Related papers: High-contrast random composites: homogenisation fr…
Wavefront shaping allows focusing light through or inside strongly scattering media, but the background intensity also increases due to long-range correlations, reducing the target's contrast. By manipulating non-local intensity…
We analyse the behaviour of the spectrum of the system of Maxwell equations of electromagnetism, with rapidly oscillating periodic coefficients, subject to periodic boundary conditions on a "macroscopic" domain $(0,T)^d, T>0.$ We consider…
Let A be a self-adjoint operator acting on a Hilbert space. The notion of second order spectrum of A relative to a given finite-dimensional subspace L has been studied recently in connection with the phenomenon of spectral pollution in the…
This paper presents an in-depth analysis of a parametrized version of the resolvent composition, an operation that combines a set-valued operator and a linear operator. We provide new properties and examples, and show that resolvent…
We prove an asymptotic expansion for the eigenvalues and eigenfunctions of Schr\"{o}dinger-type operator with a confining potential and with principle part a periodic elliptic operator in divergence form. We compare the spectrum to the…
We introduce a generalized framework for studying higher-order versions of the multiscale method known as Localized Orthogonal Decomposition. Through a suitable reformulation, we are able to accommodate both conforming and nonconforming…
We approximate an elliptic problem with oscillatory coefficients using a problem of the same type, but with constant coefficients. We deliberately take an engineering perspective, where the information on the oscillatory coefficients in the…
In this paper we provide a complete study of the spectrum of a constant coefficients differential operator on a scale of localized Sobolev spaces, $H^{s}_{loc}(I),$ which are Fr\'echet spaces. This is quite different from what we find in…
Recent experiments [Guan et al. Science 381, 766 (2023)] have demonstrated that the resolution of superlensing slabs can be significantly enhanced with complex frequency illuminations. In this study, we introduce a novel theoretical…
Higher-order exceptional points in the spectrum of non-Hermitian Hamiltonians describing open quantum or wave systems have a variety of potential applications in particular in optics and photonics. However, the experimental realization is…
We establish necessary and sufficient conditions for the boundedness and compactness of weighted composition operators acting on weighted Dirichlet spaces and determine the spectrum of a certain class of such operators. Our results extend…
This paper employs layer potential techniques to investigate wave scattering in two-dimensional elastic media exhibiting high contrasts in both Lam\'{e} parameters and density. Our contributions are fourfold. First, we construct an…
We investigate the effect of non-symmetric relatively bounded perturbations on the spectrum of self-adjoint operators. In particular, we establish stability theorems for one or infinitely many spectral gaps along with corresponding…
A set of Hamiltonians that are not self-adjoint but have the spectrum of the harmonic oscillator is studied. The eigenvectors of these operators and those of their Hermitian conjugates form a bi-orthogonal system that provides a…
High-contrast observations in optical and infrared astronomy are defined as any observation requiring a technique to reveal a celestial object of interest that is in such close angular proximity to another source brighter by a factor of at…
We consider the Dirichlet problem for elliptic systems with periodically distributed inclusions whose conduction parameter exhibits a significant contrast compared to the background media. We develop a unified method to quantify the…
In this paper we perform the analysis of the spectrum of a degenerate operator $A_\var$ corresponding to the stationary heat equation in a $\var$-periodic composite medium having two components with high contrast diffusivity. We prove that…
Strongly correlated electron systems require the development of new theoretical schemes in order to describe their unusual and unexpected properties. The usual perturbation schemes are inadequate and new concepts must be introduced. In our…
The spectrum of triangular band matrices defined on the sequence spaces where the entries of each band is a constant or convergent sequence is well studied. In this article, the spectrum and fine spectrum of a new generalised difference…
The variation of spectral subspaces for linear self-adjoint operators under an additive bounded perturbation is considered. The objective is to estimate the norm of the difference of two spectral projections associated with isolated parts…