Extensive numerical simulations on competitive growth between the Edwards-Wilkinson and Kardar-Parisi-Zhang universality classes

doi:10.1088/1674-1056/ad322e

Abstract Extensive numerical simulations and scaling analysis are performed to investigate competitive growth between the linear and nonlinear stochastic dynamic growth systems, which belong to the Edwards-Wilkinson (EW) and Kardar-Parisi-Zhang (KPZ) universality classes, respectively. The linear growth systems include the EW equation and the model of random deposition with surface relaxation (RDSR), the nonlinear growth systems involve the KPZ equation and typical discrete models including ballistic deposition (BD), etching, and restricted solid on solid (RSOS). The scaling exponents are obtained in both the ($1+1$)- and ($2+1$)-dimensional competitive growth with the nonlinear growth probability $p$ and the linear proportion $1-p$. Our results show that, when $p$ changes from 0 to 1, there exist non-trivial crossover effects from EW to KPZ universality classes based on different competitive growth rules. Furthermore, the growth rate and the porosity are also estimated within various linear and nonlinear growths of cooperation and competition.

Keywords: competitive growth scaling behavior discrete growth model Kardar-Parisi-Zhang universality class

Received: 23 January 2024
Revised: 05 March 2024
Accepted manuscript online: 11 March 2024

PACS:	05.40.-a	(Fluctuation phenomena, random processes, noise, and Brownian motion)
	05.10.Ln	(Monte Carlo methods)
	68.35.Fx	(Diffusion; interface formation)

Fund: This work was supported by Undergraduate Training Program for Innovation and Entrepreneurship of China University of Mining and Technology (CUMT) (Grant No. 202110290059Z), and Fundamental Research Funds for the Central Universities of CUMT (Grant No. 2020ZDPYMS33).

Corresponding Authors: Jun Tang, Hui Xia
E-mail: tjuns@cumt.edu.cn；hxia@cumt.edu.cn

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Chengzhi Yu(余成志), Xiao Liu(刘潇), Jun Tang(唐军), and Hui Xia(夏辉) Extensive numerical simulations on competitive growth between the Edwards-Wilkinson and Kardar-Parisi-Zhang universality classes 2024 Chin. Phys. B 33 060502

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Extensive numerical simulations on competitive growth between the Edwards-Wilkinson and Kardar-Parisi-Zhang universality classes

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