Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/4819
Title: Exact scaling in competitive growth models
Authors: Braunstein, LA
Lam, CH 
Keywords: Agglomeration
Continuum mechanics
Mathematical models
Surface roughness
Issue Date: 24-Aug-2005
Publisher: American Physical Society
Source: Physical review. E, Statistical, nonlinear, and soft matter physics, Aug. 2005, v. 72, no. 2, 026128, p. 1-5 How to cite?
Journal: Physical review. E, Statistical, nonlinear, and soft matter physics 
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.
URI: http://hdl.handle.net/10397/4819
ISSN: 1539-3755
EISSN: 1550-2376
DOI: 10.1103/PhysRevE.72.026128
Rights: Physical Review E © 2005 The American Physical Society. The Journal's web site is located at http://pre.aps.org/
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