Analytical structure factors

The analytical namespace implements a Percus–Yevick hard-sphere model. It is useful when you want a fast structure-factor calculation without generating an explicit packing configuration.

import numpy as np

from PackLab import analytical
from PackLab.units import ureg

radii = [100, 150] * ureg.nanometer
number_fractions = [0.7, 0.3]
domain = analytical.PercusYevickDomain(
    size=10 * ureg.micrometer,
    radii=radii,
    volume_fraction=0.15,
    number_fractions=number_fractions,
)
distances = np.linspace(0.2, 1.5, 300) * ureg.micrometer
solver = analytical.PercusYevickSolver(
    densities=domain.particle_densities_per_radius,
    radii=domain.radii,
    wavenumber="auto",
)
result = solver.compute(distances=distances)

The solver result contains the evaluated wavenumber grid and the associated structure factor. With wavenumber="auto", PackLab uses zero as the minimum, one twentieth of the smallest particle radius as the real-space resolution, and 12 samples per sinc-kernel oscillation at the largest requested distance. Pass radial_resolution=... or samples_per_oscillation=... to tune that selection. make_wavenumber_grid remains available when you need to provide the grid explicitly. The solver emits a RuntimeWarning when an explicit grid has fewer than eight samples per sinc-kernel oscillation.

The model assumes an idealised hard-sphere fluid. It is therefore a useful reference for Monte-Carlo results, rather than a replacement for an RSA configuration with finite size, boundaries, and a chosen radius sampler.

Examples

The analytical gallery starts with the two common equilibrium cases:

• Monodisperse Percus–Yevick fluid at several densities shows how density changes the monodisperse pair correlation.

• Binary-mixture Percus–Yevick pair correlations resolves like- and unlike-species correlations in a binary mixture.

• Percus Yevick mixture solver workflow converts a continuous size distribution to a multi-class mixture.

Use Scattering calculations when the Percus–Yevick correlation tensor is to be combined with optical single-particle amplitudes.