Cuddling Ellipsoids: Densest local structures of uniaxial ellipsoids

TL;DR

This paper investigates the densest local packings of uniaxial ellipsoids, revealing how particle shape influences local structures and their distribution in disordered packings, with implications for understanding granular and glassy systems.

Contribution

It introduces a numerical method to identify densest local structures of uniaxial ellipsoids and classifies these structures based on symmetry and coordination, extending classical packing problems.

Findings

Different local structures emerge depending on particle aspect ratio.

Voronoi volume distributions in packings can be rescaled to a $k$-Gamma distribution.

Approximate icosahedral clusters are present in random packings, but not for highly aspherical particles.

Abstract

Connecting the collective behavior of disordered systems with local structure on the particle scale is an important challenge, for example in granular and glassy systems. Compounding complexity, in many scientific and industrial applications, particles are polydisperse, aspherical or even of varying shape. Here, we investigate a generalization of the classical kissing problem in order to understand the local building blocks of packings of aspherical grains. We numerically determine the densest local structures of uniaxial ellipsoids by minimizing the Set Voronoi cell volume around a given particle. Depending on the particle aspect ratio, different local structures are observed and classified by symmetry and Voronoi coordination number. In extended disordered packings of frictionless particles, knowledge of the densest structures allows to rescale the Voronoi volume distributions onto the single-parameter family of $k$-Gamma distributions. Moreover, we find that approximate icosahedral clusters are found in random packings, while the optimal local structures for more aspherical particles are not formed.