Silent Flocks

TL;DR

This paper introduces a new continuum theory for collective motion in biological groups, revealing the existence of 'silent' flocks where information transfer via sound modes is suppressed.

Contribution

It develops a coupled velocity-density-spin field model that extends Toner-Tu theory to include inertial spin effects, explaining phenomena at smaller scales.

Findings

Second sound propagation emerges at shorter wavelengths.

A gap between first and second sound modes can create silent flocks.

Medium-sized systems can suppress information transfer modes.

Abstract

Experiments find coherent information transfer through biological groups on length and time scales distinctly below those on which asymptotically correct hydrodynamic theories apply. We present here a new continuum theory of collective motion coupling the velocity and density fields of Toner and Tu to the inertial spin field recently introduced to describe information propagation in natural flocks of birds. The long-wavelength limit of the new equations reproduces Toner-Tu theory, while at shorter wavelengths (or, equivalently, smaller damping), spin fluctuations dominate over density fluctuations and second sound propagation of the kind observed in real flocks emerges. We study the dispersion relation of the new theory and find that when the speed of second sound is large, a gap sharply separates first from second sound modes. This gap implies the existence of `silent' flocks, namely medium-sized systems across which neither first nor second sound can propagate.