Fractal analysis of ballistic deposition model with power-law distributed noise

The ballistic deposition model with power-law distributed noise (BD-PLN) has been simulated and investigated. Analysis of scaling exponents and statistical features seems essential in understanding the mechanism of noise in the phenomena. In the BD-PLN model, heterogeneous particles with rod-like shapes are deposited during growth time and lead to the forming of porous structures. By using the Hoshen-Kopelman algorithm, porous structures are converted to contour loops, and the fractal properties of the loops are considered. The fractal dimension of each loop, D_f, the fractal dimension of the contour set, d, the generalized dimensions, D_q, and the mass function, τ_q are calculated. The fractal dimension, d, increases as d = a + bμ^c versus μ exponent, and remains constant for μ >"μ" _c=۳, where μ is the decay of the noise amplitude. The results indicate that augmentation of μ exponent and conspicuity of the Gaussian ballistic deposition model prepare to decrease in structure porosity and multi-affinity, and also increase in contour loops area and perimeter.

Keywords:

Ballistic deposition model , Power-law noise , Contour loops , Frac- tal dimension