Generalisation of theory and algorithms for the configurational temperature Nosé–Hoover thermostat.
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Date
2015
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Abstract
In this dissertation we reformulate the configurational temperature Nos`e-Hoover thermostat
proposed by Braga and Travis (C. Braga and K.P. Travis, 2005), using the
antisymmetric matrix formalism found in (A. Sergi, 2003). By exploiting the properties
of this formalism, and utilising the concept behind the Nos`e-Hoover chain thermostat,
we extend our reformulated thermostat to obtain a hybrid configurational-kinetic
chain thermostat. This is done with a view to achieving an ergodic sampling of phase
space. We derive an integration algorithm, based upon the symmetric Trotter factorisation
of the Liouville operator, as well as symplectic position and velocity Verlet
integrations schemes, for purposes of comparison. In the case of systems possessing
non-harmonic and non-linear interaction potentials, a position-dependent harmonic approximation
scheme is presented. The thermostats and integration schemes were tested
on one-dimensional harmonic and quartic oscillators, where it was found that the hybrid
configurational-kinetic temperature Nos`e-Hoover chain thermostat overcame the
ergodicity problem, and the integration scheme based on the Trotter factorisation was
the best performing.
Description
Master of Science in Physics.
Keywords
Algorithms., Configurations., Thermostat., Theses -- Physics., Nosé–Hoover thermostat.