Kinetic theory of non-equilibrium growth processes

Professor Colm Connaughton, University of Warwick. Part of the Leeds Applied Nonlinear Dynamics seminar.

Professor Colm Connaughton, University of Warwick.

The kinetic theory of far from equilibrium growth-fragmentation processes provides natural mathematical models for many types of complex systems. The phenomenology of such models is very rich. They sometimes reach steady states that exhibit power law scaling of the cluster size distribution over some range of scales. However, depending on the details and the relative strength of the growth and fragmentation mechanisms, we may find a transition between a stationary stable phase in which the characteristic size is bounded and a non-stationary growing phase in which the characteristic cluster size grows indefinitely. In the growing phase, it is possible for the characteristic cluster size to diverge in a finite time - a mechanism for very rapid formation of very large clusters. Even when the characteristic cluster size is bounded, the stationary cluster size distribution is sometimes unstable. This instability produces a transition to a regime in which the kinetics become oscillatory with the largest clusters appearing and disappearing in a periodic fashion. In this talk, I will discuss recent developments in this area and try to relate them to some of the commonly discussed phenomenology of complex systems.