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Chaotic behaviors and fractal self-similar analysis of particles transport properties in RIKEN mesoscopic devices

Yang Qin-Nan Zhang Yan-Hui Cai Xiang-Ji Jiang Guo-Hui Xu Xue-You

Chaotic behaviors and fractal self-similar analysis of particles transport properties in RIKEN mesoscopic devices

Yang Qin-Nan, Zhang Yan-Hui, Cai Xiang-Ji, Jiang Guo-Hui, Xu Xue-You
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  • The theoretical model of RIKEN mesoscopic device in our study is one kind of the two-dimensional Sinai billiards, which is an ideal model to investigate the chaotic and fractal behaviors in particle escape curves. In the analysis of the escape curves, we use two methods:qualitative comparison and quantitative calculation of the fractal dimensions. Then we obtain the influence of the distribution of chaotic areas caused by the opening width, cavity length, corner positions, arc radius, etc. In the results, we find the fractal self-similar structure of the escape curves in which the similarity is very good, and they display the chaotic property of the transmission in the RIKEN device. Moreover, we use the eye-style structure analysis and the comparation between similar ratios to investagate the fractal self-similar structure.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 10774093, 10374061).
    [1]

    Hu G 1994 Random Force and Nonlinear Systems (Shanghai:Shanghai Technology and Education Press) p114 (in Chinese) [胡岗 1994 随机力与非线性系统 (上海:上海科技教育出版社) 第114页]

    [2]

    Zhong Y X 2010 Discussion on Chaos and Fractals (Beijing:Peking University Press) p5 (in Chinese) [钟云霄 2010 混沌与分形浅谈 (北京:北京大学出版社) 第5页]

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    Hansen P, Mitchell K A, Delos J B 2006 Phys. Rev. E 73 066226

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    Ree S, Reichl L E 2002 Phys. Rev. E 65 055205

    [5]

    Micolich A P, Taylor R P, Newbury R, Fromhold T M, Tench C R 2000 Europhys. Lett. 49 417

    [6]

    Jiang G H, Zhang Y H, Cai X J, Yang Q N 2011 Shandong Science 24 22 (in Chinese) [蒋国辉, 张延惠, 蔡祥吉, 杨秦男 2011 山东科学 24 22]

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    Micolich A P 2000 Ph. D. Dissertation (Australia:The University of New South Wales)

    [8]

    Fromhold T M, Tench C R, Taylor R P, Micolich A P, Newbury R 1998 Physica B 249 334

    [9]

    Zhao H J, Du M L 2007 Acta Phys. Sin. 56 3827 (in Chinese) [赵海军, 杜孟利 2007 物理学报 56 3827]

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    Zhao H J, Du M L 2007 Phys. Rev. E 76 027201

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    Song X F, Du M L, Zhao H J 2012 Sci. Sin. Phys. Mech. Astron. 42 127 (in Chinese) [宋新芳, 杜孟利, 赵海军 2012 中国科学:物理学 力学 天文学 42 127]

    [12]

    Xu X Y, Zhang Y H, Huang F Z, Lin S L, Du M L 2005 Acta Phys. Sin. 54 4538 (in Chinese) [徐学友, 张延惠, 黄发忠, 林圣路, 杜孟利 2005 物理学报 54 4538]

    [13]

    Jiang G H, Zhang Y H, Bian H T, Xu X Y 2011 Chin. Phys. Lett. 28 120507

    [14]

    Mitchell K A, Handley J P, Tighe B, Knudson S K, Delos J B 2003 Chaos 13 880

    [15]

    Mitchell K A, Handley J P, Knudson S K, Delos J B 2003 Chaos 13 892

    [16]

    Huang R S 2000 Chaos and Its Application (Wuhan:Wuhan University Press) p179 (in Chinese) [黄润生 2000 混沌及其应用 (武汉:武汉大学出版社) 第179页]

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    Taylor R P, Micolich A P, Jonas D 1999 Nature 399 422

  • [1]

    Hu G 1994 Random Force and Nonlinear Systems (Shanghai:Shanghai Technology and Education Press) p114 (in Chinese) [胡岗 1994 随机力与非线性系统 (上海:上海科技教育出版社) 第114页]

    [2]

    Zhong Y X 2010 Discussion on Chaos and Fractals (Beijing:Peking University Press) p5 (in Chinese) [钟云霄 2010 混沌与分形浅谈 (北京:北京大学出版社) 第5页]

    [3]

    Hansen P, Mitchell K A, Delos J B 2006 Phys. Rev. E 73 066226

    [4]

    Ree S, Reichl L E 2002 Phys. Rev. E 65 055205

    [5]

    Micolich A P, Taylor R P, Newbury R, Fromhold T M, Tench C R 2000 Europhys. Lett. 49 417

    [6]

    Jiang G H, Zhang Y H, Cai X J, Yang Q N 2011 Shandong Science 24 22 (in Chinese) [蒋国辉, 张延惠, 蔡祥吉, 杨秦男 2011 山东科学 24 22]

    [7]

    Micolich A P 2000 Ph. D. Dissertation (Australia:The University of New South Wales)

    [8]

    Fromhold T M, Tench C R, Taylor R P, Micolich A P, Newbury R 1998 Physica B 249 334

    [9]

    Zhao H J, Du M L 2007 Acta Phys. Sin. 56 3827 (in Chinese) [赵海军, 杜孟利 2007 物理学报 56 3827]

    [10]

    Zhao H J, Du M L 2007 Phys. Rev. E 76 027201

    [11]

    Song X F, Du M L, Zhao H J 2012 Sci. Sin. Phys. Mech. Astron. 42 127 (in Chinese) [宋新芳, 杜孟利, 赵海军 2012 中国科学:物理学 力学 天文学 42 127]

    [12]

    Xu X Y, Zhang Y H, Huang F Z, Lin S L, Du M L 2005 Acta Phys. Sin. 54 4538 (in Chinese) [徐学友, 张延惠, 黄发忠, 林圣路, 杜孟利 2005 物理学报 54 4538]

    [13]

    Jiang G H, Zhang Y H, Bian H T, Xu X Y 2011 Chin. Phys. Lett. 28 120507

    [14]

    Mitchell K A, Handley J P, Tighe B, Knudson S K, Delos J B 2003 Chaos 13 880

    [15]

    Mitchell K A, Handley J P, Knudson S K, Delos J B 2003 Chaos 13 892

    [16]

    Huang R S 2000 Chaos and Its Application (Wuhan:Wuhan University Press) p179 (in Chinese) [黄润生 2000 混沌及其应用 (武汉:武汉大学出版社) 第179页]

    [17]

    Taylor R P, Micolich A P, Jonas D 1999 Nature 399 422

  • [1] Hu Xiaoliang, Liang Hong, Wang Huili. Lattice Boltzmann method simulations of the immiscible Rayleigh-Taylor instability with high Reynolds numbers. Acta Physica Sinica, 2020, 69(4): 1-10. doi: 10.7498/aps.69.20191504
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  • Received Date:  10 October 2012
  • Accepted Date:  21 December 2012
  • Published Online:  20 April 2013

Chaotic behaviors and fractal self-similar analysis of particles transport properties in RIKEN mesoscopic devices

  • 1. College of Physics and Electronics, Shandong Normal University, Jinan 250014, China;
  • 2. Information Research Institute, Shandong Academy of Sciences, Jinan 250014, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant Nos. 10774093, 10374061).

Abstract: The theoretical model of RIKEN mesoscopic device in our study is one kind of the two-dimensional Sinai billiards, which is an ideal model to investigate the chaotic and fractal behaviors in particle escape curves. In the analysis of the escape curves, we use two methods:qualitative comparison and quantitative calculation of the fractal dimensions. Then we obtain the influence of the distribution of chaotic areas caused by the opening width, cavity length, corner positions, arc radius, etc. In the results, we find the fractal self-similar structure of the escape curves in which the similarity is very good, and they display the chaotic property of the transmission in the RIKEN device. Moreover, we use the eye-style structure analysis and the comparation between similar ratios to investagate the fractal self-similar structure.

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