Asymmetric exchange in flocks

TL;DR

This paper investigates how fore-aft asymmetry in bird flock interactions causes destabilization through spontaneous turning and explains differences in information and flock movement speeds, linking asymmetry to broken detailed balance.

Contribution

It reveals that antisymmetric exchange interactions induce flock instability and explains the speed difference between information propagation and flock movement, emphasizing the role of broken detailed balance.

Findings

Asymmetric exchange destabilizes flock via spontaneous turning.

Broken detailed balance explains the difference in information and flock speeds.

Conditions for turning instability are characterized by parameters and wavenumber.

Abstract

As the constituents of a flock are polar, one expects a fore-aft asymmetry in their interactions. We show here that the resulting antisymmetric part of the "exchange coupling" between a bird and its neighbours, if large enough, destabilizes the flock through spontaneous turning of the birds. The same asymmetry also yields a natural mechanism for a difference between the speed of advection of information along the flock and the speed of the flock itself. We show that the absence of detailed balance, and not merely the breaking of Galilean invariance, is responsible for this difference. We delineate the conditions on parameters and wavenumber for the existence of the turning instability. Lastly we present an alternative perspective based on flow-alignment effects in an active liquid crystal with turning inertia in contact with a momentum sink.