Finding What Happens in a Space of Ever So Many Dimensions

R. Stephen Berry, The University of Chicago

Atomic clusters, nanoscale particles and biomolecules are examples of systems small enough to tempt us to treat them in atomic detail but complex enough to make such an approach look a bit terrifying. This presentation will describe some of the promising ways to extract useful, important information by using microscopic approaches but in variously restricted ways. One is through the use of multiscale simulation, which shows considerable promise especially for biomolecules. Another is through the approach of kinetics, rather than dynamics, specifically by describing the system with a master equation of a particular kind. Instead of constructing and solving a full master equation for the kinetics of motion among all the vast number of minima on a potential surface, one can construct a statistical sample of the information about the topography of the energy landscape and use the corresponding statistical-sample master equation to provide the important rates governing the rearrangements of components of the complex system.