Far Eastern Mathematical Journal

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The Fourier law for a one-dimensional crystal


Guzev M.A.

2018, issue 1, P. 34-38


Abstract
For a large number of particles, an analytic representation is obtained for the heat flux of a one-dimensional harmonic crystal. It is shown that the heat flux from one particle to an another one is not linked with the temperature difference between them, i.e. the classical Fourier law is not satisfied.

Keywords:
Fourier law, one-dimensional harmonic crystal

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References

[1] A.M. Krivcov, “Rasprostranenie tepla v beskonechnom odnomernom garmonicheskom kristalle”, Doklady Akademii nauk, 464:2, (2015), 162–166.
[2] M.A. Guzev, A.A. Dmitriev, “Oscilljacionno-zatuhajuwee povedenie temperatury v kristalle”, Dal'nevost. matem. zhurn., 17:2, (2017), 170–179.
[3] S. Lepri, R. Livi, A. Politi, “Thermal conduction in classical low-dimensional lattices”, Physics Reports, 377, (2003), 1–80.
[4] Dzh.V. Gibbs, Termodinamika. Statisticheskaja mehanika, Nauka, Moskva, 1982.
[5] A.M. Krivcov, “Kolebanija jenergij v odnomernom kristalle”, Doklady Akademii nauk, 458:3, (2014), 279–281.
[6] A.P. Prudnikov, JU.A. Brychkov, O.I. Marichev, Integraly i rjady. JElementarnye funkcii, v 3 t., t. 1, Fizmatlit, Moskva, 2002.

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