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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Estimation of a 2D Fourier integral for the quarte
r-plane diffraction problem - Andrey Shanin (Mosco
w State University)
DTSTART;TZID=Europe/London:20230207T114500
DTEND;TZID=Europe/London:20230207T123000
UID:TALK194758AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/194758
DESCRIPTION:The classical problem of diffraction of a scalar m
onochromatic wave by a Dirichlet thin quarter-plan
e screen in the 3D space is studied. As it is know
n\, this problem admits separation of variables\,
but no analog of the Wiener-Hopf method for it has
been built. In [1] we propose an approach enablin
g one to study the singularities of the solution o
f the problem a priori (i.e. without building the
solution). The wave field becomes represented as a
2D Fourier integral whose transformant has an unk
nown regular part and an explicitly known singular
part. Here we address a technical but important p
roblem: we reconstruct the principal wave terms fr
om the singularities of the Fourier transformant.
As the basic technique\, we use the method develop
ed in [2].\nWe demonstrate that the locality princ
iple is applicable to the integral: the principal
wave terms are produced by the crossings of the si
ngularity components or the saddle points on the s
ingularity. After a careful analysis\, we obtain t
hat all components obtained this way correspond to
certain rays.\nThe work is co-authored by R.C.Ass
ier and A.I.Korolkov.\n[1] R.C.Assier\, A.V.Shanin
\, Diffraction by a quarter-plane. Analytical cont
inuation of spectral function // QJMAM V. 72\, 51-
85 (2019).\n[2] R.C.Assier\, A.V.Shanin\, A.I.Koro
lkov\, A contribution to the mathematical theory o
f diffraction: a note on double Fourier integrals
// QJMAM\, DOI: 10.1093/qjmam/hbac017
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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