Supersonic kinks and solitons in active solids

TL;DR

This paper introduces a model demonstrating that active matter can support stable, supersonic nonlinear waves called kinks, which are anti-dissipative and resemble solitons, expanding understanding of wave propagation in active solids.

Contribution

The paper develops a bi-stable mass-spring chain model showing that active matter can sustain stable, supersonic, anti-dissipative kinks, a phenomenon not present in passive systems.

Findings

Supersonic kinks are stable and anti-dissipative.

Active matter can support soliton-like wave bundles.

Quasi-continuum models capture key active phenomena.

Abstract

To show that steadily propagating nonlinear waves in active matter can be driven internally, we develop a prototypical model of a topological kink moving with a constant supersonic speed. We use a model of a bi-stable mass-spring (FPU) chain capable of generating active stress. In contrast to subsonic kinks in passive bi-stable chains, that are necessarily dissipative, the obtained supersonic solutions are purely anti-dissipative. Our numerical experiments point towards stability of the obtained kink-type solutions and the possibility of propagating kink-anti-kink bundles reminiscent of solitons. We show that even the simplest quasi-continuum approximation of the discrete model captures the most important features of the predicted active phenomena.