Jamming in Systems Composed of Frictionless Ellipse-Shaped Particles

TL;DR

This paper investigates the unique structural and mechanical properties of jammed ellipse-shaped particles, revealing fundamental differences from spherical particle packings, including hypostaticity, spectral gaps, and novel scaling relations.

Contribution

It introduces the first detailed analysis of jamming in ellipse particles, highlighting hypostaticity, spectral features, and mode behavior distinct from spherical systems.

Findings

Ellipse packings are hypostatic with more degrees of freedom than constraints.

The low-energy spectra have two gaps and three branches across aspect ratios.

Mode energies increase quartically with deformation amplitude at zero compression.

Abstract

We study the structural and mechanical properties of jammed ellipse packings, and find that the nature of the jamming transition in these systems is fundamentally different from that for spherical particles. Ellipse packings are generically hypostatic with more degrees of freedom than constraints. The spectra of low energy excitations possess two gaps and three distinct branches over a range of aspect ratios. In the zero compression limit, the energy of the modes in the lowest branch increases {\it quartically} with deformation amplitude, and the density of states possesses a $\delta$-function at zero frequency. We identify scaling relations that collapse the low-frequency part of the spectra for different aspect ratios. Finally, we find that the degree of hypostaticity is determined by the number of quartic modes of the packing.