Linear and anomalous front propagation in system with non Gaussian diffusion: the importance of tails

TL;DR

This paper explores how the tails of non-Gaussian probability distributions influence the long-term behavior of front propagation in diffusive and sub-diffusive systems, highlighting the importance of tail characteristics over moments.

Contribution

It demonstrates that the tail shape of the probability distribution, rather than moments, governs the asymptotic front propagation in systems with anomalous diffusion.

Findings

Tails of the distribution determine asymptotic front behavior.

Bulk properties influence pre-asymptotic dynamics.

Standard moments are insufficient to predict long-term propagation.

Abstract

We investigate front propagation in systems with diffusive and sub-diffusive behavior. The scaling behavior of moments of the diffusive problem, both in the standard and in the anomalous cases, is not enough to determine the features of the reactive front. In fact, the shape of the bulk of the probability distribution of the transport process, which determines the diffusive properties, is important just for pre-asymptotic behavior of front propagation, while the precise shape of the tails of the probability distribution determines asymptotic behavior of front propagation.