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The radiative transfer equation (RTE) for polarized light accepts a convenient exponential solution when the absorption matrix commutes with its integral. We characterize some of the matrix depth variations which are compatible with the…

Astrophysics · Physics 2007-05-23 M. Semel , A. Lopez Ariste

Compton scattering between electrons and photons plays a crucial role in astrophysical plasmas. Many important aspects of this process can be captured by using the so-called Compton scattering kernel. For isotropic media, exact analytic…

Cosmology and Nongalactic Astrophysics · Physics 2019-10-03 Abir Sarkar , Jens Chluba , Elizabeth Lee

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.…

Computational Physics · Physics 2020-01-01 Ruo Li , Weiming Li , Lingchao Zheng

Simple yet accurate results for radiative transfer in layered media with discontinuous refractive index are obtained by the method of K-integrals, originally developed for neutron transport analysis. These are certain weighted integrals…

Optics · Physics 2016-01-05 Adrian C Selden

The radiative transfer equation (RTE) has been established as a fundamental tool for the description of energy transport, absorption and scattering in many relevant societal applications, and requires numerical approximations. However,…

Numerical Analysis · Mathematics 2025-05-28 Markus Bachmayr , Riccardo Bardin , Matthias Schlottbom

In a recent article the authors showed that the radiative Transfer equations with multiple frequencies and scattering can be formulated as a nonlinear integral system. In the present article, the formulation is extended to handle reflective…

Numerical Analysis · Mathematics 2023-06-12 Olivier Pironneau , Pierre-Henri Tournier

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…

Statistical Mechanics · Physics 2009-11-11 Michael J. Caola

Rotated reference frames offer fast algorithms for the radiative transport equation (RTE). We review the singular-eigenfunction approach and related numerical methods for the multi-dimensional RTE with rotated reference frames.

Numerical Analysis · Mathematics 2024-05-16 Manabu Machida

We investigate integral formulations and fast algorithms for the steady-state radiative transfer equation with isotropic and anisotropic scattering. When the scattering term is a smooth convolution on the unit sphere, a model reduction step…

Numerical Analysis · Mathematics 2019-02-20 Yuwei Fan , Jing An , Lexing Ying

In this work, the transition matrix elements for inelastic electron--electron scattering are investigated. The angular part is given by spherical harmonics. For the weighted radial wave function overlap, analytic expressions are derived in…

Materials Science · Physics 2013-04-09 Stefan Löffler , Peter Schattschneider

This paper considers the iterative solution of linear systems arising from discretization of the anisotropic radiative transfer equation with discontinuous elements on the sphere. In order to achieve robust convergence behavior in the…

Numerical Analysis · Mathematics 2021-03-11 Jürgen Dölz , Olena Palii , Matthias Schlottbom

We consider the inverse problem of reconstructing the scattering coefficient of a simple radiative transport equation (RTE) used to model light propagation inside a scattering medium. To do so, we extract information from the second term in…

Analysis of PDEs · Mathematics 2025-08-07 Francis Chung , Faith Hensley

Within a covariant Bethe-Salpeter approach, the relativistic complex separable neutron-proton interaction kernel is proposed. The uncoupled partial-wave states with the total angular momentum $J$=0,1 are considered. The multirank separable…

Nuclear Theory · Physics 2011-06-23 S. G. Bondarenko , V. V. Burov , E. P. Rogochaya

We derive a reciprocity relation for vector radiative transport equation (vRTE) that describes propagation of polarized light in multiple-scattering media. We then show how this result, together with translational invariance of a…

This article studies the problem of approximating functions belonging to a Hilbert space $H_d$ with an isotropic or anisotropic Gaussian reproducing kernel, $$ K_d(\bx,\bt) = \exp\left(-\sum_{\ell=1}^d\gamma_\ell^2(x_\ell-t_\ell)^2\right) \…

Numerical Analysis · Mathematics 2015-01-16 Gregory E. Fasshauer , Fred J. Hickernell , Henryk Woźniakowski

A new formalism is introduced for the transfer of polarized radiation. Stokes parameters are shown to be four-vectors in a Minkowski-like space and, most strikingly, the radiative transfer equation (RTE) turns out to be an infinitesimal…

Astrophysics · Physics 2007-05-23 A. Lopez Ariste , M. Semel

In the article, new asymptotic approximation of the $n$th order is obtained and proposed to be used in calculations of radiation propagation without scattering in optically thick media; the asymptotic approximation is much simpler and more…

Instrumentation and Methods for Astrophysics · Physics 2020-12-23 S. A. Serov , S. S. Serova

Asymptotic radiative transfer (ART), like diffusion theory, assumes the angular intensity distribution incident at a boundary is identical with that in the depth of the scattering medium. However, the asymptotic intensity profile and…

Optics · Physics 2019-05-06 Adrian Selden

In this paper, an improved numerical solver to evaluate the time-dependent radiative transfer equation (RTE) for underwater optical wireless communications (UOWC) is investigated. The RTE evaluates the optical path-loss of light wave in an…

Signal Processing · Electrical Eng. & Systems 2019-05-07 Elmehdi Illi , Faissal El Bouanani , Ki-Hong Park , Fouad Ayoub , Mohamed-Slim Alouini

We discuss the implementation of physically meaningful branching ratios between the CRD and PRD contributions to the emissivity of a polarized multi-term atom in the presence of both inelastic and elastic collisions. Our derivation is based…

Solar and Stellar Astrophysics · Physics 2017-02-01 R. Casini , T. del Pino Aleman , R. Manso Sainz