Chaotic and fractal properties of deterministic diffusion-reaction processes.
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.
Gaspard
P.
P
Center for Nonlinear Phenomena and Complex Systems and Service de Chimie Physique, Faculte des Sciences, Universite Libre de Bruxelles, Campus Plaine, Code Postal 231, B-1050 Brussels, Belgium.
Klages
R.
R