Related papers: The radiative transport equation with heterogeneou…
A variety of boundary value problems in linear transport theory are expressed as a diffusion equation of the two-way, or forward-backward, type. In such problems boundary data are specified only on part of the boundary, which introduces…
This paper is devoted to proving convergence rates of variational and iterative regularization methods under variational source conditions VSCs for inverse problems whose linearization satisfies a range invariance condition. In order to…
We characterize the non-uniqueness in the inverse problem for the stationary transport model, in which the absorption "a" and the scattering coefficient "k" are to be recovered from the albedo operator. We show that "gauge equivalent" pairs…
The radiative transport equation for the Schr\"odinger equation in a periodic potential with a weak random potential in electromagnetic fields is derived using asymptotic expansion.
In previous papers of this series, we presented a formalism able to account for both statistical equilibrium of a multilevel atom and coherent and incoherent scatterings (partial redistribution). aims: This paper provides theoretical…
The chemotaxis system \begin{align*} u_t &= \Delta u - \nabla \cdot (u\nabla v), \\ v_t &= \Delta v - uv, \end{align*} is considered under the boundary conditions $\frac{\partial u}{\partial\nu}- u\frac{\partial v}{\partial\nu}=0$ and…
We present a general method to calculate radiative transfer including scattering in the continuum as well as in lines in spherically symmetric systems that are influenced by the effects of general relativity (GR). We utilize a comoving…
The fractional Boltzmann equation for resonance radiation transport in plasma is proposed. We start from the standard Boltzmann equation, averaging over frequencies leads to appearance of fractional derivative. This fact is in accordance…
It is known that classical electromagnetic radiation at a frequency in resonance with energy splittings of atoms in a dielectric medium can be described using the classical sine-Gordon equation. In this paper we quantize the electromagnetic…
The linear Boltzmann equation governs the absorption and scattering of a population of particles in a medium with an ambient field, represented by a Riemannian metric, where particles follow geodesics. In this paper, we study the possible…
We resolve a long standing question regarding the suitable effective diffusion coefficient of the spherically-symmetric transport equation, which is valid at long times. To that end, we generalize a transport solution in three dimensions…
We study the stability of the reconstruction of the scattering and absorption coefficients in a stationary linear transport equation from knowledge of the full albedo operator in dimension $n\geq3$. The albedo operator is defined as the…
The inverse source problem for the radiative transfer equation is considered, with partial data. Here it is shown that under certain smoothness conditions on the scattering and absorption coefficients, one can recover sources supported in a…
We study gradient corrections to the transport equation for energetic light partons in dense QCD environments. In the diffusion limit, the transport dynamics is solely controlled by small-angle elastic scatterings, leading to transverse…
A new numerical method for X-ray tomography for a specific case of incomplete Radon data is proposed. Potential applications are in checking out bulky luggage in airports. This method is based on the analysis of the transport PDE governing…
We present the first extension of the special-relativistic Lattice-Boltzmann Method for radiative transport developed by Weih et al. (2020), to solve the radiative-transfer equation in curved spacetimes. The novel approach is based on the…
Highly precise numerical solutions to the radiative transfer equation with polarization present a special challenge. Here, we establish a precise numerical solution to the radiative transfer equation with combined Rayleigh and isotropic…
We examine a method for solving an infinite-dimensional tensor eigenvalue problem $H x = \lambda x$, where the infinite-dimensional symmetric matrix $H$ exhibits a translational invariant structure. We provide a formulation of this type of…
We come back to the Cauchy integral equations occurring in radiative transfer problems posed in finite, plane-parallel media with light scattering taken as monochromatic and isotropic. Their solution is calculated following the classical…
The theory of nonlinear spectroscopy on randomly oriented molecules leads to the problem of averaging molecular quantities over the random rotation. We solve this problem for arbitrary tensor rank by deriving a closed-form expression for…