Kinetics of Deposition of Oriented Superdisks

TL;DR

This study uses Monte Carlo simulations to analyze the deposition kinetics of oriented superdisks, revealing a nonanalytic change in the approach to jamming at the convex-concave shape transition.

Contribution

It provides the first detailed analysis of the deposition kinetics of superdisks, highlighting the nonanalytic behavior at the shape transition point.

Findings

Discontinuous derivative in packing and jamming densities at p=0.5

Nonanalytic behavior in late-stage deposition kinetics at p=0.5

Heuristic excluded-area arguments explain the observed phenomena

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.