| The classical method for simulating chemical reaction networks is to assume that the chemical species concentrations are continuous variables and to track their evolution in time with ordinary differential equations (ODEs). Multiple time scales are ubiquitous in practical chemical reaction networks. Methods such as singular perturbation analysis (SPA) and the quasi-steady state approximation (QSSA) are used to simplify these ODE models when multiple time scales are present. When the populations of key species in the reaction network are small (e.g. proteins in cells, or adsorbed gases on a catalyst particle), the fluctuations induced by small numbers of molecules can significantly change the dynamic behavior of the species concentrations. The chemical master equation, which describes the probability of species visiting discrete states in time, can correctly account for the fluctuations induced by small numbers of molecules.; In this dissertation, singular perturbation analysis is used to develop reduced chemical master equations when multiple time scales are present. First, SPA is used to remove the highly-reactive intermediates from the master equation. This simplification generates new stoichiometry and reaction rates that are often different from those derived by simplifications of ODE models. SPA is also used to develop simplified master equations for reaction networks that have rapidly equilibrating reactions. We show how the reaction-equilibrium master equation can be used to simulate catalytic surface reactions in the fast diffusion limit.; Prediction of the thermodynamics and kinetics of crystallization are of fundamental importance to a variety of industries. Theoretical methods for quantitative prediction of crystallization properties are still in their infancy. In this dissertation, a novel molecular simulation method is demonstrated for the prediction of melting temperatures. Additionally the sensitivity of melting temperature predictions to finite-size effects and cutoff-radius are presented. Also, a full description of the melting line for the Lennard-Jones system is given. We also give quantitative data about the effect of the gas-water interface on the lifetime of gas hydrate cage structures. |
