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Related papers: Free boundary methods and non-scattering phenomena

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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

It is proved that the scattering amplitude $A(\beta, \alpha_0, k_0)$, known for all $\beta\in S^2$, where $S^2$ is the unit sphere in $\mathbb{R}^3$, and fixed $\alpha_0\in S^2$ and $k_0>0$, determines uniquely the surface $S$ of the…

Numerical Analysis · Mathematics 2017-06-15 A. G. Ramm

We propose a universal strategy to realize a broadband control on arbitrary scatterers, through multiple coherent beams. By engineering the phases and amplitudes of incident beams, one can suppress the dominant scattering partial waves,…

We apply boundary integral equations for the first time to the two-dimensional scattering of time-harmonic waves from a smooth obstacle embedded in a continuously-graded unbounded medium. In the case we solve the square of the wavenumber…

Numerical Analysis · Mathematics 2016-05-04 Alex. H. Barnett , Bradley J. Nelson , J. Matthew Mahoney

In this work we consider the method of non-linear boundary integral equation for solving numerically the inverse scattering problem of obliquely incident electromagnetic waves by a penetrable homogeneous cylinder in three dimensions. We…

Numerical Analysis · Mathematics 2024-02-23 Drossos Gintides , Leonidas Mindrinos

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…

Analysis of PDEs · Mathematics 2021-03-23 Emilia Blåsten , Hongyu Liu

The paper concerns scattering of plane waves by a bounded obstacle with complex valued impedance boundary conditions. We study the spectrum of the Neumann-to-Dirichlet operator for small wave numbers and long wave asymptotic behavior of the…

Mathematical Physics · Physics 2010-11-09 Evgeny Lakshtanov , Boris Vainberg

This paper addresses the inverse obstacle scattering problem of simultaneously reconstructing the obstacle geometry and boundary conditions from multi-frequency near-field backscattering data. We first establish rigorous high-frequency…

Analysis of PDEs · Mathematics 2026-04-14 Jialei Li , Xiaodong Liu

This paper focuses on the time-harmonic electromagnetic (EM) scattering problem in a general medium which may possess a nontrivial topological structure. We model this by an inhomogeneous and possibly anisotropic medium with embedded…

Analysis of PDEs · Mathematics 2024-08-14 Huaian Diao , Hongyu Liu , Qingle Meng , Li Wang

We study obstacle problems governed by two distinct types of diffusion operators involving interacting free boundaries. We obtain a somewhat surprising coupling property, leading to a comprehensive analysis of the free boundary. More…

Analysis of PDEs · Mathematics 2025-02-07 Damião J. Araújo , Rafayel Teymurazyan

The theory of acoustic wave scattering by many small bodies is developed for bodies with impedance boundary condition. It is shown that if one embeds many small particles in a bounded domain, filled with a known material, then one can…

Mathematical Physics · Physics 2009-11-13 A. G. Ramm

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

The aim of this lecture is to consider a concrete problem, namely the identification of situations of invisibility in waveguides, to present techniques and tools that may be useful in various fields of applied mathematics. To be more…

Analysis of PDEs · Mathematics 2025-11-13 Lucas Chesnel

In this paper, we consider the scattering theory for acoustic-type equations on non-compact manifolds with a single flat end. Our main purpose is to show an existence result of non-scattering energies. Precisely, we show a Weyl-type lower…

Mathematical Physics · Physics 2023-11-28 Hisashi Morioka , Naotaka Shoji

This paper is concerned with an inverse obstacle scattering problem of an acoustic wave for a single incident plane wave and a wave number. The Colton-Sleeman theorem states the unique recovery of sound-soft obstacles with a smooth boundary…

Analysis of PDEs · Mathematics 2019-12-12 Masaru Ikehata

In this paper we propose and analyse a hybrid numerical-asymptotic boundary element method for the solution of problems of high frequency acoustic scattering by a class of sound-soft nonconvex polygons. The approximation space is enriched…

Numerical Analysis · Mathematics 2014-01-14 David P. Hewett , Simon N. Chandler-Wilde , Stephen Langdon , Ashley Twigger

In this paper we introduce a method for solving linear and nonlinear scattering problems for wave equations using a new hybrid approach. This new approach consists of a reformulation of the governing equations into a form that can be solved…

Numerical Analysis · Mathematics 2018-07-04 Aihua Lin , Anastasiia Kuzmina , Per Kristen Jakobsen

We propose and analyse a hybrid numerical-asymptotic $hp$ boundary element method for time-harmonic scattering of an incident plane wave by an arbitrary collinear array of sound-soft two-dimensional screens. Our method uses an approximation…

Numerical Analysis · Mathematics 2014-08-12 David P. Hewett , Stephen Langdon , Simon N. Chandler-Wilde

The boundaries of waveguides and nanowires have drastic influence on their coherent scattering properties. Designing the boundary profile is thus a promising approach for transmission and band-gap engineering with many applications. By…

Mesoscale and Nanoscale Physics · Physics 2012-12-04 O. Dietz , H. -J. Stöckmann , U. Kuhl , F. M. Izrailev , N. M. Makarov , J. Doppler , F. Libisch , S. Rotter

In this paper, we study the problem of scattering by several strictly convex obstacles, with smooth boundary and satisfying a non eclipse condition. We show, in dimension 2 only, the existence of a spectral gap for the meromorphic…

Spectral Theory · Mathematics 2024-05-01 Lucas Vacossin