Structure and Dynamics of Correlated Cluster Growth Processes

摘要

The main thrust of our research has been the investigation of various aspects ofthe structure and dynamics of cluster growth processes. We have also used the concepts of cluster growth to investigate a number of other phenomena, including studies of the morphology of rough surfaces and the phenomenon of pattern formation. Self affine fractal interfaces are generated in a variety of far-from-equilibrium processes, including fluid flow in porous media, vapor deposition, and corrosion, as well as in biological systems. Recently, there has been considerable interest in the study of stochastically growing interfaces, in the context of ballistic deposition, the Eden model, and Burger's equation. Much of this interest stems from the fact that in addition to their connection to processes of fundamental practical importance, such as thin film growth and interface dynamics in random media, these models exhibit non-trivial scaling behavior. The dynamics of the interface in these models has also been shown to be intimately related to a variety of other problems, including directed polymers in random media, the large-time behavior of randomly stirred fluids, and the evolution of Sivashinski flame fronts.