Random deposition with surface relaxation model accompanied by long-range correlated noise

Abstract

The random deposition with surface relaxation model which is accompanied by a long-range power law correlated noise is introduced. The particles are deposited in a selected distance of each other by a power law relation, Δi,j=int[u−12ρ], where u is chosen randomly over the range (0,1) while ρ is called the correlation strength exponent. Each deposited particle diffuses along the surface to find the position with the lowest height. Fractal analysis of the synthetic rough surfaces performed by multifractal detrended fluctuation analysis indicates that the height fluctuations are mono-affine for all values of correlation exponents; while in the random deposition with long-range correlation noise without any short-range correlations, multi-affinity is observed which is due to the diffusion of particles. Furthermore, the growth and roughness exponents increase up to ρc=0.5 which are in agreement with the theoretical relations as β=14+ρ2 and α=2β=12+ρ. For the higher values of correlation exponents (ρ>ρc), the investigated scaling exponents keep a constant value of β=0.5 and α=1 due to the competition of the long-range power law correlation and the short-range correlation raised from the nature of the investigated model.