Geometric Model Reduction and Structure-Preserving Integrators
for Stochastic Multi-scale Hamiltonian Systems

The objective of this NSF project is to develop novel geometric model reduction methods along with computational methods for the dynamical simulation and eventual control of stochastic mechanical systems involving multiple-scales. These new dynamical and simulation tools will be applied to specific molecular and biomolecular systems, such as atomic clusters and DNAs.

An exciting development in geometric model reduction has been the development of the radii of gyration as coarse variables along with the discovery of specic fine variables that act as triggers that induce conformation changes. A further development of and deeper understanding of such triggers will be important in the eventual control of biomolecular conformation changes and reactions. Going along with these geometric model reduction techniques is the theoretical and computational development of stochastic asynchronous variational integration (SAVI) methods and their applications to the simulation and control of stochastic mechanical systems spanning many temporal-scales.

The project is funded by the National Science Foundation (NSF-CMMI-092600), starting in fall,2009. It involves Hourman Owahdi (PI), Jerrold E. Marsden (Co-PI), Wang Sang Koon , Tomohiro Yanao, and Molei Tao.