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

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 Palásti approximation.