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SUMMARY:The link between the Wiener-Hopf and the generalised Sommerfeld Ma
 lyuzhinets methods: Lecture 3 - Guido Lombardi (Politecnico di Torino\; Po
 litecnico di Torino)\; J.M.L. Bernard (ENS de Cachan)
DTSTART:20190808T131500Z
DTEND:20190808T143000Z
UID:TALK128095@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:The<br>Sommerfeld Malyuzhinets (SM) method and the Wiener Hopf
  (WH) technique are<br>different but closely related methods. In particula
 r in the paper &ldquo\;Progress and<br>Prospects in The Theory of Linear W
 aves Propagation&rdquo\; SIAM SIREV vol.21\, No.2\,<br>April 1979\, pp. 22
 9-245\, J.B. Keller posed the following question &ldquo\;What<br>features 
 of the methods account for this difference?&rdquo\;. Furthermore<br>J.B. K
 eller notes &ldquo\;it might be<br>helpful to understand this in order to 
 predict the success of other methods&rdquo\;.<br><br>We<br>agree with this
  opinion expressed by the giant of Diffraction. Furthermore we think that 
 SM and<br>WH applied to the same problems (for instance the polygon diffra
 ction) can determine a helpful synergy. In the past<br>the SM and WH metho
 ds were considered disconnected in particular because the SM<br>method was
  traditionally defined with the angular complex representation while<br>th
 e WH method was traditionally defined in the Laplace domain.<br><br>In<br>
 this course we show that the two methods have significant points of simila
 rity<br>when the representation of problems in both methods are expressed 
 in terms of<br>difference equations. The two methods show their diversity 
 in the solution<br>procedures that are completely different and effective.
 <br>Both similarity and diversity properties are of advantage in &ldquo\;P
 rogress and Prospects in The Theory of<br>Linear Waves Propagation&rdquo\;
 . Moreover<br>both methods have demonstrated their efficacy in studying pa
 rticularly complex<br>problems\, beyond the traditional problem of scatter
 ing by a wedge: in<br>particular the scattering by a three part polygon th
 at we will present. <br><br>Recent<br>progress in both methods:<br><br>One
 <br>of the most relevant recent progress in SM is the derivation of functi
 onal<br>difference equations without the use of Maliuzhinets inversion the
 orem. <br>One<br>of the most relevant recent progress in WH is transformat
 ion of WH equations<br>into integral equations for their effective solutio
 n.
LOCATION:Seminar Room 1\, Newton Institute
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