Damped-driven granular chains: An ideal playground for dark breathers and multibreathers
By applying an out-of-phase actuation at the boundaries of a uniform chain of granular particles, we demonstrate experimentally that time-periodic and spatially localized structures with a nonzero background (so-called dark breathers) emerge for a wide range of parameter values and initial conditions. We demonstrate a remarkable control over the number of breathers within the multibreather pattern that can be "dialed in" by varying the frequency or amplitude of the actuation. The values of the frequency (or amplitude) where the transition between different multibreather states occurs are predicted accurately by the proposed theoretical model, which is numerically shown to support exact dark breather and multibreather solutions. Moreover, we visualize detailed temporal and spatial profiles of breathers and, especially, of multibreathers using a full-field probing technology and enable a systematic favorable comparison among theory, computation, and experiments. A detailed bifurcation analysis reveals that the dark and multibreather families are connected in a "snaking" pattern, providing a roadmap for the identification of such fundamental states and their bistability in the laboratory.
© 2014 American Physical Society. Received 17 July 2013; revised manuscript received 3 February 2014; published 31 March 2014. The authors would like to thank G. Theocharis for useful discussions. Support from the US NSF (Grant Nos. CMMI 1310173, CMMI 1234452, and CMMI 1000337) and US AFOSR (Grant No. FA9550-12-1-0332) is appreciated. M.O.W. gratefully acknowledges support from an NSF Mathematics Sciences Postdoctoral Research Fellowship, DMS 1204783.
Submitted - 1307.4780v1.pdf
Published - PhysRevE.89.032924.pdf