Fluctuations, anisotropy and scaling in growth processes

Abstract

Some recent developments in the physics of two-dimensional growth processes are reviewed. The concept of effective anisotropy is used to explain tip stabilization and the non-trivial role of the driving force in Laplacian growth. Related experiments on viscous fingering are described. In diffusion-limited aggregation on a lattice, the anisotropy is suppressed by noise and very large clusters are needed to see its effect. By introducing the method of noise reduction, the asymptotic region is reached much earlier and a cross-over in the exponent of the radius of gyration takes place. In the case of the Eden model the anisotropy is no more relevant in the above sense but noise reduction is still useful because it improves the scaling behaviour and enables one to separate the contribution of the intrinsic width from the capillary waves.