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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URN: | urn:nbn:de:kobv:517-opus4-413140 |
DOI: | https://doi.org/10.25932/publishup-41314 |
ISSN: | 1866-8372 |
Title of parent work (English): | Postprints der Universität Potsdam : Mathematisch Naturwissenschaftliche Reihe |
Publication series (Volume number): | Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe (575) |
Publication type: | Postprint |
Language: | English |
Date of first publication: | 2019/02/05 |
Publication year: | 2011 |
Publishing institution: | Universität Potsdam |
Release date: | 2019/02/06 |
Tag: | pattern formation; reaction-advection-diffusion equation |
Issue: | 575 |
Number of pages: | 11 |
First page: | 138-147 |
Source: | Mathematical modelling of natural phenomena 6 (2011) 1, pp. 138–147 DOI 10.1051/mmnp/20116107 |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät |
DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Peer review: | Referiert |
Publishing method: | Open Access |
Grantor: | Cambridge University Press (CUP) |
License (German): | Keine öffentliche Lizenz: Unter Urheberrechtsschutz |