Stationary quasi-breathers in monatomic FCC metals
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TICAL, NONLINEAR, AND SOFT MATTER PHYSICS
Stationary Quasi-Breathers in Monatomic FCC Metals P. V. Zakharova,b,*, S. V. Dmitrievc,d, M. D. Starostenkovb, A. M. Eremina, and E. A. Korznikovac a
Shukshin Altai State Humanitarian–Pedagogical University, Biysk, 659333 Russia b Polzunov Altai State Technical University, Barnaul, 656038 Russia c Institute of Problems of Superplasticity of Metals, Russian Academy of Sciences, Ufa, 450001 Russia d National Research Tomsk State University, Tomsk, 634050 Russia *e-mail: [email protected] Received May 10, 2017
Abstract—The characteristics of quasi-breathers in monatomic fcc metals are investigated by the molecular dynamics method. The standard deviations of the frequencies of atoms constituting a breather from the fundamental frequency of oscillations are calculated. It is shown that the quasi-breather lifetime in the models under investigation depends on the initial excitation conditions as well as on the metal type. DOI: 10.1134/S1063776117100181
1. INTRODUCTION The concept of energy localization and transport in crystals by soliton-type waves has been intensely developed in recent years. In particular, discrete breathers (DBs), which are defined as spatially localized large-amplitude strictly periodic in time vibrational modes of in nonlinear lattices, aroused special interest [1, 2]. However, the search for the initial conditions leading to DB excitation corresponding to the given rigorous definition for 3D crystals that can be described by realistic interatomic potentials appears as a complicated problem (the possibility of solution of this problem has not been proved theoretically). Such an exact tuning of the initial conditions cannot be easily performed in the course of molecular dynamic simulation; the more so, such a tuning cannot be attained in any physical experiment, in which various perturbations are inevitably present [3, 4]. This circumstance led Chechin et al. [5] to develop the concept of a quasi-breather, which is a long-lived spatially localized nonlinear oscillation that does not exhibit temporal periodicity [5]. They formulated a certain criterion of closeness of a quasi-breather to the corresponding exact DB, which is based on the calculation of the standard deviation η(tk) of the oscillation frequencies of individual breather particles in a certain time interval in the vicinity of instant tk, as well as the standard deviation of oscillation frequencies of a selected DB particle on various time intervals. Such an approach makes it possible to characterize the DB evolution
with time. In the present study, quasi-breathers will be referred to as DBs for brevity. Considering the topicality of studying DBs in crystals, we note that in a number of recent publications, such objects were considered as main carriers of energy from the source of external action to the bulk of the crystal. For example, annealing of defects in the plasma treatment of germanium at a considerable distance from the crystal surface was considered in [6]. The authors of this work
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