Local Anisotropy of Fluids using Minkowski Tensors

Abstract

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 on strong 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 $0\le {\beta }_{\nu }^{a,b}\le 1$ 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 ${\beta }_{\nu }^{a,b}\approx 0.3$ for vapor phases to ${\beta }_{\nu }^{a,b}\to 1$ 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 ${\beta }_{\nu }^{a,b}$ 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.

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Cited by in corpus (13)

• Shortcomings of the Bond Orientational Order Parameters for the Analysis of Disordered Particulate Matter
• Minkowski Tensors of Anisotropic Spatial Structure
• Jammed Spheres: Minkowski Tensors Reveal Onset of Local Crystallinity
• Analyzing X-Ray tomographies of granular packings
• Non-universal Voronoi cell shapes in amorphous ellipsoid packings
• Statistical Topology of Three-Dimensional Poisson-Voronoi Cells and Cell Boundary Networks
• Characterization of maximally random jammed sphere packings: Voronoi correlation functions
• Voronoi-based estimation of Minkowski tensors from finite point samples
• Kinetics of Fluid Demixing in Complex Plasmas: Domain Growth Analysis using Minkowski Tensors
• Probing the Anisotropy and Non-Gaussianity in the Redshift Space through the Conditional Moments of the First Derivative
• papaya2: 2D Irreducible Minkowski Tensor computation
• Scale-Free Crystallization of two-dimensional Complex Plasmas: Domain Analysis using Minkowski Tensors
• Symmetry and the salience of textures