82B80 Numerical methods (Monte Carlo, series resummation, etc.) [See also 65-XX, 81T80]
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Year of publication
- 2009 (2)
Language
- English (2)
Keywords
- cluster analysis (2)
- dynamical systems (2)
- metastability (2)
- rare events (2)
- stationary distribution (1)
- transition state theory (1)
Project
- A4 (2)
Application Area
- A (2)
For the treatment of equilibrated molecular systems in a heat bath we
propose a transition state theory that is based on conformation dynamics.
In general, a set-based discretization of a Markov operator P does not
preserve the Markov property. In this article, we propose a discretization
method which is based on a Galerkin approach. This discretization
method preserves the Markov property of the operator and can be interpreted
as a decomposition of the state space into (fuzzy) sets. The
conformation-based transition state theory presented here can be seen as
a first step in conformation dynamics towards the computation of essential
dynamical properties of molecular systems without time-consuming
molecular dynamics simulations.
This article deals with an efficient sampling of the stationary distribution
of dynamical systems in the presence of metastabilities. For such
systems, standard sampling schemes suffer from trapping problems and
critical slowing down. Starting multiple trajectories in different regions of
the sampling space is a promising way out. The different samplings represent
the stationary distribution locally very well, but are still far away
from ergodicity or from the global stationary distribution. We will show
how these samplings can be joined together in order to get one global
sampling of the stationary distribution.