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SUMMARY:Transmission and reflection of energy at the boundary of a random 
 two-component composite - John Raymond Willis (University of Cambridge)
DTSTART:20230324T090000Z
DTEND:20230324T093000Z
UID:TALK195610@talks.cam.ac.uk
DESCRIPTION:A half-space $x_2 > 0$ is occupied by a two-component statisti
 cally-uniform random composite with specified volume fractions and two-poi
 nt correlation. It is bonded to a uniform half-space $x_2 < 0$ from which 
 a plane wave is incident. The problem requires the specification of the pr
 operties of three media: those of the two constituents of the composite an
 d those of the homogeneous half-space. The complexity of the problem is mi
 nimized by considering a model acoustic-wave problem in which the two medi
 a comprising the composite have the same modulus but different densities. 
 The homogeneous half-space can have any chosen modulus and density. An app
 roximate formulation based on a stochastic variational principle is formul
 ated and solved explicitly in the particular case of an exponentially deca
 ying correlation function\, generalizing a previous solution in which the 
 homogeneous medium had the same modulus as the composite. The main novelty
  of the present work is that the mean energy fluxes in the composite and r
 eflected from the boundary are calculated\, demonstrating explicitly the l
 arge backscatter associated with the mean-zero component of the reflected 
 signal and the systematic transfer of energy from the decaying mean transm
 itted waves into the mean-zero disturbance as distance from the boundary i
 ncreases.
LOCATION:Seminar Room 1\, Newton Institute
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