Dynamical arrest of topological defects in 2D hyperuniform disk packings

¹ Department of Applied Mathematics, Research School of Physics and Engineering, Australian National University, Canberra, ACT 2601, Australia
² Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
³ Mathematics and Statistics, Murdoch University, Perth, WA 6150, Australia
⁴ School of Civil Engineering, The University of Sydney, Sydney, NSW 2006, Australia

^* e-mail: sungyeon.hong@anu.edu.au
^** e-mail: nicolas.francois@anu.edu.au
^*** e-mail: mohammad.saadatfar@anu.edu.au

Published online: 7 June 2021

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.