Discrete Breathers in a Forced-Damped Array of Coupled Pendula: Modeling, Computation, and Experiment

Cuevas, J.; English, Lars Q.; Kevrekidis, P. G.; Anderson, Mara

doi:10.1103/physrevlett.102.224101

Cited by 101 publications

(117 citation statements)

References 25 publications

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“…For instance, in a pendulum setting where φ plays the role of an angular variable in the long-wavelength limit (see, e.g., [42]), a may correspond to the moment of inertia, b to the coupling between pendula, c to the torque due to gravity, and d to the dashpot type of gain/loss prefactor. The latter constitutes also the perturbation term on the right-hand side of the equation.…”

Section: The Modelmentioning

confidence: 99%

Interaction of sine-Gordon kinks and breathers with a parity-time-symmetric defect

2014

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The scattering of kinks and low-frequency breathers of the nonlinear sine-Gordon (SG) equation on a spatially localized parity-time-symmetric perturbation (defect) with a balanced gain and loss is investigated numerically. It is demonstrated that if a kink passes the defect, it always restores its initial momentum and energy, and the only effect of the interaction with the defect is a phase shift of the kink. A kink approaching the defect from the gain side always passes, while in the opposite case it must have sufficiently large initial momentum to pass through the defect instead of being trapped in the loss region. The kink phase shift and critical velocity are calculated by means of the collective variable method. Kink-kink (kink-antikink) collisions at the defect are also briefly considered, showing how their pairwise repulsive (respectively, attractive) interaction can modify the collisional outcome of a single kink within the pair with the defect. For the breather, the result of its interaction with the defect depends strongly on the breather parameters (velocity, frequency, and initial phase) and on the defect parameters. The breather can gain some energy from the defect and as a result potentially even split into a kink-antikink pair, or it can lose a part of its energy. Interestingly, the breather translational mode is very weakly affected by the dissipative perturbation, so that a breather penetrates more easily through the defect when it comes from the lossy side, than a kink. In all studied soliton-defect interactions, the energy loss to radiation of small-amplitude extended waves is negligible.

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Section: The Modelmentioning

confidence: 99%

Interaction of sine-Gordon kinks and breathers with a parity-time-symmetric defect

2014

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“…II we present the relevant model in connection to the experiments of Ref. [10], while in Sec. III we study the single-pendulum dynamical features.…”

Section: Introductionmentioning

confidence: 99%

Instability dynamics and breather formation in a horizontally shaken pendulum chain

Alexander

Sidhu

et al. 2014

Phys. Rev. E

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Inspired by the experimental results of Cuevas et al. [Phys. Rev. Lett. 102, 224101 (2009)], we consider theoretically the behavior of a chain of planar rigid pendulums suspended in a uniform gravitational field and subjected to a horizontal periodic driving force applied to the pendulum pivots. We characterize the motion of a single pendulum, finding bistability near the fundamental resonance and near the period-3 subharmonic resonance. We examine the development of modulational instability in a driven pendulum chain and find both a critical chain length and a critical frequency for the appearance of the instability. We study the breather solutions and show their connection to the single-pendulum dynamics and extend our analysis to consider multifrequency breathers connected to the period-3 periodic solution, showing also the possibility of stability in these breather states. Finally we examine the problem of breather generation and demonstrate a robust scheme for generation of on-site and off-site breathers.

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“…Although using a periodic boundary condition would also be feasible (a ring arrangement), its experimental realization is more involved than a free-free boundary condition; see, e.g., Refs. [22,24] for straightforward realizations of free boundary conditions in base-driven mechanical systems. A very good candidate for experimental realization of complete delocalization is a chain of coupled cantilevers with a controllable magnet-induced nonlinear defect force.…”

Section: Discussionmentioning

confidence: 99%

“…(1) throughout the paper: ζ = 0.005 (light damping), k c = 0.01 (weak-coupling regime), and N = 14 (finite length). While operating near the anticontinuum limit (small k c ) is not necessary, it helps capture the dispersion effects of periodicity more easily for such a short periodic system-also note that realizing this value for k c is practical [6,22,24]. The remaining parameters are free.…”

Section: Mathematical Modelmentioning

confidence: 99%

Complete delocalization in a defective periodic structure

Yousefzadeh

Daraio

2017

Phys. Rev. E

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We report on the existence of stable, completely delocalized response regimes in a nonlinear defective periodic structure. In this state of complete delocalization, despite the presence of the defect, the system exhibits in-phase oscillation of all units with the same amplitude. This elimination of defect-borne localization may occur in both the free and forced responses of the system. In the absence of external driving, the localized defect mode becomes completely delocalized at a certain energy level. In the case of a damped-driven system, complete delocalization may be realized if the driving amplitude is beyond a certain threshold. We demonstrate this phenomenon numerically in a linear periodic structure with one and two defective units possessing a nonlinear restoring force. We derive closed-form analytical expressions for the onset of complete delocalization, and we discuss the necessary conditions for its occurrence.

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Discrete Breathers in a Forced-Damped Array of Coupled Pendula: Modeling, Computation, and Experiment

Cited by 101 publications

References 25 publications

Interaction of sine-Gordon kinks and breathers with a parity-time-symmetric defect

Interaction of sine-Gordon kinks and breathers with a parity-time-symmetric defect

Instability dynamics and breather formation in a horizontally shaken pendulum chain

Complete delocalization in a defective periodic structure

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