Change of Location:
This talk will be in Room FINE 214 (second floor of Fine Hall) !

Knut Solna

Wave pulses in a heterogeneous environment

 Abstract:  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 phase 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 show how 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.