Diffusion-limited gelation

Abstract

Diffusion-limited aggregation is a means of forming continuous random networks of low density. Recent work on diffusion-limited aggregation is reviewed. These aggregates have universal power-law density correlations. This implies scaling laws relating an aggregate's size to its mass when it is grown from a point, line, or surface. The mass of the growing interface scales as a power of the total mass, but not in the way suggested by simple estimates. A mean field model of the process yields a density that falls inversely as the distance from the origin. It is speculated that the mean field solution may be stable above some spatial dimension dc.