Dynamics of a nonlinear master equation: Low-dimensional manifolds and the nature of vibrational relaxation

Abstract

The dynamics of nonlinear master equations describing vibrational relaxation in shock-heated molecules are studied. The nonlinearity results principally from inclusion of self-collisions. The master equations were derived in a previous paper by fitting experimental data and besides being nonlinear they vary according to changes in the bath temperature. It is demonstrated that, except for brief transients, the dynamics lie on one-dimensional, nonlinear manifolds, including the full time of experimental observation. The one-dimensional nature of the dynamics allows for an in depth study of vibrational relaxation. It is shown that vibrational distributions cannot be characterized accurately by a vibrational temperature until they are close to equilibrium and that one-dimensional rate laws accurately describe the dynamics on the one-dimensional manifold. The latter characteristic is important, because it allows results generated from master equations which include self-collisions to be easily incorporated into kinetic modeling.