Intrinsic Localized Modes in Anharmonic Lattices

Bickham, S. R.; Kiselev, S. A.; Sievers, A. J.

doi:10.1007/978-1-4615-5835-4_9

Cited by 3 publications

(3 citation statements)

References 26 publications

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“…For a classical nonlinear oscillator array, there are a number of characteristic ILM properties, probed theoretically, such as their interaction with an ac driver, 14,34 -36 their propagation 5,[37][38][39][40] and amplitude dependent mobility 4,6,[40][41][42] in a discrete lattice potential, 43,44 as well as their interactions with impurities, [45][46][47][48][49][50] that still need to be examined experimentally. Note that strongly excited ILMs 42 can be trapped anywhere in the lattice, so they also could approach impurity mode behavior.…”

Section: Introductionmentioning

confidence: 99%

Study of intrinsic localized vibrational modes in micromechanical oscillator arrays

Satō

Hubbard

English

et al. 2003

Chaos: An Interdisciplinary Journal of Nonlinear Science

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103

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Intrinsic localized modes ͑ILMs͒ have been observed in micromechanical cantilever arrays, and their creation, locking, interaction, and relaxation dynamics in the presence of a driver have been studied. The micromechanical array is fabricated in a 300 nm thick silicon-nitride film on a silicon substrate, and consists of up to 248 cantilevers of two alternating lengths. To observe the ILMs in this experimental system a line-shaped laser beam is focused on the 1D cantilever array, and the reflected beam is captured with a fast charge coupled device camera. The array is driven near its highest frequency mode with a piezoelectric transducer. Numerical simulations of the nonlinear Klein-Gordon lattice have been carried out to assist with the detailed interpretation of the experimental results. These include pinning and locking of the ILMs when the driver is on, collisions between ILMs, low frequency excitation modes of the locked ILMs and their relaxation behavior after the driver is turned off. © 2003 American Institute of Physics. ͓DOI: 10.1063/1.1540771͔An advance of the theory of nonlinear excitations in discrete lattices was the discovery that some localized vibrations in perfectly periodic but nonintegrable lattices could be stabilized by lattice discreteness. The modulational instability of extended large amplitude vibrational modes has been proposed as a mechanism for the realization of dynamical localization on the scale of the lattice constant. Although theoretically a variety of methods to excite the instability of a homogeneous vibrational mode have been proposed, these ideas have yet to be tested experimentally. Since the observation of nanoscale localized vibrational modes still cannot be achieved there is definite advantage to examining a macroscopic array, which is small enough so that the entire time dependence of the instability dynamics occurs in a practical measurement interval. This has been accomplished by using micromechanical silicon technology to fabricate up to 248 identical cantilevers with a 40 micron lattice constant. Optical techniques have been used to track the motion of individual cantilevers in the presence of an inertial driver. In addition to experimentally characterizing the modulational instability and identifying the best method for producing intrinsic localized modes a new discovery is the locking of the local mode amplitude with the driver frequency. Numerical simulations have been used to better understand the nature of this synchronization effect.

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Section: Introductionmentioning

confidence: 99%

Study of intrinsic localized vibrational modes in micromechanical oscillator arrays

Satō

Hubbard

English

et al. 2003

Chaos: An Interdisciplinary Journal of Nonlinear Science

Self Cite

103

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“…(12) has long been studied in the context of FPU lattice theory. Following earlier pioneering works Page, 1990] (also see in [Kiselev et al, 1995;Bickham et al, 1997] and Refs. therein), the existence of DBs in FPU chains was rigorously proven in [James, 2001]; see in [Sánchez-Rey et al, 2004;Flach & Gorbach, 2004] for two recent studies, establishing the existence of bright and dark breathers in FPU chains.…”

Section: Discrete Localized Oscillations In the Longitudinal Directionmentioning

confidence: 95%

“…Following the pioneering analytical and numerical considerations of ILM existence due to coupling anharmonicity (in discrete FPU chains) by Sievers, Takeno, Page and coworkers [Sievers & Takeno, 1988;Page, 1990] presented in the late 1980's (also see [Kiselev et al, 1995;Bickham et al, 1997] for a review), the existence of DB modes has been rigorously proven in the past, for a wide class of nonlinear discrete lattices. Two main axes of proof have been suggested so far, namely: (i) the analytic continuation from the uncoupled ("anti-continuous") limit to a weakly interacting oscillator chain [MacKay & Aubry, 1994;Aubry, 1997], and (ii) the relation of DB existence to (intersection points of) the homoclinic orbits in the phase space defined by the Fourier component amplitudes {A nk } [Flach, 1995] (also see [Bountis, 2000]).…”

Section: Intrinsic Localized Modesmentioning

confidence: 99%

Nonlinear Excitations in Strongly-Coupled Plasma Lattices: Envelope Solitons, Kinks and Intrinsic Localized Modes

Kourakis

Shukła

2006

Int. J. Bifurcation Chaos

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Ensembles of charged particles (plasmas) are a highly complex form of matter, most often modeled as a many-body system characterized by weak inter-particle interactions (electrostatic coupling). However, strongly-coupled plasma configurations have recently been produced in laboratory, either by creating ultra-cold plasmas confined in a trap or by manipulating dusty plasmas in discharge experiments. In this paper, the nonlinear aspects involved in the motion of charged dust grains in a one-dimensional plasma monolayer (crystal) are discussed. Different types of collective excitations are reviewed, and characteristics and conditions for their occurrence in dusty plasma crystals are discussed, in a quasi-continuum approximation. Dust crystals are shown to support nonlinear kink-shaped supersonic solitary longitudinal excitations, as well as modulated envelope localized modes associated with longitudinal and transverse vibrations. Furthermore, the possibility for intrinsic localized modes (ILMs) — Discrete Breathers (DBs) — to occur is investigated, from first principles. The effect of mode-coupling is also briefly considered. The relation to previous results on atomic chains, and also to experimental results on strongly-coupled dust layers in gas discharge plasmas, is briefly discussed.

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Nonlinear nanoscale localization of magnetic excitations in atomic lattices

Lai

Sievers

1999

Physics Reports

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Intrinsic Localized Modes in Anharmonic Lattices

Cited by 3 publications

References 26 publications

Study of intrinsic localized vibrational modes in micromechanical oscillator arrays

Study of intrinsic localized vibrational modes in micromechanical oscillator arrays

Nonlinear Excitations in Strongly-Coupled Plasma Lattices: Envelope Solitons, Kinks and Intrinsic Localized Modes

Nonlinear nanoscale localization of magnetic excitations in atomic lattices

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