2002 DiPerna Lectures
The 2002 DiPerna Memorial Lecture will be delivered by Andrew Stuart on February 7.
Department of Mathematics, University of California, Berkeley, presents
The DiPerna Memorial Lecture 2002
Andrew Stuart
Mathematics Institute, Warwick University
Thursday, February 7, 4 p.m.
60 EVANS
Extracting Macroscopic Dynamics
In many applications, the primary objective of numerical simulation of
time-evolving systems is the prediction of macroscopic, or
coarse-grained, quantities. Examples of such applications include
molecular dynamics and ocean-atmosphere modelling. In recent years a
number of new algorithmic approaches have been introduced to extract
effective, lower-dimensional, models for the macroscopic dynamics; the
starting point is the full, detailed, evolution equations. In many
cases the effective low-dimensional dynamics may be stochastic, even
when the original starting point is deterministic.
I will survey a number of new approaches to the problem of extracting
effective dynamics, highlighting similarities and differences between
them. I will stress the importance of model problems for the evaluation
of these new approaches, and introduce a class of model problems which I
have found useful in this regard. These model problems are high
dimensional ordinary differential equations which, when projected onto a
low dimensional subspace, exhibit stochastic behaviour, provably close
to that of a stochastic differential equation. I will conclude by
describing recent work (with Ch. Schuette and W. Huisinga, FU Berlin)
where we have used these model problems to evaluate a new algorithmic
approach for the extraction of large-scale biomolecular conformational
dynamics.
Refreshments will be served in 1015 Evans, 3:00-4:00 pm
