Related papers: Detecting a hidden obstacle via the time domain en…
We consider the inverse elastic scattering problems using the far field data due to one incident plane wave. A simple method is proposed to reconstruct the location and size of the obstacle using different components of the far field…
We solve a long-standing set of problems in optics and waves: why does a volume have only so many useful orthogonal wave channels in or out of it, why do coupling strengths fall off dramatically past this number, and, indeed, just what…
We consider wave propagation problems over 2-dimensional domains with piecewise-linear boundaries, possibly including scatterers. We assume that the wave speed is constant, and that the initial conditions and forcing terms are radially…
This paper deals with the accomplishment of total area coverage of an arbitrary region using sensors with a finite sensing radius of rs. For a given region, we aim to obtain a deterministic placement of sensors which, apart from ensuring…
An inverse source problem for the heat equation is considered. Extraction formulae for information about the time and location when and where the unknown source of the equation firstly appeared are given from a single lateral boundary…
This paper concerns an inverse elastic scattering problem which is to determine the location and the shape of a rigid obstacle from the phased or phaseless far-field data for a single incident plane wave. By introducing the Helmholtz…
Exact solutions describing trapped modes in a plane quantum waveguide with a small rigid obstacle are constructed in the form of convergent series in powers of the small parameter characterizing the smallness of the obstacle. The terms of…
The aim of this paper is to establish the framework of the enclosure method for some class of inverse problems whose governing equations are given by parabolic equations with discontinuous coefficients. The framework is given by considering…
We consider the acoustic field scattered by a bounded impenetrable obstacle and we study its dependence upon a certain set of parameters. As usual, the problem is modeled by an exterior Dirichlet problem for the Helmholtz equation $\Delta u…
Consider the scattering of a time-harmonic plane wave by a rigid obstacle embedded in a homogeneous and isotropic elastic medium in two dimensions. In this paper, a novel boundary integral formulation is proposed and its highly accurate…
This paper gives applications of the enclosure method introduced by the author to typical inverse obstacle and crack scattering problems in two dimensions. Explicit extraction formulae of the convex hull of unknown polygonal sound-hard…
We develop a new variant of the wave-packet analysis and solve the tunneling time problem for one particle. Our approach suggests an individual asymptotic description of the quantum subensembles of transmitted and reflected particles both…
This paper is devoted to a novel quantitative imaging scheme of identifying impenetrable obstacles in time-harmonic acoustic scattering from the associated far-field data. The proposed method consists of two phases. In the first phase, we…
We study numerical methods of tomography in domains with a reflecting obstacle. It will be shown that tomography with sets containing both broken rays, i.e. rays reflecting at the obstacle, as well as unbroken rays, has a smaller error…
The phenomenon of wave packet diffraction in space and time is described. It consists in a diffraction pattern whose spatial location progresses with time. The pattern is produced by wave packet quantum scattering off an attractive or…
The acoustic inverse obstacle scattering problem consists of determining the shape of a domain from measurements of the scattered far field due to some set of incident fields (probes). For a penetrable object with known sound speed, this…
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…
In quantum information theory, the reliable and effective detection of entanglement is of paramount importance. However, given an unknown state, assessing its entanglement is a challenging task. To attack this problem, we investigate the…
The water wave problem is considered for a class of semi-infinite domains each having its shore shaped as a cliffed cape. In particular, the free surface of a water domain is supposed to be an infinite sector whose vertex angle is greater…
We study the uniqueness and accuracy of the numerical solution of the problem of reconstruction of the shape and trajectory of a reflecting obstacle moving in an inhomogeneous medium from travel times, start and end points, and initial…