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.
Bibliographical noteFunding Information:
A. Scheel was partially supported through NSF grants DMS-1612441 and DMS-1311740, through a DAAD Faculty Research Visit Grant, WWU Fellowship, and a Humboldt Research Award. A. Stevens was partially supported by the DFG Excellence Cluster Cells in Motion (CiM). A. Scheel gratefully acknowledges generous hospitality during his extended research stay at the WWU Münster.
© 2017, Springer-Verlag Berlin Heidelberg.
- Balance laws
- Coupled transport equations
- Invasion fronts
- Standing wave
- Traveling wave
- Wavenumber selection