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SUMMARY:Transmission and reflection at the boundary of a random two-compon
 ent composite - Professor  John R. Willis\, University of Cambridge
DTSTART:20200611T140000Z
DTEND:20200611T153000Z
UID:TALK148636@talks.cam.ac.uk
CONTACT:Hilde Hambro
DESCRIPTION:Description: A half-space x_2 > 0 is occupied by a two-compone
 nt statistically-uniform random composite with specified volume fractions 
 and two-point correlation. It is bonded to a uniform half-space x_2 < 0 fr
 om which a plane wave is incident. The transmitted and reflected mean wave
 s are calculated via a variational formulation that makes optimal use of t
 he given statistical information. The problem requires the specification o
 f the properties of three media: those of the two constituents of the comp
 osite and those of the homogeneous half-space. The complexity of the probl
 em is minimized by considering a model acoustic-wave problem in which the 
 three media have the same modulus but different densities. It is formulate
 d as a problem of Wiener–Hopf type which is solved explicitly in the par
 ticular case of an exponentially decaying correlation. A striking feature 
 in this case is that the composite supports exactly two mean acoustic plan
 e waves in any given direction. Each decays exponentially. At low frequenc
 ies the rate of decay of one wave is much slower than that of the other\; 
 at higher frequencies the decay rates of the two waves are comparable. Thu
 s\, in general\, there are two transmission coefficients and one reflectio
 n coefficient\, and the conditions of continuity of traction and displacem
 ent of the mean waves do not suffice to determine them: the solution absol
 utely requires a more complete calculation\, such as the one presented. 
LOCATION:Venue to be confirmed
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