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SUMMARY:Elena Cherkaev (University of Utah)
DTSTART:20210930T160000Z
DTEND:20210930T170000Z
DTSTAMP:20260423T021155Z
UID:Inverse/59
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Inverse/59/"
 >Inverse homogenization: Can one hear the structure of a composite?</a>\nb
 y Elena Cherkaev (University of Utah) as part of International Zoom Invers
 e Problems Seminar\, UC Irvine\n\n\nAbstract\nInverse homogenization is a 
 problem of deriving information about the microgeometry of a finely struct
 ured medium from its known effective properties. I will discuss an approac
 h to this problem based on reconstructing the matrix-valued spectral measu
 re in the Stieltjes integral representation of the effective properties of
  a two-component composite. This integral representation relates the n-poi
 nt correlation functions of the microstructure to the moments of the spect
 ral measure of an operator depending on the composite’s geometry. I will
  show that the spectral measure which contains all information about the m
 icrostructure\, can be uniquely recovered from frequency dependent effecti
 ve data\; this allows to view the problem as an inverse spectral problem. 
 In particular\, the moments of the measure and the spectral gaps at the en
 ds of the spectral interval can be uniquely reconstructed\, which results 
 in the unique identification of the volume fractions of materials in the c
 omposite and estimates for the connectedness of its phases. I will discuss
  the recovery of microstructural parameters from electromagnetic and visco
 elastic effective measurements and show that the resulting spectroscopic i
 maging method provides an efficient way to construct spectrally matched mi
 crostructures.\n
LOCATION:https://researchseminars.org/talk/Inverse/59/
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