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EXISTENCE THEOREMS FOR TRAPPED MODES

EVANS, DV; LEVITIN, M; VASSILIEV, D; (1994) EXISTENCE THEOREMS FOR TRAPPED MODES. J FLUID MECH , 261 21 - 31. 10.1017/S0022112094000236. Green open access

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Abstract

A two-dimensional acoustic waveguide of infinite extent described by two parallel lines contains an obstruction of fairly general shape which is symmetric about the centreline of the waveguide. It is proved that there exists at least one mode of oscillation, antisymmetric about the centreline, that corresponds to a local oscillation at a particular frequency, in the absence of excitation, which decays with distance down the waveguide away from the obstruction. Mathematically, this trapped mode is related to an eigenvalue of the Laplace operator in the waveguide. The proof makes use of an extension of the idea of the Rayleigh quotient to characterize the lowest eigenvalue of a differential operator on an infinite domain.

Type: Article
Title: EXISTENCE THEOREMS FOR TRAPPED MODES
Open access status: An open access version is available from UCL Discovery
DOI: 10.1017/S0022112094000236
Publisher version: http://dx.doi.org/10.1017/S0022112094000236
Language: English
Additional information: © 1994 Cambridge University Press
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/170542
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