Intrinsic Energy Localization through Discrete Gap Breathers in One-Dimensional Diatomic Granular Crystals

TL;DR

This paper systematically studies the existence, structure, and stability of discrete gap breathers in one-dimensional diatomic granular crystals, revealing their regimes and contrasting them with FPU-type chains, highlighting the effects of tensionless interactions.

Contribution

It introduces a comprehensive analysis of discrete gap breathers in diatomic granular crystals, emphasizing their stability regimes and the impact of tensionless Hertzian interactions.

Findings

Identification of two families of discrete gap breathers with different stability properties.

Classification of breathers into four regimes based on their position in the band gap.

Highlighting the unique hybrid localized solutions due to tensionless interactions.

Abstract

We present a systematic study of the existence and stability of discrete breathers that are spatially localized in the bulk of a one-dimensional chain of compressed elastic beads that interact via Hertzian contact. The chain is diatomic, consisting of a periodic arrangement of heavy and light spherical particles. We examine two families of discrete gap breathers: (1) an unstable discrete gap breather that is centered on a heavy particle and characterized by a symmetric spatial energy profile and (2) a potentially stable discrete gap breather that is centered on a light particle and is characterized by an asymmetric spatial energy profile. We investigate their existence, structure, and stability throughout the band gap of the linear spectrum and classify them into four regimes: a regime near the lower optical band edge of the linear spectrum, a moderately discrete regime, a strongly discrete regime that lies deep within the band gap of the linearized version of the system, and a regime near the upper acoustic band edge. We contrast discrete breathers in anharmonic FPU-type diatomic chains with those in diatomic granular crystals, which have a tensionless interaction potential between adjacent particles, and highlight in that the asymmetric nature of the latter interaction potential may lead to a form of hybrid bulk-surface localized solutions.