Vlasov Equation for Phonons and its Macroscopic Consequences

Corrections to the harmonic approximation are obtained for the first order of the theory of hyperelasticity in the relaxation approximation for a cubic crystal. The Vlasov equation is constructed for a collisionless gas of phonons in a self-consistent deformation field. Collisions of phonons are con...

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Bibliographic Details
Published inMathematical models and computer simulations Vol. 13; no. 4; pp. 552 - 560
Main Authors Volkov, Yu. A., Dmitriev, A. S., Markov, M. B.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.07.2021
Springer Nature B.V
Subjects
Approximation
Computational fluid dynamics
Fluid flow
Hydrodynamics
Mathematical analysis
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Phonons
Simulation and Modeling
Thermoelasticity
Vlasov equations
deformation
phonon
Vlasov equation
thermoelasticity
crystal
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Summary:Corrections to the harmonic approximation are obtained for the first order of the theory of hyperelasticity in the relaxation approximation for a cubic crystal. The Vlasov equation is constructed for a collisionless gas of phonons in a self-consistent deformation field. Collisions of phonons are considered in the relaxation approximation to the equilibrium distribution. It is shown that the thermoelasticity equations are valid for the hydrodynamics of a phonon gas in the thermodynamic limit. The relationship between the kinetic model of a phonon gas and the equations of Cattaneo and Guyer-Crumhansl, as well as Biot’s thermoelasticity, is considered.
ISSN:2070-0482
2070-0490
DOI:10.1134/S2070048221040220