Related papers: Equilibrium and Non-Equilibrium diffusion approxim…
The one-dimensional problem of the nonlinear heat equation is considered. We assume that the heat flow in the origin of coordinates is the power function of time and the initial temperature is zero. Approximate solutions of the problem are…
In this manuscript, we propose a non-equilibrium temperature by a temperature dependent Vlasov equation for the charge particles transport through a environmental reservoir. A new damping force and a inverse damping relaxation time are…
Non-equilibrium radiation is addressed theoretically by means of a stochastic lattice-gas model. We consider a resonating transmission line composed of a chain of radiation resonators, each at a local equilibrium, whose boundaries are in…
Radiative-conductive systems are intrinsically nonlinear due to the quartic temperature dependence of thermal radiation. Under fixed total heating power, convexity arguments imply that nonuniform temperature distributions radiate more…
This paper shows how the enclosure method which was originally introduced for elliptic equations can be applied to inverse initial boundary value problems for parabolic equations. For the purpose a prototype of inverse initial boundary…
Describing particle transport at the macroscopic or mesoscopic level in non-ideal environments poses fundamental theoretical challenges in domains ranging from inter and intra-cellular transport in biology to diffusion in porous media. Yet,…
In this tutorial, we aim to directly recreate some of our "aha" moments when exploring the impact of heat diffusion on the spatial resolution limit of photothermal imaging. Our objective is also to communicate how this physical limit can…
The problem of the change of photon distribution of thermal light passing through the body surface into the vacuum is discussed. It is shown that the usual assumption that each photon passes through the boundary totally independent of…
We consider a reaction-diffusion system for two densities lying in adjacent domains of $\mathbb{R}^N$. We treat two configurations: either a cylinder and its complement, or two half-spaces. Diffusion and reaction heterogeneities for the two…
The clearing up of a wave nature of the energy and mass transfer phenomena in classical expressions of the molecular-kinetic theory has allowed to find a quantitative measure of intensity of processes of a thermal conductivity, viscosity…
We analyze the statistical properties of radiative transitions for a molecular system possessing discrete, equally spaced, energy levels, interacting with thermal radiation at constant temperature. A radiative fluctuation-dissipation…
We study the asymptotic diffusion processes with (generally nonlocal) open boundaries in one dimension which are exactly solvable by means of the recently developed recursion formula. We investigate the stationary states, which cannot be…
We discuss relativistic dynamics in a random electromagnetic field which can be considered as a high temperature limit of the quantum electromagnetic field in a heat bath (cavity) moving with a uniform velocity w. We derive diffusion…
We study heat radiation and heat transfer for pointlike particles in a system of other objects. Starting from exact many-body expressions found from scattering theory and fluctuational electrodynamics, we find that transfer and radiation…
We consider initial-boundary value problems (IBVPs) on a finite interval for the system of the energy balance equation and Guyer-Krumhansl constitutive equation. Boundary conditions comprise various models of behavior of a physical system…
To determine the electron heat flux density on macroscopic scales, the most widely used approach is to solve a diffusion equation through a multi-group technique. This method is however restricted to transport induced by temperature…
We study thermal radiation outside equilibrium. The situation considered consists of two bodies emitting photons at two different temperatures. We show that the system evolves to a stationary state characterized by an energy current which…
The near-field interaction between two neighboring particles is known to produce enhanced radiative heat transfer. We advance in the understanding of this phenomenon by including the full electromagnetic particle response, heat exchange…
Radiative transfer equation in plane parallel geometry and Kompaneets equation is solved simultaneously to obtain theoretical spectrum of 1-125 KeV photon energy range. Diffuse radiation field is calculated using time-independent radiative…
In order to constrain the models describing circumstellar environments, it is necessary to solve the radiative transfer equation in the presence of absorption and scattering, coupled with the equation for radiative equilibrium. However,…