Related papers: Three-dimensional analytical discrete-ordinates me…
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 new set of discrete ordinates is proposed for one-dimensional radiative transfer in spheres with central symmetry. The set is structured with un-normalized circular functions. This resulted in a conservative and closed set of discrete…
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…
We consider optical tomography with structured illumination in spatial-frequency domain using the three-dimensional radiative transport equation. Without the diffusion approximation, the radiative transport equation is solved by the…
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…
Case's method obtains solutions to the radiative transport equation as superpositions of elementary solutions when the specific intensity depends on one spatial variable. In this paper, we find elementary solutions when the specific…
In linear transport theory, three-dimensional equations reduce to one-dimensional equations by means of rotated reference frames. In this paper, we illustrate how the technique works and three-dimensional transport theories are obtained.
The discrete ordinates method (DOM) of solution to the 1D radiative transfer equation has been an effective method of solution for nearly 70 years. During that time, the method has experienced numerous improvements as numerical and…
The FN method is an accurate and efficient numerical method for the one-dimensional radiative transport equation. In this paper the FN method is extended to three dimensions using rotated reference frames. To demonstrate the method, the…
Particle transport through a duct by Lambertian reflection from duct walls is again considered. This popular transport example has been solved by most numerical transport methods except notably one- the method of doubling. We shall show…
A mapping is obtained relating analytical radial Coulomb systems in any dimension greater than one to analytical radial oscillators in any dimension. This mapping, involving supersymmetry-based quantum-defect theory, is possible for…
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…
An $\left( n+1\right) -$D coefficient inverse problem for the radiative stationary transport equation is considered for the first time. A globally convergent so-called convexification numerical \ method is developed and its convergence…
Any three-dimensional Riemannian metric can be locally obtained by deforming a constant curvature metric along one direction. The general interest of this result, both in geometry and physics, and related open problems are stressed.
Electromagnetism in an inhomogeneous dielectric medium at rest is described using the methods of differential geometry. In contrast to a general relativistic approach the electromagnetic fields are discussed in three-dimensional space only.…
A numerical scheme is proposed for the solution of the three-dimensional radiative transfer equation with variable optical depth. We show that time-dependent ray tracing is an attractive choice for simulations of astrophysical ionization…
An indirect, hybrid Monte Carlo discretization of general relativistic kinetic theory suitable for the development of numerical schemes for radiation transport is presented. The discretization is based on surface flux estimators obtained…
Diffusive cosmic-ray transport in nonuniform large-scale magnetic fields in the presence of boundaries is considered. Reflecting and absorbing boundary conditions are derived for a modified telegraph equation with a convective term.…
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 study the reconstruction of the attenuation and absorption coefficients in a stationary linear transport equation from knowledge of albedo operator in dimension $n\geq 3$ on a Riemannian manifold in the presence of a magnetic field. We…