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Braunstein LA, Lam CH. Exact scaling in competitive growth models. Phys Rev E Stat Nonlin Soft Matter Phys. 2005;72(2):026128doi: 10.1103/PhysRevE.72.026128.
Braunstein, L. A., & Lam, C. H. (2005). Exact scaling in competitive growth models. Physical review. E, Statistical, nonlinear, and soft matter physics, 72(2), 026128. https://doi.org/10.1103/PhysRevE.72.026128
Braunstein, L A, and Lam, Chi-Hang. "Exact scaling in competitive growth models." Physical review. E, Statistical, nonlinear, and soft matter physics vol. 72,2 (2005): 026128. doi: https://doi.org/10.1103/PhysRevE.72.026128
Braunstein LA, Lam CH. Exact scaling in competitive growth models. Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Aug;72(2):026128. doi: 10.1103/PhysRevE.72.026128. Epub 2005 Aug 24. PMID: 16196665.
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Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Aug;72(2):026128. doi: 10.1103/PhysRevE.72.026128. Epub 2005 Aug 24.

Exact scaling in competitive growth models.

Physical review. E, Statistical, nonlinear, and soft matter physics

L A Braunstein, Chi-Hang Lam

Affiliations

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

PMID: 16196665 DOI: 10.1103/PhysRevE.72.026128

Abstract

A competitive growth model (CGM) describes the aggregation of a single type of particle under two different growth rules with occurrence probabilities p and 1-p . We explain the origin of the scaling behavior of the resulting surface roughness at small p for two CGM's which describe random deposition (RD) competing with ballistic deposition and RD competing with the Edward-Wilkinson (EW) growth rule. Exact scaling exponents are derived. The scaling behavior of the coefficients in the corresponding continuum equations are also deduced. Furthermore, we suggest that, in some CGM's, the p dependence on the coefficients of the continuum equation that represents their universality class can be nontrivial. In some cases, the process cannot be represented by a unique universality class. In order to show this, we introduce a CGM describing RD competing with a constrained EW model. This CGM shows a transition in the scaling exponents from RD to a Kardar-Parisi-Zhang behavior when p is close to 0 and to a Edward-Wilkinson one when p is close to 1 at practical time and length scales. Our simulation results are in excellent agreement with the analytic predictions.

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