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.

参考文献

[1] Barabási A L and Stanley H E 1995 Fractal Concepts in Surface Growth (Cambridge: Cambridge University Press)
[2] Family F 1986 J. Phys. A: Math. Gen. 19 L441
[3] Clar S, Drossel B and Schwabl F 1996 J. Phys.: Condens. Matter 8 6803
[4] Albano E V, Salvarezza R C, Vázquez L and Arvia A J 1999 Phys. Rev. B 59 7354
[5] Tang G, Xia H, Hao D, Xun Z, Wen R and Chen Y 2011 Chin. Phys. B 20 036402
[6] Vold M J 1959 J. Colloid Sci. 14 168
[7] Vold M J 1959 J. Phys. Chem. 63 1608
[8] Kim J M and Kosterlitz J M 1989 Phys. Rev. Lett. 62 2289
[9] Hosseinabadi S, Masoudi A and Sadegh Movahed M 2010 Physica B 405 2072
[10] Neyman J 1961 Fourth Berkeley Symposium on Mathematical Statistics and Probability, June 20-July 30, 1960, Statistical Laboratory of the University of California, Berkeley, USA, Vol. 4, p. 413
[11] Rodríguez-Cañas E, Aznárez J, Oliva A and Sacedón J 2006 Surf. Sci. 600 3110
[12] Liu Z J, Shum P and Shen Y 2006 Thin Solid Films 496 326
[13] Hawkeye MM and Brett MJ 2007 J. Vac. Sci. Technol. A 25 1317
[14] Das S K, Banerjee D and Roy J N 2023 J. Inst. Eng. (India): Ser. D 105 595
[15] Forgerini F L and Figueiredo W 2009 Phys. Rev. E 79 041602
[16] Kotrla M, Krug J and Šmilauer P 2000 Phys. Rev. B 62 2889
[17] Wang W and Cerdeira H A 1993 Phys. Rev. E 47 3357
[18] Aarão Reis F D A 2003 Phys. Rev. E 68 041602
[19] Das S K, Banerjee D and Roy J N 2021 Surf. Rev. Lett. 28 2050043
[20] Oliveira T J, Dechoum K, Redinz J A and Aarão Reis F D A 2006 Phys. Rev. E 74 011604
[21] Oliveira T J 2013 Phys. Rev. E 87 034401
[22] Chame A and Aarão Reis F D A 2002 Phys. Rev. E 66 051104
[23] Silveira F A and Aarão Reis F D A 2012 Phys. Rev. E 85 011601
[24] Pellegrini Y P and Jullien R 1990 Phys. Rev. Lett. 64 1745
[25] Pellegrini Y P and Jullien R 1991 Phys. Rev. A 43 920
[26] Edwards S and Wilkinson D 1982 Proc. R. Soc. Lond. A 381 17
[27] Kardar M, Parisi G and Zhang Y C 1986 Phys. Rev. Lett. 56 889
[28] Muraca D, Braunstein L A and Buceta R C 2004 Phys. Rev. E 69 065103
[29] Horowitz C M and Albano E V 2001 J. Phys. A: Math. Gen. 34 357
[30] Braunstein L A and Lam C H 2005 Phys. Rev. E 72 026128
[31] Kolakowska A, Novotny M A and Verma P S 2004 Phys. Rev. E 70 051602
[32] Kolakowska A and Novotny M A 2015 Phys. Rev. E 91 012147
[33] Krug J 1989 J. Phys. A: Math. Gen. 22 L769
[34] de Assis T A, de Castro C P, de Brito Mota F, de Castilho C M C and Andrade R F S 2012 Phys. Rev. E 86 051607
[35] Mello B A, Chaves A S and Oliveira F A 2001 Phys. Rev. E 63 041113
[36] Family F and Vicsek T 1985 J. Phys. A: Math. Gen. 18 L75
[37] Yan H, Kessler D and Sander L M 1990 Phys. Rev. Lett. 64 926
[38] Nath P and Jana D 2015 Int. J. Mod. Phys. C 26 1550115

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

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 1

Metrics

本文评价

推荐阅读 10