Pattern Formation Induced by Time-Dependent Advection

A. V. Straube; A. Pikovsky

Mathematical Modelling of Natural Phenomena (2010)

  • Volume: 6, Issue: 1, page 138-148
  • ISSN: 0973-5348

Abstract

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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.

How to cite

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Straube, A. V., and Pikovsky, A.. "Pattern Formation Induced by Time-Dependent Advection." Mathematical Modelling of Natural Phenomena 6.1 (2010): 138-148. <http://eudml.org/doc/197708>.

@article{Straube2010,
abstract = {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 = {Straube, A. V., Pikovsky, A.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {pattern formation; reaction-advection-diffusion equation; Lyapunov-Bloch exponents; spatially periodic mixing},
language = {eng},
month = {6},
number = {1},
pages = {138-148},
publisher = {EDP Sciences},
title = {Pattern Formation Induced by Time-Dependent Advection},
url = {http://eudml.org/doc/197708},
volume = {6},
year = {2010},
}

TY - JOUR
AU - Straube, A. V.
AU - Pikovsky, A.
TI - Pattern Formation Induced by Time-Dependent Advection
JO - Mathematical Modelling of Natural Phenomena
DA - 2010/6//
PB - EDP Sciences
VL - 6
IS - 1
SP - 138
EP - 148
AB - 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.
LA - eng
KW - pattern formation; reaction-advection-diffusion equation; Lyapunov-Bloch exponents; spatially periodic mixing
UR - http://eudml.org/doc/197708
ER -

References

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  13. T. Tél, A. de Moura, C. Grebogi, G. Károlyi. Chemical and biological activity in open flows: a dynamical system approach. Physics Reports, 413 (2005), 91–196. 
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