Abstract:
We consider two transient thermal processes in uniformly heated harmonic crystals: (i) equalibration of kinetic and potential energies and (ii) redistribution of the kinetic energy among the spatial directions. Equations describing these two processes in two-dimensional and three-dimensional crystals are derived. Analytical solutions of these equations for the square and triangular lattices are obtained. It is shown that the characteristic time of the transient processes is of the order of ten periods of atomic vibrations. The difference between the kinetic and potential energies oscillates in time. For the triangular lattice, amplitude of the oscillations decays inversely proportional to time, while for the square lattice it decays inversely proportional to the square root of time. In general, there is no equipartition of the kinetic energy among spatial directions, i.e. the kinetic temperature demonstrates tensor properties. In addition, the covariance of velocities of different particles is nonzero even at the steady state. The analytical results are supported by numerical simulations. It is also shown that the obtained solutions accurately describe the transient thermal processes in weakly nonlinear crystals at short times.
Citation:
V. A. Kuzkin, A. M. Krivtsov, “An analytical description of transient thermal processes in harmonic crystals”, Fizika Tverdogo Tela, 59:5 (2017), 1023–1035; Phys. Solid State, 59:5 (2017), 1051–1062
\Bibitem{KuzKri17}
\by V.~A.~Kuzkin, A.~M.~Krivtsov
\paper An analytical description of transient thermal processes in harmonic crystals
\jour Fizika Tverdogo Tela
\yr 2017
\vol 59
\issue 5
\pages 1023--1035
\mathnet{http://mi.mathnet.ru/ftt9597}
\crossref{https://doi.org/10.21883/FTT.2017.05.44396.240}
\elib{https://elibrary.ru/item.asp?id=29405105}
\transl
\jour Phys. Solid State
\yr 2017
\vol 59
\issue 5
\pages 1051--1062
\crossref{https://doi.org/10.1134/S1063783417050201}
Linking options:
https://www.mathnet.ru/eng/ftt9597
https://www.mathnet.ru/eng/ftt/v59/i5/p1023
This publication is cited in the following 34 articles:
Sergey V. Dmitriev, Vitaly A. Kuzkin, Anton M. Krivtsov, “Nonequilibrium thermal rectification at the junction of harmonic chains”, Phys. Rev. E, 108:5 (2023)
Sergei D. Liazhkov, Vitaly A. Kuzkin, “Unsteady two-temperature heat transport in mass-in-mass chains”, Phys. Rev. E, 105:5 (2022)
Ekaterina A. Podolskaya, Anton M. Krivtsov, Vitaly A. Kuzkin, Advanced Structured Materials, 164, Mechanics and Control of Solids and Structures, 2022, 501
Rita I. Babicheva, Alexander S. Semenov, Elvira G. Soboleva, Aleksey A. Kudreyko, Kun Zhou, Sergey V. Dmitriev, “Discrete breathers in a triangular
β
-Fermi-Pasta-Ulam-Tsingou lattice”, Phys. Rev. E, 103:5 (2021)
A M Krivtsov, A S Murachev, “Transition to thermal equilibrium in a crystal subjected to instantaneous deformation”, J. Phys.: Condens. Matter, 33:21 (2021), 215403
O. S. Loboda, E. A. Podolskaya, D. V. Tsvetkov, A. M. Krivtsov, “On the fundamental solution of the heat transfer problem in one-dimensional harmonic crystals”, Continuum Mech. Thermodyn., 33:2 (2021), 485
Anton M. Krivtsov, Vitaly A. Kuzkin, Encyclopedia of Continuum Mechanics, 2020, 642
Vitaly A. Kuzkin, Sergei D. Liazhkov, “Equilibration of kinetic temperatures in face-centered cubic lattices”, Phys. Rev. E, 102:4 (2020)
A.V. Savin, E.A. Korznikova, A.M. Krivtsov, S.V. Dmitriev, “Longitudinal stiffness and thermal conductivity of twisted carbon nanoribbons”, European Journal of Mechanics - A/Solids, 80 (2020), 103920
I. Berinskii, V. A. Kuzkin, “Equilibration of energies in a two-dimensional harmonic graphene lattice”, Phil. Trans. R. Soc. A., 378:2162 (2020), 20190114
Elena A. Korznikova, Vitaly A. Kuzkin, Anton M. Krivtsov, Daxing Xiong, Vakhid A. Gani, Aleksey A. Kudreyko, Sergey V. Dmitriev, “Equilibration of sinusoidal modulation of temperature in linear and nonlinear chains”, Phys. Rev. E, 102:6 (2020)
F. Hadipour, D. Saadatmand, M. Ashhadi, A. Moradi Marjaneh, I. Evazzade, A. Askari, S.V. Dmitriev, “Interaction of phonons with discrete breathers in one-dimensional chain with tunable type of anharmonicity”, Physics Letters A, 384:4 (2020), 126100
Serge N. Gavrilov, Anton M. Krivtsov, “Steady-state kinetic temperature distribution in a two-dimensional square harmonic scalar lattice lying in a viscous environment and subjected to a point heat source”, Continuum Mech. Thermodyn., 32:1 (2020), 41
I. F. Golovnev, E. I. Golovneva, “Calculation of the Temperature Dependence of the Surface Energy
of Metal Nanoclusters in a Wide Range of Their Radii”, Phys Mesomech, 23:4 (2020), 316
D. V. Korikov, “Asymptotic description of fast thermal processes in scalar harmonic lattices”, Phys. Solid State, 62:11 (2020), 2232–2241
O.S. Loboda, E.A. Podolskaya, A.M. Krivtsov, D.V. Tsvetkov, “On the fundamental solution of the heat transfer problem in one-dimensional harmonic crystals”, Comp. Contin. Mech., 12:4 (2019), 390
S. N. Gavrilov, A. M. Krivtsov, D. V. Tsvetkov, “Heat transfer in a one-dimensional harmonic crystal in a viscous environment subjected to an external heat supply”, Continuum Mech. Thermodyn., 31:1 (2019), 255
O. S. Loboda, A. M. Krivtsov, A. V. Porubov, D. V. Tsvetkov, “Thermal processes in a one‐dimensional crystal with regard for the second neighbor interaction”, Z Angew Math Mech, 99:9 (2019)
Daxing Xiong, Sergey V. Dmitriev, Nonlinear Systems and Complexity, 26, A Dynamical Perspective on the ɸ4 Model, 2019, 281
Vitaly A. Kuzkin, “Thermal equilibration in infinite harmonic crystals”, Continuum Mech. Thermodyn., 31:5 (2019), 1401
Citation in format AMSBIB
Contact us: