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We study the existence of Feller semigroups arising in the theory of multidimensional diffusion processes. We study bounded perturbations of elliptic operators with boundary conditions containing an integral over the closure of the domain…
We present a theoretical and computational framework based on fractional calculus for the analysis of the nonlocal static response of cylindrical shell panels. The differ-integral nature of fractional derivatives allows an efficient and…
The transport properties of interacting electrons for which the spin degree of freedom is taken into account are numerically studied for small two dimensional diffusive clusters. On-site electron-electron interactions tend to delocalize the…
Photonic computing has recently become an interesting paradigm for high-speed calculation of computing processes using light-matter interactions. Here, we propose and study an electromagnetic wave-based structure with the ability to…
Dynamically encircling an exceptional point (EP) in parity-time (PT) symmetric systems shows an interesting chiral dynamics, leading to asymmetric mode switching in which the output modes are different when the encircling direction is…
We investigate the application of windowed Fourier frames (WFFs) to the numerical solution of partial differential equations, focussing on elliptic equations. The action of a partial differential operator (PDO) on a windowed plane wave is…
An explicit moving boundary method for the numerical solution of time-dependent hyperbolic conservation laws on grids produced by the intersection of complex geometries with a regular Cartesian grid is presented. As it employs directional…
Pair density waves (PDWs) are a inhomogeneous superconducting states whose Cooper pairs possess a finite momentum resulting in a oscillatory gap in space, even in the absence of an external magnetic field. There is growing evidence for the…
The modeling and control of single-phase flow systems governed by Partial Differential Equations (PDEs) present challenges, especially under transient conditions. In this work, we extend the Physics-Informed Neural Nets for Control (PINC)…
The hybrid plasmonic waveguide consists of a high-permittivity dielectric nanofiber embedded in a low-permittivity dielectric near a metal surface. This architecture is considered as one of the most perspective candidates for long-range…
Design-oriented boundary conditions for subharmonic oscillations are of great interest recently. Based on a subharmonic oscillation boundary condition reported in a PhD thesis more than a decade ago, extended new boundary conditions are…
During the past few years, metasurfaces have been used to demonstrate optical elements and systems with capabilities that surpass those of conventional diffractive optics. Here we review some of these recent developments with a focus on…
We investigate discrete fractional Laplacians defined on the half-lattice in several dimensions, allowing possibly different fractional orders along each coordinate direction. By expressing the half-lattice operator as a boundary…
We continue to develop a new approach to description of charge kinetics in disordered semiconductors. It is based on fractional diffusion equations. This article is devoted to transient processes in structures under dispersive transport…
We present a frequency domain based $H_\infty$-control strategy to solve boundary control problems for systems governed by parabolic or hyperbolic partial differential equation, where controllers are constrained to be physically…
We formulate a Maxwell version of the codimension-three Riesz/Gaussian quadratic-form representation for perfectly conducting parallel plates. This paper is the Maxwell follow-up to the scalar codimension-three Riesz/Gaussian representation…
With the discovery of new superconductors there was a running to find the justifications for the new properties found in these materials. In order to describe these new effects some theories were adapted and some others have been tried. In…
A periodic arrangement of one-dimensional slits carved in perfect electric conductor is investigated and an equivalent model based on the effective medium theory is derived. The proposed model is no longer fully homogeneous and features…
Metasurfaces offer a powerful platform for effective light manipulation, which is crucial for advanced optical technologies. While designs of polarization-independent structures have reduced the need for polarized illumination, they are…
Dielectric waveguide (DWG) interconnects frequently utilize multimode waveguides due to their low dispersion in the fundamental mode. However, these links are more vulnerable to cross-modal coupling that significantly impacts their overall…