title: Wavenumber selection in coupled transport equations.
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.
authors.affiliation: School of Mathematics, University of Minnesota, 206 Church St. S.E., Minneapolis, MN, 55455, USA. scheel@umn.edu.
authors.forename: Arnd
authors.identifier: http://orcid.org/0000-0001-6667-3003
authors.initials: A
authors.lastname: Scheel
authors.affiliation: Fachbereich Mathematik und Informatik, Universität Münster, Einsteinstrasse 62, 48149, Münster, Germany.
authors.forename: Angela
authors.initials: A
authors.lastname: Stevens
mesh_terms: D003198:Computer Simulation; D007700:Kinetics; D016014:Linear Models; D055641:Mathematical Concepts; D008954:Models, Biological; D009068:Movement / Q000502:physiology; D009231:Myxococcales / Q000166:cytology / Q000502:physiology; D017711:Nonlinear Dynamics
keywords: Balance laws; Coupled transport equations; Invasion fronts; Standing wave; Traveling wave; Wavenumber selection