English
Related papers

Related papers: On the transmission eigenvalues for scattering by …

200 papers

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…

Analysis of PDEs · Mathematics 2022-02-24 Hongyu Liu , Chun-Hsiang Tsou

The model problem of scattering of a sound wave by an infinite plane structure formed by a semi-infinite acoustically hard screen and a semi-infinite sandwich panel perforated from one side and covered by a membrane from the other is…

Mathematical Physics · Physics 2023-04-11 Y. A. Antipov

The paper considers direct and inverse elastic scattering from a cavity in homogeneous medium with Dirichlet and Neumann boundary conditions. For direct scattering, existence and uniqueness are derived by variation approach. For inverse…

Analysis of PDEs · Mathematics 2023-02-28 Tianjiao Wang , Yiwen Lin , Xiang Xu

The paper concerns the isotropic interior transmission eigenvalue (ITE) problem. This problem is not elliptic, but we show that, using the Dirichlet-to-Neumann map, it can be reduced to an elliptic one. This leads to the discreteness of the…

Mathematical Physics · Physics 2015-06-12 Evgeny Lakshtanov , Boris Vainberg

Effective interface conditions for a periodically voided thin layer separating two homogeneous bulk regions are derived for the elastic wave equation by taking the simultaneous limit of vanishing layer periodicity and layer thickness. The…

Analysis of PDEs · Mathematics 2026-03-30 Markus Gahn , Tanja Lochner , Malte A. Peter

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…

Analysis of PDEs · Mathematics 2025-12-09 Jianli Xiang , Guanghui Hu

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 inverse elastic scattering problem for a random potential in three dimensions. Interpreted as a distribution, the potential is assumed to be a microlocally isotropic Gaussian random field whose covariance…

Analysis of PDEs · Mathematics 2021-02-16 Jianliang Li , Peijun Li , Xu Wang

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…

Analysis of PDEs · Mathematics 2024-10-31 Safiere Kuijpers , Laura Scarabosio

A theory for multiple scattering of elastic waves is presented in a random medium bounded by two ideal free surfaces, whose horizontal size is infinite and whose transverse size is smaller than the mean free path of the waves. This geometry…

Mesoscale and Nanoscale Physics · Physics 2009-11-07 Nicolas P. Tregoures , Bart A. van Tiggelen

In this paper, we study the Helmholtz transmission eigenvalue problem for inhomogeneous anisotropic media with the index of refraction $n(x)\equiv 1$ in two and three dimension. Starting with a nonlinear fourth order formulation established…

Numerical Analysis · Mathematics 2023-04-26 Qing Liu , Tiexiang Li , Shuo Zhang

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…

Numerical Analysis · Mathematics 2016-06-29 Yidu Yang , Jiayu Han , Hai Bi

This paper is concerned with uniqueness, phase retrieval and shape reconstruction methods for inverse elastic scattering problems with phaseless far field data. Systematically, we study two basic models, i.e., inverse scattering of plane…

Analysis of PDEs · Mathematics 2020-01-08 Xia Ji , Xiaodong Liu

This paper concerns the reconstruction of multiple elastic parameters (Lam\'e parameters and density) of an inhomogeneous medium embedded in an infinite homogeneous isotropic background in $\mathbb{R}^2$. The direct scattering problem is…

Numerical Analysis · Mathematics 2019-02-13 Gang Bao , Tao Yin , Fang Zeng

Consider the scattering of a time-harmonic electromagnetic plane wave by an open cavity which is embedded in a perfectly electrically conducting infinite ground plane. This paper concerns the numerical solutions of the open cavity…

Numerical Analysis · Mathematics 2020-04-24 Xiaokai Yuan , Gang Bao , Peijun Li

In this paper, we present the first well-posedness result for elastic scattering by locally rough interfaces in both two and three dimensions. Inspired by the Helmholtz decomposition, we discover a fundamental identity for the stress…

Analysis of PDEs · Mathematics 2026-01-21 Chengyu Wu , Yushan Xue , Jiaqing Yang

We consider the two-dimensional Kirchhoff-Love plate equation in the context of elasticity modeling the stresses and deformations in thin plates subjected to forces and moments. We establish global recovery of the material parameters like…

Analysis of PDEs · Mathematics 2021-02-12 Sombuddha Bhattacharyya , Tuhin Ghosh

This paper is devoted to studying impedance eigenvalues (that is, eigenvalues of a particular Dirichlet-to-Neumann map) for the time harmonic linear elastic wave problem, and their potential use as target-signatures for fluid-solid…

Analysis of PDEs · Mathematics 2022-01-31 Michael Levitin , Peter Monk , Virginia Selgas

This paper is concerned with the inverse scattering problem of time-harmonic elastic waves by an unbounded rigid rough surface. A direct imaging method is developed to reconstruct the unbounded rough surface from the elastic scattered…

Numerical Analysis · Mathematics 2018-04-17 Xiaoli Liu , Bo Zhang , Haiwen Zhang

Linear problems appear in a variety of disciplines and their application for the transmission matrix recovery is one of the most stimulating challenges in biomedical imaging. Its knowledge turns any random media into an optical tool that…

Machine Learning · Statistics 2019-02-05 Daniele Ancora , Luca Leuzzi