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The major challenges for a fully polarized radiative transfer driven approach to Zeeman-Doppler imaging are still the enormous computational requirements. In every cycle of the iterative interplay between the forward process (spectral…
Hadron production at low transverse momenta in semi-inclusive deep inelastic scattering can be described by transverse momentum dependent (TMD) factorization. This formalism has also been widely used to study the Drell-Yan process and…
Accelerating the learning of Partial Differential Equations (PDEs) from experimental data will speed up the pace of scientific discovery. Previous randomized algorithms exploit sparsity in PDE updates for acceleration. However such methods…
We develop a domain-decomposition model reduction method for linear steady-state convection-diffusion equations with random coefficients. Of particular interest to this effort are the diffusion equations with random diffusivities, and the…
Partial frequency redistribution (PRD), describing the formation of the line profile, has negligible observational effects for optical depths smaller than ~10^3, at the resolving power of most current instruments. However, when the spectral…
The objective of polarization rendering is to simulate the interaction of light with materials exhibiting polarization-dependent behavior. However, integrating polarization into rendering is challenging and increases computational costs…
Aims: This paper extends previous studies in modeling time varying linear polarization due to axisymmetric magnetic fields in rotating stars. We use the Hanle effect to predict variations in net line polarization, and use geometric…
The physical interpretation of spectropolarimetric observations of lines of neutral helium, such as those of the 10830 A multiplet, represents an excellent opportunity for investigating the magnetism of plasma structures in the solar…
Several strong solar resonance lines show observable linear scattering polarization signals, holding a great potential for investigating the magnetism of the outer solar atmosphere. Accurately modeling these signals requires solving the…
The linearly-polarized solar limb spectrum that is produced by scattering processes contains a wealth of information on the physical conditions and magnetic fields of the solar outer atmosphere, but the modeling of many of its strongest…
A domain decomposition method for the solution of general variable-coefficient elliptic partial differential equations on regular domains is introduced. The method is based on tessellating the domain into overlapping thin slabs or shells,…
Polarization that is produced by coherent scattering can be modified by magnetic fields via the Hanle effect. According to standard theory the Hanle effect should only be operating in the Doppler core of spectral lines but not in the wings.…
The weak, turbulent magnetic fields that supposedly permeate most of the solar photosphere are difficult to observe, because the Zeeman effect is virtually blind to them. The Hanle effect, acting on the scattering polarization in suitable…
Polarized NLTE radiative transfer in the presence of scattering in spectral lines and/or in continua may be cast in a so-called reduced form for six reduced components of the radiation field. In this formalism the six components of the…
In his monograph Chebyshev and Fourier Spectral Methods, John Boyd claimed that, regarding Fourier spectral methods for solving differential equations, ``[t]he virtues of the Fast Fourier Transform will continue to improve as the relentless…
Removing the aberrations introduced by the Point Spread Function (PSF) is a fundamental aspect of astronomical image processing. The presence of noise in observed images makes deconvolution a nontrivial task that necessitates the use of…
This article presents an introduction to optical pumping, atomic polarization and the Hanle effect in weakly magnetized stellar atmospheres. Although the physical processes and the theoretical framework described here are of interest for…
A discrete spherical harmonics method is developed for the radiative transfer problem in inhomogeneous polarized planar atmosphere illuminated at the top by a collimated sunlight while the bottom reflects the radiation. The method expands…
The quantum theory of polarized light allows one to model scattering in the solar atmosphere for inferring its properties. This powerful approach has revealed two key long-standing problems in solar physics: the puzzling dilemmas between…
An acoustic wave propagation problem with a log normal random field approximation for wave speed is solved using a sampling-free intrusive stochastic Galerkin approach. The stochastic partial differential equation with the inputs and…