Several problems in the titled areas are discussed in terms of their multiple-time-scale properties. In particular, theories of unimolecular reactions and the description of vibrational spectra and eigenstates are mentioned. The main focus of the talk will be low-dimensional manifolds in problems involving kinetic modeling. The manifolds are generated numerically using two methods. One is the approximate method of Maas and Pope and the other is our modification of Fraser's relaxation algorithm which is able to generate exact low-dimensional manifolds under some conditions. Some simple model problems are discussed as well as applications to gas phase chemical kinetics, vibrational relaxation, and the coarsening of solid surfaces.
This is joint work with Rex T. Skodje.