Overdamped Lattice Dynamics of Sedimenting Active Cosserat Crystals

TL;DR

This paper investigates how uniaxial activity influences the dynamics of sedimenting active Cosserat crystals, revealing traveling waves and instabilities that lead to crystal melting, with implications for understanding active matter in viscous fluids.

Contribution

It introduces a novel analysis of overdamped lattice dynamics in active Cosserat crystals, highlighting the role of Poisson structures and identifying wave instabilities caused by activity.

Findings

Traveling waves of position and orientation in active crystals.

At least one polarization mode is always unstable.

Poisson structure with Hamiltonian and Casimir invariant identified.

Abstract

Micropolar active matter requires for its kinematic description both positional and orientational degrees of freedom. Activity generates dynamic coupling between these kinematic variables that are absent in micropolar passive matter, such as the oriented crystals first studied by the Cosserat brothers. Here we study the effect of uniaxial activity on the dynamics of an initially crystalline state of spheroidal colloids sedimenting slowly in a viscous fluid remote from confining boundaries. Despite frictional overdamping by the fluid, the crystalline lattice admits traveling waves of position and orientation. At long wavelengths these obey a vector wave equation with Lam\'e constants determined by the activity. We find that at least one polarization mode of these waves is always unstable, leading to the melting of the crystal. These results are elucidated by identifying an odd-dimensional Poisson structure consisting of a Hamiltonian and an associated Casimir invariant, where linear combinations of position and orientation are identified as conjugate variables. Our results suggest that Poisson structures may exist generally for active particles in slow viscous flow and thereby allow equilibrium arguments to be applied in the presence of these dissipative systems.