Dresden 2006 – wissenschaftliches Programm

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SYSS: Structure Formation and Self-Organization in non-equilibrium Systems

SYSS 1: Structure Formation and Self-Organization in non-equilibrium Systems I

SYSS 1.13: Vortrag

Donnerstag, 30. März 2006, 12:45–13:00, BAR Sch\"o

Patterns in chaotically mixing fluid flows — •Arthur Straube and Arkady Pikovsky — University of Potsdam, Am Neuen Palais 10, PF 601553, D-14415 Potsdam

We consider a reaction-diffusion system of an activator-inhibitor type and impose a periodic in space mixing flow. We fix governing parameters in a way that ensures the stability of the homogeneous steady state in reaction-diffusion system, so that without advection no Turing patterns occur. Next, we increase the advection rate and study the influence of the flow on the stability of this state. One could expect that because the flow is mixing, it should stabilize the homogeneous state. However, the instability appears as the rate of advection increases beyond a certain threshold, which results in pattern formation. We apply the Bloch theory to find out the length-scale of the patterns, which generally do not coincide with the length-scale of the imposed flow. The mechanism of the instability can be understood from a reduced model; the results are explained by means of Lyapunov exponents. We report on two situations: (i) general case when both chemical species are advected and (ii) a partial case, when only one species is advected, which is relevant to biological applications.

Since the flow and reaction terms are generic for the effects investigated, we believe that the results hold for a variety of flows and chemical reactions.