Hyperuniformity and phase enrichment in vortex and rotor assemblies

TL;DR

This paper demonstrates that vortex and rotor assemblies in 2D fluids self-organize into hyperuniform states and phase-enriched structures, revealing universal geometric conservation laws across different physical systems.

Contribution

It uncovers the spontaneous self-assembly and hyperuniformity in rotor systems, linking them to classical vortex models and revealing new insights into their structural states.

Findings

Systems develop hidden order despite chaotic dynamics

Rotational interactions suppress long-wavelength fluctuations

Mixtures exhibit phase enrichment and ordering transitions

Abstract

Ensembles of particles rotating in a two-dimensional fluid can exhibit chaotic dynamics yet develop signatures of hidden order. Such "rotors" are found in the natural world spanning vastly disparate length scales - from the rotor proteins in cellular membranes to models of atmospheric dynamics. Here we show that an initially random distribution of either ideal vortices in an inviscid fluid, or driven rotors in a viscous membrane, spontaneously self assembles. Despite arising from drastically different physics, these systems share a Hamiltonian structure that sets geometrical conservation laws resulting in distinct structural states. We find that the rotationally invariant interactions isotropically suppress long wavelength fluctuations - a hallmark of a disordered hyperuniform material. With increasing area fraction, the system orders into a hexagonal lattice. In mixtures of two co-rotating populations, the stronger population will gain order from the other and both will become phase enriched. Finally, we show that classical 2D point vortex systems arise as exact limits of the experimentally accessible microscopic membrane rotors, yielding a new system through which to study topological defects.