MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Wavenumber selection in coupled transport equations

Arnd Scheel and Angela Stevens


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.

traveling wave, standing wave, balance laws, coupled transport equations, invasion fronts, wavenumber selection

Related publications

2017 Repository Open Access
Arnd Scheel and Angela Stevens

Wavenumber selection in coupled transport equations

In: Journal of mathematical biology, 75 (2017) 5, pp. 1047-1073