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SUMMARY:Homogenization of quasi-periodic photonic crystals: The cut-and-pr
 oject multiple scale method - Sebastian Guenneau (CNRS (Centre national de
  la recherche scientifique))
DTSTART:20230316T133000Z
DTEND:20230316T150000Z
UID:TALK198013@talks.cam.ac.uk
DESCRIPTION:An asymptotic procedure based upon the method of multiple scal
 es has been developed by Elena Cherkaev (\nDepartment of Mathematics\, Uni
 versity of Utah\, USA)\, Niklas Wellander (Swedish Defence Research Agency
 \, Linkoping\, Sweden)\, Frederic Zolla (Institut Fresnel\, Aix-Marseille 
 University\, CNRS\, Marseille\, France) and the speaker for homogenization
  of wave equations in quasiperiodic inhomogeneous media deduced from a cut
 -and-projection [1]. Partial differential operators (gradient\, divergence
  and curl) acting on periodic functions with m variables in a higher-dimen
 sional space are projected onto operators acting on quasiperiodic function
 s with n variables in the physical space (m>n). When the wave wavelength i
 s much larger than the periodic cell in the m-dimensional space\, heteroge
 neous photonic quasicrystals can be approximated by homogeneous media desc
 ribed by anisotropic tensors of permittivity and permeability\, deduced fr
 om the resolution of annex problems of electrostatic type on the periodic 
 cell in m-dimensional space. We point out that this cut-and-project multip
 le scale method can be applied to other wave problems described by systems
  of linear partial differential equations in quasiperiodic structures dedu
 ced from a cut-and-projection.\n&nbsp\;\n[1] S. Guenneau\, F. Zolla\, E. C
 herkaev and N. Wellander\, Multiple scale method applied to homogenization
  of irrational metamaterials\, IEEE Proceedings of the Fourteenth Internat
 ional Congress on Artificial Materials for Novel Wave Phenomena\, 162-164\
 , 2020.\n&nbsp\;\n&nbsp\;
LOCATION:Seminar Room 2\, Newton Institute
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