Particle aggregation versus cluster aggregation in high dimensions

This work shows that physical limits on the aggregation rate impose a lower bound on the fractal dimensionD0 of the aggregate, and presents a soluble model that should agree with Sutherland's binary aggregation model in high dimensions.

Abstract

We distinguish two different types of irreversible aggregation-accretion of individual particles and successive aggregation of clusters of comparable size. In aggregation of particles which follow trajectories of fractal dimensionD 1, we show that physical limits on the aggregation rate impose a lower bound on the fractal dimensionD 0 of the aggregate. Ind-dimensional space,D 0{⩾d−D}1 + 1. Thus aggregation of ballistic particles, withD 1 = 1, is not fractal. By contrast, cluster aggregates appear to attain a finite, limitingD 0 in high dimensions. We present a soluble model with this property, and argue that it should agree with Sutherland's binary aggregation model in high dimensions. For this model,D 0 depends continuously on a parameter; the exponent is not universal.