Theory of packings of identical hard disks generated by ballistic deposition

Abstract

Recent simulations of the deposition of hard disks in a box according to a rule in which each added disk seeks a gravitationally stable position yielded several surprising results. The packings exhibit an asymptotic approach to a topologically ordered state at large heights, a rapid decay of topological defects with height, and nontrivial periodicities induced by periodic or hard-wall boundary conditions. It is shown here that much of the observed phenomenology can be understood via simple analysis of local configurations of disks. It is also demonstrated that deposition of identical disks onto an initially bare, flat floor does not result in a close-packed crystalline structure in the large system limit. © 1992 IOP Publishing Ltd.