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Distributions of the volume of Voronoi cells have attracted considerable attention for the study of jamming in dense granular systems and of phase transitions in simple liquid/gas models. Here we demonstrate that higher-order shape measures of the Voronoi cells, in particular measures
of their anisotropy, provide clear signatures of various structural transitions. We define versatile and robust measures of intrinsic anisotropy, derived from so-called Minkowsi Tensors [1]. These are applied to characterize the structural anisotropy of particle configurations obtained from X-ray tomography experiments, Monte Carlo and Molecular Dynamics simulations in both 2D and 3D. In bead packs in 3D, the average anisotropy of the Voronoi cells changes qualitatively when the system enters a jammed state and when it undergoes partial crystallization at RCP [2]. In disk packs in 2D, anisotropy also reflects the poly-crystalline nature of the denser states. In equilibrium hard sphere and disk ensembles, there is a distinct change in anisotropy of the free-volume cells at the crystallization transition. Further, in the ordered phases anisotropy as function of packing fraction $\phi$ is qualitatively different in 2D and 3D. In particular, while the relative standard deviation of all anisotropy measures decreases with $\phi$ in 2D, it increases in 3D. This implies very different scenarios for cell shape fluctuations. References: [1] G.E. Schröder-Turk, S. Kapfer, B. Breidenbach, C. Beisbart, K. Mecke: "Tensorial Minkowski functionals and anisotropy measures for planar patterns" in J. Mic., 238(1), 57-74 (2010) [2] G.E. Schröder-Turk, W. Mickel, M. Schröter, G. W. Delaney, M. Saadatfar, T.J. Senden, K. Mecke and T. Aste: "Disordered Spherical Bead Packs are Anisotropic" to be submitted (2010) [3] G.E. Schröder-Turk, W. Mickel, B. Breidenbach, D. Hug, S. Kapfer and K. Mecke: "Minkowski Tensors of Anisotropic Spatial Structure" to be submitted (2010) |
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