ANALYSIS OF STATISTICAL CHARACTERISTICS OF QUASI-BREATHER IN MONOATOMIC FCC METALS Au, Cu, Ni, Pd AND Pt

Alexander M. Eremin; Pavel V. Zakharov; Mikhail D. Starostenkov; Alexey S. Vdovin

doi:10.17308/kcmf.2018.20/628

Alexander M. Eremin Cand. Sci. (Phys.-Math.), Associate Professor, Shukshin Altai State Humanities Pedagogical University, Biysk, Russia; tel.: +7 (3854) 337438, e-mail: eam77@yandex.ru
Pavel V. Zakharov Cand. Sci. (Phys.-Math.), Associate Professor, Shukshin Altai State Humanities Pedagogical University, Biysk, Russia; tel.: +7 (3854) 337438, e-mail: zakharovpvl@rambler.ru
Mikhail D. Starostenkov Dr. Sci. (Phys.-Math.), Full Professor, Head of the Department of Physics, Polzunov Altai State Technical University, Barnaul, Russia; tel.: +7 (3852) 290852, e-mail: genphys@mail.ru
Alexey S. Vdovin Senior Lecturer, Shukshin Altai State Humanities Pedagogical University, Biysk, Russia; tel.: +7 (3854) 337438, e-mail: ronin_78@mail.ru

DOI: https://doi.org/10.17308/kcmf.2018.20/628

Keywords: crystal, quasi-breather, discrete breather, nonlinear dynamics, soliton, molecular dynamics.

Abstract

The molecular dynamics method is used to calculate and analyze the statistical characteristics of a quasi-breather with a hard type of nonlinearity in monoatomic FCC metals, for example, Cu, Au, Pt, Ni and Pd. Within the framework of this model, the following statistical characteristics and dependencies were calculated for quasi-breathers: a grouped statistical series of absolute and relative frequencies, a polygon of absolute and relative frequencies, a histogram of relative frequencies, an empirical distribution function, an estimate of the mathematical expectation and variance of the original sample. The densities of phonon states are calculated for all crystals. Statistics allow you to understand the causes of the destruction of breathers and more fully describe the process of their dissipation of energy.

ACKNOWLEDGMENTS

For AME, PVZ, the study was carried out with the financial support of the Russian Federal Property Fund and the Altai Territory within the framework of the scientific project No. 18-42-220002; The MDS is grateful to the Ministry of Education and Science of the basic part of the state task, project No. 3.4820.2017/BC.

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