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采用Purwins的三变量模型, 在二维空间对气体放电系统中多臂螺旋波的形成和转化进行了数值研究. 通过分析方程参数对系统空间的影响, 确定了系统获得稳定螺旋波的参数空间; 得到了斑图由简单静态六边形到螺旋波的演化过程, 分析了螺旋波的形成机制和时空特性; 进一步获得六种不同臂数的多臂螺旋波斑图(例如: 双臂、三臂、四臂、五臂、六臂和七臂螺旋波). 结果表明: 螺旋波斑图出现在图灵-霍普夫(Turing-Hopf)空间, 是Turing模和Hopf模相互竞争、相互作用的结果; 不同臂数的螺旋波波头均在持续地旋转运动, 其运动速度随螺旋波臂数的增加而增大; 随着螺旋波臂数的增加, 其波头的运动形式愈加复杂; 由于受微扰及边界条件的影响, 多臂螺旋波可以向臂数少一的螺旋波发生转变, 数值模拟结果与实验结果符合较好.The process of formation or transformation of multi-armed spiral patterns in gas discharge system is investigated numerically by using H.-G. Purwins model with three components. The parameter space is obtained though analyzing the influence of system parameters on system space, where a stable spiral appears. Besides, the formation mechanism and spatiotemporal characteristics of spiral pattern are studied. In addition, the evolution process of pattern from simple hexagon to spiral wave is numerically simulated, and various kinds of spirals are obtained (including two-armed, three-armed, four-armed, five-armed, six-armed, and seven-armed spirals). It is found that the stable spiral only survives in Turing-Hopf space, which is the result of interaction between Turing mode and Hopf mode. Furthermore, the spiral tips constantly rotate for various spiral patterns, and the velocity increases with the number of spiral arm increasing. For the influences of perturbation and boundary conditions, the multi-armed spiral pattern can lose one arm and become a new spiral in the rotating process. In conclusion, the numerical simulation results are in good agreement with those obtained in gas discharge experiment.
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Keywords:
- spiral pattern /
- numerical simulation /
- gas discharge
[1] Thakur P, Ann H B, Jiang I 2009 Astrophys. J. 69 3586
[2] Cysyk J, Tung L 2008 Biophys. J. 94 1533
[3] Sawai S, Thomason P A, Cox E C 2005 Nature 433 323
[4] Vasiev B, Siegert F, Weijer C 1997 Phys. Rev. Lett. 78 2489
[5] de Bruyn J R, Lewis B C, Shattuck M D, Swinney H L 2001 Phys. Rev. E 63 041305
[6] Zaritski R M, Pertsov A M 2002 Phys. Rev. E 66 066120
[7] Guo H Y, Li L, Ouyang Q 2003 J. Chem. Phys. 118 5038
[8] Zhang H, Ruan X S, Hu B, Ouyang Q 2004 Phys. Rev. E 70 016202
[9] Aranson L S, Aranson L, Kramer L, Weber A 1992 Phys. Rev. A 46 R2992
[10] Zaikin A N, Zhabotinsky A M 1970 Nature 225 535
[11] Bruyn J R, Lewis B C S, Swinney H L 2001 Phys. Rev. E 63 041305
[12] Gao J H, Wang Y, Zhang C, Yang H P, Ge Z C 2014 Acta Phys. Sin. 63 020503 (in Chinese) [高继华, 王宇, 张超, 杨海朋, 戈早川 2014 63 020503]
[13] Wang C N, Ma J 2013 Acta Phys. Sin. 62 084501 (in Chinese) [王春妮, 马军 2013 62 084501]
[14] Hagan P S 1982 Siam. J. Appl. Math. 42 762
[15] Plapp B B, Bodenschatz E 1996 Phys. Scripta. 67 111
[16] Bursac N, Aguel F, Tung L 2004 Proc. Natl. Acad. Sci. 101 15530
[17] Deng L Y, Zhang H, Li Y Q 2009 Phys. Rev. E 79 036107
[18] Hu B, Ma J, Tang J 2013 Plos One 8 0069251
[19] He Y F, Ai B Q, Liu F C 2013 Phys. Rev. E 87 052913
[20] Li B, Dong L F, Zhang C, Shen Z K, Zhang X P 2014 J. Phys. D: Appl. Phys. 47 055205
[21] Dong L F, Shen Z K, Li B, Bai Z G 2013 Phys. Rev. E 87 042914
[22] Astrov Y A, Mller I, Ammelt E, Purwins H G 1998 Phys. Rev. Lett. 80 5341
[23] Dong L F, Wang H F, Liu F C, He Y F 2007 New J. Phys. 9 330
[24] Dong L F, Li B, Shen Z K, Liu L 2012 Phys. Rev. E 86 056217
[25] Dong L F, Liu F C, Liu S H, He Y F, Fan W L 2005 Phys. Rev. E 72 046215
[26] Yin Z Q, Wang L, Dong L F, Li X C, Chai Z F 2003 Acta Phys. Sin. 52 929 (in Chinese) [尹增谦, 王龙, 董丽芳, 李雪辰, 柴志方 2003 52 929]
[27] Radehaus C, Willebrand H, Dohmen R, Niedernostheide F, Bengel G, Purwins H 1992 Phys. Rev. A 45 2546
[28] Schenk C P, Or-Guil M, Bode M, Purwins H 1997 Phys. Rev. Lett. 78 3781
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[1] Thakur P, Ann H B, Jiang I 2009 Astrophys. J. 69 3586
[2] Cysyk J, Tung L 2008 Biophys. J. 94 1533
[3] Sawai S, Thomason P A, Cox E C 2005 Nature 433 323
[4] Vasiev B, Siegert F, Weijer C 1997 Phys. Rev. Lett. 78 2489
[5] de Bruyn J R, Lewis B C, Shattuck M D, Swinney H L 2001 Phys. Rev. E 63 041305
[6] Zaritski R M, Pertsov A M 2002 Phys. Rev. E 66 066120
[7] Guo H Y, Li L, Ouyang Q 2003 J. Chem. Phys. 118 5038
[8] Zhang H, Ruan X S, Hu B, Ouyang Q 2004 Phys. Rev. E 70 016202
[9] Aranson L S, Aranson L, Kramer L, Weber A 1992 Phys. Rev. A 46 R2992
[10] Zaikin A N, Zhabotinsky A M 1970 Nature 225 535
[11] Bruyn J R, Lewis B C S, Swinney H L 2001 Phys. Rev. E 63 041305
[12] Gao J H, Wang Y, Zhang C, Yang H P, Ge Z C 2014 Acta Phys. Sin. 63 020503 (in Chinese) [高继华, 王宇, 张超, 杨海朋, 戈早川 2014 63 020503]
[13] Wang C N, Ma J 2013 Acta Phys. Sin. 62 084501 (in Chinese) [王春妮, 马军 2013 62 084501]
[14] Hagan P S 1982 Siam. J. Appl. Math. 42 762
[15] Plapp B B, Bodenschatz E 1996 Phys. Scripta. 67 111
[16] Bursac N, Aguel F, Tung L 2004 Proc. Natl. Acad. Sci. 101 15530
[17] Deng L Y, Zhang H, Li Y Q 2009 Phys. Rev. E 79 036107
[18] Hu B, Ma J, Tang J 2013 Plos One 8 0069251
[19] He Y F, Ai B Q, Liu F C 2013 Phys. Rev. E 87 052913
[20] Li B, Dong L F, Zhang C, Shen Z K, Zhang X P 2014 J. Phys. D: Appl. Phys. 47 055205
[21] Dong L F, Shen Z K, Li B, Bai Z G 2013 Phys. Rev. E 87 042914
[22] Astrov Y A, Mller I, Ammelt E, Purwins H G 1998 Phys. Rev. Lett. 80 5341
[23] Dong L F, Wang H F, Liu F C, He Y F 2007 New J. Phys. 9 330
[24] Dong L F, Li B, Shen Z K, Liu L 2012 Phys. Rev. E 86 056217
[25] Dong L F, Liu F C, Liu S H, He Y F, Fan W L 2005 Phys. Rev. E 72 046215
[26] Yin Z Q, Wang L, Dong L F, Li X C, Chai Z F 2003 Acta Phys. Sin. 52 929 (in Chinese) [尹增谦, 王龙, 董丽芳, 李雪辰, 柴志方 2003 52 929]
[27] Radehaus C, Willebrand H, Dohmen R, Niedernostheide F, Bengel G, Purwins H 1992 Phys. Rev. A 45 2546
[28] Schenk C P, Or-Guil M, Bode M, Purwins H 1997 Phys. Rev. Lett. 78 3781
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