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This document contains working annotations on the Virtual Element Method (VEM) for the approximate solution of diffusion problems with variable coefficients. To read this document you are assumed to have familiarity with concepts from the…
Volume or statistical averaging of the microscopic Maxwell equations (MEs), i.e. transition from microscopic MEs to their macroscopic counterparts, is one of the main steps in electrodynamics of materials. In spite of the fundamental…
Aberration-corrected Scanning Transmission Electron Microscopy (STEM) has become an essential tool in understanding materials at the atomic scale. However, tuning the aberration corrector to produce a sub-{\AA}ngstr\"om probe is a complex…
The mesoscopic concept is a way to deal with complex materials with an internal structure within continuum mechanics. It consists of extending the domain of the balance equations by mesoscopic variables and of introducing a local…
It is demonstrated that, making minimal changes in ordinary quantum mechanics, a reasonable irreversible quantum mechanics can be obtained. This theory has a more general spectral decompositions, with eigenvectors corresponding to unstable…
Microelectromechanical systems (MEMS) resonators serve as frequency selective components in applications ranging from biology to communications. In this paper, the dynamic behavior of an RF MEMS disk resonator is formulated using an…
Fractional differential operators provide an attractive mathematical tool to model effects with limited regularity properties. Particular examples are image processing and phase field models in which jumps across lower dimensional subsets…
The advantages of convergent beam electron diffraction for symmetry determination at the scale of a few nm are well known. In practice, the approach is often limited due to the restriction on the angular range of the electron beam imposed…
In this article, the piecewise-linear finite element method (FEM) is applied to approximate the solution of time-fractional diffusion equations on bounded convex domains. Standard energy arguments do not provide satisfactory results for…
A number of visions for a new generation of dose-efficient electron microscopes have been advanced. These proposals, while inspired by quantum principles, make little contact with the broader field of quantum metrology. We discuss a…
In quantum computing systems the quantum states of qubits can be modified among others by applying light pulses. In order to achieve low computing error rates these pulses have to be precisely shaped in magnitude and phase. In practical…
Structured electron beams carrying orbital angular momentum are currently of considerable interest, both from a fundamental point of view and for application in electron microscopy and spectroscopy. Until recently, most studies have focused…
Metasurfaces are arrays of subwavelength meta-atoms that shape waves in a compact and planar form factor. Analysis and design of metasurfaces require methods for modeling their interactions with waves. Conventional modeling techniques…
We compare the light extinction spectra of elongated gold nanoparticles with different shapes (cylinder, spherocylinder and ellipsoid) and sizes of 10 to 100~nm. We argue that the equivalence of the various moments of mass distribution is…
We consider the linear regression problem of estimating an unknown, deterministic parameter vector based on measurements corrupted by colored Gaussian noise. We present and analyze blind minimax estimators (BMEs), which consist of a bounded…
Recently, modal expansion methods (MEMs) were developed to accurately predict the extinction and scattering spectra of bare and coated plasmonic particles. However, it remains uncertain whether the accuracy of analytical models is preserved…
We report the characterization of an achromatic focusing metasurface at oblique incident angles. We show that in addition to the inherent off-axis aberrations that occurs due to the hyperbolic phase profile of the metasurface, the focusing…
We present a mathematical formalism describing the propagation of a completely general electromagnetic wave in a birefringent medium. Analytic formulas for the refraction and reflection from a plane interface are obtained. As a particular…
Particle beam eigen-emittances comprise the lowest set of rms-emittances that can be imposed to a beam through symplectic optical elements. For cases of practical relevance this paper introduces an approximation providing a very simple and…
The focusing of atoms interacting with both far-detuned and resonant standing wave fields in the thin lens regime is considered. The thin lens approximation is discussed quantitatively from a quantum perspective. Exact quantum expressions…