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

doi:10.1088/1674-1056/ad322e

中国物理B ›› 2024, Vol. 33 ›› Issue (6): 60502-060502.doi: 10.1088/1674-1056/ad322e

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

Chengzhi Yu(余成志), Xiao Liu(刘潇), Jun Tang(唐军)†, and Hui Xia(夏辉)‡

School of Materials Science and Physics, China University of Mining and Technology, Xuzhou 221116, China

收稿日期:2024-01-23 修回日期:2024-03-05 接受日期:2024-03-11 出版日期:2024-06-18 发布日期:2024-06-18
通讯作者: Jun Tang, Hui Xia E-mail:tjuns@cumt.edu.cn；hxia@cumt.edu.cn
基金资助:
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).

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

Chengzhi Yu(余成志), Xiao Liu(刘潇), Jun Tang(唐军)†, and Hui Xia(夏辉)‡

School of Materials Science and Physics, China University of Mining and Technology, Xuzhou 221116, China

Received:2024-01-23 Revised:2024-03-05 Accepted:2024-03-11 Online:2024-06-18 Published:2024-06-18
Contact: Jun Tang, Hui Xia E-mail:tjuns@cumt.edu.cn；hxia@cumt.edu.cn
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: competitive growth, scaling behavior, discrete growth model, Kardar-Parisi-Zhang universality class

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.

Key words: competitive growth, scaling behavior, discrete growth model, Kardar-Parisi-Zhang universality class

中图分类号: (Fluctuation phenomena, random processes, noise, and Brownian motion)

05.40.-a

05.10.Ln (Monte Carlo methods) 68.35.Fx (Diffusion; interface formation)

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[J]. 中国物理B, 2024, 33(6): 60502-060502.

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

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

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