Random deposition with a power-law noise model: Multiaffine analysis.

ABSTRACT

We study the random deposition model with power-law distributed noise and rare-event dominated fluctuation. In this model instead of particles with unit sizes, rods with variable lengths are deposited onto the substrate. The length of each rod is chosen from a power-law distribution P(l)∼l^{-(µ+1)}, and the site at which each rod is deposited is chosen randomly. The results show that for µ<µ_{c}=3 the log-log diagram of roughness, W(t), versus deposition time, t, increases as a step function, where the roughness in each interval acts as W_{loc}(t)≈t^{ß_{loc}}. The local growth exponent, ß_{loc}, is zero for µ=1. By increasing the µ exponent, the value of ß_{loc} is increased. It tends to the growth exponent of the random distribution model with Gaussian noise, ß=1/2, at µ_{c}=3. The fractal analysis of the height fluctuations for this model was performed by multifractal detrended fluctuation analysis algorithm. The results show multiaffinity behavior for the height fluctuations at µ<µ_{c} and the multiaffinity strength is greater for smaller values of the µ exponent.