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In this paper, we study the so-called clamped transmission eigenvalue problem. This is a new transmission eigenvalue problem that is derived from the scattering of an impenetrable clamped obstacle in a thin elastic plate. The scattering…

Analysis of PDEs · Mathematics 2025-11-21 Isaac Harris , Andreas Kleefeld , Heejin Lee

The impact of surface reflection on the statistics of transmission eigenvalues is a largely unexplored subject of fundamental and practical importance in statistical optics. Here, we develop a first-principles theory and confirm numerically…

Disordered Systems and Neural Networks · Physics 2014-05-20 Xiaojun Cheng , Chushun Tian , Azriel Z. Genack

For the direct problem, we give the asymptotic distribution of the (real and non-real) transmission eigenvalues for the Schrodinger operator on the half line. For the inverse problem, we prove that the potential can be uniquely determined…

Mathematical Physics · Physics 2020-05-07 Xiao-Chuan Xu

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.…

Analysis of PDEs · Mathematics 2025-02-04 Isaac Harris , Heejin Lee , Andreas Kleefeld

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

We consider the direct and inverse scattering problem for a penetrable, isotropic obstacle with a second-order Robin boundary condition, which asymptotically models the delamination of the boundary of the scatterer. We develop a direct…

Analysis of PDEs · Mathematics 2026-01-22 Govanni Granados , Isaac Harris , Andreas Kleefeld

In this paper we show that the eigenfunctions can be found exactly for systems whose delay-Doppler spread function is concentrated along a straight line and they can be found in approximate sense for systems having a spread function…

Information Theory · Computer Science 2015-10-15 Sergio Barbarossa , Mikhail Tsitsvero

This paper is concerned with the invisibility cloaking in acoustic wave scattering from a new perspective. We are especially interested in achieving the invisibility cloaking by completely regular and isotropic mediums. It is shown that an…

Analysis of PDEs · Mathematics 2016-04-20 Xia Ji , Hongyu Liu

In this paper, we investigate on the direct and inverse scattering problem by an unbounded penetrable rough surface in a lossless medium. The cases that the transmission coefficient $\mu\neq1$ and $\mu=1$, which creates certain difficulties…

Analysis of PDEs · Mathematics 2025-11-25 Chengyu Wu , Jiaqinq Yang

This paper is concerned with the invisibility cloaking in electromagnetic wave scattering from a new perspective. We are especially interested in achieving the invisibility cloaking by completely regular and isotropic mediums. Our study is…

Mathematical Physics · Physics 2017-01-20 Jingzhi Li , Xiaofei Li , Hongyu Liu , Yuliang Wang

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

We describe the asymptotic distribution of the eigenvalues of interior transmission problem in absorbing medium. We apply the Cartwright's theory and the technique from asymptotic periodic entire function theory. We find a Weyl's type of…

Functional Analysis · Mathematics 2013-07-02 Lung-Hui Chen

We describe analytical and numerical results on the statistical properties of complex eigenvalues and the corresponding non-orthogonal eigenvectors for non-Hermitian random matrices modeling one-channel quantum-chaotic scattering in systems…

Condensed Matter · Physics 2009-11-07 Y. V. Fyodorov , B. Mehlig

This paper is about perfectly electrically conducting structures designed to produce negligible scattered power when exposed to a time-harmonic plane electromagnetic wave. The structures feature cavities capable of concealing objects.…

Computational Physics · Physics 2025-10-01 Johan Helsing , Anders Karlsson

We consider the interior transmission problem associated with the scattering by an inhomogeneous (possibly anisotropic) highly oscillating periodic media. We show that, under appropriate assumptions, the solution of the interior…

Analysis of PDEs · Mathematics 2015-10-12 Fioralba Cakoni , Houssem Haddar , Isaac Harris

This paper is concerning the inverse conductive scattering of acoustic waves by a bounded inhomogeneous object with possibly embedded obstacles inside. A new uniqueness theorem is proved that the conductive object is uniquely determined by…

Analysis of PDEs · Mathematics 2026-01-19 Chengyu Wu , Jiaqing Yang

We provide a new analytical and computational study of the transmission eigenvalues with a conductive boundary condition. These eigenvalues are derived from the scalar inverse scattering problem for an inhomogeneous material with a…

Analysis of PDEs · Mathematics 2020-04-15 Isaac Harris , Andreas Kleefeld

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

A discrete analog is considered for the inverse transmission eigenvalue problem, having applications in acoustics. We provide a well-posed inverse problem statement, develop a constructive procedure for solving this problem, prove…

Spectral Theory · Mathematics 2021-11-01 Natalia P. Bondarenko , Vjacheslav A. Yurko

In this paper, we study the transmission eigenvalue problem for an anisotropic material with a conductive boundary. We prove that the transmission eigenvalues for this problem exist and are at most a discrete set. We also study the…

Analysis of PDEs · Mathematics 2023-11-02 Victor Hughes , Isaac Harris , Jiguang Sun