The Vold-Sutherland and Eden models of cluster formation

Abstract

Large clusters or flocs have been grown on the computer using the models introduced by Vold and Sutherland and by Eden. Some of the properties of these clusters have been analyzed and compared with the same properties of clusters grown using the diffusion limited growth process of Witten and Sander. For all three models the radius of gyration ( R g) is related to the number of particles in the cluster ( N) by an expression of the form R g N β (in the limit of large cluster sizes). In two-dimensional simulations the Eden (surface growth) model gives compact clusters with a radius of gyration exponent (β) very close to 1 2 . For the Vold-Sutherland (linear particle trajectory) model the exponent β has a value close to 1 2 for two-dimensional clusters and close to 1 3 for three-dimensional clusters, if they are sufficiently large. For the Witten-Sander model β is definitely larger than 1 2 in two dimensions ( ∼3 5 ) and larger than 1 3 in three dimensions ( ∼2 5 ). Other geometric properties of the clusters have been determined such as the density-density correlation function and the number of particles N( l) within a distance ( l) of the center of mass. For the two dimensional Witten-Sander model the dependence of R g on N 1 the dependence of N( l) on l, and the density-density correlation function can be described in terms of a single parameter (the Hausdorff dimensionality— D). The significance of the Hausdorff dimensionality is outlined and the concept of Hausdorff dimensionality is used in the discussion of the structures generated using all three models.