Scaling properties of the number of random sequential adsorption iterations needed to generate saturated random packing

TL;DR

This paper investigates how the number of iterations in random sequential adsorption (RSA) to achieve saturated packings scales with size and dimension, revealing a Pareto distribution and power-law behavior.

Contribution

It provides analytical and numerical insights into the distribution and scaling of RSA iterations across dimensions, aiding in simulation design.

Findings

Number of RSA iterations follows a Pareto distribution with exponent -1-1/d.

Median iterations scale with packing size as a power-law with exponent d.

Results are supported by analytical calculations valid for any dimension.

Abstract

The properties of the number of iterations in random sequential adsorption protocol needed to generate finite saturated random packing of spherically symmetric shapes were studied. Numerical results obtained for one, two, and three dimensional packings were supported by analytical calculations valid for any dimension $d$. It has been shown that the number of iterations needed to generate finite saturated packing is subject to Pareto distribution with exponent $-1-1/d$ and the median of this distribution scales with packing size according to the power-law characterized by exponent $d$. Obtained resultscan be used in designing effective RSA simulations.