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The general space-time evolution of the scattering of an incident acoustic plane wave pulse by an arbitrary configuration of targets is treated by employing a recently developed non-singular boundary integral method to solve the Helmholtz…
In this paper, a time domain enclosure method for an inverse obstacle scattering problem of electromagnetic wave is introduced. The wave as a solution of Maxwell's equations is generated by an applied volumetric current having an {\it…
We present a new methodology, based on the WKB approximation and Fast Fourier Transforms, for the evaluation of wave propagation through inhomogeneous media. This method can accurately resolve fields containing caustics, while still…
Scalar wave scattering by many small particles with impedance boundary condition and creating material with a desired refraction coefficient are studied. The acoustic wave scattering problem is solved asymptotically and numerically under…
We study the propagation in three dimensions of internal waves using ray tracing methods and traditional dynamical systems theory. The wave propagation on a cone that generalizes the Saint Andrew's cross justifies the introduction of an…
A 3-D inverse medium problem in the frequency domain is considered. Another name for this problem is Coefficient Inverse Problem. The goal is to reconstruct spatially distributed dielectric constants from scattering data. Potential…
We introduce a direct, linear sampling approach to imaging in an acoustic waveguide with sound hard walls. The waveguide terminates at one end and has unknown geometry due to compactly supported wall deformations. The goal of imaging is to…
Gravitational-wave analyses depend heavily on waveforms that model the evolution of compact binary coalescences as seen by observing detectors. In many cases these waveforms are given by waveform approximants, models that approximate the…
The dynamics of solitary gravity-capillary water waves propagating on the surface of a three-dimensional fluid domain is studied numerically. In order to accurately compute complex time dependent solutions, we simplify the full potential…
The scattering of scalar waves by a set of scatterers is considered. It is proven that the scattered field can be represented as an integral supported by any smooth surface enclosing the scatterers. This is a generalization of the series…
Energy transmission over long distances by waves is a key mechanism for many natural processes. This possibility arises when an inhomogeneous medium is arranged in such a manner that it enables a certain type of wave to propagate with…
Although frames, which are a generalization of bases, are important tools used in signal processing, their potential in other fields of engineering and applied mathematics (e.g. acoustics) has not been fully explored yet. Gabor frames, that…
One of the greatest theoretical challenges in the build-up to the era of second-generation gravitational-wave detectors is the modeling of generic binary waveforms. We introduce an approximation that has the potential to significantly…
The reflection and transmission amplitudes of waves in disordered multimode waveguides are studied by means of numerical simulations based on the invariant embedding equations. In particular, we analyze the influence of surface-type…
This paper describes a numerical formulation for calculating wave propagation with high precision in a three-dimensional system. Yee's discretization scheme is used to formulate a frequency domain method that is compatible with the…
Inverse scattering is the process of estimating the spatial distribution of the scattering potential of an object by measuring the scattered wavefields around it. In this paper, we consider reflection tomography of high contrast objects…
This paper considers an inverse problem for the classical wave equation in an exterior domain. It is a mathematical interpretation of an inverse obstacle problem which employs the dynamical scattering data of acoustic wave over a finite…
We formulate a finite-difference time-domain (FDTD) approach to simulate electromagnetic wave scattering from scatterers embedded in layered dielectric or dispersive media. At the heart of our approach is a derivation of an equivalent…
We establish space-time dispersive estimates for solutions to the wave equation on compact Riemannian manifolds with bounded sectional curvature, with the same exponents as for $C^\infty$ metrics. The estimates are for bounded time…
We consider the propagation of acoustic waves in a 2D waveguide unbounded in one direction and containing a compact obstacle. The wavenumber is fixed so that only one mode can propagate. The goal of this work is to propose a method to cloak…