Related papers: Modeling of a heat equation with a Dirac density
The specific heat capacity of a two-dimensional electron gas is derived for two types of the density of states, namely, the Dirac delta function spectrum and that based on a Gaussian function. For the first time, a closed form expression of…
The thermodynamic properties of strongly correlated system with binary type of disorder are investigated using the combination of the coherent potential approximation and dynamical mean-field theory. The specific heat has a peak at small…
We present the computer simulation results of a chain of hard point particles with alternating masses interacting on its extremes with two thermal baths at different temperatures. We found that the system obeys Fourier's law at the…
We propose a model with a quantized degree of freedom to study the heat transport in quasi-one dimensional system. Our simulations reveal three distinct temperature regimes. In particular, the intermediate regime is characterized by heat…
We study the fully nonlinear heat equation $b(\partial_tu)\partial_tu=\Delta u$ posed in a bounded domain with Dirichlet boundary conditions. Here $b(s)=b^-$ if $s<0$, $b(s)=b^+$ if $s>0$, $b^-\neq b^+$ being two positive constants. This…
The aim of this paper is to verify the new numerical implementation of a binary fluid, heat conduction dominated solidification model. First, we extend a semi-analytical solution to the heat diffusion equation, next, the range of its…
Phase separation of binary fluids quenched by contact with cold external walls is considered. Navier-Stokes, convection-diffusion, and energy equations are solved by lattice Boltzmann method coupled with finite-difference schemes. At high…
We study fluids of hard rods in the vicinity of hard spherical and cylindrical surfaces at densities below the isotropic-nematic transition. The Onsager second virial approximation is applied, which is known to yield exact results for the…
Hybrid resonance is a physical mechanism for the heating of a magnetic plasma. In our context hybrid resonance is a solution of the time harmonic Maxwell's equations with smooth coefficients, where the dielectric tensor is a non diagonal…
This work deals with the problem of determining a non-homogeneous heat conductivity profile in a steady-state heat conduction boundary-value problem with mixed Dirichlet-Neumann boundary conditions over a bounded domain in $\mathbb{R}^n$,…
We consider a nearly-elastic model system with one degree of freedom. In each collision with the "wall", the system can either lose or gain a small amount of energy due to stochastic perturbation. The weak limit of the corresponding slow…
One-dimensional hard rod gases are explicitly constructed as the limits of discrete systems: exclusion processes involving particles of arbitrary length. Those continuum many-body systems in general do not exhibit the same hydrodynamic…
This paper is concerned with an interaction problem between a full compressible, electrically conducting fluid and a thermoelastic shell in a two-dimensional setting. The shell is modelled by linear thermoelasticity equations, and…
In this short paper, periodic homogenization of a steady heat flow in two-component media with highly adhesive contact is performed via the two-scale convergence technique. Our micro-model is based on mass conservation for the heat flow in…
In this article, a finite element model is implemented to analyze hydro-thermal convective flow in a porous medium. The mathematical model encompasses Darcy's law for incompressible fluid behavior, which is coupled with a…
The linearization around one of its equilibrium of a system that describes the correlations between the superfluid component and the normal fluid part of a condensed Bose gas in the approximation of very low temperature and small condensate…
Heat exchangers are devices that typically transfer heat between two fluids. The performance of a heat exchanger such as heat transfer rate and pressure loss strongly depends on the flow regime in the heat transfer system. In this paper, we…
This paper concerns a diffuse interface model for the flow of two incompressible viscoelastic fluids in a bounded domain. More specifically, the fluids are assumed to be macroscopically immiscible, but with a small transition region, where…
Large-scale electrical and thermal currents in ordinary metals are well approximated by effective medium theory: global transport properties are governed by the solution to homogenized coupled diffusion equations. In some metals, including…
We study a two-component reaction-diffusion system in which one of the reaction terms becomes singularly large. Assuming that the initial data are nonnegative and mutually segregated, we prove that the solution converges to that of the heat…