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Thermal processes in a one‐dimensional crystal with regard for the second neighbor interaction
Author(s) -
Loboda O. S.,
Krivtsov A. M.,
Porubov A. V.,
Tsvetkov D. V.
Publication year - 2019
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201900008
Subject(s) - thermal , group velocity , front (military) , perturbation (astronomy) , lattice (music) , heat transfer , k nearest neighbors algorithm , front velocity , mechanics , vertical velocity , crystal (programming language) , physics , thermal velocity , classical mechanics , condensed matter physics , materials science , optics , thermodynamics , flow velocity , quantum mechanics , meteorology , computer science , programming language , flow (mathematics) , artificial intelligence , acoustics
An influence of the second neighbor interaction on the process of heat propagation in a one‐dimensional crystal is studied. Previously developed model of the ballistic nature of the heat transfer is used. It is shown that the initial thermal perturbation evolves into two consecutive thermal wave fronts propagating with finite and different velocities. The velocity of the first front corresponds to the maximum group velocity of the discrete crystalline model. The velocity of the second front is determined by the second group‐velocity extremum, which arises at a certain ratio between the stiffnesses of the first and second neighbor interaction in the lattice.