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Colloquium, Spring 2005

Day: Thursday April 28th Time: 4:00pm Place: BH 227 Title: Characterization of Spatiotemporal Chaos Speaker: Ralf Wittenberg, Simon Fraser University Abstract: Many concepts and techniques from finite-dimensional dynamical systems have been extended to nonlinear spatially extended systems displaying complex spatial and temporal dynamics and pattern formation. However, the nature and origins of such complex spatiotemporal behaviour are still incompletely understood. I will discuss some aspects of spatiotemporal chaos (STC) in a class of one-dimensional partial differential equations including the Kuramoto-Sivashinsky (KS) equation, and I will show how a wavelet projection and numerical experiments may be used to study features of the dynamics in space and scale. I will particularly focus on the importance of large spatial scales, which act as a Gaussian "heat bath" maintaining the spatiotemporal disorder, and will illustrate this with two additional examples: The KS equation in the presence of an additional destabilizing linear term, which displays a transition from STC to a stationary shock-like solution due to excitation at large scales; and a sixth-order analogue of the KS equation in which STC is maintained by the coupling to large scales. Cookies: In BH 300 at 3:30pm.