Numerical measurements of the shape and dispersion relation for moving one-dimensional anharmonic localized modes

Bickham, S. R.; Sievers, A. J.; Takeno, Sachio

doi:10.1103/physrevb.45.10344

Cited by 81 publications

(38 citation statements)

References 13 publications

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“…Simulations demonstrate that the mobility of localized modes decreases with increasing amplitude, 37 and if the amplitude becomes large enough, the localized mode is trapped at a site. 42 Although the nonlinear KG lattice does not support a Peierls-Nabarro potential 43,44 due to the presence of internal degrees of freedom, 40,69 a pinning potential of some sort still appears to be a valid concept.…”

Section: Discussionmentioning

confidence: 99%

“…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%

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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: Discussionmentioning

confidence: 99%

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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“…Here u n -displacement of atom n from it's equilibrium position, V (2) , V (3) , ... are the harmonic and anharmonic force constants; the subscripts n include both the site number and the number of the Cartesian component. A localized solution of the (9.1) describing a DB reads…”

Section: Mean Field Theory Of Discrete Breathersmentioning

confidence: 99%

Standing and Moving Discrete Breathers with Frequencies Above the Phonon Spectrum

et al. 2015

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It is found that discrete breathers with frequencies above the top of the phonon spectrum may exist in some metals (Ni, Fe, Cu) and semiconductors (Ge, diamond). It is shown that these excitations in metals may propagate in crystals along crystallographic directions transferring energy of 1 eV over large distances. IntroductionIt is well known already for few decades that anharmonicity of crystal lattices may result in long living small size vibrational excitations of rather high energy. These excitations are usually called as discrete breathers (DBs), intrinsic localized modes, vibrational solitons, or quodons [1-3, 7-9, 11, 12, 22, 24, 25, 27, 31-35, 37, 38]. In numerical studies of DBs different two-body potential models (Lennard-Jones, BornMayer-Coulomb, Toda, and Morse potentials and their combinations) have been used. All these potentials show strong softening at increasing vibrational amplitudes. The DBs, found in such simulations, always drop down from the optical band(s) into the phonon gap, if such a gap exists in the spectrum (see [20,21,23], where DBs have been studied in the alkali halide crystals). Consequently, it has been assumed that the

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“…Thus, a possibility can arise to appear well-localized DBs with rather large vibrational amplitudes. The static changes of the lengths of the interatomic bonds in the actual central region of such a DB are not proportional to 2 A , the basic assumption of the criterion (4). The contribution of the higher harmonics may also become significant in such DBs.…”

Section: Discrete Breathers Above the Phonon Spectrummentioning

confidence: 99%

“…These excitations are called as discrete breathers (DBs), intrinsic localized modes, vibrational solitons, or quodons [2,4,7,11,13,14,16,17,29,31,32,34,42,43,46,47,48,51,52]. In numerical studies of DBs different twobody potential models (Morse, Lennard-Jones, Born-MayerCoulomb and other potentials) have been used.…”

Section: Introductionmentioning

confidence: 99%

Discrete breathers above phonon spectrum

Hizhnyakov¹,

Shelkan²,

Haas³

et al. 2016

LoM

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It is shown that in some metals (Ni, Nb, Fe, Cu) may exist discrete breathers with frequencies above the top of the phonon spectrum. These excitations are mobile: they may propagate along the crystallographic directions transferring energy of > 1 eV over large distances. The discrete breathers with the frequencies above the top of the phonon bands may also exist in covalent crystals (diamond, Si and Ge). It is also found that in monatomic chains and planes (e.g. in graphene), the transverse discrete breathers may be excited above the spectrum of corresponding phonons. Although these vibrations are in resonance with longitudinal (chain) or in-plane (graphene) phonons the lifetime of them may be very long.

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Numerical measurements of the shape and dispersion relation for moving one-dimensional anharmonic localized modes

Cited by 81 publications

References 13 publications

Study of intrinsic localized vibrational modes in micromechanical oscillator arrays

Study of intrinsic localized vibrational modes in micromechanical oscillator arrays

Standing and Moving Discrete Breathers with Frequencies Above the Phonon Spectrum

Discrete breathers above phonon spectrum

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