Kinetics of Deposition of Oriented Superdisks

Abstract

We use numerical Monte Carlo simulation to study kinetics of deposition of oriented superdisks, bounded by the Lame curves of the form $|x|^{2p}+|y|^{2p}=1$, on regular planar substrate. It was recently shown that the maximum packing density, as well as jamming density $\rho_{J}$, exhibit discontinuous derivative at $p=0.5$, when the shape changes from convex to concave form. By careful examination of the late-stage approach to the jamming limit, we find that the leading term in temporal development is also nonanalytic at $p=0.5$, and offer heuristic excluded-area arguments for this behavior.