Related papers: A 3D radiative transfer framework: III. periodic b…
We reduce the solution of the scattering problem defined on the half-line $[0,\infty)$ by a real or complex potential $v(x)$ and a general homogenous boundary condition at $x=0$ to that of the extension of $v(x)$ to the full line that…
We propose a new colour transfer method with Optimal Transport (OT) to transfer the colour of a sourceimage to match the colour of a target image of the same scene that may exhibit large motion changes betweenimages. By definition OT does…
Direct and inverse scattering problem for an operator with non-local potential is solved in the paper. The method is based on the Riemann boundary value problem on a bundle of three straight lines. Description of scattering problem data is…
The paper continues the analysis, started in [1] (Part I,arXiv:2302.04353), of the model open wave-guide problem defined by 2 semi-infinite, rectangular wave-guides meeting along a common perpendicular line. In Part I we reduce the solution…
Polarized NLTE radiative transfer in the presence of scattering in spectral lines and/or in continua may be cast in a so-called reduced form for six reduced components of the radiation field. In this formalism the six components of the…
Multi-level non-local thermodynamic equilibrium (NLTE) radiation transfer calculations have become standard throughout the stellar atmospheres community and are applied to all types of stars as well as dynamical systems such as novae and…
This paper presents an efficient parallel radiative transfer-based inverse-problem solver for time-domain optical tomography. The radiative transfer equation provides a physically accurate model for the transport of photons in biological…
We solve the classic albedo and Milne problems of plane-parallel illumination of an isotropically-scattering half-space when generalized to a Euclidean domain $\mathbb{R}^d$ for arbitrary $d \ge 1$. A continuous family of pseudo-problems…
Scalar wave scattering by many small particles of arbitrary shapes with impedance boundary condition is studied. The problem is solved asymptotically and numerically under the assumptions a << d << lambda, where k = 2pi/lambda is the wave…
Observations and theoretical calculations have shown the importance of non-spherically symmetric structures in supernovae. Thus, the interpretation of observed supernova spectra requires the ability to solve the transfer equation in 3-D…
Accurate angular quadratures are crucial for the numerical solution of three-dimensional (3D) radiative transfer problems, especially when the spectral line polarisation produced by the scattering of anisotropic radiation is included. There…
The radiation condition is the key question in the mathematical modelling for scattering problems in unbounded domains. Mathematically, it plays the role as the "boundary condition" at the infinity, which guarantees the well-posedness of…
We consider the numerical solution of the scattering of time-harmonic plane waves from an infinite periodic array of reflection or transmission obstacles in a homogeneous background medium, in two dimensions. Boundary integral formulations…
The boundary integral method is an efficient approach for solving time-harmonic obstacle scattering problems by a bounded scatterer. This paper presents the directional preconditioner for the iterative solution of linear systems of the…
The transfer matrix formalism is widely used in modeling heat diffusion in layered structures.Due to an intrinsic numerical instability issue, which has not yet drawn enough attention to the heat transfer community,this formalism fails at…
The linearly-polarized solar limb spectrum that is produced by scattering processes contains a wealth of information on the physical conditions and magnetic fields of the solar outer atmosphere, but the modeling of many of its strongest…
3D non-LTE radiative transfer problems are computationally demanding, and this sets limits on the size of the problems that can be solved. So far Multilevel Accelerated Lambda Iteration (MALI) has been to the method of choice to perform…
We study the stationary scattering theory for the matrix Schr\"odinger equation on the half line, with the most general boundary condition at the origin, and with integrable selfadjoint matrix potentials. We prove the limiting absorption…
The inverse scattering transform for a special case of the 3-wave resonant interaction equations with non-vanishing boundary conditions is studied. The Jost solutions and the fundamental analytic solutions (FAS) for the associated spectral…
We review a recently developed transfer matrix formulation of the stationary scattering in two and three dimensions where the transfer matrix is a linear operator acting in an infinite-dimensional function space. We discuss its utility in…