Non-universal Voronoi cell shapes in amorphous ellipsoid packings

In particulate systems with short-range interactions, such as granular matter or simple fluids, local structure plays a pivotal role in determining the macroscopic physical properties. Here, we analyse local structure metrics derived from the Voronoidiagram of configurations of oblate ellipsoids, for various aspect ratios $alpha$ and global volume fractions $phi_g$. We focus on jammed static configurations of frictional ellipsoids, obtained by tomographic imaging and by discrete element method simulations. In particular, we consider the local packing fraction $phi_l$, defined as the particles volume divided by its Voronoi cell volume. We find that the probability $P(phi_l)$ for a Voronoi cell to have a given local packing fraction shows the same scaling behaviour as function of $phi_g$ as observed for random sphere packs. Surprisingly, this scaling behaviour is further found to be independent of the particle aspect ratio. By contrast, the typical Voronoi cell shape, quantified by the Minkowski tensor anisotropy index $beta=beta_0^{2,0}$, points towards a significant difference between random packings of spheres and those of oblate ellipsoids. While the average cell shape $beta$ of all cells with a given value of $phi_l$ is very similar in dense and loose jammed sphere packings, the structure of dense and loose ellipsoid packings differs substantially such that this does not hold true. This non-universality has implications for our understanding of jamming of aspherical particles.

Local Anisotropy of Fluids using Minkowski Tensors

Statistics of the free volume available to individual particles have previously been studied for simple and complex fluids, granular matter, amorphous solids, and structural glasses. Minkowski tensors provide a set of shape measures that are based onstrong mathematical theorems and easily computed for polygonal and polyhedral bodies such as free volume cells (Voronoi cells). They characterize the local structure beyond the two-point correlation function and are suitable to define indices $0leq beta_ u^{a,b}leq 1$ of local anisotropy. Here, we analyze the statistics of Minkowski tensors for configurations of simple liquid models, including the ideal gas (Poisson point process), the hard disks and hard spheres ensemble, and the Lennard-Jones fluid. We show that Minkowski tensors provide a robust characterization of local anisotropy, which ranges from $beta_ u^{a,b}approx 0.3$ for vapor phases to $beta_ u^{a,b}to 1$ for ordered solids. We find that for fluids, local anisotropy decreases monotonously with increasing free volume and randomness of particle positions. Furthermore, the local anisotropy indices $beta_ u^{a,b}$ are sensitive to structural transitions in these simple fluids, as has been previously shown in granular systems for the transition from loose to jammed bead packs.