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.
Author details: | Arthur V. Straube, Arkadij PikovskijORCiDGND |
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DOI: | https://doi.org/10.1051/mmnp/20116107 |
ISSN: | 0973-5348 |
Title of parent work (English): | Mathematical modelling of natural phenomena |
Publisher: | EDP Sciences |
Place of publishing: | Les Ulis |
Publication type: | Article |
Language: | English |
Year of first publication: | 2011 |
Publication year: | 2011 |
Release date: | 2017/03/26 |
Tag: | pattern formation; reaction-advection-diffusion equation |
Volume: | 6 |
Issue: | 1 |
Number of pages: | 11 |
First page: | 138 |
Last Page: | 148 |
Funding institution: | German Science Foundation, DFG [SPP 1164, STR 1021/1-2] |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
Peer review: | Referiert |
Publishing method: | Open Access |