Dr. Katherine Newhall, Assistant Professor of Mathematics at the University of North Carolina at Chapel Hill, will present the next Math Lecture, on Friday, February 23th. She will discuss “Metastability of the Nonlinear Wave Equation.” This free lecture is open to all. The event begins at 11:20 a.m. in Armitage Hall, Room 121.
The abstract is as follows:
“Dr. Newhall will discuss the long-time dynamics of infinite energy solutions to a wave equation with nonlinear forcing. Of particular interest is when these solutions display metastability in the sense that they spend long periods of time in disjoint regions of phase-space and only rarely transition between them. This phenomenon is quantified by calculating exactly via Transition State Theory (TST) the mean frequency at which the solutions of the nonlinear wave equation with initial conditions drawn from its invariant measure cross a dividing surface lying in between the metastable sets. Numerical results suggest a regime for which the dynamics are not fundamentally different from that observed in the stochastic counterpart in which random noise and damping terms are added to the equation, as well as a regime for which successive transitions between the metastable sets are correlated and the coarse-graining to a Markov chain fails.”