An informal Discussion on Invariant Manifold Methods

Dept. of Chemistry and Biochemistry, CU Boulder

Low-dimensional manifold can simplify the description of complicated systems of kinetics equations. 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 new technique, the global eigenvalue method, is derived. This method combines the conceptual advantages of some earlier methods 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.

See R.Skodje and M. Davis, J. Phys. Chem. 105, 10356 (2001).