Title: Phase locking for interface propagation in periodic media

Speaker: Viktor Roytburd

Abstract:

Sharp-interface models with energy deposition at the interface provide a
rather accurate description for many phase transition type phenomena, such
as freezing or burning. Numerical simulations reveal a huge variety of
dynamical scenarios, including period doubling, chaos etc. Nonetheless,
although described by partial differential equations, asymptotic dynamics
are essentially finite-dimensional. Moreover, numerical estimation shows
that the correlation dimension is very low indeed.
For propagation in periodic media we also examine phase-locking effects
(which are analogous to the ones observed for the classical van der Pol
oscillator). In some sense the PDE system behaves like a fancy nonlinear
oscillator. Amazingly, many features of PDE dynamics are reproduces in a
^3-dimensional projection^ of the original dynamical system. This is a
joint work with Michael Frankel of Indiana University-Purdue University
Indianapolis.