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Summary: The Center for Control, Dynamical Systems, and Computation
Spring Seminars
Presents
Computational Dynamics via Set Oriented
Numerics -- from Transport Phenomena to
Multiobjective Optimization
by
Professor Michael Dellnitz
Institute for Mathematics
University of Paderborn, Germany
Friday, April 14th, 2006 3:00 - 4:00 PM Engineering II Pavilion
Abstract:
Over the last years so-called set oriented numerical methods have been developed for dynamical systems. The basic idea
is to cover the objects of interest -- for instance invariant manifolds or invariant measures -- by outer approximations which
are created via adaptive multilevel subdivision techniques. These schemes allow for an efficient discretization of the phase
space.
In this talk we will show that set oriented techniques particularly be useful for the approximation of transport processes. We
will focus on two related applications. First, we analyze the transport of asteroids in the solar system -- motivated by the
asteroid belt between Mars and Jupiter. Second, we can show how to analyze transport phenomena in ocean dynamics.
Here the related mathematical models depend explicitly on time which makes the numerical treatment inherently more
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