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Four-dimensional scanning transmission electron microscopy (4D-STEM) enables mapping of diffraction information with nanometer-scale spatial resolution, offering detailed insight into local structure, orientation, and strain. However, as…
The convergence of iterative schemes to achieve self-consistency in mean field problems such as the Schr\"odinger-Poisson equation is notoriously capricious. It is particularly difficult in regimes where the non-linearities are strong such…
An approach for the crystallographic mapping of two-phase alloys on the nanoscale using a combination of scanned precession electron diffraction and open-source python libraries is introduced in this paper. This method is demonstrated using…
Anderson localization of classical waves in disordered media is a fundamental physical phenomenon that has attracted attention in the past three decades. More recently, localization of polar excitations in nanostructured metal-dielectric…
A rigorous approach for solving canonical circular open-ended dielectric-lined waveguide diffraction problems is presented. This is continuation of our recent paper [1] where a simpler case of uniform dielectric filling has been considered.…
Schwinger-Dyson equations (SDEs) provide a natural staring point to study non-perturbative phenomena such as dynamical chiral symmetry breaking in gauge field theories. We briefly review this research in the context of quenched quantum…
This paper introduces the sparsifying preconditioner for the pseudospectral approximation of highly indefinite systems on periodic structures, which include the frequency-domain response problems of the Helmholtz equation and the…
A nonlinear Schrodinger equation arising from light propagation down an inhomogeneous medium is considered. The inhomogeneity is reflected through a non-uniform coefficient of the non-linear term in the equation. In particular, a…
A novel variant of spectral phase interferometry for direct electric-field reconstruction (SPIDER) is introduced and experimentally demonstrated. Other than most previously demonstrated variants of SPIDER, our method is based on a…
Chen et al. (1) applied three-dimensional (3D) Fourier filtering together with equal-slope tomographic reconstruction for an observation of nearly all the atoms in a multiply twinned platinum nanoparticle. However, their methodology suffers…
Advancements in fast electron detectors have enabled the statistically significant sampling of crystal structures on the nanometre scale by means of Scanning Electron Nanobeam Diffraction (SEND). Characterisation of structural similarity…
Motivated by the discrete dipole approximation (DDA) for the scattering of electromagnetic waves by a dielectric obstacle that can be considered as a simple discretization of a Lippmann-Schwinger style volume integral equation for…
This work studies a stabilization technique for first-order hyperbolic differential equations used in DNA transcription modeling. Specifically we use the Lighthill-Whitham-Richards Model with a nonlinear Greenshield's velocity proposed in…
Optical imaging methods are typically restricted to a resolution of order of the probing light wavelength $\lambda_p$ by the Rayleigh diffraction limit. This limit can be circumvented by making use of multiphoton detection of correlated…
An efficient low-order scaling method is presented for large-scale electronic structure calculations based on the density functional theory using localized basis functions, which directly computes selected elements of the density matrix by…
We propose a method for obtaining effective lifetimes of scattering electronic states for avoiding the artificially confinement of the wave function due to the use of incomplete basis sets in time-dependent electronic-structure calculations…
A high-order convergent and robust numerical solver is constructed and used to find complex eigenwavenumbers and electromagnetic eigenfields of dielectric objects with axial symmetry. The solver is based on Fourier--Nystr\"om discretization…
Various properties of the general two-center two-electron integral over the explicitly correlated exponential function are analyzed for the potential use in high precision calculations for diatomic molecules. A compact one dimensional…
This paper describes the implementation of the direct solution method (DSM) using radial spectral elements for the calculation of synthetic seismograms in self-gravitating, spherically symmetric, non-rotating, anelastic, and transversely…
The displacement field in highly non uniformly strained crystals is obtained by addition of constraints to an iterative phase retrieval algorithm. These constraints include direct space density uniformity and also constraints to the sign…