Geodesic
Vlasov equation for phonons and its macroscopic consequences
Matematičeskoe modelirovanie, Tome 32 (2020) no. 11, pp. 16-28

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Amendments are obtained to the harmonic approximation for the first order of the hyperelasticity theory in the relaxation approximation for a cubic crystal. The Vlasov equation is constructed for a collisionless phonon gas in a self-consistent deformation field. Collisions are considered in the approximation of relaxation to the equilibrium distribution. It is shown that the equations of thermo-elasticity are valid in the thermodynamic limit for the hydrodynamics of a phonon gas. The connection of the kinetic model with the equations of Cattaneo, Guyer-Crumhansl and thermoelasticity in the Bio form is considered.
Keywords: crystal, deformation, thermoelasticity.
Mots-clés : phonon, Vlasov equation 
@article{MM_2020_32_11_a1,
     author = {Yu. A. Volkov and A. S. Dmitriev and M. B. Markov},
     title = {Vlasov equation for phonons and its macroscopic consequences},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {16--28},
     publisher = {mathdoc},
     volume = {32},
     number = {11},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2020_32_11_a1/}
}
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Yu. A. Volkov; A. S. Dmitriev; M. B. Markov. Vlasov equation for phonons and its macroscopic consequences. Matematičeskoe modelirovanie, Tome 32 (2020) no. 11, pp. 16-28. http://geodesic.mathdoc.fr/item/MM_2020_32_11_a1/