PMID: 15244651Jul 13, 2004Paper

Universal behavior of the coefficients of the continuous equation in competitive growth models

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
D MuracaR C Buceta

Abstract

The competitive growth models (CGM) involving only one kind of particles, are a mixture of two processes, one with probability p and the other with probability 1-p. The p dependence produce crossovers between two different regimes. We demonstrate that the coefficients of the continuous equation, describing their universality classes, are quadratic in p (or 1-p ). We show that the origin of such dependence is the existence of two different average time rates. Thus, the quadratic p dependence is a universal behavior of all the (CGM). We derive analytically the continuous equations for two CGM, in 1+1 dimensions, from the microscopic rules using a regularization procedure. We propose generalized scalings that reproduce the scaling behavior in each regime. In order to verify the analytic results and the scalings, we perform numerical integrations of the derived analytical equations. The results are in excellent agreement with those of the microscopic CGM presented here and with the proposed scalings.

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Citations

Mar 10, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·F A Silveira, F D A Aarão Reis
Oct 8, 2014·Journal of Physics. Condensed Matter : an Institute of Physics Journal·C P de CastroR F S Andrade
Feb 14, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·A Kolakowska, M A Novotny
Jun 13, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Yen-Liang Chou, Michel Pleimling
Apr 12, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·F D A Aarão Reis
Aug 11, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·R C Buceta
Oct 4, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·L A Braunstein, Chi-Hang Lam
Aug 16, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·T J OliveiraF D A Aarão Reis

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