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Register a new userNon-universal Voronoi cell shapes in amorphous ellipsoid packings
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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 Voronoi diagram 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.
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Characterizing structural inhomogeneity is an essential step in understanding the mechanical response of amorphous materials. We introduce a threshold-free measure based on the field of vectors pointing from the center of each particle to the centroid of the Voronoi cell in which the particle resides. These vectors tend to point in toward regions of high free volume and away from regions of low free volume, reminiscent of sinks and sources in a vector field. We compute the local divergence of these vectors, for which positive values correspond to overpacked regions and negative values identify underpacked regions within the material. Distributions of this divergence are nearly Gaussian with zero mean, allowing for structural characterization using only the moments of the distribution. We explore how the standard deviation and skewness vary with packing fraction for simulations of bidisperse systems and find a kink in these moments that coincides with the jamming transition.
We measure the two-point correlation of free Voronoi volumes in binary disc packings, where the packing fraction $phi_{rm avg}$ ranges from 0.8175 to 0.8380. We observe short-ranged correlations over the whole range of $phi_{rm avg}$ and anti-correlations for $phi_{rm avg}>0.8277$. The spatial extent of the anti-correlation increases with $phi_{rm avg}$ while the position of the maximum of the anti-correlation and the extent of the positive correlation shrink with $phi_{rm avg}$. We conjecture that the onset of anti-correlation corresponds to dilatancy onset in this system.
We show that non-Brownian suspensions of repulsive spheres below jamming display a slow relaxational dynamics with a characteristic time scale that diverges at jamming. This slow time scale is fully encoded in the structure of the unjammed packing and can be readily measured via the vibrational density of states. We show that the corresponding dynamic critical exponent is the same for randomly generated and sheared packings. Our results show that a wide variety of physical situations, from suspension rheology to algorithmic studies of the jamming transition are controlled by a unique diverging timescale, with a universal critical exponent.
We compare the elastic response of spring networks whose contact geometry is derived from real packings of frictionless discs, to networks obtained by randomly cutting bonds in a highly connected network derived from a well-compressed packing. We find that the shear response of packing-derived networks, and both the shear and compression response of randomly cut networks, are all similar: the elastic moduli vanish linearly near jamming, and distributions characterizing the local geometry of the response scale with distance to jamming. Compression of packing-derived networks is exceptional: the elastic modulus remains constant and the geometrical distributions do not exhibit simple scaling. We conclude that the compression response of jammed packings is anomalous, rather than the shear response.
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