Cluster-particle aggregation with fractal (Levy flight) particle trajectories

The effects of particle trajectories on the structure of aggregates formed by cluster-particle aggregation have been explored by computer simulation. With the use of Levy-flight particle trajectories, clusters with a continuous range of effective dimensionalities between the limits of the Witten-Sander (D5/3 for $d=2$) and Vold-Sutherland models (D2.0 for $d=2$) can be generated. The effective dimensionality varies continuously with the exponent which describes the distribution of step lengths in the Levy-flight trajectory, but there does not seen to be a unique (1:1) relationship between the dimensionality of the trajectory and the dimensionality of the cluster.