Thesis (Ph. D.)--Hong Kong University of Science and Technology, 2004. / Includes bibliographical references (leaves 80-82). Also available in electronic version. Access restricted to campus users.

published_or_final_version / abstract / Mathematics / Master / Master of Philosophy

Thesis (M. Phil.)--University of Hong Kong, 2006. / Title proper from title frame. Also available in printed format.

Thesis (M. Phil.)--University of Hong Kong, 2006. / Also available online.

Predicting the kinetics of a chemical reaction is a challenging task, particularly for systems in states far from equilibrium. This work discusses the use of a relatively new theory known as intrinsic quantum thermodynamics (IQT) and its mathematical framework steepest-entropy-ascent quantum thermodynamics (SEA-QT) to predict the reaction kinetics at atomistic levels of chemically reactive systems in the non-equilibrium realm. IQT has emerged over the last three decades as the theory that not only unifies two of the three theories of physical reality, namely, quantum mechanics (QM), and thermodynamics but as well provides a physical basis for both the entropy and entropy production. The SEA-QT framework is able to describe the evolution in state of a system undergoing a dissipative process based on the principle of steepest-entropy ascent or locally-maximal-entropy generation. The work presented in this dissertation demonstrates for the first time the use of the SEA-QT framework to model the evolution in state of a chemically reactive system as its state relaxes to stable equilibrium. This framework brings a number of benefits to the field of reaction kinetics. Among these is the ability to predict the unique non-equilibrium (kinetic) thermodynamic path which the state of the system follows in relaxing to stable equilibrium. As a consequence, the reaction rate kinetics at every instant of time is known as are the chemical affinities, the reaction coordinates, the direction of reaction, the activation energies, the entropy, the entropy production, etc. All is accomplished without any limiting assumption of stable or pseudo-stable equilibrium. The objective of this work is to implement the SEA-QT framework to describe the chemical reaction process as a dissipative one governed by the laws of quantum mechanics and thermodynamics and to extract thermodynamic properties for states that are far from equilibrium. The F+H2-->HF+H and H+F2-->HF+F reaction mechanisms are used as model problems to implement this framework. / Ph. D.

The path of steepest ascent can used to optimize a response in an experiment, but problems can occur with multiple responses. Past approaches to this issue such as Del Castillo’s overlap of confidence cones and Mee and Xiao’s Pareto Optimality, have not considered the correlations of the responses or parameter uncertainty. We propose a new method using the Bayesian reliability to calculate this direction. We utilize this method with four examples: a 2 factor, 2-response experiment where the paths of steepest ascent are similar, ensuring our results match Del Castillo’s and Mee and Xiao’s; a 2 factor, 2-response experiment with disparate paths of steepest ascent illustrating the importance of the Bayesian reliability; two simulation examples, showing parameter uncertainty is considered; and a 5 factor, 2-response experiment proving this method is not dimensional limited. With a Bayesian reliable point, a direction in multivariate steepest ascent can be found.

Thesis (Ph. D.)--University of Washington, 2002. / Vita. Includes bibliographical references (p. 119-123).

Thesis (Ph. D.)--Duke University, 2007.

The method of steepest descent is used to solve partial differential equations of mixed type. In the main hypothesis for this paper, H, L, and S are Hilbert spaces, T: H -> L and B: H -> S are functions with locally Lipshitz Fréchet derivatives where T represents a differential equation and B represents a boundary condition. Define ∅(u) = 1/2 II T(u) II^2. Steepest descent is applied to the functional ∅. A new smoothing technique is developed and applied to Tricomi type equations (which are of mixed type). Finally, the graphical outputs on some test boundary conditions are presented in the table of illustrations.

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