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SUMMARY:Scattering of a sound wave by a two-sided sandwich membrane - Yuri
  Antipov (Louisiana State University)
DTSTART:20230210T114500Z
DTEND:20230210T123000Z
UID:TALK194842@talks.cam.ac.uk
DESCRIPTION:Scattering of a sound plane wave by an infinite thin structure
  is considered. The structure is composed of a semi-infinite two-sided san
 dwich membrane perforated on one side and a semi-infinite acoustically har
 d screen. On the perforated and continuous sides\, the velocity potential 
 satisfies the first order Leppington and third order membrane boundary con
 ditions\, respectively. Two ways of applying the Fourier transforms to the
  boundary value problem lead to distinct governing systems of two Wiener-H
 opf functional equations. It is shown that both Wiener-Hopf problems share
  the same characteristic polynomial and elliptic surface but reduce to dif
 ferent genus-1 scalar Riemann-Hilbert problems. The associated Jacobi inve
 rsion problem is solved in terms of&nbsp\;the genus-1 Riemann theta functi
 on. Exact formulas for the Wiener-Hopf matrix factors are presented. The s
 olvability of the problem and the discontinuity of the solution at the scr
 eens junction are discussed.
LOCATION:Seminar Room 1\, Newton Institute
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