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Scattering from a non-smooth random field on the time domain is studied for plane waves that propagate simultaneously through the potential in variable angles. We first derive sufficient conditions for stochastic moments of the field to be…

Analysis of PDEs · Mathematics 2018-12-26 Pedro Caro , Tapio Helin , Antti Kujanpää , Matti Lassas

We propose a globally convergent computational technique for the nonlinear inverse problem of reconstructing the zero-order coefficient in a parabolic equation using partial boundary data. This technique is called the "reduced dimensional…

Numerical Analysis · Mathematics 2023-09-27 Ray Abney , Thuy T. Le , Loc H. Nguyen , Cam Peters

The monotonicity method for the inverse acoustic scattering problem is to understand the inclusion relation between an unknown object and artificial one by comparing the far field operator with artificial operator. This paper introduces the…

Analysis of PDEs · Mathematics 2021-06-16 Tomohiro Daimon , Takashi Furuya , Ryuji Saiin

The Newton-Sabatier method for solving inverse scattering problem with fixed-energy phase shifts for a sperically symmetric potential is discussed. It is shown that this method is fundamentally wrong: in general it cannot be carried…

Analysis of PDEs · Mathematics 2007-05-23 A. G. Ramm

We study the direct and inverse scattering problems when the incident electromagnetic field is a time harmonic point- generated wave in a chiral medium and the scatterer is a perfectly conducting sphere. The exact Green s function and the…

Classical Physics · Physics 2008-12-12 Nikolaos Berketis , Christodoulos Athanasiadis

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,…

Two-dimensional problem of evanescent wave scattering by dielectric or metallic cylinders near the interface between two dielectric media is solved numerically by boundary integral equations method. A special Green function was proposed to…

Optics · Physics 2017-04-17 O. V. Belai , L. L. Frumin , S. V. Perminov , D. A. Shapiro

A new numerical method is proposed for a 1-D inverse medium scattering problem with multi-frequency data. This method is based on the construction of a weighted cost functional. The weight is a Carleman Weight Function (CWF). In other…

Numerical Analysis · Mathematics 2017-03-24 Michael V. Klibanov , Aleksandr E. Kolesov , Lam Nguyen , Anders Sullivan

We present a framework to solve the open problem of formulating the inverse scattering method (ISM) for an integrable PDE on a star-graph. The idea is to map the problem on the graph to a matrix initial-boundary value (IBV) problem and then…

Mathematical Physics · Physics 2015-06-02 Vincent Caudrelier

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

The inverse scattering problem from the multi-frequency backscattering data is a long-standing open problem. We advance the theory by proving a local uniqueness result. Moreover, we introduce a direct sampling method for quantitatively…

Numerical Analysis · Mathematics 2026-04-29 Yukun Guo , Xiaodong Liu

The inverse acoustic scattering problems using multi-frequency backscattering far field patterns at isolated directions are studied. The underlying object could be point like scatterers, small scatterers, extended inhomogeneities and…

Analysis of PDEs · Mathematics 2019-10-18 Xia Ji , Xiaodong Liu

We are interested in the inverse problem of the determination of the potential $p(x), x\in\Omega\subset\mathbb{R}^n$ from the measurement of the normal derivative $\partial_\nu u$ on a suitable part $\Gamma_0$ of the boundary of $\Omega$,…

Analysis of PDEs · Mathematics 2011-10-21 Lucie Baudouin

We consider one-dimensional inverse scattering in attenuating media where both the reflectivity and loss distributions are unknown. Mathematically, this corresponds to recovering the coefficients of a damped wave operator, or equivalently,…

Numerical Analysis · Mathematics 2025-11-20 Jorn Zimmerling , Mikhail Zaslavsky , Alexander V. Mamonov , Vladimir Druskin , Anarzhan Abilgazy

We develop a unified scattering approach to dynamical Casimir problems which can be applied to both accelerating boundaries, as well as dispersive objects in relative motion. A general (trace) formula is derived for the radiation from…

Quantum Physics · Physics 2013-01-14 Mohammad F. Maghrebi , Ramin Golestanian , Mehran Kardar

In this article, the inverse scattering problem (ISP) of recovering the matrix coefficient of a first order system of ordinary differential equations on the half-axis from its scattering matrix is considered. In the case of a triangular…

Spectral Theory · Mathematics 2013-07-02 Mansur I. Ismailov

The theory of inverse scattering is developed to study the initial-value problem for the modified matrix Korteweg-de Vries (mmKdV) equation with the $2m\times2m$ $(m\geq 1)$ Lax pairs under the nonzero boundary conditions at infinity. In…

Exactly Solvable and Integrable Systems · Physics 2020-05-04 Jin-Jie Yang , Shou-Fu Tian , Zhi-Qiang Li

This work is concerned with a direct sampling method (DSM) for inverse acoustic scattering problems using far-field data. The method characterizes some unknown obstacles, inhomogeneous media or cracks, directly through an indicator function…

Mathematical Physics · Physics 2012-12-27 Jingzhi Li , Jun Zou

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

This paper investigates the inverse scattering problems using sampling methods with near field measurements. The near field measurements appear in two classical inverse scattering problems: the inverse scattering for obstacles and the…

Numerical Analysis · Mathematics 2021-07-02 Xiaodong Liu , Shixu Meng , Bo Zhang