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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:The link between the Wiener-Hopf and the generalis
ed Sommerfeld Malyuzhinets methods: Lecture 1 - Gu
ido Lombardi (Politecnico di Torino\; Politecnico
di Torino)\; J.M.L. Bernard (ENS de Cachan)
DTSTART;TZID=Europe/London:20190807T103000
DTEND;TZID=Europe/London:20190807T114500
UID:TALK128164AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/128164
DESCRIPTION:The
Sommerfeld Malyuzhinets (SM) method and the
Wiener Hopf (WH) technique are
different but c
losely related methods. In particular in the paper
&ldquo\;Progress and
Prospects in The Theory o
f Linear Waves Propagation&rdquo\; SIAM SIREV vol.
21\, No.2\,
April 1979\, pp. 229-245\, J.B. Kel
ler posed the following question &ldquo\;What
f
eatures of the methods account for this difference
?&rdquo\;. Furthermore
J.B. Keller notes &ldquo
\;it might be
helpful to understand this in ord
er to predict the success of other methods&rdquo\;
. We
agree with this opinion expressed by the g
iant of Diffraction. Furthermore we think that SM
and
WH applied to the same problems (for instan
ce the polygon diffraction) can determine a helpfu
l synergy. In the past
the SM and WH methods we
re considered disconnected in particular because t
he SM
method was traditionally defined with the
angular complex representation while
the WH me
thod was traditionally defined in the Laplace doma
in.
In
this course we show that the two met
hods have significant points of similarity
when
the representation of problems in both methods ar
e expressed in terms of
difference equations. T
he two methods show their diversity in the solutio
n
procedures that are completely different and
effective.
Both similarity and diversity proper
ties are of advantage in &ldquo\;Progress and Pros
pects in The Theory of
Linear Waves Propagation
&rdquo\;. Moreover
both methods have demonstrat
ed their efficacy in studying particularly complex
problems\, beyond the traditional problem of s
cattering by a wedge: in
particular the scatter
ing by a three part polygon that we will present.
Recent
progress in both methods:
One
of the most relevant recent progress in SM
is the derivation of functional
difference equ
ations without the use of Maliuzhinets inversion t
heorem.
One
of the most relevant recent
progress in WH is transformation of WH equationsinto integral equations for their effective solu
tion
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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