Wavenumber selection in coupled transport equations

TL;DR

This paper investigates how nonlinear tumbling rates in a minimal run-and-tumble model lead to diverse wave patterns and a wavenumber selection mechanism, with potential relevance to bacterial colony rippling.

Contribution

It reveals a new nonlinear mechanism for wavenumber selection in run-and-tumble dynamics, expanding understanding of pattern formation in active matter models.

Findings

Nonlinear tumbling induces multiple wave patterns

A subtle wavenumber selection mechanism is identified

Implications for bacterial rippling patterns are discussed

Abstract

We study mechanisms for wavenumber selection in a minimal model for run-and-tumble dynamics. We show that nonlinearity in tumbling rates induces the existence of a plethora of traveling- and standing-wave patterns, as well as a subtle selection mechanism for the wavenumbers of spatio-temporally periodic waves. We comment on possible implications for rippling patterns observed in colonies of myxobacteria.