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We consider the transmission eigenvalues for a bounded scatterer with a periodically varying index of refraction, and derive the first order corrections to the limiting transmission eigenvalues. We assume the scatterer contrast to be of one…

Analysis of PDEs · Mathematics 2025-09-01 Fioralba Cakoni , Shari Moskow

We consider the time-harmonic scattering wave problem in a 2D waveguide at wavenumber $k$ such that one mode is propagating in the far field. In a first step, for a given $k$, playing with one scattering branch of finite length, we…

Analysis of PDEs · Mathematics 2019-05-22 Lucas Chesnel , Vincent Pagneux

This paper is concerned with uniqueness for reconstructing a periodic inhomogeneous medium covered on a perfectly conducting plate. We deal with the problem in the frame of time-harmonic Maxwell systems without TE or TM polarization. An…

Analysis of PDEs · Mathematics 2010-03-17 Guanghui Hu , Jiaqing Yang , Bo Zhang

The reflection matrix R=S^{\dagger}S, with S being the scattering matrix, differs from the unit one, when absorption is finite. Using the random matrix approach, we calculate analytically the distribution function of its eigenvalues in the…

Mesoscale and Nanoscale Physics · Physics 2007-05-23 D. V. Savin , H. -J. Sommers

We transform an inverse scattering problem to be an interior transmission problem. We find an inverse uniqueness on the scatterer with a knowledge of a fixed interior transmission eigenvalue. By examining the solution in a series of…

Mathematical Physics · Physics 2015-08-06 Lung-Hui Chen

This paper is concerned with the problem of scattering of time-harmonic electromagnetic waves from an impenetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is established, employing the integral…

Analysis of PDEs · Mathematics 2015-05-18 Xiaodong Liu , Bo Zhang , Jiaqing Yang

The linear system of differential equations for determination of transmission and reflection amplytudes of scattered electron in the field of one dimensional arbitrary potential is obtained. It is shown that in general the scattering…

Disordered Systems and Neural Networks · Physics 2019-08-17 David M. Sedrakian , Ashot Zh. Khachatrian

This paper is concerned with the inverse problem of time-harmonic acoustic scattering by an unbounded, locally rough interface which is assumed to be a local perturbation of a plane. The purpose of this paper is to recover the local…

Analysis of PDEs · Mathematics 2020-08-05 Jianliang Li , Jiaqing Yang , Bo Zhang

In this paper we survey some recent results concerning scattering and non-scattering in the context of the linear Helmholtz equation and inhomogeneities of nontrivial contrast. We examine isotropic as well as anisotropic media. Part of the…

Analysis of PDEs · Mathematics 2026-02-09 Fioralba Cakoni , Michael S. Vogelius

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…

Analysis of PDEs · Mathematics 2023-10-26 Narek Hovsepyan

This paper investigates a distinctive spectral pattern exhibited by transmission eigenfunctions in wave scattering theory. Building upon the discovery in [7, 8] that these eigenfunctions localize near the domain boundary, we derive sharp…

Analysis of PDEs · Mathematics 2026-03-24 Yan Jiang , Hongyu Liu , Kai Zhang , Haoran Zheng

In this paper, we consider the obstacle scattering problem for biharmonic equations with a Dirichlet boundary condition in both two and three dimensions. Some basic properties are first derived for the biharmonic scattering solutions, which…

Analysis of PDEs · Mathematics 2025-10-16 Chengyu Wu , Jiaqing Yang

This paper is devoted to the discreteness of the transmission eigenvalue problems. It is known that this problem is not self-adjoint and a priori estimates are non-standard and do not hold in general. Two approaches are used. The first one…

Analysis of PDEs · Mathematics 2016-10-25 Hoai-Minh Nguyen , Quoc Hung Nguyen

The goal of this paper is to develop numerical methods computing a few smallest elasticity transmission eigenvalues, which are of practical importance in inverse scattering theory. The problem is challenging since it is nonlinear,…

Numerical Analysis · Mathematics 2018-02-13 Xia Ji , Peijun Li , Jiguang Sun

The scattering matrix approach is employed to determine a joint probability density function of reflection eigenvalues for chaotic cavities coupled to the outside world through both ballistic and tunnel point contacts. Derived under…

Mesoscale and Nanoscale Physics · Physics 2012-05-17 Pedro Vidal , Eugene Kanzieper

This paper concerns the inverse shape problem of recovering an unknown clamped cavity embedded in a thin infinite plate. The model problem is assumed to be governed by the two-dimensional biharmonic wave equation in the frequency domain.…

Analysis of PDEs · Mathematics 2025-01-22 Isaac Harris , Heejin Lee , Peijun Li

The paper concerns the discreteness of the eigenvalues and the solvability of the interior transmission problem for anisotropic media. Conditions for the ellipticity of the problem are written explicitly, and it is shown that they do not…

Mathematical Physics · Physics 2012-04-19 Evgeny Lakshtanov , Boris Vainberg

In this paper we study the interior transmission problem and transmission eigenvalues for multiplicative perturbations of linear partial differential operator of order $\ge 2$ with constant real coefficients. Under suitable growth…

Mathematical Physics · Physics 2015-03-17 Michael Hitrik , Katsiaryna Krupchyk , Petri Ola , Lassi Päivärinta

This paper addresses the inverse scattering problem of a random potential associated with the polyharmonic wave equation in two and three dimensions. The random potential is represented as a centered complex-valued generalized microlocally…

Analysis of PDEs · Mathematics 2025-07-02 Jianliang Li , Peijun Li , Xu Wang , Guanlin Yang

Assume a time-harmonic elastic wave is incident onto a penetrable anisotropic body embedded into a homogeneous isotropic background medium. We propose an equivalent variational formulation in a truncated bounded domain and show the…

Analysis of PDEs · Mathematics 2016-12-21 Gang Bao , Guanghui Hu , Jiguang Sun , Tao Yin