Thermal processes in a one‐dimensional crystal with regard for the second neighbor interaction

Abstract

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.

Unsteady ballistic heat transport in two-dimensional harmonic graphene lattice

“…Significant progress in the analytical description of unsteady ballistic heat transfer has been achieved in the harmonic approximation [10][11][12][13][14][15][16][17][18][19]. In particular, an equation describing unsteady ballistic heat transfer in the Hooke's crystal 4 was derived in papers [12,13].…”

“…Generalization of results [12] for the case of one-and two-dimensional scalar lattices with arbitrary harmonic interactions was carried out in paper [14]. The influence of interactions with non-nearest neighbors on heat transfer in harmonic one-dimensional chains was studied in paper [15]. Unsteady heat transfer problems with heat supply were solved e.g.…”