Measure-preserving and time-reversible integration algorithms for constant temperature molecular dynamics.
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Date
2011
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Abstract
This thesis concerns the formulation of integration algorithms for non-Hamiltonian
molecular dynamics simulation at constant temperature. In particular, the
constant temperature dynamics of the Nosé-Hoover, Nosé-Hoover chain, and
Bulgac-Kusnezov thermostats are studied. In all cases, the equilibrium statistical
mechanics and the integration algorithms have been formulated using
non-Hamiltonian brackets in phase space. A systematic approach has been
followed in deriving numerically stable and efficient algorithms. Starting from
a set of equations of motion, time-reversible algorithms have been formulated
through the time-symmetric Trotter factorization of the Liouville propagator.
Such a time-symmetric factorization can be combined with the underlying non-
Hamiltonian bracket-structure of the Liouville operator, preserving the measure
of phase space. In this latter case, algorithms that are both time-reversible
and measure-preserving can be obtained. Constant temperature simulations of
low-dimensional harmonic systems have been performed in order to illustrate
the accuracy and the efficiency of the algorithms presented in this thesis.
Description
Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2011.
Keywords
Molecular dynamics., Mathematical physics., Physics--Computer simulation., Theses--Physics.