Related papers: Equilibrium-diffusion limit of the radiation model
A theory of thermal and nonthermal radiation in a vacuum background of arbitrary temperature generated by relativistic polarizable particle with spin is proposed. When the particle rotates, radiation is produced by vacuum fluctuations even…
Based on the phenomenological theory of heat diffusion, we show that the generated peak temperature $T_{\text{max}}$ after absorption of a laser pulse strongly depends on the pulse duration. We identify three different heat conduction…
Typically, aggregation-diffusion is modeled by parabolic equations that combine linear or nonlinear diffusion with a Fokker-Planck convection term. Under very general suitable assumptions, we prove that radial solutions of the evolution…
The numerical approximation of an inverse problem subject to the convection--diffusion equation when diffusion dominates is studied. We derive Carleman estimates that are on a form suitable for use in numerical analysis and with explicit…
We solve for a system that emits acceleration radiation at two different temperatures. The equilibrium states occur asymptotically in Planck distributions and transition non-thermally. The model is simple enough to obtain a global solution…
We derive an explicit representation of the fundamental solution to the heat equation in a half-space of ${\mathbb R}^N$ with a diffusive dynamical boundary condition, and establish sharp pointwise upper and lower bounds. We also…
We study the blow up solutions of a semilinear reaction diffusion system coupled in both equations and boundary conditions. The main purpose is to understand how the reaction terms and the absorption terms affect the blow-up properties. We…
We provide an explicit analytical calculation that shows the asymptotic approach of the one dimensional Caldeira-Leggett model to thermal equilibrium in the high temperature and weak coupling limit. We investigate a free particle and a…
A non-equilibrium thermodynamics model able to analyze the combined effect of diffusion and adsorption in porous materials is proposed. The model considers the coupled dynamics of the diffusive phase, described by a diffusion type equation,…
We show that, for any spatially discretized system of reaction-diffusion, the approximate solution given by the explicit Euler time-discretization scheme converges to the exact time-continuous solution, provided that diffusion coefficient…
Consider the initial-boundary value problem for the 2-speed Carleman model of the Boltzmann equation of the kinetic theory of gases set in some bounded interval with boundary conditions prescribing the density of particles entering the…
A communication theory for a transmitter broadcasting to many receivers is presented. In this case energetic considerations cannot be neglected as in Shannon theory. It is shown that, when energy is assigned to the information bit,…
The effects of radiation on the structure of shocks in a fully-ionized plasma are investigated by solving the steady-state fluid equations for ions, electrons, and radiation. The electrons and ions are assumed to have the same bulk velocity…
We present high-resolution thermal diffusivity measurements on several near optimally doped electron- and hole-doped cuprate systems in a temperature range that passes through the Mott-Ioffe-Regel limit, above which the quasiparticle…
We develop a microscopic theory of thermalisation for a thermometer coupled to a many-body bath beyond standard Markovian and Fermi-golden-rule assumptions. By modeling interaction matrix elements in the non-interacting basis as independent…
We consider a diffusion process on an evolving surface with a piecewise Lipschitz-continuous boundary from an energetic point of view. We employ an energetic variational approach with both surface divergence and transport theorems to derive…
A system of diffusion-reaction equations coupled with a dissolution-precipitation model is discussed. We start by introducing a microscale model together with its homogenized version. In the present paper, we first derive the corrector…
We show that observing the trajectories of confined particles in a thermal equilibrium state yields an estimate on the free-space diffusion coefficient. For generic trapping potentials and interactions between particles, the estimate comes…
The line of phase equilibrium between the hot and cold phases of a plasma is derived from the intensity of thermal radiation as a function of the plasma density and temperature. The last function is obtained with the help of the condition…
In this paper we study the rate of convergence to the complex balanced equilibrium for some chemical reaction-diffusion systems with boundary equilibria. We first analyze a three-species system with boundary equilibria in some…