Related papers: Rotated reference frames in radiative transport th…
It is of great interest to solve the inverse problem of stationary radiative transport equation (RTE) in optical tomography. The standard way is to formulate the inverse problem into an optimization problem, but the bottleneck is that one…
Computation of the spherical harmonic rotation coefficients or elements of Wigner's d-matrix is important in a number of quantum mechanics and mathematical physics applications. Particularly, this is important for the Fast Multipole Methods…
Biomedical optical imaging has a possibility of a comprehensive diagnosis of thyroid cancer in conjunction with ultrasound imaging. For improvement of the optical imaging, this study develops a higher order scheme for solving the…
Recent modern space missions deliver invaluable information about origin of our universe, physical processes in the vicinity of black holes and other exotic astrophysical objects, stellar dynamics of our galaxy, etc. On the other hand,…
Reduced rank extrapolation (RRE) is an acceleration method typically used to accelerate the iterative solution of nonlinear systems of equations using a fixed-point process. In this context, the iterates are vectors generated from a…
We describe a new algorithm to solve the time dependent, frequency integrated radiation transport (RT) equation implicitly, which is coupled to an explicit solver for equations of magnetohydrodynamics (MHD) using {\sf Athena++}. The…
The method of moving frames (rep\`ere mobile) was used by Elie Cartan as a way of organizing the identification of differential invariants and solving equivalence problems. In this expository paper, we discuss how moving frames are used to…
We give a convenient representation for any map that is covariant with respect to an irreducible representation of SU(2), and use this representation to analyze the evolution of a quantum directional reference frame when it is exploited as…
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…
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…
In this paper we present a novel method for the numerical solution of linear transport equations, which is based on ridgelets. Such equations arise for instance in radiative transfer or in phase contrast imaging. Due to the fact that…
Due to their high cross field mobility, neutral atoms can have a strong effect on transport even at the low relative densities found inside the separatrix. We use a charge-exchange dominated model for the neutrals, coupled to neoclassical…
The radiative transfer equation (RTE) is a fundamental mathematical model to describe physical phenomena involving the propagation of radiation and its interactions with the host medium. Deterministic methods can produce accurate solutions…
In recent years, the first author has developed three successful numerical methods to solve the 1D radiative transport equation yielding highly precise benchmarks. The second author has shown a keen interest in novel solution methodologies…
We present a new method for the numerical solution of the radiative-transfer equation (RTE) in multidimensional scenarios commonly encountered in computational astrophysics. The method is based on the direct solution of the Boltzmann…
Radiative backpropagation-based (RB) methods efficiently compute reverse-mode derivatives in physically-based differentiable rendering by simulating the propagation of differential radiance. A key assumption is that differential radiance is…
We present the first extension of the special-relativistic Lattice-Boltzmann Method for radiative transport developed by Weih et al. (2020), to solve the radiative-transfer equation in curved spacetimes. The novel approach is based on the…
We present recurrent transformer networks (RTNs) for obtaining dense correspondences between semantically similar images. Our networks accomplish this through an iterative process of estimating spatial transformations between the input…
This paper provides a theoretical and numerical approach to show existence, uniqueness, and the numerical determination of metalenses refracting radiation with energy patterns. The theoretical part uses ideas from optimal transport and for…
We present a critical review of the relativistic rotation transformation of Trocheris and Takeno. A new transformation is proposed which is free from the drawbacks of the former. Some applications are presented.