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Published April 2013 | Published + Submitted
Journal Article Open

Dark breathers in granular crystals


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.

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.

Attached Files

Published - PhysRevE.87.042202.pdf

Submitted - 1210.5173.pdf


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August 19, 2023
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