Strategies for Optimize Off-Lattice Aggregate Simulations

Growth processes occurring far from equilibrium are widespread in nature and technology. Examples include electrodeposition [1], viscous fingering [2], bacterial colonies [3], and neurite formation [4]. Computer models for the growth of clusters, generally constituted of identical particles, are useful tools for the understanding of aggregation phenomena. The main contribution of such models is to provide pathways to investigate the underlying physical ingredients ruling the properties observed in growth phenomena. One of the most intriguing features of the fractal structures found in nature and computer models is the scale invariance emerging without fine-tuning of any parameter, in contrast with usual critical phenomena in which scale invariance only emerges at a critical point [5]. The foremost example of nonequilibrim growth model is the diffusion-limited aggregation (DLA) model introduced by Witten and Sander [6] in 1981. The rules of the DLA model are based on an iterative stochastic process in which the particles, one at a time, follow Brownian trajectories until they touch and stick in an aggregate. Despite its simple rules, the DLA model leads to very complex aggregates with multiscale properties [7, 8] and multifractality in the growth-site probability distribution [9, 10]. If the random walks in the DLA model are replaced by ballistic trajectories at random directions, we have the ballistic aggregation (BA) model [11, 12] proposed by Vold to describe colloid aggregation. Differently from DLA, the BA model generates asymptotically non-fractal clusters (fractal dimension equal to the space dimension) characterized by a power law approach to the asymptotic regime [13, 14]. Finally, a third standard aggregation process was proposed by Eden [15] as a basic model for the biological pattern formation as, for instance, tumor growth and bacterial colonies. In this model, new particles are sequentially added to the empty neighborhood of the cluster without overlap with previously aggregated particles [16, 17]. Although the Eden model is unrealistic from the biological point of view, it produces com-