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We study an inverse uniqueness with a knowledge of spectral data in the interior transmission problem defined by an index of refraction in a simple domain. We expand the solution in such a domain into a series of one dimensional problems.…

Analysis of PDEs · Mathematics 2015-08-10 Lung-Hui Chen

In this paper, we provide an analytical study of the transmission eigenvalue problem in the context of biharmonic scattering with a penetrable obstacle. We will assume that the underlying physical model is given by an infinite elastic…

Analysis of PDEs · Mathematics 2025-10-10 Rafael Ceja Ayala , Isaac Harris , Andreas Kleefeld

Transmission eigenchannels are building blocks of coherent wave transport in diffusive media, and selective excitation of individual eigenchannels can lead to diverse transport behavior. An essential yet poorly understood property is the…

Optics · Physics 2019-08-06 Hasan Yılmaz , Chia Wei Hsu , Alexey Yamilov , Hui Cao

We consider inverse obstacle and transmission scattering problems where the source of the incident waves is located on a smooth closed surface that is a boundary of a domain located outside of the obstacle/inhomogeneity of the media. The…

Mathematical Physics · Physics 2017-10-12 Evgeny Lakshtanov , Boris Vainberg

Transmission eigenfunctions are certain interior resonant modes that are of central importance to the wave scattering theory. In this paper, we present the discovery of novel global rigidity properties of the transmission eigenfunctions…

Optics · Physics 2021-04-15 Youjun Deng , Hongyu Liu , Xianchao Wang , Wei Wu

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

The eigenvalues of the transmission matrix provide the basis for a full description of the statistics of steady-state transmission and conductance. At the same time, the ability to excite the sample with the waveform of specific…

Disordered Systems and Neural Networks · Physics 2015-11-25 Zhou Shi , Azriel Z. Genack

The paper contains lower bounds on the counting function of the positive eigenvalues of the interior transmission problem when the latter is elliptic. In particular, these bounds justify the existence of an infinite set of interior…

Mathematical Physics · Physics 2015-06-05 Evgeny Lakshtanov , Boris Vainberg

The inverse electromagnetic scattering problem for anisotropic media in general does not have a unique solution. A possible approach to this problem is through the use of appropriate "target signatures," i.e. eigenvalues associated with the…

Analysis of PDEs · Mathematics 2018-05-21 Samuel Cogar , David Colton , Peter Monk

In this paper, we investigate two transmission eigenvalue problems associated with the scattering of a media with a coated boundary. In recent years, there has been a lot of interest in studying these eigenvalue problems. It can be shown…

Analysis of PDEs · Mathematics 2019-08-19 Isaac Harris

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

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…

Optics · Physics 2015-02-13 Matthieu Davy , Zhou Shi , Jongchul Park , Chushun Tian , Azriel Z. Genack

This work deals with the interior transmission eigenvalue problem: $y'' + {k^2}\eta \left( r \right)y = 0$ with boundary conditions ${y\left( 0 \right) = 0 = y'\left( 1 \right)\frac{{\sin k}}{k} - y\left( 1 \right)\cos k},$ where the…

Spectral Theory · Mathematics 2019-10-01 Xiao-Chuan Xu , Chuan-Fu Yang , Sergey A. Buterin , Vjacheslav A. Yurko

This paper considers the inverse problem of scattering of time-harmonic acoustic and electromagnetic plane waves by a bounded, inhomogeneous, penetrable obstacle with embedded objects inside. A new method is proposed to prove that the…

Analysis of PDEs · Mathematics 2017-06-14 Jiaqing Yang , Bo Zhang , Haiwen Zhang

Light-matter interactions inside turbid medium can be controlled by tailoring the spatial distribution of energy density throughout the system. Wavefront shaping allows selective coupling of incident light to different transmission…

Optics · Physics 2017-09-06 M. Koirala , R. Sarma , H. Cao , A. Yamilov

A stabilized version of the fundamental solution method to catch ill-conditioning effects is investigated with focus on the computation of complex-valued elastic interior transmission eigenvalues in two dimensions for homogeneous and…

Numerical Analysis · Mathematics 2019-09-06 Andreas Kleefeld , Lukas Pieronek

In this paper, we consider an interior transmission eigenvalue (ITE) problem on some compact $C^{\infty }$-Riemannian manifolds with a common smooth boundary. In particular, these manifolds may have different topologies, but we impose some…

Spectral Theory · Mathematics 2019-05-27 Hisashi Morioka , Naotaka Shoji

The transmission eigenvalues corresponding to the half-line Schr\"odinger equation with the general selfadjoint boundary condition is analyzed when the potential is real valued, integrable, and compactly supported. It is shown that a…

Spectral Theory · Mathematics 2016-10-06 Tuncay Aktosun , Vassilis G. Papanicolaou

In this paper we consider the transmission eigenvalue problem for Maxwell's equations corresponding to non-magnetic inhomogeneities with contrast in electric permittivity that has fixed sign (only) in a neighborhood of the boundary. We…

Analysis of PDEs · Mathematics 2021-04-05 Houssem Haddar , Shixu Meng

In this paper, we provide an analytical study of the transmission eigenvalue problem with two conductivity parameters. We will assume that the underlying physical model is given by the scattering of a plane wave for an isotropic scatterer.…

Analysis of PDEs · Mathematics 2022-09-16 Rafael Ceja Ayala , Isaac Harris , Andreas Kleefeld , Nikolaos Pallikarakis