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Analytic Mode-Matching at an Exceptional Point

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MWSW01 - Canonical scattering problems

Exceptional points (which occur when two or more modes coalesce) have long been associated with optimal attenuation in lined acoustic waveguides.  In recent years, with a view to optimising sound absorption, some effort has gone into designing liners that generate exceptional points (EPs) at specified frequencies. However, analytic modelling of acoustic scattering in the presence of an EP is not well developed, with most authors relying on standard methods applied close to (but not at) EP conditions. Indeed, exact treatment requires care since the mathematical system under-pinning the scattering process is degenerate. This talk presents an analytic mode-matching approach to modelling the scattering of a plane wave travelling towards the junction of a rigid duct with a lined duct at EP conditions. Both EP2 and EP3 (coalescence of two and three modes respectively) are considered. The enhanced mode-matching scheme is shown to be valid and numerically robust, and it is anticipated that it will be straightforward to adapt to a wide range of applications involving complex symmetric operators. [In collaboration with E Perrey-Debain and B Nennig.]

This talk is part of the Isaac Newton Institute Seminar Series series.

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