Validation and comparison#
These examples make three complementary validation checks:
compare an ensemble of explicit, finite RSA packings with a matching Percus–Yevick reference, including the RSA standard error;
compare samples from a fixed-volume Metropolis hard-sphere chain with the same Percus–Yevick reference;
compare PackLab’s binary-mixture Percus–Yevick solution with digitised Percus–Yevick curves from Tsang et al. (2001);
compare PackLab’s monodisperse Percus–Yevick solution at $f=0.2$ and $f=0.3$ with digitised curves from the same reference;
verify convergence of the numerical Percus–Yevick inverse transform by refining its wavenumber grid.
RSA is an irreversible, history-dependent packing process. Metropolis samples the equilibrium hard-sphere ensemble only after adequate burn-in and sampling. Percus–Yevick is an analytical equilibrium reference, so agreement with RSA is informative but is not an expectation of exact equality.
Metropolis hard-sphere samples versus Percus–Yevick
PackLab Percus–Yevick versus the Tsang et al. reference
PackLab monodisperse Percus–Yevick versus Tsang et al.
