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SUMMARY:Scattering of waves by finite periodic arrays - Richard Porter (Un
 iversity of Bristol)
DTSTART:20230207T094500Z
DTEND:20230207T103000Z
UID:TALK194752@talks.cam.ac.uk
DESCRIPTION:It will be shown how solutions to problems involving scatterin
 g of waves by a finite periodic array of scatterers can be reduced to a pa
 ir of scalar equations. These arise from matching solutions in the two sem
 i-infinite domains either side of the array at appropriately chosen interf
 aces at the two ends of the array to a general solution within the array. 
 The form of the scalar equations that result depends upon how the matching
  at these interfaces is performed. The multiple wave scattering that takes
  place between elements in the finite array can be encoded in the general 
 solution within a single period of the array using an expansion in the eig
 enfunctions of the infinite periodic Bloch-Floquet problem. The key is the
  construction of an orthogonality relation for these eigenfunctions which 
 allows the information in one period of the array to be propagated\, witho
 ut mode coupling\, to any other period of the array. The absence of mode c
 oupling sets it apart from transfer or scattering matrix approaches. Two e
 xamples will be presented to illustrate its application in two different s
 ettings. The connection to homogenisation will also be touched upon.
LOCATION:Seminar Room 1\, Newton Institute
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