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Our ability to numerically model and understand the complex flow behavior of solid-bearing suspensions has increased significantly over the last couple of years, partly due to direct numerical simulations that compute flow around individual…
High-Sfrequency (HF) ray tracing in the complex ionospheric medium generally faces a fundamental trade-off between path accuracy and computational efficiency. This paper presents a high-fidelity Ray Tracing Method (RTM) synergistically…
The implementation of an efficient self-consistent field (SCF) method including both scalar relativistic effects and spin-orbit interaction in density functional theory (DFT) is presented. We make use of Gaussian-type orbitals (GTOs) and…
We investigate the absorption and scattering of charged massive scalar waves by the Kerr-Newman black-bounce spacetime when the waves are incident along the rotation axis. Our findings indicate that a faster (slower) rotating spacetime or a…
Two methods are developed for solving the steady-state spherically symmetric radiative transfer equation for resonance line radiation emitted by a point source in the Intergalactic Medium. One method is based on solving the ray and moment…
The key information about any nanoscale system are orientations and conformations of its parts. Unfortunately, these details are often hidden below the diffraction limit and elaborate techniques must be used to optically probe them. Here,…
A new approach is described to the evaluation of the S-matrix in three-dimensional atom-diatom reactive quantum scattering theory. The theory is developed based on natural collision coordinates where progress along the reaction coordinate…
Spectral dimensionality reduction algorithms are widely used in numerous domains, including for recognition, segmentation, tracking and visualization. However, despite their popularity, these algorithms suffer from a major limitation known…
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…
Problems with dominant advection, discontinuities, travelling features, or shape variations are widespread in computational mechanics. However, classical linear model reduction and interpolation methods typically fail to reproduce even…
We propose a communication- and computation-efficient distributed optimization algorithm using second-order information for solving ERM problems with a nonsmooth regularization term. Current second-order and quasi-Newton methods for this…
The experimental consequences of different order parameters in iron-based superconductors are theoretically analyzed. We consider both nodeless and nodal order parameters, with an emphasis on the $\cos(k_x)\cdot \cos(k_y)$ nodeless order…
In this paper we develop a time reversal method for the radiative transport equation to solve two problems: an inverse problem for the recovery of an initial condition from boundary measurements, and the exact boundary controllability of…
Neutron stars (NSs) in low-mass X-ray binaries rotate at frequencies high enough to significantly deviate from sphericity ($\nu_* \sim$ 200--600 Hz). We investigate the effects of rapid rotation on the observational appearance of a NS. We…
Efficient numerical methods are required for the design of optimised devices. In magnonics, the primary computational tool is micromagnetic simulations, which solve the Landau-Lifshitz equation discretised in time and space. However, their…
This article is concerned with the numerical solution of subspace optimization problems, consisting of minimizing a smooth functional over the set of orthogonal projectors of fixed rank. Such problems are encountered in particular in…
On the base of a 1D Shr\"{o}dinger equation the non-linear first-order differential equation (Ricatti type) for a quantum wave impedance function was derived. The advantages of this approach were discussed and demonstrated for a case of a…
Spectral deferred corrections (SDC) are a class of iterative methods for the numerical solution of ordinary differential equations. SDC can be interpreted as a Picard iteration to solve a fully implicit collocation problem, preconditioned…
A first-principles theory of resonant magnetic scattering of x rays is presented. The scattering amplitudes are calculated using a standard time-dependent perturbation theory to second order in the electron-photon interaction vertex. In…
This paper studies the shallow Ritz method for solving the one-dimensional diffusion problem. It is shown that the shallow Ritz method improves the order of approximation dramatically for non-smooth problems. To realize this optimal or…