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Published August 2010 | Published
Journal Article Open

Nonlinear waves in disordered diatomic granular chains


We investigate the propagation and scattering of highly nonlinear waves in disordered granular chains composed of diatomic (two-mass) units of spheres that interact via Hertzian contact. Using ideas from statistical mechanics, we consider each diatomic unit to be a "spin," so that a granular chain can be viewed as a spin chain composed of units that are each oriented in one of two possible ways. Experiments and numerical simulations both reveal the existence of two different mechanisms of wave propagation: in low-disorder chains, we observe the propagation of a solitary pulse with exponentially decaying amplitude. Beyond a critical level of disorder, the wave amplitude instead decays as a power law, and the wave transmission becomes insensitive to the level of disorder. We characterize the spatiotemporal structure of the wave in both propagation regimes and propose a simple theoretical interpretation for a transition between the two regimes. Our investigation suggests that an elastic spin chain can be used as a model system to investigate the role of heterogeneities in the propagation of highly nonlinear waves.

Additional Information

© 2010 The American Physical Society. Received 2 April 2009; revised manuscript received 24 June 2010; published 12 August 2010. We thank D. Allwright, D. K. Campbell, E. J. Hinch, E. López, and G. Refael for useful discussions and K. Whittaker for help with experiments. We also thank the European Union's (PhyCracks project) Marie Curie outgoing fellowship (L.P.), NSF-CMMI (C.D.), NSF-CAREER (C.D., P.G.K.), NSF-DMS (P.G.K.), the Jardine Foundation (Y.M.L.), and Exeter College in Oxford (Y.M.L.) for support.

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Published - Ponson2010p11159Phys_Rev_E.pdf


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