Excitations of Ellipsoid Packings near Jamming

Abstract

We study the vibrational modes of three-dimensional jammed packings of soft ellipsoids of revolution as a function of particle aspect ratio $ε$ and packing fraction. At the jamming transition for ellipsoids, as distinct from the idealized case using spheres where $ε= 1$, 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 $|ε- 1|$ increases. Quite surprisingly, as this new band is separated from zero frequency by a gap, and lies below the onset frequency for translational vibrations, $ω^*$, 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, $ω^*$ depends solely on coordination as it does for compressed packings of spheres. We also discuss the regime of large $|ε- 1|$, where the two bands merge.

6 pages, 4 figures