Browsing by Author "Obaga, Emmanuel Omboga."
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Item Measure-preserving and time-reversible integration algorithms for constant temperature molecular dynamics.(2011) Obaga, Emmanuel Omboga.; Sergi, Alessandro.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.Item Simulating thermal fluctuations in soft matter models.(2015) Obaga, Emmanuel Omboga.; Sergi, Alessandro.; Petruccione, Francesco.The research carried out in this work is in two parts: In the first part, we derive a configurational temperature Nosé-Hoover thermostat by reformulating the original Braga and Travis thermostat [J. Chem. Phys. 123 (134101), 2005] in phase space using a quasi- Hamiltonian approach introduced by Sergi and Ferrario [Phys. Rev. E 64 (056125), 2001]. We also present a reversible integrator based on the symmetric Trotter decomposition of propagator for harmonic potentials and for more complicated potentials, a harmonic approximation of the potential is performed locally resulting in a positiondependent harmonically approximated propagator for a general system. In the second part of our work, we present a phonostat methodology based on classical molecular dynamics and Wigner approach to quantum mechanics. We introduce quantum effects into our system by generating a thermal profile using different ’effective’ temperature for the modes and coupling each one of the modes to a thermal bath. We test our phonostat algorithm against the range of temperatures and densities explored by Mausbach and May [Fluid Phase Equil. 249 (17), 2006].