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Aging in a two-dimensional swarmalator crystal with delayed interactions

Chanin Kumpeerakij1,2,*, Thiparat Chotibut3,4,†, and Oleg Kogan5,‡

  • *Contact author: chanin.kumpeerakij@colorado.edu
  • †Contact author: thiparatc@gmail.com
  • ‡Contact author: oleg.kogan@qc.cuny.edu
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Phys. Rev. Research 8, 023335 – Published 26 June, 2026

DOI: https://doi.org/10.1103/bx11-ktk3

Abstract

Time delay can have a significant impact on the properties of collective organization of active matter. In the previous paper [Phys. Rev. E 109, 014205 (2024)], we discussed delay-induced breathing in a system of swarmalators—a model coupling particles’ internal phases to spatial interactions. Here, we build on that study to investigate the aging phenomenon in this system. It is the aging of a two-dimensional crystal with defects and inhomogeneous lattice constants and takes place after the breathing transients subside. We show that aging proceeds through the gradual elimination of fivefold and sevenfold coordination number defects, which merge pairwise or migrate to the cluster boundary, incrementally increasing the hexatic order parameter in the bulk. Despite this process, defects usually do not fully disappear; some residual number of defects remain frozen in the interior. However, we found that it is possible to achieve a nearly total elimination of coordination number defects at sufficiently low delay—when the surface of the cluster develops a sufficeintly thick fluidized “boiling layer.” This mechanism of boundary-mediated annealing reveals a nonequilibrium pathway to achieving high crystalline order in the bulk and raises a tantalizing possibility for controlling defects in active matter with free boundaries.

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Phys. Rev. Research 8, 023335– Published 26 June, 2026
  • Received 6 August 2025
  • Accepted 6 April 2026
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