Dynamics of random sequential adsorption

Abstract

The coverage of a two-dimensional surface by the random sequential adsorption of hard disks is shown to approach the "jamming limit" with time as ${t}^{\ensuremath{-}\frac{1}{2}}$ (or ${t}^{\ensuremath{-}\frac{1}{d}}$ for general dimension $d$), confirming a conjecture by Feder. The same argument predicts a logarithmic divergence of the two-particle correlation function at contact, confirming a second conjecture by Feder. The effects of placing squares on the surface instead of disks, and the consequences of these results for future numerical work on related problems are discussed.