Chaotic and fractal properties of deterministic diffusion-reaction processes

Chaos
Pierre Gaspard, Rainer Klages

Abstract

We study the consequences of deterministic chaos for diffusion-controlled reaction. As an example, we analyze a diffusive-reactive deterministic multibaker and a parameter-dependent variation of it. We construct the diffusive and the reactive modes of the models as eigenstates of the Frobenius-Perron operator. The associated eigenvalues provide the dispersion relations of diffusion and reaction and, hence, they determine the reaction rate. For the simplest model we show explicitly that the reaction rate behaves as phenomenologically expected for one-dimensional diffusion-controlled reaction. Under parametric variation, we find that both the diffusion coefficient and the reaction rate have fractal-like dependences on the system parameter. (c) 1998 American Institute of Physics.

References

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Citations

Jul 5, 2012·Chaos·Georgie KnightRainer Klages
Jun 5, 2003·Chaos·Wolfgang BreymannJurgen Vollmer
Apr 20, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·I Claus, P Gaspard
Apr 24, 2002·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·R Klages, J R Dorfman
Dec 12, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·L MátyásJ Vollmer
Sep 21, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Takahisa HarayamaPierre Gaspard
Oct 15, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·A YadavWerner Horsthemke
Mar 10, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Jaison NovickJohn B Delos
Oct 3, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·T Harayama, P Gaspard
May 21, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·László Mátyás, Pierre Gaspard
Sep 21, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·R Klages
Dec 21, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Georgie Knight, Rainer Klages

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