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SUMMARY:Two-scale 'micro-resonant' homogenisation of periodic (and some er
 godic) problems - Smyshlyaev\, V (University College London)
DTSTART:20150326T113000Z
DTEND:20150326T123000Z
UID:TALK58606@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Co-author: Ilia Kamotski (University College London) \n\nThere
  has been lot of recent interest in composite materials whose macroscopic 
 physical properties can be radically different from those of conventional 
 materials\, often due to effects of the so-called "micro-resonances". Math
 ematically this leads to studying high-contrast homogenization of (periodi
 c or not) problems with a `critically scaled high contrast\, where the res
 ulting two-scale asymptotic behaviour appears to display a number of inter
 esting effects. Mathematical analysis of these problems requires developme
 nt of  "two-scale" versions of operator and spectral convergences\, of com
 pactness\, etc. We will review some background\, as well as some more rece
 nt generalizations and applications. One is two-scale analysis of general 
 "partially-degenerating" periodic problems\, where strong two-scale resolv
 ent convergence appears to hold under a rather generic decomposition assum
 ptions\, implying in particular (two-scale) convergence of se migroups wit
 h applications to a wide class of micro-resonant dynamic problems. Another
  is two-scale homogenization with random micro-resonances\, which appears 
 to yield macroscopic dynamics effects akin to Anderson localization. Some 
 of the work is joined with Ilia Kamotski. \n
LOCATION:Seminar Room 1\, Newton Institute
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