Related papers: A pseudospectral method for solution of the radiat…
We solve the radiative transfer equation (RTE) in anisotropically scattering media as an infinite series. Each series term represents a distinct number of scattering events, with analytical solutions derived for zero and single scattering.…
Addressing the problem of photon multiple scattering interference caused by turbid media in optical measurements, biomedical imaging, environmental monitoring and other fields, existing Monte Carlo light scattering simulations widely adopt…
We explore the application of Monte Carlo transport methods to solving coupled radiation-hydrodynamics problems. We use a time-dependent, frequency-dependent, 3-dimensional radiation transport code, that is special relativistic and includes…
The radiative transfer equation (RTE) is a cornerstone for describing the propagation of electromagnetic radiation in a medium, with applications spanning atmospheric science, astrophysics, remote sensing, and biomedical optics. Despite its…
This paper introduces a mathematical approach that allows one to numerically solve the nonclassical transport equation in a deterministic fashion using classical numerical procedures. The nonclassical transport equation describes particle…
We study the travel time tomography problem for transversely isotropic media using the artificial boundary method used in works in X-ray tomography and boundary rigidity problems. The analysis involved requires a modification of the…
We give a new and constructive proof of the existence of global-in-time weak solutions of the 3-dimensional incompressible semi-geostrophic equations (SG) in geostrophic coordinates, for arbitrary initial measures with compact support. This…
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…
We present a numerical method for handling the resolution of a general transport equation for radiative particles, aimed at physical problems with a general spherical geometry. Having in mind the computational time difficulties encountered…
We propose a neural network-based real-time volume rendering method for realistic and efficient rendering of volumetric media. The traditional volume rendering method uses path tracing to solve the radiation transfer equation, which…
We derive new equations using the mixed-frame approach for one- and two-dimensional (axisymmetric) time-dependent radiation transport and the associated couplings with matter. Our formulation is multi-group and multi-angle and includes…
A method for the fast and accurate solution of the radiative transfer equation in plane-parallel media with coherent isotropic scattering is presented. This largely analytical approach uses the formalism of meromorphic functions in order to…
Pseudospectral numerical schemes for solving the Dirac equation in general static curved space are derived using a pseudodifferential representation of the Dirac equation along with a simple Fourier-basis technique. Owing to the presence of…
In order to choose a numerical method for solving the time dependent equations of radiative transport, we obtain an exact solution for the time dependent radiation field in a one dimensional infinite medium with monochromatic, isotropic…
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, we present an open-source, automated, and multi-faceted computational-statistical platform to obtain synthetic homogeneous isotropic turbulent flow and passive scalar transport. A parallel implementation of the well-known…
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…
We describe a mesh-free three-dimensional numerical scheme for solving the incompressible semi-geostrophic equations based on semi-discrete optimal transport techniques. These results generalise previous two-dimensional implementations. The…
The nonclassical transport equation models particle transport processes in which the particle flux does not decrease as an exponential function of the particle's free-path. Recently, a spectral approach was developed to generate…
The transport of energetic particles in a spatially varying magnetic field is described by the focused transport equation. In the past two versions of this equation were investigated. The more commonly used standard form described a…