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Pattern formation induced by time-dependent advection

  • We study pattern-forming instabilities in reaction-advection-diffusion systems. We develop an approach based on Lyapunov-Bloch exponents to figure out the impact of a spatially periodic mixing flow on the stability of a spatially homogeneous state. We deal with the flows periodic in space that may have arbitrary time dependence. We propose a discrete in time model, where reaction, advection, and diffusion act as successive operators, and show that a mixing advection can lead to a pattern-forming instability in a two-component system where only one of the species is advected. Physically, this can be explained as crossing a threshold of Turing instability due to effective increase of one of the diffusion constants.

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Metadaten
Author:Arthur V. Straube, Arkady S. PikovskyORCiDGND
DOI:https://doi.org/10.1051/mmnp/20116107
ISSN:0973-5348 (print)
Parent Title (English):Mathematical modelling of natural phenomena
Publisher:EDP Sciences
Place of publication:Les Ulis
Document Type:Article
Language:English
Year of first Publication:2011
Year of Completion:2011
Release Date:2017/03/26
Tag:pattern formation; reaction-advection-diffusion equation
Volume:6
Issue:1
Pagenumber:11
First Page:138
Last Page:148
Funder:German Science Foundation, DFG [SPP 1164, STR 1021/1-2]
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie
Peer Review:Referiert
Publication Way:Open Access