05w5052 Mathematical Issues in Molecular Dynamics

Arriving Saturday, June 4 and departing Thursday, June 9, 2005

Organizers: Robert Skeel (Purdue University), Paul Tupper (McGill University).

Confirmed Participants

Information for Participants

Schedule and Abstracts (PDF file)

Final Report (PDF file)

Workshop Videos

Objectives

This workshop will bring together molecular dynamics (MD) specialists, numerical analysts and other applied mathematicians to study the mathematical problems in molecular dynamics. We hope that with this interaction progress will be made on outstanding theoretical problems, new problems in MD will be brought the attention of mathematicians and insight will be gained into how to better design algorithms for MD. The workshop will focus on several topics.



Why Does MD work?



Molecular Dynamics is an extremely important area in Physics, Chemistry, and Biochemistry, as a glance recent publications in these fields will show. Despite MD being around for a few decades, there is almost no mathematically rigorous justification of the practice. However, we believe that many of the pieces are ready to be put into place.



Computational Artifacts



Very few researchers are considering these effects. Their investigation is long overdue. The time now is particularly ripe for an assessment of the relative merits of Langevin and Nose thermostats. These two techniques for constant temperature simulation are used by two separate groups, often to accomplish the same things.



Convergence of MD/MC



In Summer of 2003, a highly successful workshop on Markov Chains was held in Durham, England. One particular focus of the workshop was on understanding Monte Carlo simulation. Our workshop will continue with the momentum generated in Durham and focus more directly on the problem of Monte Carlo methods for molecular simulation. Furthermore, we will extend the scope by considering the analogous issues for MD, as well as considering Hybrid Monte Carlo, which is an especially hot topic at present.



Multiscale Simulation



Multiscale simulation is widely agreed to be the future of material simulation. (SIAM has recently launched a new journal devoted to it.) There is an urgent need for a clear statement of the problems in this area, so that the many new techniques for multiscale simulation can be understood and assessed.