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SUMMARY:Effective constitutive relations for waves in composites and metam
 aterials - Professor J Willis\, DAMTP
DTSTART:20090501T130000Z
DTEND:20090501T140000Z
UID:TALK17203@talks.cam.ac.uk
CONTACT:Ms Helen Gardner
DESCRIPTION:The description of waves propagating through strongly-heteroge
 neous material requires some kind of averaging to be performed. Here\, the
  material is taken to be random and ensemble averaging is considered\; it 
 is noted in this context that\, although the ensemble average is not seen 
 in any one realisation\, it nevertheless provides a scaffold upon which th
 e solution in any particular realisation can in principle be built. In pra
 ctice\, resort must be made to approximations. This work establishes exact
  variational principles which the ensemble averaged solutions must satisfy
 \, and from which “effective constitutive relations” follow. It is dem
 onstrated also that a similar variational structure follows if weighted en
 semble averages are employed. Such weighted averages are relevant to so-ca
 lled metamaterials which contain micro-resonators\, whose displacements ar
 e best excluded from the averaging process.
LOCATION:Oatley Seminar Room\, Department of Engineering
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