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SUMMARY:Homogenisation of resonators via a two-scale transform\, and gener
 alisations - Valery Smyshlyaev (University College London)
DTSTART:20240705T094500Z
DTEND:20240705T101500Z
UID:TALK215440@talks.cam.ac.uk
DESCRIPTION:For a basic model of wave propagation in a matrix containing a
 n infinite periodic array of high-contrast ``soft'' inclusions\,&nbsp\; th
 e macro and micro-scales are coupled reflecting the effect of the inclusio
 n resonances. This leads to two-scale descriptions displaying in an asympt
 otically explicit way such effects as formation of band gaps due to the re
 sonances. One can obtain refined two-scale type approximations accompanied
  by rigorous error estimates via asymptotic analysis of a scaled Floquet-B
 loch-Gelfand transform combined with an (inverse scaled) Fourier transform
 . The latter combined transform appears to be a two-scale version of a cla
 ssical Whittaker-Shannon interpolation. It has several interesting propert
 ies\, and the approach allows generalisations in various directions beyond
  the infinite periodic and PDE settings. Based on a joint work with Shane 
 Cooper and Ilia Kamotski (UCL).&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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