Related papers: Bifurcations in Interior Transmission Eigenvalues:…
This work investigates spectrum and root functions (that is, eigen- and associated functions) of a Sturm-Liouville problem involving an abstract linear operator (nonselfadjoint in general) in the equation together with supplementary…
The transmission eigenvalue problem is an important and challenging topic arising in the inverse scattering theory. In this paper, for the Helmholtz transmission eigenvalue problem, we give a weak formulation which is a nonselfadjoint…
The nonlinear Fourier transform (NFT) decomposes waveforms propagating through optical fiber into nonlinear degrees of freedom, which are preserved during transmission. By encoding information on the nonlinear spectrum, a transmission…
Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what factors contribute to the stability of complex dynamical…
We observe that the reflection and transmission coefficients of a particle within a double, PT symmetric heterojunction with spatially varying mass, show interesting features, depending on the degree of non Hermiticity, although there is no…
Identifying the collection of scalars that represent a non-negative matrix's eigenvalues is known as the non-negative inverse eigenvalue problem (NIEP). Conditions for the existence of a non-negative matrix with a certain spectrum are…
It is well established that the physical phenomenon of intermittency can be investigated via the spectral analysis of a transfer operator associated with the dynamics of an interval map with indifferent fixed point. We present here for the…
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.…
The topological invariant of a topological insulator (or superconductor) is given by the number of symmetry-protected edge states present at the Fermi level. Despite this fact, established expressions for the topological invariant require…
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…
In this paper, we consider the problem of the scattering of in-plane waves at an interface between a homogeneous medium and a metamaterial. The relevant eigenmodes in the two regions are calculated by solving a recently described non…
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…
We consider the non-self-adjoint Sturm-Liouville operator on a finite interval. The inverse spectral problem is studied, which consists in recovering this operator from its eigenvalues and generalized weight numbers. We prove local…
The basic inverse problem in spectral graph theory consists in determining the graph given its eigenvalue spectrum. In this paper, we are interested in a network of technological agents whose graph is unknown, communicating by means of a…
This article investigates the unique determination of a radial refractive index n from spectral data. First, we demonstrate that for piecewise twice continuously differentiable functions, n is not uniquely determined by the special…
Photon transport through a diffusing slab can be described by the radiative transfer equation (RTE). When the slab is highly scattering and weakly absorbing, the RTE simplifies to the diffusion equation. In this paper, an inverse diffusion…
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…
Symplectic geometry plays an increasingly important role in mathematics, physics and applications, and naturally gives rise to interesting matrix families and properties. One of these is the notion of symplectic eigenvalues, whose existence…
Bispectral analysis of the nonlinear resonant interaction known as parametric subharmonic instability (PSI) for a coherence semidiurnal internal tide demonstrates the ability of the bispectrum to identify and quantify the transfer rate.…
We analyze the scattering of linear internal waves in a two dimensional channel with subcritical bottom topography. We construct the scattering matrix for the internal wave problem in a channel with straight ends, mapping incoming data to…