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In this paper we develop a framework for moment-based adaptive time integration of deterministic multifrequency thermal radiation transpot (TRT). We generalize our recent semi-implicit-explicit (IMEX) integration framework for gray TRT to…

Numerical Analysis · Mathematics 2026-02-11 Ben S. Southworth , Steven Walton , Steven B. Roberts , HyeongKae Park

We propose in this work a fast numerical algorithm for solving the equation of radiative transfer (ERT) in isotropic media. The algorithm has two steps. In the first step, we derive an integral equation for the angularly averaged ERT…

Numerical Analysis · Mathematics 2019-07-09 Kui Ren , Rongting Zhang , Yimin Zhong

A method is presented which allows one to introduce collective coordinates self-consistently, in distinction to the Caldeira-Leggett model. It is demonstrated how the partition function Z for the total nuclear system can be calculated to…

Nuclear Theory · Physics 2009-11-10 Christian Rummel , Helmut Hofmann

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…

Statistical Mechanics · Physics 2010-09-17 Thomas Christen , Frank Kassubek , Rudolf Gati

The opacity of FRTE depends on not only the material temperature but also the frequency, whose values may vary several orders of magnitude for different frequencies. The gray radiation diffusion and frequency-dependent diffusion equations…

Numerical Analysis · Mathematics 2023-08-16 Xiaojiang Zhang , Peng Song , Yi Shi , Min Tang

Thermal radiation transport (TRT) is a time dependent, high dimensional partial integro-differential equation. In practical applications such as inertial confinement fusion, TRT is coupled to other physics such as hydrodynamics, plasmas,…

Numerical Analysis · Mathematics 2024-08-14 Ben S. Southworth , Samuel S. Olivier , HyeongKae Park , Tommaso Buvoli

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…

Numerical Analysis · Mathematics 2019-03-21 J. C. H. Blake , I. G. Graham , F. Scheben , A. Spence

In this paper we present a multilevel projection-based iterative scheme for solving thermal radiative transfer problems that performs iteration cycles on the high-order Boltzmann transport equation (BTE) and low-order moment equations.…

Numerical Analysis · Mathematics 2026-03-18 Joseph M. Coale , Dmitriy Y. Anistratov

Real-world physical systems, like composite materials and porous media, exhibit complex heterogeneities and multiscale nature, posing significant computational challenges. Computational homogenization is useful for predicting macroscopic…

Computational Engineering, Finance, and Science · Computer Science 2024-07-29 Yuki Sato , Yuto Lewis Terashima , Ruho Kondo

In this work, we prove rigorous error estimates for a hybrid method introduced in [15] for solving the time-dependent radiation transport equation (RTE). The method relies on a splitting of the kinetic distribution function for the…

Numerical Analysis · Mathematics 2023-06-09 Andrés Galindo-Olarte , Victor P. DeCaria , Cory D. Hauck

To determine the electron heat flux density on macroscopic scales, the most widely used approach is to solve a diffusion equation through a multi-group technique. This method is however restricted to transport induced by temperature…

A simplified transient energy-transport system for semiconductors subject to mixed Dirichlet-Neumann boundary conditions is analyzed. The model is formally derived from the non-isothermal hydrodynamic equations in a particular vanishing…

Analysis of PDEs · Mathematics 2012-06-26 Ansgar Jüngel , René Pinnau , Elisa Röhrig

We consider in this contribution a simplified idealized one-dimensional model in a nuclear core reactor coupling the diffusion equation on the neutron flux withthe enthalpy equation for the water which collects the heat produced by this…

Numerical Analysis · Mathematics 2025-03-11 Olivier Lafitte , François Dubois

A new variable Eddington factor (VEF) model is presented for nonlinear problems of thermal radiative transfer (TRT). The VEF model is a data-driven one that acts on known (a-priori) radiation-diffusion solutions for material temperatures in…

Numerical Analysis · Mathematics 2025-08-06 Joseph M. Coale , Dmitriy Y. Anistratov

A new method for the determination of environmental Gd by neutron transmission (NT) experiments is proposed. The NT method is based on the measurements of neutron spectra passing through a target. From the attenuation neutron spectra new…

Nuclear Experiment · Physics 2014-06-04 Cristiana Oprea , Ioan Alexandru Oprea , Alexandru Mihul

A novel method for solving the linear radiative transport equation (RTE) in a three-dimensional homogeneous medium is proposed and illustrated with numerical examples. The method can be used with an arbitrary phase function A(s,s') with the…

Mathematical Physics · Physics 2007-05-23 George Panasyuk , John C. Schotland , Vadim A. Markel

We test approximate approaches to solving a neutrino transport problem that presents itself in the analysis of some accretion-disk models. Approximation #1 consists of replacing the full, angular- dependent, distribution function by a…

Astrophysics · Physics 2016-08-30 R. F. Sawyer

Tensor network techniques, known for their low-rank approximation ability that breaks the curse of dimensionality, are emerging as a foundation of new mathematical methods for ultra-fast numerical solutions of high-dimensional Partial…

The neutron transport equation (NTE) describes the flux of neutrons across a planar cross-section in an inhomogeneous fissile medium when the process of nuclear fission is active. Classical work on the NTE emerges from the applied…

Probability · Mathematics 2020-03-18 Simon C. Harris , Emma Horton , Andreas E. Kyprianou

This paper introduces the use of statistical distributions based on transport differential equations for clear distinction of transport modes within transient kinetic experiments. More specifically,novel techniques are developed for the…

Applications · Statistics 2025-01-08 M. Ross Kunz , Debtanu Maiti , Gregory Yablonsky , Rebecca Fushimi