Related papers: Eigenfunctions of Underspread Linear Communication…
This paper presents a diffusion based probabilistic interpretation of spectral clustering and dimensionality reduction algorithms that use the eigenvectors of the normalized graph Laplacian. Given the pairwise adjacency matrix of all…
Given a set of transmission eigenvalues, we describe the connection of such a set to the indicator functions in entire function theory. The indicator functions control the asymptotic growth rate of the solution of the Sturm-Liouville…
We analyze an approximate interior transmission eigenvalue problem in ${\mathbb R}^d$ for $d=2$ or $d=3$, motivated by the transmission problem of a transformation optics-based cloaking scheme and obtained by replacing the refractive index…
Sloshing eigenvalues and eigenfunctions are studied for vertical cylinders of constant, finite depth occupied by a two-layer fluid. Two families of eigenfrequencies are obtained in the form expressing them explicitly via the eigenvalues of…
We develop a compact theory that can be applied to a variety of time-varying dispersive materials. The continuous wave reflection and transmission coefficients are replaced with equivalent operator expressions. In addition to comparing this…
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…
In this paper, we consider a new transmission eigenvalue problem derived from the scattering by a clamped cavity in a thin elastic material. Scattering in a thin elastic material can be modeled by the Kirchhoff--Love infinite plate problem.…
Motivated by the need to localise faults along electrical power lines, this paper adopts a frequency-domain approach to parameter estimation for an infinite-dimensional linear dynamical system with one spatial variable. Since the time of…
This paper is concerned with the intrinsic geometric structure of interior transmission eigenfunctions arising in wave scattering theory. We numerically show that the aforementioned geometric structure can be much delicate and intriguing.…
We have studied the soliton propagation through a segment containing random point-like scatterers. In the limit of small concentration of scatterers when the mean distance between the scatterers is larger than the soliton width, a method…
We study the distribution of transmission eigenvalues of a quantum point contact with nearby impurities. In the semi-classical case (the chemical potential lies at the conductance plateau) we find that the transmission properties of this…
The frequency selectivity of wireless communication channels can be characterized by the delay spread Ds of the channel impulse response. If the delay spread is small compared to the bandwidth W of the input signal, that is, Ds*W…
This paper presents a novel dynamic coverage control algorithm allowing a group of robots to track an optimal-deployment configuration for arbitrary time-varying density functions. Building on singular perturbation theory, the proposed…
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…
Because the desire to explore opaque materials is ordinarily frustrated by multiple scattering of waves, attention has focused on the transmission matrix of the wave field. This matrix gives the fullest account of transmission and…
Scattering hinders the passage of light through random media and consequently limits the usefulness of optical techniques for sensing and imaging. Thus, methods for increasing the transmission of light through such random media are of…
Multilayer networks are widespread in natural and manmade systems. Key properties of these networks are their spectral and eigenfunction characteristics, as they determine the critical properties of many dynamics occurring on top of them.…
We consider the reflection-transmission problem in a waveguide with obstacle. At certain frequencies, for some incident waves, intensity is perfectly transmitted and the reflected field decays exponentially at infinity. In this work, we…
We study the eigenvalues and eigenfunctions of the time-frequency localization operator $H_\Omega$ on a domain $\Omega$ of the time-frequency plane. The eigenfunctions are the appropriate prolate spheroidal functions for an arbitrary domain…
In this paper, we apply angle-domain Doppler compensation for high-mobility wideband massive multi-input multi-output (MIMO) uplink transmission. The time-varying multipath channel is considered between high-speed terminal and static base…