Assumptions and limitations

PackLab provides complementary models, not interchangeable ways to obtain the same result. Record the physical inputs and choose the workflow whose assumptions match the question.

Common inputs

Radii, number fractions, volume fraction, domain dimensions, and boundary conditions define the physical system. Use explicit units for every dimensional input. A radius distribution is not merely a numerical setting: it changes the mixture composition and its structure.

RSA

Random sequential adsorption produces non-overlapping configurations by irreversible deposition. Accepted spheres never move, so early random choices can block later placements. RSA is appropriate for deposition-like packings and for workflows that require explicit sphere centres. It is not an equilibrium hard-sphere sampler.

Check the stopping criterion, random seed, realised packing fraction, and box size. A configuration can be valid yet still be too small or too sparse for a stable bulk correlation estimate.

Metropolis Monte Carlo

Metropolis moves target an equilibrium hard-sphere system at fixed particle count and volume. A valid RSA packing is a convenient initial state, but its deposition history must be forgotten through burn-in before collecting data. Assess stationarity, autocorrelation, acceptance rate, and sensitivity to box size; a fixed sweep count alone is not evidence of equilibration.

Percus–Yevick

The analytical workflow is a Percus–Yevick approximation for an equilibrium hard-sphere mixture. It supplies pair correlations and structure factors quickly, but does not create centres, represent deposition history, or remove finite-size effects from a simulation. Verify numerical resolution by refining the wavenumber grid when real-space correlations are important.

Scattering

Scattering is optional and uses PyMieSim for the single-particle optical amplitudes. A mixture phase function additionally depends on the supplied structure tensor. When that tensor comes from Percus–Yevick, the scattering result is structure-aware but remains an analytical equilibrium prediction, not a scattering calculation from an RSA configuration.

Comparisons

When comparing workflows, match radii, composition, total volume fraction, boundary conditions, and the definition and resolution of the observable. Agreement between equilibrated Metropolis samples and Percus–Yevick tests an analytical approximation. Differences between RSA and Percus–Yevick are often expected because they describe different physical processes.