Related papers: Radiative Transfer with long-range interactions in…
In this paper we study the distribution of the temperature within a body where the heat is transported only by radiation. Specifically, we consider the situation where both emission-absorption and scattering processes take place. We study…
Albeit the past intensive research, the governing equation of anomalous diffusion which is observed for the transport of particles underground is still an open problem. In this paper, as a governing equation, the advection-diffusion…
Inspired by many examples in nature, stochastic resetting of random processes has been studied extensively in the past decade. In particular, various models of stochastic particle motion were considered where upon resetting the particle is…
Many important transport phenomena are described by simple mathematical models rooted in the diffusion equation. Geometrical constraints present in such phenomena often have influence of a universal sort and manifest themselves in scaling…
We study existence of random elements with partially specified distributions. The technique relies on the existence of a positive extension for linear functionals accompanied by additional conditions that ensure the regularity of the…
Effective medium theory of transport in disordered systems, whose basis is the replacement of spatial disorder by temporal memory, is extended in several practical directions. Restricting attention to a 1-dimensional system with bond…
This work inspects the thermally activated transfer of solute particles across the interface between two interstitial solid solution phases that equilibrate internally by fast diffusion on conserved arrays of sites. When each phase is…
Efficient numerical approximation of the polarized radiative transfer equation is challenging because this system of ordinary differential equations exhibits stiff behavior, which potentially results in numerical instability. This…
We derive from first principles a one-way radiative transfer equation for the wave intensity resolved over directions (Wigner transform of the wave field) in random media. It is an initial value problem with excitation from a source which…
This paper is devoted to deal with some mathematical and numerical aspects of the radiative integral transfer equations. First, the properties of the raidative integral operators are analyzed. Based on these results, the existence and…
The problem of radio wave reflection from an optically thick plane monotonous layer of magnetized plasma is considered at present work. The plasma electron density irregularities are described by spatial spectrum of an arbitrary form. The…
We derive radiative transport equations for solutions of a Schr\"odinger equation in a periodic structure with small random inhomogeneities. We use systematically the Wigner transform and the Bloch wave expansion. The streaming part of the…
We consider the lattice dynamics in the half-space. The initial data are random according to a probability measure which enforces slow spatial variation on the linear scale $\varepsilon^{-1}$. We establish two time regimes. For times of…
We develop a dynamical theory of heat transfer between two nano systems. In particular, we consider the resonant heat transfer between two nanoparticles due to the coupling of localized surface modes having a finite spectral width. We model…
We generalize known results on transport equations associated to a Lipschitz field $\mathbf{F}$ on some subspace of $\mathbb{R}^N$ endowed with some general space measure $\mu$. We provide a new definition of both the transport operator and…
We consider the classical integral equation reformulation of the radiative transport equation (RTE) in a heterogeneous medium, assuming isotropic scattering. We prove an estimate for the norm of the integral operator in this formulation…
This paper is concerned with quasilinear parabolic reaction-diffusion-advection systems on extended domains. Frameworks for well-posedness in Hilbert spaces and spaces of continuous functions are presented, based on known results using…
We present a study of sound wave propagation in a time dependent random medium and an application to imaging. The medium is modeled by small temporal and spatial random fluctuations in the wave speed and density, and it moves due to an…
Analytical and numerical solutions are obtained for the equation of radiative transfer in ultra-relativistic opaque jets. The solution describes the initial trapping of radiation, its adiabatic cooling, and the transition to transparency.…
In this work, we study the instability of an inverse problem of radiative transport equation with angularly averaged measurement near the diffusion limit, i.e. the normalized mean free path (the Knudsen number) $0 < \eps \ll 1$. It is…