# 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*