Multiscaling in Random Cluster-cluster Aggregates


Two-point density correlation functions are studied numerically in computergenerated three-dimensional lattice cluster-cluster aggregates with the number of particles up to 20,000. The “pure” aggregation algorithm is used, where subclusters of all possible sizes are allowed to collide. We find that large cluster-cluster aggregates demonstrate pronounced multiscaling, i.e., the power-law exponents in the pair-correlation function p(r) are not constants, but depend on r and the number of particles in a cluster. In particular, the fractal dimension determined from the slope of the two-point correlation function at small distances differs from that found from the dependence of the radius of gyration on the number of monomers (1.8 and 2.0, respectively, according to our data). We also consider different functional forms of p(r) and their general properties. We find that if the fractal dimension for the cluster-cluster aggregates can be defined as a continuous function D = D(r/Rg), where Rg is the radius of gyration, it must have a maximum at some value of r/Rg = xm, where D(xm) > 2.

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@inproceedings{MarkelMultiscalingIR, title={Multiscaling in Random Cluster-cluster Aggregates}, author={Vadim A. Markel} }