Random packing of spheres in Menger sponge

TL;DR

This study investigates the properties of randomly packed spheres within fractal collectors of non-integer dimension using RSA, focusing on saturation limits, scaling behaviors, and validating dimensional relations for such complex systems.

Contribution

It provides the first detailed numerical analysis of sphere packing saturation and autocorrelation scaling in fractal collectors with non-integer dimensions.

Findings

Saturation density follows phenomenological relations with collector dimension.

RSA kinetics coefficients are quantified.

Dimensional relations hold for non-integer dimensions below 3.

Abstract

Random packing of spheres inside fractal collectors of dimension 2 < d < 3 is studied numerically using Random Sequential Adsorption (RSA) algorithm. The paper focuses mainly on the measurement of random packing saturation limit. Additionally, scaling properties of density autocorrelations in the obtained packing are analyzed. The RSA kinetics coefficients are also measured. Obtained results allow to test phenomenological relation between random packing saturation density and collector dimension. Additionally, performed simulations together with previously obtained results confirm that, in general, the known dimensional relations are obeyed by systems having non-integer dimension, at least for d < 3.