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.

• Control of a Model of DNA Division via Parametric Resonance, Chaos, 23, 013117 (2013).(Koon, W.S., H. Owhadi, M. Tao, and T. Yanao,[2013].pdf)
  
  
• A Nonequilibrium Rate Formula for Collective Motions of Complex Molecular Systems, Proceedings of ICNAAM, Numerical Analysis and Applied Mathematics, International Conference 2010.(Yanao, T., W.S. Koon, and J.E. Marsden,[2010].pdf)
  
  
• Intramolecular energy transfer and the driving mechanisms for large-amplitude collective motions of clusters, Journal of Chemical Physics, 130, 144111.(Yanao, T., W.S. Koon, and J.E. Marsden, [2009].pdf)
  
  
• Gyration-Radius Dynamics in Structural Transitions of Atomic Clusters, Journal of Chemical Physics, 126, 124102. (Yanao, T., W.S. Koon, J.E. Marsden, and I.G. Kevrekidis [2007].pdf)
  
  
• Mass Effects and Internal Space Geometry in Triatomic Reaction Dynamics, Physical Review A, 73, 052704. (Yanao, T., W.S. Koon, and J.E. Marsden [2006]. pdf)
  
  
• Application of Tube Dynamics to Non-statistical Reaction Processes, Few-Body Systems, Volume 38, Numbers 2-4, pages 167 - 172. (Gabern F., W. S. Koon, J. E. Marsden, S. D. Ross, and T. Yanao, [2006]. pdf)
  
  
• Mass-Related Dynamical Barriers in Triatomic Reactions, Few-Body Systems, Volume 38, Numbers 2-4, pages 161 - 166. (Yanao, T., W.S. Koon, and J.E. Marsden [2006], pdf)
  
  
• Theory and Computation of Non-RRKM Lifetime Distributions and Rates of Chemical Systems with Three and More Degrees of Freedom, Physica D, volume 211, issue 3-4, pages 391-406. (Gabern, F., W.S. Koon, J.E. Marsden, and S.D. Ross [2005], pdf)
  
  

• Effects of an intrinsic metric of molecular internal space on chemical reaction dynamics, Advances in Chemical Physics 130 B, 87-128. (T. Yanao and K. Takatsuka [2005])
  
  
• Set-oriented computation of transport rates in 3-degree of freedom systems: the Rydberg atom in crossed fields, Regular and Chaotic Dynamics, 10, 173-192. (Dellnitz, M., K. Grubits, J. E. Marsden, K. Padberg, and B. Thiere [2005], pdf)
  
  
• Kinematic effects associated with molecular frames in structural isomerization dynamics of clusters, Journal of Chemical Physics 120, 8924-8936. (T. Yanao and K. Takatsuka [2004], pdf)
  
  
• Collective coordinates and an accompanying metric force in structural isomerization dynamics of molecules, Physical Review A 68, 032714 (1-16). (T. Yanao and K. Takatsuka [2003], pdf)