Unsteady ballistic heat transport in infinite harmonic crystals
arXiv:1808.07255 · doi:10.1007/s00161-019-00802-1
Abstract
We study thermal processes in infinite harmonic crystals having a unit cell with arbitrary number of particles. Initially particles have zero displacements and random velocities, corresponding to some initial temperature profile. Our main goal is to calculate spatial distribution of kinetic temperatures, corresponding to degrees of freedom of the unit cell, at any moment in time. An approximate expression for the temperatures is derived from solution of lattice dynamics equations. It is shown that the temperatures are represented as a sum of two terms. The first term describes high-frequency oscillations of the temperatures caused by local transition to thermal equilibrium at short times. The second term describes slow changes of the temperature profile caused by ballistic heat transport. It is shown, in particular, that local values of temperatures, corresponding to degrees of freedom of the unit cell, are generally different even if their initial values are equal. Analytical findings are supported by results of numerical solution of lattice dynamics equations for diatomic chain and graphene lattice. Presented theory may serve for description of unsteady ballistic heat transport in real crystals with low concentration of defects. In particular, solution of the problem with sinusoidal temperature profile can be used for proper interpretation of experimental data obtained by the transient thermal grating technique. Keywords: ballistic heat transport; heat transfer; harmonic crystal; harmonic approximation; polyatomic crystal lattice; complex lattice; kinetic temperature; transient processes; temperature matrix; unsteady heat transport.
arXiv comment34 pages; 11 figures. arXiv admin note: text overlap with arXiv:1808.00504
References in corpus (21)
- Thermal Properties of Graphene, Carbon Nanotubes and Nanostructured Carbon Materials
- Thermal conduction in classical low-dimensional lattices
- Length-dependent thermal conductivity in suspended single-layer graphene
- Heat Transport in low-dimensional systems
- Direct Measurement of Room Temperature Non-diffusive Thermal Transport Over Micron Distances in a Silicon Membrane
- Phonon Transport in Graphene
- Observation of second sound in graphite at temperatures above 100 K
- Fourier's Law for a Harmonic Crystal with Self-consistent Stochastic Reservoirs
- A stochastic model of anomalous heat transport: analytical solution of the steady state
- Non-equilibrium stationary state of a harmonic crystal with alternating masses
- Fast and slow thermal processes in harmonic scalar lattices
- Non-stationary heat conduction in one-dimensional chains with conserved momentum
- Energy transport by acoustic modes of harmonic lattices
- Transverse intrinsic localized modes in monatomic chain and in graphene
- Heat transfer in a one-dimensional harmonic crystal in a viscous environment subjected to an external heat supply
- Hamiltonian Thermostats Fail to Promote Heat Flow
- High-frequency thermal processes in harmonic crystals
- Steady-state kinetic temperature distribution in a two-dimensional square harmonic scalar lattice lying in a viscous environment and subjected to a point heat source
- Approach to thermal equilibrium in harmonic crystals with polyatomic lattice
- Heat wave propagation in a nonlinear chain
- Thermal echo in a finite one-dimensional harmonic crystal
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- Steady-state ballistic thermal transport associated with transversal motions in a damped graphene lattice subjected to a point heat source
- Non-stationary elastic wave scattering and energy transport in a one-dimensional harmonic chain with an isotopic defect