Related papers: Passivity constraints on the relations between tra…
In this work, we show that the eigenvalue continuation approach introduced recently in [Phys. Rev. Lett. {\bf 121}, 032501 (2018)], despite its many advantages, has some fundamental limitations which cannot be overcome when strongly…
We analyze statistical properties of the complex system with conditions which manifests through specific constraints on the column/row sum of the matrix elements. The presence of additional constraints besides symmetry leads to new…
In this paper we study the concentration properties for the eigenvalues of kernel matrices, which are central objects in a wide range of kernel methods and, more recently, in network analysis. We present a set of concentration inequalities…
This paper introduces the problem of passive control of a chain of N identical masses in which there is an identical passive connection between neighbouring masses and a similar connection to a movable point. The problem arises in the…
We revisit the relative perturbation theory for invariant subspaces of positive definite matrix pairs. As a prototype model problem for our results we consider parameter dependent families of eigenvalue problems. We show that new estimates…
Energy of propagating electromagnetic waves can be fully absorbed in a thin lossy layer, but only in a narrow frequency band, as follows from the causality principle. On the other hand, it appears that there are no fundamental limitations…
The electrical and optical properties of ordered passive arrays, constituted of inductive and capacitive components, are usually deduced from Kirchhoff's rules. Under the assumption of periodic boundary conditions, comparable results may be…
An inverse obstacle problem for the wave governed by the wave equation in a two layered medium is considered under the framework of the time domain enclosure method. The wave is generated by an initial data supported on a closed ball in the…
The problem of the emergence of wave dispersion due to the heterogeneity of a transmission line (TL) is considered. An exactly solvable model helps to better understand the physical process of a signal passing through a non-uniform section…
The passivity index, a quantitative measure of a system's passivity deficiency or excess, has been widely used in stability analysis and control. Existing studies mostly rely on scalar forms of indices, which are restrictive for…
This work investigates the consequences of imposing a volume constraint on the maximum power that can be absorbed from progressive regular incident waves by an attenuating line absorber heaving in a travelling wave mode. Under assumptions…
Past work has considered the analytic properties of the reflection coefficient for a metal-backed slab. The primary result established a fundamental relationship for the minimal layer thickness to bandwidth ratio achievable for an absorber.…
Absorption of electromagnetic energy by a material is a phenomenon that underlies many applied problems, including molecular sensing, photocurrent generation and photodetection. Commonly, the incident energy is delivered to the system…
In the framework of the pseudophotons method and under the hypothesis of the far field approximation the formal evaluation of the transition radiation spectrum produced by a three-dimensional charged beam interacting with a metallic target…
Compressed sensing allows for the recovery of sparse signals from few measurements, whose number is proportional to the sparsity of the unknown signal, up to logarithmic factors. The classical theory typically considers either random linear…
This paper continues the preceding paper on the problem of quantum dynamics on the lattice. Firstly we consider the multiple reflections of the wave function (Loschmidt echo). The phenomenon of wave function concentration on the impurity…
A theory is presented (and supported by numerical simulations) for phase-coherent reflection of light by a disordered medium which either absorbs or amplifies radiation. The distribution of reflection eigenvalues is shown to be the Laguerre…
The interior transmission eigenvalue problem (ITP) plays a central role in inverse scattering theory and in the spectral analysis of inhomogeneous media. Despite its smooth dependence on the refractive index at the PDE level, the…
Information transfer through electromagnetic waves is an important problem that touches a variety of technologically relevant applications, including computing and telecommunications. Prior attempts to establish limits on optical…
The reflection, transmission and absorption of a symmetric electromagnetic pulse, which carrying frequency is close to the frequency of an interband transition in a QW (QW), are obtained. The energy levels of a QW are assumed discrete, one…