r_min = {r_min}')
ax[1].axis(False);