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Exact scaling in competitive growth models.

L A Braunstein1, Chi-Hang Lam

  • 1Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes 3350, 7600 Mar del Plata, Argentina.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 4, 2005
PubMed
Summary

This study analyzes competitive growth models (CGMs) for particle aggregation. Researchers derived exact scaling exponents for surface roughness, revealing transitions in growth behaviors like random deposition and Edward-Wilkinson.

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Area of Science:

  • Statistical Physics
  • Materials Science
  • Surface Growth Phenomena

Background:

  • Competitive Growth Models (CGMs) are crucial for understanding particle aggregation dynamics.
  • Surface roughness in CGMs exhibits complex scaling behavior influenced by competing growth rules.
  • Existing models often assume a single universality class, which may not always hold.

Purpose of the Study:

  • To elucidate the origin of scaling behavior in surface roughness for specific CGMs at small probabilities (p).
  • To derive exact scaling exponents and analyze continuum equation coefficients.
  • To investigate CGMs where a unique universality class may not apply, demonstrating transitions in scaling behavior.

Main Methods:

  • Analytical derivation of exact scaling exponents for surface roughness.

Related Experiment Videos

  • Analysis of scaling behavior for coefficients in corresponding continuum equations.
  • Introduction and simulation of a novel CGM (RD competing with constrained EW) to observe scaling transitions.

    • Main Results:

    • Exact scaling exponents were derived for random deposition (RD) competing with ballistic deposition and Edward-Wilkinson (EW) growth.
    • The p-dependence of continuum equation coefficients, representing universality classes, can be nontrivial.
    • A new CGM demonstrated a transition from RD to Kardar-Parisi-Zhang (KPZ) and then to EW scaling as p varied.

    Conclusions:

    • The study provides a comprehensive understanding of scaling behavior in CGMs, particularly at small p.
    • It highlights that some CGMs do not conform to a single universality class, exhibiting transitions.
    • Simulation results strongly support the analytic predictions, validating the developed models and findings.