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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Transmission and reflection of energy at the bound
ary of a random two-component composite - John Ray
mond Willis (University of Cambridge)
DTSTART;TZID=Europe/London:20230324T090000
DTEND;TZID=Europe/London:20230324T093000
UID:TALK195610AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/195610
DESCRIPTION:A half-space $x_2 > 0$ is occupied by a two-compon
ent statistically-uniform random composite with sp
ecified volume fractions and two-point correlation
. It is bonded to a uniform half-space $x_2 < 0$ f
rom which a plane wave is incident. The problem re
quires the specification of the properties of thre
e media: those of the two constituents of the comp
osite and those of the homogeneous half-space. The
complexity of the problem is minimized by conside
ring a model acoustic-wave problem in which the tw
o media comprising the composite have the same mod
ulus but different densities. The homogeneous half
-space can have any chosen modulus and density. An
approximate formulation based on a stochastic var
iational principle is formulated and solved explic
itly in the particular case of an exponentially de
caying correlation function\, generalizing a previ
ous solution in which the homogeneous medium had t
he same modulus as the composite. The main novelty
of the present work is that the mean energy fluxe
s in the composite and reflected from the boundary
are calculated\, demonstrating explicitly the lar
ge backscatter associated with the mean-zero compo
nent of the reflected signal and the systematic tr
ansfer of energy from the decaying mean transmitte
d waves into the mean-zero disturbance as distance
from the boundary increases.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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