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Related papers: Free boundary methods and non-scattering phenomena

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We consider a fixed angle inverse scattering problem in the presence of a known Riemannian metric. First, assuming a no caustics condition, we study the direct problem by utilizing the progressing wave expansion. Under a symmetry assumption…

Analysis of PDEs · Mathematics 2021-07-21 Shiqi Ma , Mikko Salo

Shock waves are steep wave fronts that are fundamental in nature, especially in high-speed fluid flows. When a shock hits an obstacle, or a flying body meets a shock, shock reflection/diffraction phenomena occur. In this paper, we show how…

Analysis of PDEs · Mathematics 2016-02-17 Gui-Qiang G. Chen , Mikhail Feldman

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…

Analysis of PDEs · Mathematics 2022-10-13 Peijun Li , Xu Wang

In this series of papers, we investigate the spreading and vanishing dynamics of time almost periodic diffusive KPP equations with free boundaries. Such equations are used to characterize the spreading of a new species in time almost…

Analysis of PDEs · Mathematics 2015-07-08 Fang Li , Xing Liang , Wenxian Shen

The scalar scattering of the plane wave by a strictly convex obstacle with impedance boundary conditions is considered. The uniform boundedness of the Total Cross Section for all values of frequencies is proved. The high frequency limit of…

Mathematical Physics · Physics 2010-09-13 A. I. Aleksenko , J. P. Cruz , E. L. Lakshtanov

We study the backward scatterings of plane waves by reciprocal scatterers and reveal that $n$-fold ($n\geq3$) rotation symmetry is sufficient to secure invariant backscattering for arbitrarily-polarized incident plane waves. It is further…

Optics · Physics 2021-01-27 Weijin Chen , Qingdong Yang , Yuntian Chen , Wei Liu

An inverse obstacle problem for the wave equation in a two layered medium is considered. It is assumed that the unknown obstacle is penetrable and embedded in the lower half-space. The wave as a solution of the wave equation is generated by…

Analysis of PDEs · Mathematics 2018-08-07 Masaru Ikehata , Mishio Kawashita

We consider the light scattering problem for a Gaussian beam and a (spherical) particle at arbitrary location. Within the beam cross section, the total electromagnetic field is the superposition of the incident beam and the scattered wave.…

Optics · Physics 2025-04-09 Jonas Gienger

The possibility of asymmetric absorption and reflection for flexural waves is demonstrated though analytical and numerical examples. We focus on the 1D case of flexural motion of a beam and consider combinations of point scatterers which…

Classical Physics · Physics 2019-09-04 Andrew N. Norris , Pawel Packo

We consider the problem of fixed frequency acoustic scattering from a sound-soft flat screen. More precisely the obstacle is restricted to a two-dimensional plane and interacting with a arbitrary incident wave, it scatters acoustic waves to…

Analysis of PDEs · Mathematics 2020-07-20 Emilia Blåsten , Lassi Päivärinta , Sadia Sadique

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.…

Classical Physics · Physics 2023-12-27 M. J. Nieves , B. L. Sharma

We consider the solvability of the direct scattering problem of an obliquely incident time-harmonic electromagnetic wave by a piecewise constant inhomogeneous, penetrable and infinitely long cylinder. We prove the existence and uniqueness…

Analysis of PDEs · Mathematics 2024-02-23 Drossos Gintides , Sotiris Giogiakas , Leonidas Mindrinos

Effective field theory descriptions of surface waves on flowing fluids have tended to assume that the flow is irrotational, but this assumption is often impractical due to boundary layer friction and flow recirculation. Here we develop an…

General Relativity and Quantum Cosmology · Physics 2024-09-26 Alessia Biondi , Scott Robertson , Germain Rousseaux

In the frequency domain wave scattering problems, obstacles can be effectively replaced by point scatterers as soon as the wavelength of the incident wave exceeds significantly their diameter. The situation is less clear in the time domain,…

Analysis of PDEs · Mathematics 2025-12-18 Maryna Kachanovska , Adrian Savchuk

We consider inverse potential scattering problems where the source of the incident waves is located on a smooth closed surface outside of the inhomogeneity of the media. The scattered waves are measured on the same surface at a fixed value…

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

This paper is devoted to the algorithmic development of inverse elastic scattering problems. We focus on reconstructing the locations and shapes of elastic scatterers with known dictionary data for the nearly incompressible materials. The…

Analysis of PDEs · Mathematics 2017-11-02 Li Jingzhi , Liu Hongyu , Sun Hongpeng

Formulas are derived for solutions of many-body wave scattering problems by small particles in the case of acoustically soft, hard, and impedance particles embedded in an inhomogeneous medium. The case of transmission (interface) boundary…

Mathematical Physics · Physics 2012-09-03 A. G. Ramm

In this paper, we consider the inverse scattering problem associated with an inhomogeneous media with a conductive boundary. First, we discuss the inverse conductivity problem of reconstructing the conductivity parameter from scattering…

Analysis of PDEs · Mathematics 2017-12-12 Isaac Harris , Andreas Kleefeld

We consider the scattering problem governed by the Helmholtz equation with inhomogeneity in both `conductivity' in the divergence form and `potential' in the lower order term. The support of the inhomogeneity is assumed to contain a convex…

Analysis of PDEs · Mathematics 2020-09-14 Fioralba Cakoni , Jingni Xiao

We study 4 problems in the area of scattering of time harmonic acoustic or electromagnetic waves by unbounded rough surfaces/inhomogeneous layers. Specifically we study: i) a boundary value problem (BVP) for the Helmholtz equation, in both…

Analysis of PDEs · Mathematics 2019-04-09 Thomas Baden-Riess