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We consider the space-fractional operator with order $0<\alpha<1$ on the metric star graph. The boundary conditions at the vertices of the metric star graph providing the self-adjointness of the operator are derived. The obtained result is…
Sufficient conditions of the existence of electric or magnetic walls on dielectric interfaces are given for a multizone uniform dielectric waveguiding system. If one of two adjacent dielectric zones supports a TEM field distribution while…
We shall construct two boundary states which are corresponding to a dynamical fractional D$p$-brane in the presence of the fluxes of the Kalb-Ramond field and a $U(1)$ gauge potential, in the partially orbifold spacetime $\mathbb{R}^{1,…
Time-reversal symmetry (TRS) may be broken in superconductors with three or more condensates interacting repulsively, yielding two degenerate states specified by chirality of gap functions. We consider a loop of such superconductor with two…
We consider the Dirichlet Laplacian in a waveguide of uniform width and infinite length which is ideally divided into three parts: a "vertex region", compactly supported and with non zero curvature, and two "edge regions" which are…
We design compact waveguide couplers via impedance-tunable transformation optics. By tuning impedance coefficients in the original space, two-dimensional metallic and dielectric waveguide couplers are designed with a high efficiency.…
Recent numerical simulations of flat band models with interactions which show clear evidence of fractionalized topological phases in the absence of a net magnetic field have generated a great deal of interest. We provide an explanation for…
In this paper, an incommensurate fractional order (FO) model has been proposed to generate ECG like waveforms. Earlier investigation of ECG like waveform generation is based on two identical Van-der Pol (VdP) family of oscillators which are…
We analyze an optimal control problem with pointwise tracking for a fractional semilinear elliptic partial differential equation. The diffusion is characterized by the spectral fractional Laplacian $(-\Delta)^s$ with $s \in (1/2,1)$, a…
We demonstrate the appearance of unexpected reflection resonances in corrugated dielectric waveguides. These are due to the curvature of the boundary. The effect is as strong as the ordinary Bragg resonances, and reduces the transmission…
The electrostatic modeling of conductors is a fundamental challenge in various applications, including the prediction of parasitic effects in electrical interconnects, the design of biasing networks, and the modeling of biological,…
For characterizing the Brownian motion in a bounded domain: $\Omega$, it is well-known that the boundary conditions of the classical diffusion equation just rely on the given information of the solution along the boundary of a domain; on…
Hard surfaces or magnetic surfaces can be used to propagate quasi-TEM modes inside closed waveguides. The interesting feature of these modes is an almost uniform field distribution inside the waveguide. But the mechanisms governing how…
Piezoelectric appliances have become hugely important in the past century and computer simulations play an essential part in the modern design process thereof. While much work has been invested into the practical simulation of piezoelectric…
Recently, metamaterials-inspired diffraction gratings (or metagratings) have demonstrated unprecedented efficiency in wavefront manipulation by means of relatively simple structures. Conventional one-dimensional (1D) gratings have a profile…
From measurements of fluctuation spectroscopy and weak nonlinear transport on the semimetallic ferromagnet EuB$_6$ we find direct evidence for magnetically-driven electronic phase separation consistent with the picture of percolation of…
We propose an experimental technique based on all-electric measurements to retrieve the frequency response of a one-dimensional piezoelectric phononic crystal plate, structured periodically with millimeter-scaled metallic strips on its two…
In this paper presents the results obtained in the field of spectral theory operators of fractional differentiation. Proven a number of propositions which represents independent interest in the theory of fractional calculus. Introduced…
It is shown that the dielectric properties of interaction site models of polar fluids can be investigated in computer experiment using not only the charge fluctuations but also correlations corresponding to a current of moving charges. This…
We consider a quantum particle in a waveguide which consists of an infinite straight Dirichlet strip divided by a thin semitransparent barrier on a line parallel to the walls which is modeled by a $\delta$ potential. We show that if the…