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APS » Journals » Phys. Rev. Lett. » Volume 102 » Issue 2
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Phys. Rev. Lett. 102, 024102 (2009) [4 pages]

Dissipative Solitary Waves in Granular Crystals

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R. Carretero-González1, D. Khatri2, Mason A. Porter3, P. G. Kevrekidis4, and C. Daraio2,*
1Department of Mathematics and Statistics, San Diego State University, San Diego, California 92182-7720, USA
2Graduate Aeronautical Laboratories (GALCIT) and Department of Applied Physics, California Institute of Technology, Pasadena, California 91125, USA
3Oxford Center for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, OX1 3LB, United Kingdom
4Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA

Received 12 August 2008; published 16 January 2009

We provide a quantitative characterization of dissipative effects in one-dimensional granular crystals. We use the propagation of highly nonlinear solitary waves as a diagnostic tool and develop optimization schemes that allow one to compute the relevant exponents and prefactors of the dissipative terms in the equations of motion. We thereby propose a quantitatively accurate extension of the Hertzian model that encompasses dissipative effects via a discrete Laplacian of the velocities. Experiments and computations with steel, brass, and polytetrafluoroethylene reveal a common dissipation exponent with a material-dependent prefactor.

© 2009 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevLett.102.024102
DOI:
10.1103/PhysRevLett.102.024102
PACS:
45.70.−n, 05.45.Yv, 43.25.+y, 46.40.Cd

*Corresponding author.

daraio@caltech.edu

 
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