Please wait a minute...
Chin. Phys. B, 2009, Vol. 18(2): 0686    DOI: 10.1088/1674-1056/18/2/047
CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES Prev   Next  

Three-dimensional interfacial wave theory of dendritic growth: (II). non-axi-symmetric global wave modes and selection criterion of pattern formation

Chen Yong-Qianga, Xu Jian-Junb, Tang Xiong-Xinc
a School of Mathematical Science, Nankai University, Tianjin 300071, China;Department of Fundamental Subject, Tianjin Institute of Urban Construction, Tianjin 300384, China; b School of Mathematical Science, Nankai University, Tianjin 300071, China;Department of mathematics and Statistics, McGill University, H3A2K6 Montreal, Canada; c School of Mathematical Science, Nankai University, Tianjin 300071, China;School of materials Science and Engineering, University of Science and Technology Beiji
Abstract  This paper is the continuation of part (I), which completes the derivations of the 3D global wave modes solutions, yields the stability criterion and, on the basis of the results obtained, demonstrates the selection criterion of pattern formation.
Keywords:  selection criterion      dendritic growth      pattern formation      interfacial waves  
Received:  04 July 2008      Revised:  29 August 2008      Published:  20 February 2009
PACS:  68.70.+w (Whiskers and dendrites (growth, structure, and nonelectronic properties))  
  47.35.-i (Hydrodynamic waves)  
Fund: Project supported by the Nankai University, China and in part by NSERC Grant of Canada.

Cite this article: 

Chen Yong-Qiang, Tang Xiong-Xin, Xu Jian-Jun Three-dimensional interfacial wave theory of dendritic growth: (II). non-axi-symmetric global wave modes and selection criterion of pattern formation 2009 Chin. Phys. B 18 0686

[1] A lattice Boltzmann-cellular automaton study on dendrite growth with melt convection in solidification of ternary alloys
Dong-Ke Sun(孙东科), Zhen-Hua Chai(柴振华), Qian Li(李谦), Guang Lin(林光). Chin. Phys. B, 2018, 27(8): 088105.
[2] Pattern formation in superdiffusion Oregonator model
Fan Feng(冯帆), Jia Yan(闫佳), Fu-Cheng Liu(刘富成), Ya-Feng He(贺亚峰). Chin. Phys. B, 2016, 25(10): 104702.
[3] Numerical simulation and analysis of complex patterns in a two-layer coupled reaction diffusion system
Li Xin-Zheng, Bai Zhan-Guo, Li Yan, He Ya-Feng, Zhao Kun. Chin. Phys. B, 2015, 24(4): 048201.
[4] Control of the patterns by using time-delayed feedback near the codimension-three Turing–Hopf–Wave bifurcations
Wang Hui-Juan, Wang Yong-Jie, Ren Zhi. Chin. Phys. B, 2013, 22(12): 120503.
[5] Controlling the transition between Turing and antispiral patterns by using time-delayed-feedback
He Ya-Feng,Liu Fu-Cheng,Fan Wei-Li,Dong Li-Fang. Chin. Phys. B, 2012, 21(3): 034701.
[6] Spatial pattern formation of a ratio-dependent predator–prey model
Lin Wang. Chin. Phys. B, 2010, 19(9): 090206.
[7] Dendritic sidebranches of a binary system with enforced flow
Li Xiang-Ming, Wang Zi-Dong. Chin. Phys. B, 2010, 19(12): 126401.
[8] Three-dimensional interfacial wave theory of dendritic growth: (I). multiple variables expansion solutions
Chen Yong-Qiang, Tang Xiong-Xin, Xu Jian-Jun. Chin. Phys. B, 2009, 18(2): 671-685.
[9] Second-order solutions for random interfacial waves in N-layer density-stratified fluid with steady uniform currents
Chen Xiao-Gang, Guo Zhi-Ping, Song Jin-Bao. Chin. Phys. B, 2008, 17(9): 3387-3393.
[10] RAPID DENDRITIC GROWTH INVESTIGATED WITH ARTIFICIAL NEURAL NETWORK METHOD
Wang Nan, Zhang Jun, Wei Bing-bo, Dai Guan-zhong. Chin. Phys. B, 2000, 9(7): 532-536.
No Suggested Reading articles found!