Dark Breathers in Granular Crystals

TL;DR

This paper investigates dark breather solutions in a one-dimensional granular crystal chain, analyzing their existence, stability, bifurcations, and potential physical detection methods, revealing novel nonlinear instabilities.

Contribution

The study introduces the existence and stability analysis of dark breathers in granular crystals, including bifurcation structures and a new nonlinear instability not seen in classical lattices.

Findings

Large amplitude solutions bifurcate with small amplitude solutions.

A nonlinear instability unique to this system is identified.

Dark breathers can be physically detected via end actuation and destructive interference.

Abstract

We present a study of the existence, stability and bifurcation structure of families of dark breathers in a one-dimensional uniform chain of spherical beads under static load. A defocus- ing nonlinear Schrodinger equation (NLS) is derived for frequencies that are close to the edge of the phonon band and is used to construct targeted initial conditions for numerical computations. Salient features of the system include the existence of large amplitude solutions that bifurcate with the small amplitude solutions described by the NLS equation, and the presence of a nonlinear instability that, to the best of the authors knowledge, has not been observed in classical Fermi- Pasta-Ulam lattices. Finally, it is also demonstrated that these dark breathers can be detected in a physically realistic way by merely actuating the ends of an initially at rest chain of beads and inducing destructive interference between their signals.