Front propagation into unstable states in discrete media

TL;DR

This paper analyzes front propagation into unstable states in discrete media, providing analytical and numerical insights into front speed and oscillatory behavior, and introduces a generalized Peierls-Nabarro potential for better understanding discreteness effects.

Contribution

It offers the first analytical calculation of front speed in discrete media and generalizes the Peierls-Nabarro potential to describe oscillatory front propagation.

Findings

Analytical expression for front speed in discrete media

Numerical characterization of oscillatory front behavior

Generalized Peierls-Nabarro potential for discreteness effects

Abstract

Non-equilibrium dissipative systems usually exhibit multistability, leading to the presence of propagative domain between steady states. We investigate the front propagation into an unstable state in discrete media. Based on a paradigmatic model of coupled chain of oscillators and populations dynamics, we calculate analytically the average speed of these fronts and characterize numerically the oscillatory front propagation. We reveal that different parts of the front oscillate with the same frequency but with different amplitude. To describe this latter phenomenon we generalize the notion of the Peierls-Nabarro potential, achieving an effective continuous description of the discreteness effect.