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Asymptotic function for multigrowth surfaces using power-law noise.

Hiroaki Katsuragi1, Haruo Honjo

  • 1Department of Applied Science for Electronics and Materials, Interdisciplinary Graduate School of Engineering Science, Kyushu University, 6-1 Kasugakoen, Kasuga, Fukuoka 816-8580, Japan. katsurag@asem.kyushu-u.ac.jp

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 15, 2003
PubMed
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This study explores ballistic deposition growth with power-law noise, finding its multigrowth exponent aligns with theory. Large rare events may disrupt Kardar-Parisi-Zhang scaling at higher orders.

Area of Science:

  • Physics
  • Statistical Mechanics
  • Complex Systems

Background:

  • Ballistic deposition is a fundamental model for surface growth.
  • Understanding noise effects is crucial for predicting growth dynamics.
  • Power-law noise introduces complex, intermittent behaviors.

Purpose of the Study:

  • Investigate multiaffine exponent alpha(q) and multigrowth exponent beta(q) in ballistic deposition.
  • Analyze the impact of power-law distributed noise on growth dynamics.
  • Compare simulation results with theoretical predictions and scaling laws.

Main Methods:

  • Numerical simulations of ballistic deposition growth.
  • Analysis of noise obeying a power-law distribution.
  • Comparison of simulated exponents beta(q) and alpha(q) with theoretical functions.

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Main Results:

  • Simulated beta(q) values show good agreement with the asymptotic function beta(q)=1/q for large q.
  • The multiaffine exponent alpha(q) was found to be in the range 1/q <= alpha(q) <= 2/(q+1).
  • Discrepancies suggest large, rare events can break Kardar-Parisi-Zhang universality at higher orders.

Conclusions:

  • Ballistic deposition with power-law noise exhibits specific scaling behaviors for beta(q).
  • The observed range for alpha(q) indicates deviations from standard universality due to extreme events.
  • Findings highlight the importance of considering rare events in growth models.