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NJIT Applied Mathematics Colloquium

Friday, March 26, 2010, 11:30am
Cullimore Lecture Hall II
New Jersey Institute of Technology

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Transitory Dynamical Systems and Transport

James Meiss

University of Colorado, Boulder

A transitory system is steady sufficiently far in the past and in the future, but undergoes a transition between these two steady states. They provide perhaps the simplest example of nonautonomous and aperiodic dynamical systems. Nonautonomous dynamical systems have received much study recently using the concepts of "Lagrangian coherent structures" (LCS) and finite time Lyapunov exponents (FTLE) especially for application to fluid mixing in the context of atmospheric and oceanic flows. For the transitory case, the coherent structures are precisely defined for the past and future systems, and the natural question is "what is the transport between these structures?" This is a natural testbed for understanding LCS. A simple example corresponds to a 2D fluid flow with a pair of gyres that transition to a new pair. Another corresponds to the acceleration of a particle trapped in a moving potential well. The interesting quantity to compute is the flux from the past to the future coherent structures. We show how these fluxes can be finding particular heteroclinic orbits and computing integrals along these orbits to determine their "actions". We will compare these results to those obtained by the FTLE technique.