Fractal and Multifractal Approaches to Clustering Phenomena

摘要

Recently considerable efforts have been made in understanding the dynamics of non-equilibrium interface growth in the context of a variety of fractal clustering models. Many recent investigations have concentrated on the dynamic scaling properties of interfaces obtained in experiments and in various cluster growth models. Particular attention has been devoted to the scaling properties of the rms interface width. It has been widely believed that many such problems belong to the same universality class as the Kardar-Parisi-Zhang (KPZ) equation. There have recently appeared several experiments on surface growth. Roughening with Power Law Distributed Noise: Recently Zhang suggested that the anomalous roughening found in experiments can be explained by an uncorrelated 'noise' obeying a power-law distribution.