相关论文: Surface concentration of transmission eigenfunctio…
We investigate thermoelectric transport in monolayer graphene across a finite complex barrier within a Landauer scattering framework. Solving the Dirac-Weyl problem exactly, we show that the imaginary part of the barrier renders the…
Three-dimensional geophysical fluids support both internal and boundary-trapped waves. To obtain the normal modes in such fluids we must solve a differential eigenvalue problem for the vertical structure (for simplicity, we only consider…
Cakoni and Nguyen recently proposed very general conditions on the coefficients of Maxwell equations for which they established the discreteness of the set of eigenvalues of the transmission problem and studied their locations. In this…
The Steklov eigenvalue problem, first introduced over 125 years ago, has seen a surge of interest in the past few decades. This article is a tour of some of the recent developments linking the Steklov eigenvalues and eigenfunctions of…
In this paper, we investigate the eigenvalue problem for a non-local dispersal operator defined on a bounded spatial domain with Neumann-type boundary conditions. Unlike the classical Laplacian, the non-local operator lacks compactness,…
We develop a field-theoretic framework, called radiant field theory, to calculate the distribution of transmission eigenvalues for coherent wave propagation in disordered media. At its core is a self-consistent transport equation for a…
This work addresses the Galerkin isogeometric discretization of the one-dimensional Laplace eigenvalue problem subject to homogeneous Dirichlet boundary conditions on a bounded interval. We employ GLT theory to analyze the behavior of the…
We extend classical time-frequency limiting analysis, historically applied to one-dimensional finite signals, to the multidimensional discrete setting. This extension is relevant for images, videos, and other multidimensional signals, as it…
Anisotropic thin sheets of materials possess intriguing properties because of their ability to modify the phase, amplitude and polarization of incident waves. Such sheets are usually modeled by imposing transmission conditions of resistive…
We consider the transmission problem for the Laplace equation on an infinite three-dimensional wedge, determining the complex parameters for which the problem is well-posed, and characterizing the infinite multiplicity nature of the…
We study the relation between quasi-normal modes (QNMs) and transmission resonances (TRs) in one-dimensional (1D) disordered systems. We show for the first time that while each maximum in the transmission coefficient is always related to a…
We consider the propagation of surface shear waves in a half-plane, whose shear modulus $\mu(y)$ and density $\rho(y)$ depend continuously on the depth coordinate $y$. The problem amounts to studying the parametric Sturm-Liouville equation…
The transmission eigenvalue problem (TEP) plays a central role in inverse scattering theory. Despite substantial theoretical progress, the numerical solution of direct and inverse TEP in spherically symmetric domains with variable…
The problem of diffraction of a waveguide mode by a thin Neumann screen is considered. The incident mode is assumed to have frequency close to the cut-off. The problem is reduced to a propagation problem on a branched surface and then is…
In this paper we are concerned with a new class of BVP' s consisting of eigendependent boundary conditions and two supplementary transmission conditions at one interior point. By modifying some techniques of classical Sturm-Liouville theory…
Based on the functional-discrete technique (FD-method), an algorithm for eigenvalue transmission problems with discontinuous flux and integrable potential is developed. The case of the potential as a function belonging to the functional…
We prove a Weyl-type fractal upper bound for the spectrum of the damped wave equation, on a negatively curved compact manifold. It is known that most of the eigenvalues have an imaginary part close to the average of the damping function. We…
The time periodic circuit theory is exploited to introduce an appropriate translation operator that is invariant under the change of the spatial unit cell. Useful properties of the operator are derived. By casting the problem in an…
Invariance in duality transformation, the self-dual property, has important applications in electromagnetic engineering. In the present paper, the problem of most general linear and local boundary conditions with self-dual property is…
We discuss the properties of the transmission function in the k-space for a generic multi-layered structure. In particular we analytically demonstrate that a transmission greater than one in the evanescent spectrum (amplification of the…