Nonstationary heat conduction in one-dimensional models with substrate potential

Abstract

The paper investigates non-stationary heat conduction in one-dimensional models with substrate potential. In order to establish universal characteristic properties of the process, we explore three different models --- Frenkel-Kontorova (FK), phi4+ (${\varphi }^4$+) and phi4- (${\varphi }^4-$). Direct numeric simulations reveal in all these models a crossover from oscillatory decay of short-wave perturbations of the temperature field to smooth diffusive decay of the long-wave perturbations. Such behavior is inconsistent with parabolic Fourier equation of the heat conduction and clearly demonstrates the necessity of hyperbolic models. The crossover wavelength decreases with increase of average temperature. The decay patterns of the temperature field almost do not depend on the amplitude of the perturbations, so the use of linear evolution equations for temperature field is justified. In all model investigated, the relaxation of thermal perturbations is exponential -- contrary to linear chain, where it follows a power law. However, the most popular lowest-order hyperbolic generalization of the Fourier law, known as Cattaneo-Vernotte (CV) or telegraph equation (TE) is not valid for description of the observed behavior of the models with on-site potential. In part of the models a characteristic relaxation times exhibit peculiar scaling with respect to the temperature perturbation wavelength. Quite surprisingly, such behavior is similar to that of well-known model with divergent heat conduction (Fermi-Pasta-Ulam chain) and rather different from the model with normal heat conduction (chain of rotators). Thus, the data on the non-stationary heat conduction in the systems with on-site potential do not fit commonly accepted concept of universality classes for heat conduction in one-dimensional models.

9 pages, 7 figures, corrected version

References in corpus (5)

• Heat conduction in a three dimensional anharmonic crystal
• Normal Heat Conduction in a Chain with Weak Interparticle Anharmonic Potential
• Non-stationary heat conduction in one-dimensional chains with conserved momentum
• Thermal conductivity of a classical one dimensional spin-phonon system
• Heat wave propagation in a nonlinear chain

Cited by in corpus (5)

• Fast and slow thermal processes in harmonic scalar lattices
• Heat transfer in a one-dimensional harmonic crystal in a viscous environment subjected to an external heat supply
• 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
• Scaling of energy spreading in a disordered Ding-Dong lattice
• Mechanical control of heat conductivity in microscopic models of dielectrics