Excitations of Ellipsoid Packings near Jamming

TL;DR

This paper investigates how vibrational modes in jammed ellipsoid packings evolve with particle shape and packing density, revealing new rotational modes and their impact on the vibrational spectrum near jamming.

Contribution

It introduces the analysis of rotational degrees of freedom in ellipsoid packings and their influence on vibrational modes, extending understanding beyond spherical particles.

Findings

Rotational modes form a new band separated by a gap from zero frequency.

The translational vibrational spectrum depends only on contact number, not on rotational modes.

At large aspect ratios, rotational and translational bands merge.

Abstract

We study the vibrational modes of three-dimensional jammed packings of soft ellipsoids of revolution as a function of particle aspect ratio $\epsilon$ and packing fraction. At the jamming transition for ellipsoids, as distinct from the idealized case using spheres where $\epsilon = 1$, there are many unconstrained and non-trivial rotational degrees of freedom. These constitute a set of zero-frequency modes that are gradually mobilized into a new rotational band as $|\epsilon - 1|$ increases. Quite surprisingly, as this new band is separated from zero frequency by a gap, and lies below the onset frequency for translational vibrations, $\omega^*$, the presence of these new degrees of freedom leaves unaltered the basic scenario that the translational spectrum is determined only by the average contact number. Indeed, $\omega^*$ depends solely on coordination as it does for compressed packings of spheres. We also discuss the regime of large $|\epsilon - 1|$, where the two bands merge.