Discrete and continuum fundamental solutions describing heat conduction in 1D harmonic crystal: Discrete-to-continuum limit and slow-and-fast motions decoupling

Abstract

In the recent paper by Sokolov et al. (Int. J. of Heat and Mass Transfer 176, 2021, 121442) ballistic heat propagation in 1D harmonic crystal is considered and the properties of the exact discrete solution and the solution of the ballistic heat equation introduced by Krivtsov are numerically compared. The aim of this note is to demonstrate that the latter continuum fundamental solution can be formally obtained as the slow time-varying component of the large-time asymptotics for the exact discrete solution on a moving point of observation.

11 pages, 1 figure

References in corpus (1)

• Kapitza thermal resistance in linear and nonlinear chain models: isotopic defect

Cited by in corpus (5)

• Unsteady ballistic heat transport in a 1D harmonic crystal due to a source on an isotopic defect
• The anti-localization of non-stationary linear waves and its relation to the localization. The simplest illustrative problem
• Non-stationary elastic wave scattering and energy transport in a one-dimensional harmonic chain with an isotopic defect
• Unsteady thermal transport in an instantly heated semi-infinite free end Hooke chain
• Anti-localization of non-stationary quasi-waves in a strongly nonlinear $\beta$-FPUT chain