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.


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