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SUMMARY:Model reduction for the Dirichlet Laplacian in thin domains - Luca
 s  Chesnel  (INRIA Saclay - Île-de-France)
DTSTART:20260415T091500Z
DTEND:20260415T101500Z
UID:TALK244009@talks.cam.ac.uk
DESCRIPTION:In this talk\, we are interested in the spectrum of the Dirich
 let Laplacian in thin domains. First\, we consider broken strips of thickn
 ess &epsilon\;>0 small with an angle &alpha\;. We construct an asymptotic 
 expansion of the first eigenvalues and corresponding eigenfunctions when &
 epsilon\; tends to zero. By studying the dependence of this expansion with
  respect to &alpha\;\, we highlight a curious phenomenon of "diving eigenv
 alues": when the strip is more and more broken\, at certain critical angle
 s\, an eigenvalue moves down rapidly below the pack of other eigenvalues. 
 By exploiting this analysis\, in a second step\, we present another intrig
 uing phenomenon of "spectral breathing" in quasi 1D periodic waveguides: w
 hen changing continuously the geometry around certain configurations\, spe
 ctral brands\, which are generically very short due to the Dirichlet bound
 ary conditions\, can grow to a considerable length.\nThis is a joint work 
 with S.A. Nazarov.
LOCATION:Seminar Room 1\, Newton Institute
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