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A spectral element method (SEM) is developed to solve polarized radiative transfer in multidimensional participating medium. The angular discretization is based on the discrete-ordinates approach, and the spatial discretization is conducted…
This work concerns the modeling of radiative transfer in anisotropic turbid media using diffusion theory. A theory for the relationship between microscopic scattering properties (i.e., an arbitrary differential scattering cross-section) and…
We present a comprehensive analytical study of radiative transfer using the method of moments and include the effects of non-isotropic scattering in the coherent limit. Within this unified formalism, we derive the governing equations and…
We provide the first mathematically complete derivation of the Nystr\"om method for low-rank approximation of indefinite kernels and propose an efficient method for finding an approximate eigendecomposition of such kernel matrices. Building…
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,…
The well-known spatial integration schemes in molecular electronic structure theory, immune to cusps and point singularities of some kind at atomic positions, use a set of weighting functions to split the integrand into a sum of…
In this contribution, kernel approximations are applied as ansatz functions within the Deep Ritz method. This allows to approximate weak solutions of elliptic partial differential equations with weak enforcement of boundary conditions using…
Radiative transfer is essential in astronomy, both for interpreting observations and simulating various astrophysical phenomena. However, self-consistent line radiative transfer is computationally expensive, especially in 3D. To reduce the…
A nonsingular analytical solution for the transfer equation in a pure absorber is obtained in central symmetry and in a monochromatic radiation field. The native regular singularity of the equation is removed by applying a linear…
The frequency distribution of photons in frequency that results from single Compton scattering of monochromatic radiation on thermal electrons is derived in the mildly relativistic limit. Algebraic expressions are given for (1) the photon…
The report deals with classical and quantum descriptions of particles that interact with smooth random potentials, for example ultracold atoms in the dipole potential of an optical speckle pattern. In addition, a discussion of the link…
We consider the vector emissivity of the polarized radiation transfer in a $\Lambda$-type atomic transition, which we recently proposed in order to account for both CRD and PRD contributions to the scattered radiation. This expression can…
We present a numerical tool for solving the non-relativistic Kohn-Sham problem for spherically-symmetric atoms. It treats the Schr\"{o}dinger equation as an integral equation relying heavily on convolutions. The solver supports different…
The highly convergent iterative methods developed by Trujillo Bueno and Fabiani Bendicho (1995) for radiative transfer (RT) applications are generalized to spherical symmetry with velocity fields. These RT methods are based on Jacobi,…
Many naturally-occuring models in the sciences are well-approximated by simplified models, using multiscale techniques. In such settings it is natural to ask about the relationship between inverse problems defined by the original problem…
This paper presents approximation methods for time-dependent thermal radiative transfer problems in high energy density physics. It is based on the multilevel quasidiffusion method defined by the high-order radiative transfer equation (RTE)…
F\"orster's theory of resonant energy transfer (FRET) predicts the strength and range of exciton transport between separated molecules. We introduce an exactly soluble model for FRET which reproduces F\"orster's results as well as…
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…
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 nearly optimal explicitly-sparse representation for oscillatory kernels is presented in this work by developing a curvelet based method. Multilevel curvelet-like functions are constructed as the transform of the original nodal basis. Then…