Computer simulation of fractal growth via a 2D-MECA percolative system representing an extended nutrient releasing source (NRS)

Monte Carlo simulations are investigated to study the effects of the nutrient releasing source (NRS) on fractal patterns developed by a generalized dynamic fractal growth model (GDFGM). The morphology of the simulated structures reveals, in cylinder geometry, a strong correlation with the source parameters, especially its extent, its relative position to the principal growing interface (PGI), its effective concentration, and its releasing flow. Particularly, a randomly dispersed source (“particles” sea) is relevant to better understand the development of many dispersed fractal patterns in degraded thin-film materials (Gy. Radnoczi et al., Phys. Rev. A 35 (9) (1987) 4012). In such growth process, the source should be identified with the crystal lattice itself, and may be of finite concentration. Thus, it can be represented by 2D-percolative systems that capture the salient fractal features observed in real morphologies, especially the self-organized criticality (SOC), the universal columnar multiclustering, and the surface roughness. Such systems are simulated by the many eden cluster aggregation model (MECA), which allows a perfect control of their morphological characteristics. These systems affect to a large extent both static and dynamic characteristics of the grown structures, and introduce a yet non-trivial aggregation process presenting a richness in the dynamical behaviour. In fact, they represent: (i) a mechanical barrier network, which partially screens the principal growing interface (PGI); (ii) an invading medium confining the arborescence propagation via some active grain boundaries representing short paths for diffusion; (iii) an aggregation system on some dispersed grain cavities; and (iv) an extended source of finite concentration, which releases from its external surface a certain concentration of nutrients according to the Dilution (or Disintegration) rate (DR). On the other hand, they undergo many alterations marked by: (i) the widening of their grain boundaries; (ii) a bootstrap relaxation (F. Babalievski, Physica A 221 (1994) 1) that rounds the grain surface for low DRs; and (iii) the development of some fractal fractures initiated by the infiltration of some trees inside the grains, especially for high DRs. All these effects are coupled, and embody this interplay between the percolative system and the fractal growth kinetics.