TY  - JOUR
A1  - Straube, Arthur V.
A1  - Pikovskij, Arkadij
T1  - Pattern formation induced by time-dependent advection
JF  - Mathematical modelling of natural phenomena
N2  - 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.
KW  - pattern formation
KW  - reaction-advection-diffusion equation
Y1  - 2011
U6  - https://doi.org/10.1051/mmnp/20116107
SN  - 0973-5348
VL  - 6
IS  - 1
SP  - 138
EP  - 148
PB  - EDP Sciences
CY  - Les Ulis
ER  - 
TY  - GEN
A1  - Straube, Arthur V.
A1  - Pikovskij, Arkadij
T1  - Pattern formation induced by time-dependent advection
T2  - Postprints der Universität Potsdam : Mathematisch Naturwissenschaftliche Reihe
N2  - 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.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 575 
KW  - pattern formation
KW  - reaction-advection-diffusion equation
Y1  - 2019
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-413140
SN  - 1866-8372
IS  - 575
SP  - 138-147
ER  -