Related papers: Radiative Transfer with long-range interactions in…
We consider the boundary value problem of the stationary transport equation in the slab domain of general dimensions. In this paper, we discuss the relation between discontinuity of the incoming boundary data and that of the solution to the…
The atmospheres of planets (including Earth) and the outer layers of stars have often been treated in radiative transfer as plane-parallel media, instead of spherical shells, which can lead to inaccuracy, e.g. limb darkening. We give an…
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 the transmission problem in bounded domains with dissipative boundary conditions. Under some natural assumptions, we prove uniform bounds of the corresponding resolvents on the real axis at high frequency, and as a consequence, we…
We discuss transport equations resulting from relativistic diffusions in the proper time. We show that a solution of the transport equation can be obtained from the solution of the diffusion equation by means of an integration over the…
Quantum transport in a class of nonlinear extensions of the Rudner-Levitov model is numerically studied in this paper. We show that the quantization of the mean displacement, which embodies the quantum coherence and the topological…
We study the approximation of the radiative transfer equation with a relatively few moments in the spherically symmetric case. We propose a three-moment model based on choosing the beta distribution as the ansatz for the specific intensity.…
Half-space problems in the kinetic theory of gases are of great importance in the study of the asymptotic behavior of solutions of boundary value problems for the Boltzmann equation for small Knudsen numbers. In this work a generally…
We consider the well-posedness of a class of hyperbolic partial differential equations on a one dimensional spatial domain. This class includes in particular infinite-dimensional networks of transport, wave and beam equations, or even…
In this paper, we study the temperature distribution of a body when the heat is transmitted only by radiation. The heat transmitted by convection and conduction is ignored. We consider the stationary radiative transfer equation in the local…
Let $u=u(t,{\bf x},{\bf p})$ satisfy the transport equation $\frac {\partial u}{\partial t}+\frac {{\bf p}}{p_0}\frac{\partial u}{\partial{\bf x}}=f$, where $f=f(t,\bf x,\bf p)$ belongs to $ L^{p}((0,T)\times {\bf R}^{3}\times {\bf R}^{3})$…
We study the kinetic mean-field limits of the discrete systems of interacting particles used for halftoning of images in the sense of continuous-domain quantization. Under mild assumptions on the regularity of the interacting kernels we…
New mathematical and numerical results are given for the coupling of the temperature equation of a fluid with Radiative Transfer: existence and uniqueness and a convergent monotone numerical scheme. The technique is shown to be feasible for…
We develop a general theory of radiative heat exchange between dipoles with time-modulated optical properties. This framework extends fluctuational electrodynamics beyond equilibrium by incorporating nonstationary correlations and memory…
We consider the numerical approximation of boundary conditions in radiative transfer problems by a perfectly matched layer approach. The main idea is to extend the computational domain by an absorbing layer and to use an appropriate…
The transport of energetic particles in a spatially varying magnetic field is described by the focused transport equation. In the past two versions of this equation were investigated. The more commonly used standard form described a…
This work is concerned with the broad question of propagation of regularity for smooth solutions to non-linear Vlasov equations. For a class of equations (that includes Vlasov-Poisson and relativistic Vlasov-Maxwell), we prove that higher…
In this article we study a class of hyperbolic partial differential equations of order one on the semi-axis. The so-called port-Hamiltonian systems cover for instance the wave equation and the transport equation, but also networks of the…
We shall study special regularity properties of solutions to some nonlinear dispersive models. The goal is to show how regularity on the initial data is transferred to the solutions. This will depend on the spaces where regularity is…
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…