Related papers: The hyperbolic heat transfer equation and the abla…
Thermoacoustic tomography is a term for the inverse problem of determining of one of initial conditions of a hyperbolic equation from boundary measurements. In the past publications both stability estimates and convergent numerical methods…
We investigate the convective cooling of a fluid with a quadratic equation of state by performing three-dimensional direct numerical simulations of a flow with a fixed top-boundary temperature, which is lower than the initial fluid…
We consider the problem of fast forward evolution of the processes described in terms of the heat equation. The matter is considered on an adiabatically expanding time-dependent box. Attention is paid to acceleration of heat transfer…
The calculation of the heating rate of cold atoms in vibrating traps requires a theory that goes beyond the Kubo linear response formulation. If a strong "quantum chaos" assumption does not hold, the analysis of transitions shows…
Superconductors like other solids cannot relax instantaneously from excited states to thermodynamic equilibrium. In this paper, relaxation from thermal excitations is investigated, like after absorption of radiation or, under conductor…
We study the relaxation times for a parabolic differential equation whose solution represents the atom dislocation in a crystal. The equation that we consider comprises the classical Peierls-Nabarro model as a particular case, and it allows…
In this paper, we observe how the heat equation in a non-cylindrical domain can arise as the asymptotic limit of a parabolic problem in a cylindrical domain, by adding a potential that vanishes outside the limit domain. This can be seen as…
This paper investigates the numerical modeling of a time-dependent heat transmission problem by the convolution quadrature boundary element method. It introduces the latest theoretical development into the error analysis of the numerical…
Stability of a set of travelling wave solutions to the hyperbolic generalization of the convection-reaction-diffusion equation is studied by means of the qualitative methods and numerical simulation.
Usually, the relaxation times of a gas are estimated in the frame of the Boltzmann equation. In this paper, instead, we deal with the relaxation problem in the frame of the dynamical theory of Hamiltonian systems, in which the definition…
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 study the phenomenon of diffusive radiative heat waves (Marshak waves) under general boundary conditions. In particular, we derive full analytic solutions for the subsonic case, that include both the ablation and the shock wave regions.…
We investigate the large-time behavior of solutions to an outflow problem of the full compressible Navier-Stokes equations in the half line. The non-degenerate stationary solution is shown to be asymptotically stable under large initial…
The exact master equation for a harmonic oscillator coupled to a heat bath, derived recently by Hu, Paz and Zhang, is simplified by taking the weak-coupling, late-time limit. The unique time-independent solution to this simplified master…
We present a new analytic expression for the heat current through a general harmonic network coupled with Ohmic reservoirs. We use a new method that enables us to express the stationary state of the network in terms of the eigenvectors and…
Lasers are becoming a more and more important tool in cutting and shaping materials. Improving precision and effectivity is an ongoing demand in science and industry. One possibility are double pulses. Here we study laser ablation of…
Hydraulic accumulators play a central role as energy storage in nearly all fluid power systems. The accumulators serve as pulsation dampers or energy storage devices in hydro-pneumatic suspensions. The energy carrying gas is compressed and…
NaCl solvation turns the fS portion molecules into the hydrating supersolid phase by ionic polarization and leaves the rest fO portion ordinary. Polarization shortens and stiffens the HO bond and does the O:H nonbond contrastingly in the…
We consider time-independent solutions of hyperbolic equations such as $\d_{tt}u -\Delta u= f(x,u)$ where $f$ is convex in $u$. We prove that linear instability with a positive eigenfunction implies nonlinear instability. In some cases the…
This paper investigates the asymptotic behavior of a hyperbolic relaxation system designed for homogeneous two-phase flows in the limit of vanishing relaxation time. The governing equations comprise conservation laws for mixture mass and…