Non-universal Voronoi cell shapes in amorphous ellipsoid packs

Abstract

In particulate systems with short-range interactions, such as granular matter\nor simple fluids, local structure plays a pivotal role in determining the\nmacroscopic physical properties. Here, we analyse local structure metrics\nderived from the Voronoi diagram of configurations of oblate ellipsoids, for\nvarious aspect ratios $\\alpha$ and global volume fractions $\\phi_g$. We focus\non jammed static configurations of frictional ellipsoids, obtained by\ntomographic imaging and by discrete element method simulations. In particular,\nwe consider the local packing fraction $\\phi_l$, defined as the particle's\nvolume divided by its Voronoi cell volume. We find that the probability\n$P(\\phi_l)$ for a Voronoi cell to have a given local packing fraction shows the\nsame scaling behaviour as function of $\\phi_g$ as observed for random sphere\npacks. Surprisingly, this scaling behaviour is further found to be independent\nof the particle aspect ratio. By contrast, the typical Voronoi cell shape,\nquantified by the Minkowski tensor anisotropy index $\\beta=\\beta_0^{2,0}$,\npoints towards a significant difference between random packings of spheres and\nthose of oblate ellipsoids. While the average cell shape $\\beta$ of all cells\nwith a given value of $\\phi_l$ is very similar in dense and loose jammed sphere\npackings, the structure of dense and loose ellipsoid packings differs\nsubstantially such that this does not hold true. This non-universality has\nimplications for our understanding of jamming of aspherical particles.\n