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We study the fundamental limit on the localization precision for a subwavelength scatterer embedded in a strongly scattering environment, using the external degrees of freedom provided by wavefront shaping. For a weakly scattering target,…

Optics · Physics 2020-11-05 Dorian Bouchet , Rémi Carminati , Allard P. Mosk

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 limiting case is considered, when the size…

Mathematical Physics · Physics 2011-05-10 Alexander G. Ramm

In this work, we consider the time-harmonic inverse elastic source problem of a fixed frequency for the Navier equation in two dimensions. We show that a convex polygon can be uniquely determined by a single far field measurement. Our…

Analysis of PDEs · Mathematics 2025-06-04 Jianli Xiang

We determine the uniqueness on starlike obstacles by using the cross section data. We see cross section data as spectral measure in polar coordinate at far field. Cross section scattering data suffice to give the local behavior of the wave…

Analysis of PDEs · Mathematics 2010-11-15 Lung-Hui Chen

A review of the author's results is given. Inversion formulas and stability estimates for the solutions to 3D inverse scattering problems with fixed-energy data are obtained. Inversions of exact and noisy data are stidied. The inverse…

Mathematical Physics · Physics 2007-05-23 Alexander G. Ramm

An inverse scattering problems for the 3-D generalized Helmholtz equation is considered. Only the modulus of the complex valued scattered wave field is assumed to be measured and the phase is not measured. Uniqueness theorem is proved.

Mathematical Physics · Physics 2016-07-15 Michael V. Klibanov

A condition, at which the one-dimensional inverse power potential becomes reflectionless during propagation through it of a plane wave, is obtained on the basis of SUSY QM methods. A scattering of a particle on spherically symmetric inverse…

Quantum Physics · Physics 2007-05-23 Sergei P. Maydanyuk

We consider fractional diffusion-wave equations with source term which is represented in a form of a product of a temporal function and a spatial function. We prove the uniqueness for inveres source problem of determining spatially varying…

Analysis of PDEs · Mathematics 2023-01-18 Masahiro Yamamoto

Let $q(x)$ be real-valued compactly supported sufficiently smooth function. It is proved that the scattering data $A(-\beta,\beta,k)$ $\forall \beta\in S^2$, $\forall k>0,$ determine $q$ uniquely.

Mathematical Physics · Physics 2010-07-20 A. G. Ramm

This paper concerns time-harmonic inverse source problems with a single far-field pattern in two dimensions, where the source term is compactly supported in an a priori given inhomogeneous background medium. For convex-polygonal source…

Analysis of PDEs · Mathematics 2020-03-13 Guanghui Hu , Jingzhi Li

The inverse scattering problem for the Schr$\mathrm{\ddot{o}}$dinger operators on the line is considered when the potential is real valued and integrable and has a finite first moment. It is shown that the potential on the line is uniquely…

Spectral Theory · Mathematics 2018-02-14 Yongxia Guo , Guangsheng Wei

The statistical theory of certain complex wave interference phenomena, like the statistical fluctuations of transmission and reflection of waves, is of considerable interest in many fields of physics. In this article we shall be mainly…

Disordered Systems and Neural Networks · Physics 2016-08-16 P. A. Mello , M. Yépez , L. S. Froufe , J. J. Sáenz

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

It is proved that a general polyhedral perfect conducting obstacle in $\mathbb{R}^3$, possibly consisting of finitely many solid polyhedra, is uniquely determined by the far-field pattern corresponding to a single incident wave. This…

Analysis of PDEs · Mathematics 2009-11-13 Hongyu Liu

In this study, the inverse problem of the scattering theory on the half line for a piecewise continuous Sturm-Liouville equation with boundary condition depending quadratic on the spectral parameter is considered. The scattering data of the…

Spectral Theory · Mathematics 2015-02-06 Kh. R. Mamedov , Nida P. Kosar , F. Ayca Cetinkaya

We prove that the inverse scattering problem for the Schr\"odinger operator with the separable potential can be reduced to the solving of a certain singular integral equation. We establish the uniqueness of the potential corresponding to…

Mathematical Physics · Physics 2007-05-23 Yu. P. Chuburin

An alternative description of quantum scattering processes rests on inhomogeneous terms amended to the Schroedinger equation. We detail the structure of sources that give rise to multipole scattering waves of definite angular momentum, and…

Quantum Physics · Physics 2007-05-23 Christian Bracher , Tobias Kramer , Manfred Kleber

We consider the inverse scattering on the quantum graph associated with the hexagonal lattice. Assuming that the potentials on the edges are compactly supported and symmetric, we show that the S-matrix for all energies in any given open set…

Mathematical Physics · Physics 2023-11-28 Kazunori Ando , Hiroshi Isozaki , Evgeny Korotyaev , Hisashi Morioka

This work investigates both direct and inverse problems of the variable-exponent sub-diffusion model, which attracts increasing attentions in both practical applications and theoretical aspects. Based on the perturbation method, which…

Numerical Analysis · Mathematics 2025-01-31 Zhiyuan Li , Chunlong Sun , Xiangcheng Zheng

This paper concerns an inverse elastic scattering problem which is to determine a rigid obstacle from time domain scattered field data for a single incident plane wave. By using Helmholtz decomposition, we reduce the initial-boundary value…

Numerical Analysis · Mathematics 2022-03-14 Lu Zhao , Heping Dong , Fuming Ma