Related papers: Free boundary methods and non-scattering phenomena
This paper is concerned with the uniqueness in inverse acoustic scattering problems with the modulus of the far-field patterns co-produced by the obstacle (resp. medium) and the point sources. Based on the superposition of point sources as…
In this paper a mathematical model is given for the scattering of an incident wave from a surface covered with microscopic small Helmholtz resonators, which are cavities with small openings. More precisely, the surface is built upon a…
This article is concerned with the time-harmonic electromagnetic (EM) scattering from a generic inhomogeneous medium. It is shown that if there is a right corner on the support of the medium, then it scatters every pair of incident EM…
We deal with the problem of the linearized and isotropic elastic inverse scattering by interfaces. We prove that the scattered $P$-parts or $S$-parts of the far field pattern, corresponding to all the incident plane waves of pressure or…
This paper investigates the inverse biharmonic scattering problems of identifying the shape and location of the obstacle with phased and phaseless measurement data. A direct imaging method based on reverse time migration is proposed for…
Starting from fundamental multiple scattering theory it is shown that negative refraction indices are feasible for matter waves passing a well-defined ensemble of scatterers. A simple approach to this topic is presented and explicit…
This paper investigates the problem of time-harmonic acoustic scattering in an inhomogeneous medium with a complex topological structure. Specifically, the medium is anisotropic and contains several disjoint sound-soft obstacles. This model…
By large-distance asymptotics, in conventional scattering theory, at the cost of losing the information of the distance between target and observer, one arrives at an explicit expression for scattering wave functions represented by a…
The characterization problem of the existence of an unknown obstacle behind a known obstacle is considered by using a singe observed wave at a place where the wave is generated. The unknown obstacle is invisible from the place by using…
We obtain a nonperturbative, analytical solution to integral equation of scattering theory by assuming the field within the scattering object is a spherical wave with a scattering amplitude equal to that of the far field. This approximation…
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…
Reflection of a normal incident matter wave by a perfectly reflecting wall moving with a constant velocity is investigated. A surprising phenomenon is found-that if the the wall moves faster than the phase velocity of the incident wave,…
This paper is concerned with the inverse acoustic scattering problems by an obstacle or a cavity with a sound-soft or a sound-hard boundary. A direct imaging method relying on the boundary conditions is proposed for reconstructing the shape…
Generalized impedance boundary conditions are effective, approximate boundary conditions that describe scattering of waves in situations where the wave interaction with the material involves multiple scales. In particular, this includes…
We investigate fixed energy scattering from conical potentials having an irregular cross-section. The incident wave can be any arbitrary non-trivial Herglotz wave. We show that a large number of such local conical scatterers scatter all…
We develop a new boundary condition for the weak inverse mean curvature flow, which gives canonical and non-trivial solutions in bounded domains. Roughly speaking, the boundary of the domain serves as an outer obstacle, and the evolving…
Wave propagation and acoustic scattering problems require vast computational resources to be solved accurately at high frequencies. Asymptotic methods can make this cost potentially frequency independent by explicitly extracting the…
It is shown that the potential perturbation that shifts a chosen standing wave in space is a block of potential barrier and well for every wave bump between neighbouring knots. The algorithms shifting the range of the primary localization…
We study a reaction-diffusion system of partial differential equations, which can be taken to be a basic model for criminal activity. We show that the assumption of a populations natural tendency towards crime significantly changes the…
This paper is concerned with uniqueness in inverse acoustic scattering with phaseless far-field data at a fixed frequency. In our previous work ({\em SIAM J. Appl. Math. \bf78} (2018), 1737-1753), by utilizing spectral properties of the…