Thermal conductivity in two-dimensional monatomic non-linear lattices

Abstract

The authors investigate the validity of Fourier's law in a two-dimensional monoatomic Toda lattice using the molecular dynamics method. The temperature profiles in the lattice exhibit an exponential behaviour with lattice position. The temperature dependence of thermal conductivity is necessarily derived from the spatial variation of the local temperature, and found to be inversely proportional to the local temperature. The validity of Fourier's law is confirmed by excluding the non-diffusive heat flow from the total heat currents.

Finite Heat Conduction in a 2D Disorder Lattice

“…Based on these studies, several sufficient or necessary conditions of the normal thermal conductivity in a 1D lattices are suggested, such as "nonintegrability is not sufficient to guarantee the normal thermal conductivity in a 1D lattices", "in the Fourier law the phonon-lattice interaction is the key factor in 1D on-site potential or mass disorder lattice", and recently Ref [3] proved rigorously that the conductivity as given by the Green-Kubo formula always diverges in one dimensional momentum conserving systems, Ref [4] and Ref [5] give 1D models where momentum is conserved and yet the conductivity is finite. Several models have been studied on 2D lattices heat conduction, for instant, in Ref [6] a 2D Lorenctz gas, which describes a gas of non-interacting point particles moving in a box, is presented, in Ref [7] numerical simulations are performed for the 2D Toda-lattice. And the divergence of the heat conductivity in the thermodynamic limit is investigated in 2D lattices models of anharmonic solids with nearest-neighbor interaction from single-well potentials by A.Lippi and R.Livi [8].…”

Finite-size effect of the thermal conductivity in one dimensional chain

“…The calculation shows that 1/κ dependent on 1/L linearly under the condition of L l w  ( )and/or L l w  ( ), the relation has been identified and extrapolated to general cases [28,29,[39][40][41][42][43][44][45][46]. However, in our study, the slops (as well as the intercepts) of the two limit cases are not equal, with ).…”

“…In addition to traditional interests, bearing the potential applications in thermoelectrics [3][4][5], the finite-size effect is one of the most hot topics in the study of thermal conductivity . In the early study of molecular dynamics [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45] (which has been used widely for decades), a linear dependence [41,42,45] of the thermal resistance 1/κ on the reciprocal length of the system 1/L was proposed and extrapolated to infinite systems [45,46]. Such relation is supported by some experimental observations [47,48] and is used comprehensively.…”

Soliton dynamics in damped and forced Boussinesq equations

“…(10). In order to compact the calculations we consider here a dissipation term D n containing both the Stokes and the hydrodynamical damping.…”

“…Due to their robust character the soliton excitations are important in the coherent energy transfer and they have been used to explain energy transport in DNA [7]. There is also a growing evidence that nonlinear excitations participate in the heat conduction of anisotropic dielectric crystals [8,9,10,11]. The non-diffusive heat flow was attributed to modified Korteweg-de-Vries solitons in [11].…”