Chaotic and fractal properties of deterministic diffusion-reaction processes

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.

14 pages (revtex), 12 figures (postscript), to appear in CHAOS

References in corpus (1)

• Stability ordering of cycle expansions

Cited by in corpus (18)

• Simple deterministic dynamical systems with fractal diffusion coefficients
• Density-dependent diffusion in the periodic Lorentz gas
• Fractal structures of normal and anomalous diffusion in nonlinear nonhyperbolic dynamical systems
• Understanding deterministic diffusion by correlated random walks
• Deterministic diffusion in flower shape billiards
• Dependence of chaotic diffusion on the size and position of holes
• The fractality of the relaxation modes in deterministic reaction-diffusion systems
• Steady state fluctuation relation and time-reversibility for non-smooth chaotic maps
• Continuity properties of transport coefficients in simple maps
• Entropy production in diffusion-reaction systems: The reactive random Lorentz gas
• Shear flow, viscous heating, and entropy balance from dynamical systems
• Linear and fractal diffusion coefficients in a family of one dimensional chaotic maps
• Comment on ``Analysis of chaotic motion and its shape dependence in a generalized piecewise linear map''
• A multibaker map for shear flow and viscous heating
• Capturing correlations in chaotic diffusion by approximation methods
• Energy-dependent diffusion in a soft periodic Lorentz gas
• Fractal fractal dimensions of deterministic transport coefficients
• Fractal dimension of transport coefficients in a deterministic dynamical system