Acoustically invisible gateways

Brian Sleeman; Evgeny Lakshtanov

doi:10.3934/ipi.2011.5.203

Article Contents

2011, Volume 5, Issue 1: 203-217. Doi: 10.3934/ipi.2011.5.203

This issue Previous Article On rational approximation methods for inverse source problems Next Article Structural stability in a minimization problem and applications to conductivity imaging

Acoustically invisible gateways

Brian Sleeman^1, and
Evgeny Lakshtanov^2,

1.
School of Mathematics, University of Leeds, Leeds, LS2 9JT
2.
Department of Mathematics, Aveiro University, Aveiro 3810

Received: April 30, 2010

Revised: August 31, 2010

Published: January 2011

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Abstract

In recent years considerable interest has been directed at devising obstacles which appear "invisible" to various types of wave propagation. That is; suppose for example we can construct an obstacle coated with an appropriate material such that when illuminated by an incident field (e.g plane wave) the wave scattered by the obstacle has zero cross section (equivalently radiation pattern)for all incident directions and frequencies then the obstacle appears to have no effect on the illuminating wave and the obstacle can be considered invisible. Such an electromagnetic cloaking device has been constructed by Schurig et. al [18]. Motivated by recent work [1] concerning the problem of a parallel flow of particles falling on a body with piecewise smooth boundary and leaving no trace the analogous problem of acoustic scattering of a plane wave illuminating the same body, a gateway, is considered. It is shown that at high frequencies, with use of the Kirchoff approximation and the geometrical theory of diffraction, the scattered far field in a range of observed directions, e. g the back scattered direction, is zero for a discrete set of wave numbers. That is the gateway is acoustically "invisible" in that direction.

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Mathematics Subject Classification: Primary: 74J20, 78A45; Secondary: 34L25.

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