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

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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.

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Authors and Affiliations

  1. Peter the Great St. Petersburg Polytechnic University, St. Petersburg, 195251, Russia

    M. B. Babenkov, A. M. Krivtsov & D. V. Tsvetkov

  2. Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, 199178, Russia

    M. B. Babenkov, A. M. Krivtsov & D. V. Tsvetkov

Authors
  1. M. B. Babenkov
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  2. A. M. Krivtsov
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  3. D. V. Tsvetkov
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Correspondence to A. M. Krivtsov.

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Original Russian Text © M.B. Babenkov, A.M. Krivtsov, D.V. Tsvetkov, 2016, published in Fizicheskaya Mezomekhanika, 2016, Vol. 19, No. 1, pp. 60-67.

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Babenkov, M.B., Krivtsov, A.M. & Tsvetkov, D.V. Energy oscillations in a one-dimensional harmonic crystal on an elastic substrate. Phys Mesomech 19, 282–290 (2016). https://doi.org/10.1134/S1029959916030061

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