Nonlinear Sciences – Pattern Formation and Solitons
Scientific paper
2009-04-02
Nonlinear Sciences
Pattern Formation and Solitons
10 pages, 8 figures (some with multiple parts), to appear in Physical Review E; summary of changes: new title, one new figure,
Scientific paper
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 spatio-temporal structure of the wave in both propagation regimes and propose a simple theoretical interpretation for such a transition. 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.
Boechler Nicholas
Daraio Chiara
Kevrekidis Panagiotis G.
Lai Yi Ming
Ponson Laurent
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