Related papers: Singular eigenfunctions for the three-dimensional …
The linear Boltzmann equation can be solved with separation of variables in one dimension, i.e., in three-dimensional space with planar symmetry. In this method, solutions are given by superpositions of eigenmodes which are sometimes called…
The radiative transport equation in a three-dimensional infinite medium is considered. The coefficients of the radiative transport equation are assumed to be constant. For a pencil beam, we extend the analytical discrete-ordinates method to…
In one-dimensional transport theory, the method of analytical discrete ordinates (ADO) is known to be a concise and fast numerical scheme to solve the radiative transport equation. However, the extension of ADO to three dimensions has been…
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…
In this paper, the photon stationary transport equation has been extended from $\mathbb{R}^3$ to $\mathbb{C}^3$. A solution of the inverse problem is obtained on a hyper-sphere and a hyper-cylinder as X-ray and Radon transform,…
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…
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.
The paper considers a class of linear Boltzmann transport equations which models a charged particle transport. The equation is an approximation of the original exact transport equation which involves hyper-singular integrals in their…
An analytical solution to the the three-dimensional telegraph equation is presented. This equation has recently received some attention but so far the treatment has been one-dimensional. By using the structural similarity to the…
In the classical one-dimensional solution of fluid dynamics equations all unknown functions depend only on time t and Cartesian coordinate x. Although fluid spreads in all directions (velocity vector has three components) the whole picture…
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…
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…
The paper considers existence results of solution for a linear coupled system of Boltzmann transport equations and related inverse problem. The system models the evolution of three species of particles, photons, electrons and positrons.…
We present a new ray bending approach, referred to as the Eigenray method, for solving two-point boundary-value kinematic and dynamic ray tracing problems in 3D smooth heterogeneous general anisotropic elastic media. The proposed Eigenray…
We describe traveling waves in a basic model for three-dimensional water-wave dynamics in the weakly nonlinear long-wave regime. Small solutions that are periodic in the direction of translation (or orthogonal to it) form an…
The radiative transport equation accurately describes light transport in participating media such as biological tissues, though analytic solutions are known only for simple geometries. We present a pseudospectral technique to efficiently…
This work considers the propagation of high-frequency waves in highly-scattering media where physical absorption of a nonlinear nature occurs. Using the classical tools of the Wigner transform and multiscale analysis, we derive semilinear…
The decay behavior of the specific intensity is studied for the spatial-frequency domain imaging (SFDI). It is shown using the radiative transport equation that the decay is given by a superposition of different decay modes, and the decay…
An explicit numerical scheme is proposed for solving the initial-boundary value problem for the radiative transport equation in a rectangular domain with completely absorbing boundary condition. An upwind finite difference approximation is…
We consider two classes of linear kinetic equations: with constant collision frequency and constant mean free path of gas molecules (i.e., frequency of molecular collisions, proportional to the modulus molecular velocity). Based homogeneous…