Time reversal of waves in random media
4:10 pm, SS 5017A
Lenya Ryzhik, University of Chicago
We present a mathematical theory of time-reversal experiments. In such
experiments a signal emitted by a localized source is recorded by an
array of receivers-transducers and re-emitted into the medium reversed
in time. The new signal refocuses approximately on the location of the
original source despite the small size of the array. Surprisingly,
medium heterogeneities improve significantly the quality of
refocusing. We will explain how this phenomenon may be understood in
the general framework of refocusing of re-transmitted high frequency
acoustic waves recorded at a single time. We will discuss in
particular the self-averaging properties of the re-transmitted signal
that appear due to wave mixing and relate them to the self-averaging
properties of the phase space energy density of waves in random media.
Reaction-diffusion fronts in flows: speed-up and quenching
5:10 pm, SS 5017A
Lenya Ryzhik, University of Chicago
Traveling waves in reaction-diffusion equations have been very useful
in modeling various propagation phenomena in physics, biology and
other sciences. Recently there has been a lot of mathematical works on
the possible effect of a fluid flow or wind on front propagation, when
the flow is prescribed. Such a flow may significantly enhance the
front speed as well as extinguish a flame depending on the geometry of
the flow, its amplitude, and the relation of the flow scales to those
of the reaction front. We will review our results that exhibit and
quantify these phenomena in shear, cellular and other flows. We will
also discuss our recent results in the analysis of the reactive
Boussinesq system when the flow is generated by the temperature
differences.