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Dark breathers in granular crystals

Chong, C. and Kevrekidis, P. G. and Theocharis, G. and Daraio, Chiara (2013) Dark breathers in granular crystals. Physical Review E, 87 (4). Art. No. 042202. ISSN 1539-3755. doi:10.1103/PhysRevE.87.042202. https://resolver.caltech.edu/CaltechAUTHORS:20130509-102231427

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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 defocusing nonlinear Schrödinger 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 emerge from 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 experimental settings by merely actuating the ends of an initially at rest chain of beads and inducing destructive interference between their signals.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1103/PhysRevE.87.042202DOIArticle
http://link.aps.org/doi/10.1103/PhysRevE.87.042202PublisherArticle
https://arxiv.org/abs/1210.5173arXivDiscussion Paper
ORCID:
AuthorORCID
Kevrekidis, P. G.0000-0002-7714-3689
Daraio, Chiara0000-0001-5296-4440
Additional Information:© 2013 American Physical Society. Received 18 October 2012; published 8 April 2013. The authors would like to thank G. James, J. Cuevas, B. Sánchez Rey, R. Goodman, and M. A. Porter for useful discussions. C.D. acknowledges support from the National Science Foundation, Grant No. CMMI-844540 (CAREER) and No. NSF 1138702. P.G.K. gratefully acknowledges support from the US National Science Foundation under Grant No. CMMI-1000337, the US Air Force under Grant No. FA9550-12-1-0332, the Alexander von Humboldt Foundation, as well as the Alexander S. Onassis Public Benefit Foundation.
Funders:
Funding AgencyGrant Number
NSFCMMI-844540
NSFCMMI-1138702
NSFCMMI-1000337
Air Force Office of Scientific Research (AFOSR)FA9550-12-1-0332
Alexander von Humboldt FoundationUNSPECIFIED
Alexander S. Onassis Public Benefit FoundationUNSPECIFIED
Issue or Number:4
Classification Code:PACS: 45.70.-n, 63.20.Ry, 63.20.Pw, 46.40.-f
DOI:10.1103/PhysRevE.87.042202
Record Number:CaltechAUTHORS:20130509-102231427
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20130509-102231427
Official Citation:Chong, C., P. G. Kevrekidis, et al. (2013). "Dark breathers in granular crystals." Physical Review E 87(4): 042202.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:38380
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:10 May 2013 16:49
Last Modified:09 Nov 2021 23:37

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