It's a thoughtful review of recent results in the field,
using the simplest terms to explain the underlying ideas, so
it's meant to be readable for a wide audience.
Does
it describe a new discovery or new methodology that's useful to
others?
It describes recent discoveries (since 1990), and
methodologies i.e., asymptotic methods for wave fronts in
multiscale (periodic orrandom) media. It also explores results
by different researchers, and points out currently open research
problems.
Is
it a condensation of previous literature on the subject?
It is not a condensation, rather an exposition of thoughts
and ideas behind the main results and conceptual advances—such
as where to expect to go from deterministic to stochastic
problems, and how to relate random wave properties to basic laws
of probability etc.
Could
you summarize the significance of your paper in layman's terms?
It is the first major review of asymptotic methods on wave
fronts in heterogeneous media, e.g. how to characterize and
estimate flame velocity when there is wind blowing, and how to
find statistics of pollutant motion in a nonuniform porous
media.
Jack Xin
Professor of Mathematics and TICAM
University of Texas at Austin
