Computing transition paths for rare events

Applied and Computational Mathematics Seminar
Monday, August 23, 2010 - 13:00
1 hour (actually 50 minutes)
Skiles 002
U Maryland

I will propose two numerical approaches for minimizing the MFF. Approach
I is good for high-dimensional systems and fixed endpoints. It is
based on temperature relaxation strategy and Broyden's method. Approach
II is good for low-dimensional systems and only one fixed endpoint. It
is based on Sethian's Fast Marching Method.I will show the
application of Approaches I and II to the problems of rearrangement of
Lennard-Jones cluster of 38 atoms and of CO escape from the Myoglobin protein

At low temperatures, a system evolving according to the overdamped Langevin equation spends most of the time near the potential minima and performs rare transitions between them. A number of methods have been developed to study the most likely transition paths.  I will focus on one of them: the MaxFlux Functional (MFF), introduced by Berkowitz in 1983.I will reintepret the MFF  from the point of view of the Transition Path Theory (W. E & E. V.-E.) and show that the  MaxFlux approximation is equivalent to the Eikonal Approximation of the Backward Kolmogorov Equation for the committor function.