Related papers: Unsteady heat conduction processes in a harmonic c…
An analytical model of unsteady heat transfer in a one-dimensional harmonic crystal is presented. A nonlocal temperature is introduced as a generalization of the kinetic temperature. A closed equation determining unsteady thermal processes…
We consider unsteady heat transfer in a one-dimensional harmonic crystal surrounded by a viscous environment and subjected to an external heat supply. The basic equations for the crystal particles are stated in the form of a system of…
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…
The features for the unsteady process of thermal equilibration ("the fast motions") in a one-dimensional harmonic crystal lying in a viscous environment (e.g., a gas) are under investigation. It is assumed that initially the displacements…
We consider two high-frequency thermal processes in uniformly heated harmonic crystals relaxing towards equilibrium: (i) equilibration of kinetic and potential energies and (ii) redistribution of energy among spatial directions. Equation…
In the paper we apply asymptotic technique based on the method of stationary phase and obtain the approximate analytical description of thermal motions caused by a source on an isotopic defect of an arbitrary mass in a 1D harmonic crystal.…
We study transient thermal processes in infinite harmonic crystals with complex (polyatomic) lattice. Initially particles have zero displacements and random velocities such that distribution of temperature is spatially uniform. Initial…
In the present communication we consider the one-dimensional (1D) isotopically disordered lattice with the harmonic potential. Our analytical method is adequate for any 1D lattice where potential energy can be presented as the quadratic…
Unsteady heat transfer in a harmonic chain is analyzed. Two types of thermal perturbations are considered: 1) initial instant temperature perturbation, 2) external heat supply. Closed equations describing the heat propagation are obtained…
Analytic expressions for the energy eigenvalues and eigenfunctions of a one-dimensional harmonic crystal are obtained. The average energy and density profiles are obtained numerically as a function of temperature. A surprisingly large…
In the present chapter, we discuss an approach for transition from discrete to continuum description of thermomechanical behavior of solids. The transition is carried out for several anharmonic systems: one-dimensional crystal,…
Classical density-functional theory is employed to study finite-temperature trends in the relative stabilities of one-component quasicrystals interacting via effective metallic pair potentials derived from pseudopotential theory. Comparing…
We propose a new simple way to evaluate the effect of anharmonicity on a system's thermodynamic functions such as heat capacity. In this approach, the contribution of all potentially complicated anharmonic effects to constant-volume heat…
A combination of classical density-functional theory and thermodynamic perturbation theory is applied to a survey of finite-temperature trends in the relative stabilities of one-component crystals and quasicrystals interacting via effective…
An instant homogeneous thermal perturbation in the finite harmonic one-dimensional crystal is studied. Previously it was shown that for the same problem in the infinite crystal the kinetic temperature oscillates with decreasing amplitude…
Thermotropic liquid crystals are versatile optical materials that exhibit a state of matter intermediate between liquids and solids. Their properties can change significantly with temperature, pressure, or other external factors, leading to…
In this work exact solutions for the equation that describes anomalous heat propagation in 1D harmonic lattices are obtained. Rectangular, triangular, and sawtooth initial perturbations of the temperature field are considered. The solution…
The fundamental dynamic stability of heat conduction theories beyond Fourier is analyzed in the framework of nonequilibrium thermodynamics. It is shown, that the thermodynamic framework, concave entropy and nonnegative entropy production,…
We analyze the non-equilibrium steady states (NESS) of a one dimensional harmonic chain of $N$ atoms with alternating masses connected to heat reservoirs at unequal temperatures. We find that the temperature profile defined through the…
Transition to thermal equilibrium in a uniformly heated two-dimensional harmonic triangular lattice with nearest neighbor interactions is investigated. Initial conditions, typical for molecular dynamics simulations, are considered.…