Highly symmetric discrete breather in a two-dimensional Morse crystal

Korznikova, Elena A.; Fomin, S Yu; Soboleva, E. G.; Dmitriev, Sergey V.

doi:10.1134/s0021364016040081

Cited by 63 publications

(38 citation statements)

References 42 publications

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“…In fact, it is possible to obtain another, high-symmetry DB in 2D monatomic Morse lattice [14], as it is shown in Fig. 4(a).…”

Section: Introductionmentioning

confidence: 89%

“…Stresses decrease as R −2 . Radial compressive stress σ RR does not allow the free expansion of the DB core, making the contribution of the hard core of the Morse potential sufficient for the hard type nonlinearity DB to exist [12,14]. Note that in 3D crystal similar consideration of a DB with spherical symmetry and under assumption of isotropic elastic media (though in 3D case all crystals are anisotropic) the equilibrium equation in terms of the radial displacement obtains the form…”

Section: Introductionmentioning

confidence: 99%

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Discrete breathers in metals and ordered alloys

Dmitriev

2017

NOLTA

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It has been rigorously proved that nonlinear lattices can support spatially localized and periodic in time vibrational modes called either discrete breathers (DBs) or intrinsic localized modes (ILMs). DB does not radiate its energy because its frequency does not belong to the spectrum of small-amplitude running waves. Discreteness and nonlinearity are often said to be the two major necessary conditions for the existence of DBs. Interatomic interactions are nonlinear and the discovery of DBs in crystals, which are nonlinear lattices at the atomic scale, was just a question of time. The first successful attempt to excite DB in alkali-halide NaI crystal in molecular dynamics simulations dates back to 1997. However, the first report on DBs in pure metals was delayed till 2011. In this review we discuss the reason of this delay, describe the latest results on DBs in pure metals and ordered alloys, and outline the open problems in this area.

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“…In fact, it is possible to obtain another, high-symmetry DB in 2D monatomic Morse lattice [14], as it is shown in Fig. 4(a).…”

Section: Introductionmentioning

confidence: 89%

Section: Introductionmentioning

confidence: 99%

Discrete breathers in metals and ordered alloys

Dmitriev

2017

NOLTA

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“…Оказалось, что возможно получить и другой, высо-косимметричный ДБ в 2D моноатомной решетке Морзе [25], как это показано на рис. 4а.…”

Section: дискретные бризеры в двумерных и трех-мерных моноатомных криunclassified

“…4. Высокосимметричный ДБ в моноатомной 2D решетке Морзе [25]. Предположим, что ядро ДБ имеет радиус a и оно оказывает давление p на внешнюю упругую среду.…”

Section: дискретные бризеры в двумерных и трех-мерных моноатомных криunclassified

“…Из выражения (6) видно, что ДБ создают дальнодей-ствующие радиальные перемещения, которые медленно затухают, как R . Ради-альное напряжение сжатия не позволяет ядру ДБ сво-бодно расширяться, что делает вклад жесткого ядра по-тенциала Морзе достаточно существенным для создания ДБ с жестким типом нелинейности [23,25].…”

Section: дискретные бризеры в двумерных и трех-мерных моноатомных криunclassified

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The reason for existence of discrete breathers in 2D and 3D Morse crystals

Korznikova¹,

Kistanov²,

Sergeev³

et al. 2016

LoM

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It is known that crystals can support discrete breathers (DBs) -periodic in time and spatially localized vibrational modes. DB does not radiate energy, as its frequency does not lie within the spectrum of small-amplitude traveling waves (phonons). DB frequency can leave the spectrum of low-amplitude oscillations due to the nonlinearity of the interatomic potentials, as it is well known that the frequency of a nonlinear oscillator depends on the amplitude. Theoretically, it was shown that DB cannot exist in a one-dimensional chain of identical point masses interacting with each other through the Toda, Born-Mayer, Lennard-Jones or Morse potential. The reason of non-existence of DB is the softness of the considered potentials, which does not allow to form a spatially localized mode with frequency above the phonon spectrum. On the basis of this rigorous result, it was concluded that because of the softness of the interatomic interactions in crystals with a simple structure (e.g., in pure metals) existence of DB is very unlikely. Attention should be paid to crystals with a gap in phonon spectrum. In such crystals localized vibrational modes may have frequencies decreasing with amplitude and entering the gap of the phonon spectrum. The first successful attempt to excite a gap DB in alkali halide NaI crystal dates back to 1997, for this purpose, the method of molecular dynamics was used. However, in 2011 DBs with frequencies higher than the phonon spectrum were discovered in pure metals, which poses the question about the conditions of the existence of DBs in crystals with realistic interatomic potentials. In this paper we show that the dimension of the crystal is important, and the Morse crystals of dimension higher than one can support DBs with frequencies above the phonon spectrum. Известно, что кристаллы могут поддерживать существование дискретных бризеров (ДБ) -периодических во вре-мени пространственно-локализованных колебательных мод. ДБ не излучают энергию, так как их частота не лежит в спектре малоамплитудных бегущих волн (фононов). Выход частоты ДБ из спектра малоамплитудных колебаний происходит за счет нелинейности во взаимодействии атомов, ведь известно, что частота нелинейных осцилляторов зависит от амплитуды колебаний. Теоретически было показано, что ДБ не могут существовать в одномерной це-почке одинаковых точечных масс, взаимодействующих друг с другом посредством потенциалов Тоды, Борн-Маера,

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Delocalized Nonlinear Vibrational Modes in Graphene: Second Harmonic Generation and Negative Pressure

Korznikova

Shcherbinin

Ryabov

et al. 2018

Physica Status Solidi (b)

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With the help of molecular dynamics simulations, delocalized nonlinear vibrational modes (DNVM) in graphene are analyzed. Such modes are dictated by the lattice symmetry, they are exact solutions to the atomic equations of motion, regardless the employed interatomic potential and for any mode amplitude (though for large amplitudes they are typically unstable). In this study, only one-and two-component DNVM are analyzed, they are reducible to the dynamical systems with one and two degrees of freedom, respectively. There exist 4 one-component and 12 two-component DNVM with in-plane atomic displacements. Any two-component mode includes one of the one-component modes. If the amplitudes of the modes constituting a two-component mode are properly chosen, periodic in time vibrations are observed for the two degrees of freedom at frequencies ω and 2ω, that is, second harmonic generation takes place. For particular DNVM, the higher harmonic can have frequency nearly two times larger than the maximal frequency of the phonon spectrum of graphene. Excitation of some of DNVM results in the appearance of negative in-plane pressure in graphene. This counterintuitive result is explained by the rotational motion of carbon hexagons. Our results contribute to the understanding of nonlinear dynamics of the graphene lattice.

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Highly symmetric discrete breather in a two-dimensional Morse crystal

Cited by 63 publications

References 42 publications

Discrete breathers in metals and ordered alloys

Discrete breathers in metals and ordered alloys

The reason for existence of discrete breathers in 2D and 3D Morse crystals

Delocalized Nonlinear Vibrational Modes in Graphene: Second Harmonic Generation and Negative Pressure

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