Random deposition with spatially correlated noise (RD-SCN) model: Multi-affine analysis. (February 2021)

• Record Type: Journal Article
• Authors: Hosseinabadi, S.; Masoudi, A.A.
• Is Part Of: Chaos, solitons and fractals. Volume 143(2021)
• Publication Date: 2021-02
• Subjects: Random deposition model -- Spatially correlated noise -- Multi-affine analysis; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2020.110596
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: Random deposition model with long-range spatially correlated noise is investigated. In spite of other correlated growth equations, beta is an unchangeable value. In a critical correlation exponent, multi-affinity is occurred. Enhancement of correlation exponent increases the strength of multi-affinity. Abstract: We study the random deposition model with long-range spatially correlated noise. In this model the particles deposit in a power-law distance of each other as Δ i, j = i n t [ u − 1 2 ρ ], where u is chosen randomly over the range (0, 1) and ρ is the correlation strength. The results show that the enhancement of ρ exponent is accompanied by the appearance of irregularities and jumps in the height fluctuations. In spite of scaling exponents dependent to correlation strength in other linear and non-linear growth equations, enhancement of the correlation strength, does not change the growth exponent β = 1 / 2 . As the short-range correlations in growth equations result in roughness saturation, the results show that the long-range correlations in this growth model does not saturate the interface width for any system size. The fractal analysis of the height fluctuations performed via the multi-fractal detrended fluctuation analysis (MF-DFA) revealed that the synthetic rough surfaces with ρ = 0 are mono-fractal with the Hurst exponent H = 0.5 . It verifies the un-correlated fluctuations in the simple random deposition model. For the correlation strengths in the range [0, 1], the Hurst exponent increases in the range [ 1 2, 1 ) with a mono-fractal behavior. In the critical exponent of ρ c, multi-affinity is occurred. For ρ > ρ c = 1 the mono-fractal feature of the height fluctuations tends to the multi-affine one and the strength of multi-affinity increases by enhancement of ρ exponent. The results show that the observed multi-affinity is because of deviation from the normal distribution and appearance of correlations among small and large fluctuations.