Related papers: Equilibrium and Non-Equilibrium diffusion approxim…
The subject matter of this paper concerns anisotropic diffusion equations: we consider heat equations whose diffusion matrix have disparate eigenvalues. We determine first and second order approximations, we study the well-posedness of them…
We consider a spatially homogeneous advection-diffusion equation in which the diffusion tensor and drift velocity are time-independent, but otherwise general. We derive asymptotic expressions, valid at large distances from a steady point…
We describe a general radiative equilibrium and temperature correction procedure for use in Monte Carlo radiation transfer codes with sources of temperature-independent opacity, such as astrophysical dust. The technique utilizes the fact…
In this paper, we study the diffusive limit of the steady state radiative heat transfer system for non-homogeneous Dirichlet boundary conditions in a bounded domain with flat boundaries. A composite approximate solution is constructed using…
A formal derivation is presented of the energy transfer rate between radiation and matter due to the scattering of an isotropic distribution of resonant photons. The derivation is developed in the context of the two-level atom in the…
The theory of heat transfer by electromagnetic radiation is based on the radiative transfer equation (RTE) for the radiation intensity, or equivalently on the Boltzmann transport equation (BTE) for the photon distribution. We focus in this…
We study non--equilibrium ensemble corrections to particle masses and the effective potential in the early universe, using a uniform momentum distribution as an example. The resulting thermalization temperature is computed assuming \sm…
This paper concerns the derivation of radiative transfer equations for acoustic waves propagating in a randomly fluctuating half-space in the weak-scattering regime, and the study of boundary effects through an asymptotic analysis of the…
We study the heat equation on a half-space or on an exterior domain with a linear dynamical boundary condition. Our main aim is to establish the rate of convergence to solutions of the Laplace equation with the same dynamical boundary…
The heat equation is considered in the complex medium consisting of many small bodies (particles) embedded in a given material. On the surfaces of the small bodies an impedance boundary condition is imposed. An equation for the limiting…
We present a comprehensive analytical study of radiative transfer using the method of moments and include the effects of non-isotropic scattering in the coherent limit. Within this unified formalism, we derive the governing equations and…
We study the heat equation on a half-space with a linear dynamical boundary condition. Our main aim is to show that, if the diffusion coefficient tends to infinity, then the solutions converge (in a suitable sense) to solutions of the…
We study the thermal insulation of a bounded body $\Omega\subset\mathbb{R}^n$, under a prescribed heat source $f>0$, via a bulk layer of insulating material. We consider a model of heat transfer between the insulated body and the…
We study the radiative heat transfer and the Casimir-Lifshitz force occurring between two bodies in a system out of thermal equilibrium. We consider bodies of arbitrary shape and dielectric properties, held at two different temperatures,…
This paper investigates shape optimization problems in the context of heat transfer, with a focus on the stability and non-optimality of round domains under Robin boundary conditions. Using the flow approach and Steklov eigenvalue…
We study the Radiative Transfer equations coupled with the time dependent temperature equation of a fluid: existence, uniqueness, a maximum principle are established. A short numerical section illustrates the pros and cons of the method.
We examine the non-equilibrium radiative heat transfer between a plate and finite cylinders and cones, making the first accurate theoretical predictions for the total heat transfer and the spatial heat flux profile for three-dimensional…
We present a transport equation for the incoherent propagation of radiation inside a quasi-resonant atomic gas at low temperature. The derivation is based on a generalized Bethe-Salpeter equation taking into account the motion of the atoms.…
We present an effective thermal open boundary condition for convective heat transfer problems on domains involving outflow/open boundaries. This boundary condition is energy-stable, and it ensures that the contribution of the open boundary…
In the present article, we study the diffusion equations with fractional time derivatives. The aim of this paper is to investigate the best possible regularity for the initial value/boundary value problems with non-homogeneous Dirichlet…