Autocatalytic Reactions in Systems with Hyperbolic Mixing: Exact Results for the Active Baker Map

Details Autocatalytic Reactions in Systems with Hyperbolic Mixing: Exact Results for the Active Baker Map Autocatalytic Reactions in Systems with Hyperbolic Mixing: Exact Results for the Active Baker Map

2001-01-22

arxiv.org/abs/nlin/0101040v1

Nonlinear Sciences

Chaotic Dynamics

24 pages, 9 figures

Scientific paper

10.1088/0305-4470/34/25/305

We investigate the effects of hyperbolic hydrodynamical mixing on the reaction kinetics of autocatalytic systems. Exact results are derived for the two dimensional open baker map as an underlying mixing dynamics for a two-component autocatalytic system, $A+B \to 2B$. We prove that the hyperboliticity exponentially enhances the productivity of the reaction which is due the fact that the reaction kinetics is catalyzed by the fractal unstable manifold of the chaotic set of the reaction-free dynamics. The results are compared with phenomenological theories of active advection.

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