Random Sequential Adsorption of Oriented Superdisks

TL;DR

This paper investigates the jammed state of superdisks in random sequential adsorption, revealing a special point at p=1/2 where the jamming density's derivative changes discontinuously, using simulations and geometric analysis.

Contribution

It extends previous studies to the jammed state of superdisks, identifying a unique geometric and statistical property at p=1/2 through simulations and theoretical insights.

Findings

Discontinuous derivative of jamming density at p=1/2

Identification of a special geometric point in superdisk packing

Monte Carlo simulations support theoretical predictions

Abstract

In this work we extend recent study of the properties of the dense packing of "superdisks," by Y. Jiao, F. H. Stillinger and S. Torquato, Phys. Rev. Lett. 100, 245504 (2008), to the jammed state formed by these objects in random sequential adsorption. The superdisks are two-dimensional shapes bound by the curves of the form |x|^(2p) + |y|^(2p) = 1, with p > 0. We use Monte Carlo simulations and theoretical arguments to establish that p = 1/2 is a special point at which the jamming density has a discontinuous derivative as a function of p. The existence of this point can be also argued for by geometrical arguments.