[Amath-seminars] Upcoming Boeing Lecture

Joel Zylberberg joelzy at uw.edu
Wed Oct 15 14:29:00 PDT 2014

Hi All,

Our first Boeing lecture of the quarter will be next week (Oct. 23),
details below. Faculty / staff should please sign up on this google docs
meetings (and meals) with the speaker.

Speaker Kevin Zumbrun
Thurs, Oct 23, 4pm
Smith Hall 205

*Modulation of spatially periodic patterns and behavior of thin film flows*
Periodic patterns and traveling waves arise quite generally in optics,
biology, chemistry, and many other applications. A great success story
over the past couple decades for the dynamical systems approach to PDE has
been the rigorous treatment of modulation of periodic patterns in reaction
diffusion systems. However, the techniques used were designed for
modulations with a single degree of freedom. For systems possessing one or
more conservation laws, hence two or more degrees of freedom in particular,
the Kuramoto-Sivashinsky, Saint Venant, and other equations governing thin
film flow- these methods do not apply. Here, we present an approach
applying also to this more general situation, rigorously verifying an
associated ``Whitham system'' formally governing slow modulations under
suitable numerically verifiable stability assumptions on the spectra of the
linearized operator about the background pattern. This verifies/explains a
number of numerically observed phenomena in thin film flow, including
`viscoelastic behavior'' in cellular Kuramoto-Sivashinsky behavior, and
the ``homoclinic paradox'' in inclined thin-film flow, the latter
concerning the puzzling phenomenon that asymptotic behavior appears to
consist of solitary waves, despite that solitary waves are readily seen to
be exponentially unstable. We conclude by discussing verification of our
spectral assumptions in weakly and strongly unstable (corresponding to
small and large Froude number) regimes, giving simple power-law formulae
describing the stability boundaries in each case. The latter, strongly
unstable description, relevant in applications to hydraulic engineering/dam
spillway construction, was unexpected and to our knowledge is completely

Joel Zylberberg

Acting Assistant Professor
Department of Applied Mathematics
University of Washington
Seattle, WA


~ The neuroscience is theoretical, but the fun is real
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