Crossover effects and dynamic scaling properties from Eden growth to diffusion-limited aggregation

Abstract

The diffusion-limited aggregation (DLA) model is a classical fractal aggregation model that describes numerous fractal phenomena, and the Eden model is a typical discrete growth model for investigating cell clusters, such as bacteria or tissue cultures. There is a significant difference between these two discrete models in their growth rules and dynamic scaling properties. In this paper, we introduce a generalized growth theory to describe effectively these two distinct growth classes based on the competitive growth rules. By controlling the adhesion coefficient, a continuous transition exists from dense polymerization to finger growth, i.e., the evolution from Eden growth to DLA in both two-dimensional and three-dimensional cases. To simulate effectively the generalized growth system in the most physically relevant case of three-dimensions, we employ a proper technique named the Marsaglia method for correctly obtaining distributed points to avoid the inappropriate simulation schemes commonly used. Furthermore, the crossover of these competitive growth exhibits non-trivial scaling behavior, and the quantitative relation between the corresponding critical exponents and the adhesion parameter is also investigated. Concurrently, the porosities of the generalized growth system are calculated, which exhibit obviously nontrivial dynamic properties depending on the growth dimensions.