Sound waves and the absence of Galilean invariance in flocks

TL;DR

This study numerically investigates flocking behavior, revealing anisotropic sound modes and a unique velocity component due to the absence of Galilean invariance, aligning with continuum theory predictions.

Contribution

It demonstrates the existence of anisotropic sound modes and a novel velocity component in flocking, explicitly linked to the lack of Galilean invariance, supported by large-scale simulations.

Findings

Velocity and density fluctuations are carried by propagating sound modes.

Sound velocity is anisotropic, with distinct speeds for different directions.

A third velocity component arises from the absence of Galilean invariance.

Abstract

We study a model of flocking for a very large system (N=320,000) numerically. We find that in the long wavelength, long time limit, the fluctuations of the velocity and density fields are carried by propagating sound modes, whose dispersion and damping agree quantitatively with the predictions of our previous work using a continuum equation. We find that the sound velocity is anisotropic and characterized by its speed $c$ for propagation perpendicular to the mean velocity $<\vec{v}>$, $<\vec{v}>$ itself, and a third velocity $\lambda <\vec{v}>$, arising explicitly from the lack of Galilean invariance in flocks.