ISSN:
1572-9613
Keywords:
Fractals
;
aggregation
;
dendritic growth
;
critical phenomena
;
upper critical dimension
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01012946
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