On the random filling of $R^d$ by non-\-overlapping d-dimensional cubes

TL;DR

This paper analyzes the coverage dynamics of randomly placed, non-overlapping aligned d-dimensional cubes in Euclidean space, providing analytical predictions validated by simulations.

Contribution

It introduces a seventh-order series expansion for coverage prediction in random sequential adsorption of cubes in multiple dimensions, extending previous approximations.

Findings

Series expansion accurately predicts coverage at jamming.

Results agree with Monte Carlo simulations.

Generalizes Palásti approximation for this context.

Abstract

We compute the time-dependent coverage in the random sequential adsorption of aligned d-dimensional cubes in $R^d$ using time-series expansions. The seventh-order series in 2, 3 and 4 dimensions is resummed in order to predict the coverage at jamming. The result is in agreement with Monte-Carlo simulations. A simple argument, based on a property of the perturbative expansion valid at arbitrary orders, allows us to analytically derive some generalizations of the Pal\'asti approximation.