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

Area of Science:

• Surface science
• Statistical physics
• Materials science

Background:

• The random deposition model is a fundamental concept in surface growth.
• Understanding noise and fluctuation effects is crucial for modeling real-world deposition processes.
• Previous models often assume unit-sized particles, limiting applicability.

Purpose of the Study:

• To investigate the random deposition model with power-law distributed rod lengths.
• To analyze the impact of variable rod lengths on surface roughness and fractal characteristics.
• To characterize rare-event dominated fluctuations in deposition systems.

Main Methods:

• Simulation of a random deposition model with rods of power-law distributed lengths.
• Analysis of surface roughness W(t) as a function of deposition time t.
• Application of multifractal detrended fluctuation analysis (MF-DFA) for height fluctuation analysis.

Main Results:

• Surface roughness increases in a step-wise manner for μ < 3, with local growth exponents βloc dependent on μ.
• The local growth exponent βloc approaches 1/2 (Gaussian noise case) as μ approaches 3.
• Height fluctuations exhibit multiaffinity for μ < 3, with stronger multiaffinity at smaller μ values.

Conclusions:

• The distribution of particle (rod) size significantly influences surface growth dynamics.
• The model captures complex behaviors like multiaffinity, relevant for understanding disordered systems.
• Results provide a more nuanced understanding of surface evolution under non-uniform deposition conditions.