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SUMMARY:Wave propagation in periodic media and dispersive effects - Grégo
 ire Allaire\, Ecole Polytechnique
DTSTART:20150327T150000Z
DTEND:20150327T160000Z
UID:TALK58640@talks.cam.ac.uk
CONTACT:Harsha Hutridurga
DESCRIPTION:We study high frequency wave propagation in a periodic medium\
 nfor times long enough so that dispersive effects are important.\nIn other
  words\, we consider the homogenization of the wave\nequation in a periodi
 c medium for long times of the order\nof the inverse of the period\, and f
 or inital data that are\nBloch wave packets\, i.e. that are the product of
  a fast\noscillating Bloch wave and of a smooth envelope function.\nWe pro
 ve that the solution is approximately equal to two waves\npropagating in o
 pposite directions at a large group velocity with\nenvelope functions whic
 h obey a Schrodinger type equation.\nOur analysis extends the usual WKB ap
 proximation by adding a\ndispersive\, or diffractive\, effect due to the n
 on uniformity\nof the group velocity which yields the dispersion tensor of
 \nthe homogenized Schrodinger equation.\nThis is a joint work with Mariapi
 a Palombaro and Jeff Rauch.
LOCATION:CMS\, MR13
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