ARRHENIUS SYSTEMS - DYNAMICS OF JUMP DUE TO SLOW PASSAGE THROUGH CRITICALITY

Reactive systems involving Arrhenius kinetics often exhibit multiple steady states. A typical response is an S-curve, whose turnaround points correspond to ignition or extinction. This paper describes the dynamics of transition from the extinguished to the ignited state as the reaction-rate parameter is slowly varied through the critical value. Both lumped and spatially distributed models are studied. The asymptotic analysis is based on the largeness of two parameters, one characterizing the activation energy and the other the slow passage.