Excitations of Ellipsoid Packings near Jamming

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.