Local anisotropy of fluids using Minkowski tensors

Abstract

Statistics of the free volume available to individual particles have\npreviously been studied for simple and complex fluids, granular matter,\namorphous solids, and structural glasses. Minkowski tensors provide a set of\nshape measures that are based on strong mathematical theorems and easily\ncomputed for polygonal and polyhedral bodies such as free volume cells (Voronoi\ncells). They characterize the local structure beyond the two-point correlation\nfunction and are suitable to define indices $0\\leq \\beta_\\nu^{a,b}\\leq 1$ of\nlocal anisotropy. Here, we analyze the statistics of Minkowski tensors for\nconfigurations of simple liquid models, including the ideal gas (Poisson point\nprocess), the hard disks and hard spheres ensemble, and the Lennard-Jones\nfluid. We show that Minkowski tensors provide a robust characterization of\nlocal anisotropy, which ranges from $\\beta_\\nu^{a,b}\\approx 0.3$ for vapor\nphases to $\\beta_\\nu^{a,b}\\to 1$ for ordered solids. We find that for fluids,\nlocal anisotropy decreases monotonously with increasing free volume and\nrandomness of particle positions. Furthermore, the local anisotropy indices\n$\\beta_\\nu^{a,b}$ are sensitive to structural transitions in these simple\nfluids, as has been previously shown in granular systems for the transition\nfrom loose to jammed bead packs.\n