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Physical Mesomechanics

, Volume 19, Issue 3, pp 282–290 | Cite as

Energy oscillations in a one-dimensional harmonic crystal on an elastic substrate

  • M. B. Babenkov
  • A. M. KrivtsovEmail author
  • D. V. Tsvetkov
Article

Abstract

A one-dimensional harmonic crystal on an elastic substrate is considered as a stochastic system into which randomness is introduced through initial conditions. The use of the particle velocity and displacement covariances reduces the stochastic problem to a closed deterministic problem for statistical characteristics of particle pairs. An equation of rapid motion that describes oscillations of potential and kinetic energy components of the system has been derived and solved. The obtained solutions are used to determine the character and to estimate the time of decay of the transient process that brings the system to thermodynamic equilibrium.

Keywords

one-dimensional crystal thermal conductivity covariances energy oscillations elastic substrate 

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Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  • M. B. Babenkov
    • 1
    • 2
  • A. M. Krivtsov
    • 1
    • 2
    Email author
  • D. V. Tsvetkov
    • 1
    • 2
  1. 1.Peter the Great St. Petersburg Polytechnic UniversitySt. PetersburgRussia
  2. 2.Institute of Problems of Mechanical EngineeringRussian Academy of SciencesSt. PetersburgRussia

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