Related papers: Analysis of the transmission eigenvalue problem fo…
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…
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…
This paper is concerned with the cavity scattering problem in an infinite thin plate, where the out-of-plane displacement is governed by the two-dimensional biharmonic wave equation. Based on an operator splitting, the scattering problem is…
We consider the scattering of in-plane waves that interact with an edge of a structured {penetrable (inertial)} line defect contained in a triangular lattice, composed of periodically placed masses interconnected by massless elastic rods.…
We consider the time-harmonic acoustic wave scattering by a bounded {\it anisotropic inhomogeneity} embedded in an unbounded {\it anisotropic} homogeneous medium. The material parameters may have discontinuities across the interface between…
We consider the inverse random potential scattering problem for the two- and three-dimensional biharmonic wave equation in lossy media. The potential is assumed to be a microlocally isotropic Gaussian rough field. The main contributions of…
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…
In this paper, we study an inverse problem of determining the cross section of an infinitely long cylindrical-like material structure from the transverse electromagnetic scattering measurement. We establish a sharp logarithmic stability…
In this paper, we consider the numerical approximation of the Steklov eigenvalue problem that arises in inverse acoustic scattering. The underlying scattering problem is for an inhomogeneous isotropic medium. These eigenvalues have been…
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…
We consider the Bayesian approach to the inverse problem of recovering the shape of an object from measurements of its scattered acoustic field. Working in the time-harmonic setting, we focus on a Helmholtz transmission problem and then…
In this note, we present some interesting observations on the Schiffer's conjecture, interior transmission eigenvalue problem and their connections to singular and nonsingular invisibility cloaking problems of acoustic waves.
We prove a quantum version of the Sabine law from acoustics describing the location of resonances in transmission problems. This work extends the author's previous work to a broader class of systems. Our main applications are to scattering…
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,…
We analyze the propagation of waves in unbounded photonic crystals, the waves are described by a Helmholtz equation with $x$-dependent coefficients. The scattering problem must be completed with a radiation condition at infinity, which was…
We consider several intriguingly connected topics in the theory of wave propagation: geometrical characterizations of radiationless sources, non-radiating incident waves, interior transmission eigenfunctions, and their applications to…
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…
In this paper, we investigate two types of time-harmonic elastic wave scattering problems. The first one involves the scattered wave generated by an active elastic source with compact support. The second one concerns elastic wave scattering…
This paper addresses an inverse cavity scattering problem associated with the biharmonic wave equation in two dimensions. The objective is to determine the domain or shape of the cavity. The Green's representations are demonstrated for the…
We study time harmonic scattering problems in linear elasticity in $\mathbb{R}^{2}$. We show that certain penetrable scatterers with rectangular corners scatter every incident wave nontrivially. Even though these scatterers have interior…