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SUMMARY:The link between the Wiener-Hopf and the generalised Sommerfeld Ma
 lyuzhinets methods: Lecture 2 - Guido Lombardi (Politecnico di Torino\; Po
 litecnico di Torino)\; J.M.L. Bernard (ENS de Cachan)
DTSTART:20190808T093000Z
DTEND:20190808T104500Z
UID:TALK128227@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:<span><span>The Sommerfeld Malyuzhinets (SM) method and the Wi
 ener Hopf (WH) technique are different but closely related methods. In par
 ticular in the paper &ldquo\;Progress and Prospects in The Theory of Linea
 r Waves Propagation&rdquo\; SIAM SIREV vol.21\, No.2\, April 1979\, pp. 22
 9-245\, J.B. Keller posed the following question &ldquo\;What features of 
 the methods account for this difference?&rdquo\;.&nbsp\; Furthermore&nbsp\
 ; <a target="_blank" rel="nofollow">J.B. Keller</a> notes &ldquo\;it might
  be helpful to understand this in order to predict the success of other me
 thods&rdquo\;.</span> <br></span><br><span>We agree with this opinion expr
 essed by the giant of&nbsp\; Diffraction. Furthermore we think that SM and
  WH applied to the same problems (for instance the polygon diffraction)&nb
 sp\; can determine a helpful synergy. In the past the SM and WH methods we
 re considered disconnected in particular because the SM method was traditi
 onally defined with the angular complex representation while the WH method
  was traditionally defined in the Laplace domain. <br></span><br><span> In
  this course we show that the two methods have significant points of simil
 arity when the representation of problems in both methods are expressed in
  terms of difference equations. The two methods show their diversity in th
 e solution procedures that are completely different and effective. Both si
 milarity and diversity properties are of advantage in&nbsp\; &ldquo\;Progr
 ess and Prospects in The Theory of Linear Waves Propagation&rdquo\;. <br><
 /span><br><span>Moreover both methods have demonstrated their efficacy in 
 studying particularly complex problems\, beyond the traditional problem of
  scattering by a wedge: in particular the scattering by a three part polyg
 on that we will present.   Recent progress in both methods:  One of the mo
 st relevant recent progress in SM is the derivation of functional differen
 ce equations without the use of Maliuzhinets inversion theorem.  <br></spa
 n><br>One of the most relevant recent progress in WH is transformation of 
 WH equations into integral equations for their effective solution<br>
LOCATION:Seminar Room 1\, Newton Institute
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