I. Numerical nonlinear analysis: differential methods and optimization applied to chemical reaction rate determination

The primary emphasis of this work on kinetics is to illustrate the a posteriori approach to applied nonlinear analysis, where focus on data may also lead to novel outcomes, as may also be the case with the current a priori tendencies of applied analysis, which relies on axioms or constructs concerning the nature of the observable. Here, methods for the determination of chemical rate constants are developed and discussed utilizing nonlinear analysis which does not require exact knowledge of initial reactant concentrations. These methods are compared with those derived from standard methodology for known chemical reactions studied by eminent kineticists and in one case with a reaction whose initial reactant concentration was in doubt. These gradient methods are shown to be consistent with the standard methods on average, and could readily serve as alternatives for standard conditions and can be used for studies where there are limits or unknowns in the initial conditions, such as in the burgeoning fields of astrophysics and astrochemistry, forensics, archeology and biology where the standard methods are not applicable. All four reactions studied exhibited semi-sinusoidal-like change with reactant concentration change which standard integral methods have not highlighted, and which seems to constitute the observation of a new effect. Reasons based on two mechanisms are given for this observation, and experiments are suggested that can discriminate between these two factors. Although first and second order reactions were investigated here, the method applies to arbitrary fractional orders by polynomial expansion of the rate decay curves where closed form integrated expressions do not exist at present. Integral methods for the above will be investigated next.