Geometrical simplification of complex kinetic systems

The use of low-dimensional manifolds to simplify the description of complicated systems of kinetics equations is investigated. Many models exhibit a generic behavior, whereby kinetic trajectories rapidly approach a surface of much lower dimension than that of the full phase space of concentrations, and subsequently show slow relaxation to equilibrium restricted to the surface. Traditional methods, such as the quasi-steady-state approximation, can be viewed as approximate schemes to construct the low dimensional manifolds., A number of techniques for the construction of low-dimensional manifolds are discussed and compared. A more general formulation of several previous methods is provided. A new technique, the global eigenvalue method, is derived. This method combines the conceptual advantages of the Maas-Pope algorithm with the accuracy of global trajectory propagation. One- and two-dimensional manifolds are constructed using the global eigenvalue method for a 38-reaction mechanism for hydrogen combustion. A new formulation of sensitivity analysis is provided which allows testing a reduced mechanism to changes in the rate constants.