The fractality of the relaxation modes in deterministic reaction-diffusion systems

TL;DR

This paper investigates the fractal structure of relaxation modes in chaotic reaction-diffusion systems, establishing a relationship with Lyapunov exponents and diffusion coefficients, and confirms it through numerical tests.

Contribution

It introduces a theoretical relationship linking fractal dimensions of relaxation modes to dynamical system properties and validates it with numerical simulations.

Findings

Fractal dimensions of relaxation modes relate to Lyapunov exponents and diffusion coefficients.

Numerical tests on multibaker and Lorentz gas models confirm the theoretical predictions.

The relationship holds for long wavelength modes in chaotic reaction-diffusion systems.

Abstract

In chaotic reaction-diffusion systems with two degrees of freedom, the modes governing the exponential relaxation to the thermodynamic equilibrium present a fractal structure which can be characterized by a Hausdorff dimension. For long wavelength modes, this dimension is related to the Lyapunov exponent and to a reactive diffusion coefficient. This relationship is tested numerically on a reactive multibaker model and on a two-dimensional periodic reactive Lorentz gas. The agreement with the theory is excellent.