Highly degenerate diffusions for sampling molecular systems
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Date
29/06/2010Author
Noorizadeh, Emad
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Abstract
This work is concerned with sampling and computation of rare events in molecular
systems. In particular, we present new methods for sampling the canonical ensemble
corresponding to the Boltzmann-Gibbs probability measure. We combine an equation
for controlling the kinetic energy of the system with a random noise to derive a highly
degenerate diffusion (i.e. a diffusion equation where diffusion happens only along one
or few degrees of freedom of the system). Next the concept of hypoellipticity is used to
show that the corresponding Fokker-Planck equation of the highly degenerate diffusion
is well-posed, hence we prove that the solution of the highly degenerate diffusion is
ergodic with respect to the Boltzmann-Gibbs measure. We find that the new method is
more efficient for computation of dynamical averages such as autocorrelation functions
than the commonly used Langevin dynamics, especially in systems with many degrees
of freedom. Finally we study the computation of free energy using an adaptive method
which is based on the adaptive biasing force technique.