Mathematics Colloquia and Seminars
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Wave Pulses in a Heterogeneous EnvironmentOptimization
|Speaker: ||Prof. Knut Solna, UC Irvine|
|Location: ||693 Kerr|
|Start time: ||Fri, Apr 19 2002, 2:10PM|
We consider two problems related to propagation of
wave pulses in a heterogeneous environment with
rapidly changing medium parameters.
The shape of pulse and also its speed of propagation
may be affected by the heterogeneities and we want
to characterize how.
First we consider propagation of elecromagnetic
signals through a composite structure made up of two phases
and derive bounds for the group velocity of the signal.
We show that the group velocity of a pulse in fact can be higher
in the composite structure than in either of the two
phases and give the microstructures with the maximum relative increase
and decrease in velocity.
Next we consider propagation of acoustic waves through
a multiscale or fractal medium with medium parameters
modeled in terms of fractional Brownian motion. We sho whow the
modification in the pulse shape depends on the roughness of the
medium and can be described in a deterministic way when the pulse
is observed at its random arrival time. For very rough media the
wave is localized to a surface layer.