Abstract
A closed system of differential-difference equations describing thermal processes in one-dimensional harmonic crystals is obtained in the paper. An equation connecting the heat flow and the kinetic temperature is obtained as a solution of the system. The obtained law of heat conduction is different from Fourier’s law and results in an equation that combines properties of the standard heat equation and the wave equation. The resulting equation is an analytic consequence from the dynamical equations for the particles in the crystal. Unlike equations of hyperbolic heat conduction, this equation is time-reversible and has only one independent parameter. A general analytical solution of this differential equations is obtained, and the analytical results are confirmed by computer simulations.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
D. S. Chandrasekharaiah, Appl. Mech. Rev. 39 (3), 355 (1986).
K. V. Poletkin, G. G. Gurzadyan, J. Shang, and V. Kulish, Appl. Phys., Ser. B 107, 137 (2012).
Z. Rieder, J. L. Lebowitz, and E. Lieb, J. Math. Phys. 8 (5), 1073 (1967).
A. Dhar, Adv. Phys. 57 (5), 457 (2008).
A. A. Le-Zakharov and A. M. Krivtsov, Dokl. Phys. 53 (5), 261 (2008).
A. M. Krivtsov, Deformation and Fracture of Solids with Microstructure (Fizmatlit, Moscow, 2007), p. 304 (in Russian).
Mechanics—from Discrete to Continuous, Ed. by V. M. Fomin (Izd. SO RAN, Novosibirsk, 2008), p. 243 (in Russian).
W. G. Hoover and C. G. Hoover, Time Reversibility, Computer Simulations, Algorithms, Chaos, Advanced Series in Nonlinear Dynamics 13 (World Scientific, 2012), p. 397.
R. V. Goldstein and N. F. Morozov, Phys. Mesomechan. 10 (5–6), 235 (2007).
A. M. Krivtsov and N. F. Morozov, Phys. Solid State 44 (12), 2260 (2002).
A. M. Krivtsov, Dokl. Phys. 59 (9), 427 (2014).
A. M. Krivtsov, in Proc. of XXXIV Summer School “Advanced Problems in Mechanics” (St. Petersburg, Russia, 2007), pp. 261–273.
M. Born and K. Huang, Dynamical Theory of Crystal Lattices (Clarendon Press, Oxford, 1954), p. 432.
M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Government Printing Office, U.S., 1972), p. 1046.
M. B. Babenkov and E. A. Ivanova, Cont. Mechan. Thermodynam. 26 (4), 483 (2013).
Author information
Authors and Affiliations
Corresponding author
Additional information
Published in Russian in Doklady Akademii Nauk, 2015, Vol. 464, No. 2, pp. 162–166.
Presented by Academician N.F. Morozov November 24, 2014
Rights and permissions
About this article
Cite this article
Krivtsov, A.M. Heat transfer in infinite harmonic one-dimensional crystals. Dokl. Phys. 60, 407–411 (2015). https://doi.org/10.1134/S1028335815090062
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1028335815090062