Applied Mathematics Seminar

Date: 

Tuesday, 8th March 2005

On the Approximation of Transport Phenomena

Speaker: Prof. Dr. Michael Dellnitz
Chair of Applied Mathematics
University of Paderborn, Germany

Date: Thursday March 17th
Time: 11am
Room: RC-4082

Abstract: Over the last years so-called 'set oriented' numerical methods have been developed in the context of the numerical treatment of 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 extremely memory and time efficient discretisation of the phase space and have the flexibility to be applied to several problem types.

In this talk it will be shown that these numerical techniques can particularly be useful for the approximation of 'transport phenomena.' In this context we will mainly focus on two related applications: first we will show how to analyse (time dependent) transport phenomena in ocean dynamics. Here we will illustrate the strength of these techniques by a study of transport in Monterey Bay which is based on real data. Secondly, we will analyse the transport of asteroids in the solar system -- this work is mainly motivated by the explanation of the existence of the asteroid belt between Mars and Jupiter.

The talk touches joint projects with the California Institute of Technology, Princeton University and Harvard University.

The basic idea is to cover the objects
of interest for instance 'invariant manifolds'
orinvariant measures'by outer approximations which are created via adaptive multilevel subdivision techniques. These schemes allow for an extremely memory and time efficient discretisation of the phase space and have the flexibility to be applied to several problem types.

n this talk it will be shown that these numerical techniques can
particularly be useful for the approximation of 'transport
phenomena.' In this context we will mainly focus on two related
applications: first we will show how to analyse (time dependent)
transport phenomena in ocean dynamics. Here we will illustrate the
strength of these techniques by a study of transport in Monterey Bay
which is based on real data. Secondly, we will analyse the transport
of asteroids in the solar system -- this work is mainly motivated by
the explanation of the existence of the asteroid belt between Mars
and Jupiter.

The talk touches joint projects with the California Institute of
Technology, Princeton University and Harvard University.