Front Propagation in Reaction-Superdiffusion Dynamics - Taming L\'evy Flights with Fluctuations

TL;DR

This paper studies how reaction fronts propagate in a system with particles performing Levy flights, revealing that fluctuations cause constant velocity propagation contrary to mean field predictions, with velocity scaling analyzed.

Contribution

It introduces a fractional reaction-diffusion model incorporating fluctuations in Levy flight systems and characterizes the velocity scaling with particle number.

Findings

Wave fronts propagate at constant velocities despite superdiffusion.

Velocity scales with particle number, with a specific scaling exponent.

Fluctuations significantly influence front propagation dynamics.

Abstract

We investigate front propagation in a reacting particle system in which particles perform scale-free random walks known as Levy flights. The system is described by a fractional generalization of a reaction-diffusion equation. We focus on the effects of fluctuations caused by a finite number of particles. We show that, inspite of superdiffusive particle dispersion and contrary to mean field theoretical predictions, wave fronts propagate at constant velocities, even for very large particle numbers. We show that the asymptotic velocity scales with the particle number and obtain the scaling exponent.