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Wavenumber selection in coupled transport equations. (English) Zbl 1387.92064

Summary: 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.

MSC:

92C99 Physiological, cellular and medical topics
82C70 Transport processes in time-dependent statistical mechanics
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