Dynamical arrest of topological defects in 2D hyperuniform disk packings

Sungyeon Hong,Mohammad Saadatfar,Michael A Klatt,Gerd Schröder-Turk,Nicolas François,M.A Aguirre,L.A Pugnaloni,S Luding,R Soto

doi:10.1051/epjconf/202124915002

Sungyeon Hong, Mohammad Saadatfar + Show 7 more

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https://doi.org/10.1051/epjconf/202124915002

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Abstract

We investigate collective motions of points in 2D systems, orchestrated by Lloyd algorithm. The algorithm iteratively updates a system by minimising the total quantizer energy of the Voronoi landscape of the system. As a result of a tradeoff between energy minimisation and geometric frustration, we find that optimised systems exhibit a defective landscape along the process, where strands of 5- and 7-coordinated dislocations are embedded in the hexatic phase. In particular, dipole defects, each of which is the simplest possible pair of a pentagon and a heptagon, come into the picture of dynamical arrest, as the system freezes down to a disordered hyperuniform state. Moreover, we explore the packing fractions of 2D disk packings associated to the obtained hyperuniform systems by considering the maximum inscribed disks in their Voronoi cells.

Highlights

1 Introduction process that homogenises a spatial distribution of points as follows: for a given point configuration at step t ≥ 0, the Disordered hyperuniformity describes an amorphous state algorithm considers the corresponding Voronoi decompoof matter that suppresses variations in the density of parti- sition and computes the centroid of each Voronoi cell to cles on large length scales
We show that 2D hyperuniform configurations obtained by Lloyd algorithm possess defective landscapes, where 5- or 7-coordinated topological defects take part in settling down the competition between energy minimisation and geometric frustration on a flat surface
With the aim of unveiling structural motifs that mediate point-point interactions and drive a dynamical arrest into a defective landscape along the course of quantizer energy minimisation of 2D point patterns, we highlight that dipole defects, each of which is a single pair of a pentagon and a heptagon, exhibit higher number density than other defect components of different sizes

Summary

Introduction

1 Introduction process that homogenises a spatial distribution of points as follows: for a given point configuration at step t ≥ 0, the Disordered hyperuniformity describes an amorphous state algorithm considers the corresponding Voronoi decompoof matter that suppresses variations in the density of parti- sition and computes the centroid of each Voronoi cell to cles on large length scales. The been utilised as a framework to describe glassy states of algorithm optimises the space coverage by maximising the jammed granular materials [2,3,4, 6, 8] giving us a deeper distance between points, while at the same time, minimisunderstanding of their out-of-equilibrium structures while ing quantizer energy associated with the Voronoi cells conbeing maximally disordered yet mechanically rigid. Hyperuniform point patterns can be constructed using Lloyd’s centroidal Voronoi diagram algorithm In this proceedings, we show that 2D hyperuniform configurations obtained by Lloyd algorithm possess defective landscapes, where 5- or 7-coordinated topological defects take part in settling down the competition between energy minimisation and geometric frustration on a flat surface.

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