Hyperuniform Jammed Sphere Packings Have Anomalous Material Properties

TL;DR

This paper introduces a method to generate hyperuniform jammed sphere packings with unique mechanical properties, revealing atypical low-frequency phononic excitations and collective modes.

Contribution

It presents a novel rescaling transformation using Voronoi tessellation to produce hyperuniform, mechanically stable sphere packings in simulations.

Findings

Generated hyperuniform packings exhibit a band-gap in low-frequency phononic modes.

Packings show highly collective vibrational modes at specific frequencies.

Demonstrated the ability to impose hyperuniformity on arbitrary point processes.

Abstract

A spatial distribution is hyperuniform if it has local density fluctuations that vanish in the limit of long length scales. Hyperuniformity is a well known property of both crystals and quasicrystals. Of recent interest, however, is disordered hyperuniformity: the presence of hyperuniform scaling without long-range configurational order. Jammed granular packings have been proposed as an example of disordered hyperuniformity, but recent numerical investigation has revealed that many jammed systems instead exhibit a complex set of distinct behaviors at long, emergent length scales. We use the Voronoi tesselation as a tool to define a set of rescaling transformations that can impose hyperuniformity on an arbitrary weighted point process, and show that these transformations can be used in simulations to iteratively generate hyperuniform, mechanically stable packings of athermal soft spheres. These hyperuniform jammed packings display atypical mechanical properties, particularly in the low-frequency phononic excitations, which exhibit an isolated band of highly collective modes and a band-gap around zero frequency.