Generalized
Langevin Equations and non-Markovian Fokker-Planck Equations for Molecular Systems
Eric Darve
(Stanford)
Abstract:
Modeling molecular systems is often very expensive because of the large
number of degrees of freedom, such as all the coordinates of the atoms,
which are required to describe the system and because of the presence
of multiple time scales (femtosecond to millisecond). This often
results in significant computational costs. One approach to address
this issue is to formulate stochastic differential equations or Fokker-Planck equations in terms of a small number
of resolved variables, which can be order parameters or reaction
coordinates. In particular, such methods can predict slow reaction
rates which are beyond the time scales which can be resolved using
direct molecular dynamics. We will present new techniques to calculate
such equations based on the Mori-Zwanzig projection formalism.
Numerical examples from benchmark problems to solvated proteins will be
presented.