Extended series expansions for random sequential adsorption

TL;DR

This paper develops extended series expansions for the coverage in two-dimensional lattice RSA models, enabling precise estimation of jamming coverage through high-order analysis of the series.

Contribution

The authors improved an existing algorithm to generate the longest series expansions for RSA models, allowing more accurate coverage and jamming estimates.

Findings

Longest series expansions for RSA models achieved

Accurate estimates of jamming coverage derived

Enhanced algorithm enables high-order analysis

Abstract

We express the coverage (occupation fraction) $\theta$, in powers of time $t$ for four models of two-dimensional lattice random sequential adsorption (RSA) to very high orders by improving an algorithm developed by the present authors [J. Phys. A 29, L177 (1996)]. Each of these series is, to the best of our knowledge, the longest at the present. We analyze the series and deduce accurate estimates for the jamming coverage of the models.