Intrinsic energy localization through discrete gap breathers in one-dimensional diatomic granular crystals

Theocharis, G.; Boechler, Nicholas; Kevrekidis, P. G.; Job, Stéphane; Porter, Mason A.; Daraio, Chiara

doi:10.1103/physreve.82.056604

Cited by 86 publications

(75 citation statements)

References 74 publications

(102 reference statements)

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“…For that reason the latter have only been identified in heterogeneous configurations with different periodicities [19][20][21], or in monomer settings bearing defects [18]. In the latter case, localization is not intrinsic to the chain but rather is supported as an impurity mode by the defect.…”

Section: Introductionmentioning

confidence: 99%

“…1 for an example. Although bright discrete breathers are known to exist in granular crystals (in dimer or higher periodic configurations, and in monomer chains with defects, for example [18][19][20][21]), the * chong@math.umass.edu; http://www.math.umass.edu/∼chong properties of dark discrete breathers in granular crystals remain an open question and are the subject of this work.…”

Section: Introductionmentioning

confidence: 99%

“…These topics form the focus of the present work. Although the homogeneous chain is the sole configuration considered here, it is important to note that dark breathers may exist in other configurations, such as the defect [18] and periodic chains [19][20][21] mentioned above.…”

Section: Introductionmentioning

confidence: 99%

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Dark breathers in granular crystals

et al. 2013

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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.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Dark breathers in granular crystals

et al. 2013

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“…They were originally suggested as excitations of anharmonic nonlinear lattices [3], but the rigorous proof of their persistence under general conditions [4] led to their investigation in a diverse host of applications. These include, among others, antiferromagnets [5], charge-transfer solids [6], photonic crystals [7], superconducting Josephson junctions [8], micromechanical cantilever arrays [9], granular crystals [10], and biopolymers [11]. More recently, the direct manipulation and control of such states has been enabled through suitable experimental techniques [12].…”

Section: Introductionmentioning

confidence: 99%

Discrete breathers in a nonlinear electric line: Modeling, computation, and experiment

et al. 2011

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We study experimentally and numerically the existence and stability properties of discrete breathers in a periodic nonlinear electric line. The electric line is composed of single cell nodes, containing a varactor diode and an inductor, coupled together in a periodic ring configuration through inductors and driven uniformly by a harmonic external voltage source. A simple model for each cell is proposed by using a nonlinear form for the varactor characteristics through the current and capacitance dependence on the voltage. For an electrical line composed of 32 elements, we find the regions, in driver voltage and frequency, where n-peaked breather solutions exist and characterize their stability. The results are compared to experimental measurements with good quantitative agreement. We also examine the spontaneous formation of n-peaked breathers through modulational instability of the homogeneous steady state. The competition between different discrete breathers seeded by the modulational instability eventually leads to stationary n-peaked solutions whose precise locations is seen to sensitively depend on the initial conditions.

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“…Granular crystals have been proposed for a variety of engineering applications; some of these include shock energy trapping [4][5][6], vibration filtering [7,8], focusing [9], energy harvesting [10], and nonlinear localization [11]. In addition, granular crystals have been shown to support metastable breathers in material systems characterized as "sonic vacuum" [12], and localized oscillations in diatomic crystals [13] and in systems with defects [14,15].…”

Section: Introductionmentioning

confidence: 99%

Frequency bands of strongly nonlinear homogeneous granular systems

et al. 2013

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Recent numerical studies on an infinite number of identical spherical beads in Hertzian contact showed the presence of frequency bands [Jayaprakash, Starosvetsky, Vakakis, Peeters, and Kerschen, Nonlinear Dyn. 63, 359 (2011)]. These bands, denoted here as propagation and attenuation bands (PBs and ABs), are typically present in linear or weakly nonlinear periodic media; however, their counterparts are not intuitive in essentially nonlinear periodic media where there is a complete lack of classical linear acoustics, i.e., in "sonic vacua." Here, we study the effects of PBs and ABs on the forced dynamics of ordered, uncompressed granular systems. Through numerical and experimental techniques, we find that the dynamics of these systems depends critically on the frequency and amplitude of the applied harmonic excitation. For fixed forcing amplitude, at lower frequencies, the oscillations are large in amplitude and governed by strongly nonlinear and nonsmooth dynamics, indicating PB behavior. At higher frequencies the dynamics is weakly nonlinear and smooth, in the form of compressed low-amplitude oscillations, indicating AB behavior. At the boundary between the PB and the AB large-amplitude oscillations due to resonance occur, giving rise to collisions between beads and chaotic dynamics; this renders the forced dynamics sensitive to initial and forcing conditions, and hence unpredictable. Finally, we study asymptotically the near field standing wave dynamics occurring for high frequencies, well inside the AB.

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Intrinsic energy localization through discrete gap breathers in one-dimensional diatomic granular crystals

Cited by 86 publications

References 74 publications

Dark breathers in granular crystals

Dark breathers in granular crystals

Discrete breathers in a nonlinear electric line: Modeling, computation, and experiment

Frequency bands of strongly nonlinear homogeneous granular systems

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