Autocatalytic reactions in systems with hyperbolic mixing: exact results for the active Baker map

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Published 15 June 2001 • Published under licence by IOP Publishing Ltd
, , Citation Z Toroczkai et al 2001 J. Phys. A: Math. Gen. 34 5215 DOI 10.1088/0305-4470/34/25/305

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Author affiliations

1 Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM 87545, USA

2 Department of Structural Mechanics, Budapest University of Technology and Economics, Muegyetem rkp. 3, H-1521 Budapest, Hungary

3 Marine Physical Laboratory, Scripps Institution of Oceanography, University of California at San Diego, La Jolla, CA 92093-0238, USA

4 Institute for Theoretical Physics, Eötvös University, PO Box 32, H-1518 Budapest, Hungary

Dates

  1. Received 24 January 2001
  2. Published

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Abstract

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→2B. We prove that chaotic advection modelled by the Baker map enhances the productivity of the reaction which is due to the fact that the reaction kinetics is catalysed 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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