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Published November 2010 | Published
Journal Article Open

Intrinsic energy localization through discrete gap breathers in one-dimensional diatomic granular crystals


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 Fermi-Pasta-Ulam (FPU)-type diatomic chains with those in diatomic granular crystals, which have a tensionless interaction potential between adjacent particles, and note that the asymmetric nature of the tensionless interaction potential can lead to hybrid bulk-surface localized solutions.

Additional Information

© 2010 American Physical Society. Received 27 August 2010; published 8 November 2010. We thank Michael Weinstein and Vassilis Koukouloyannis for useful discussions. This work has been supported from "A.S. Onasis" Foundation, Grant No. RZG 003/2010-2011 (G.T. and P.G.K.). P.G.K. gratefully acknowledges support from the National Science Foundation Grants No. NSF-DMS-0349023 (CAREER), No. NSF-DMS-0806762, and No. NSF-CMMI-1000337 as well as from the Alexander von Humboldt Foundation. C.D. acknowledges support from the Army Research Office MURI (Dr. David Stepp) and from the National Science Foundation Grant No. NSF-CMMI-0844540 (CAREER).

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