Wavenumber selection in coupled transport equations

Arnd Scheel; Angela Stevens

doi:10.1007/s00285-017-1107-8

Wavenumber selection in coupled transport equations

Arnd Scheel, Angela Stevens

School of Mathematics

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

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.

Original language	English (US)
Pages (from-to)	1047-1073
Number of pages	27
Journal	Journal of Mathematical Biology
Volume	75
Issue number	5
DOIs	https://doi.org/10.1007/s00285-017-1107-8
State	Published - Nov 1 2017

Bibliographical note

Publisher Copyright:
© 2017, Springer-Verlag Berlin Heidelberg.

Keywords

Balance laws
Coupled transport equations
Invasion fronts
Standing wave
Traveling wave
Wavenumber selection

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10.1007/s00285-017-1107-8

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keywords = "Balance laws, Coupled transport equations, Invasion fronts, Standing wave, Traveling wave, Wavenumber selection",

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AU - Stevens, Angela

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AB - 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.

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KW - Coupled transport equations

KW - Invasion fronts

KW - Standing wave

KW - Traveling wave

KW - Wavenumber selection

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Wavenumber selection in coupled transport equations

Abstract

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