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讨论了分数阶Frenkel-Kontorova模型的物理意义, 并应用该模型刻画了耦合粒子链在记忆性介质中的输运现象, 研究了各参数对粒子链运动状态的影响. 数值仿真结果表明: 系统的记忆性对粒子链的运动有显著影响, 尤其出现了在非记忆性情况下所不具有的反向流. 同时发现粒子链的平均流速会随耦合强度、分数阶的阶数变化而产生广义共振; 此外, 平均流速还会随噪声强度的变化出现广义随机共振现象.
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关键词:
- 分数阶Frenkel-Kontorova模型 /
- 记忆性介质 /
- 随机共振 /
- 定向输运反向流
In this paper, we first discuss the physical meaning of the fractional Frenkel-Kontorova model and depict the transport phenomenon of elastically coupled particles in a memorable medium, then give the effects of various parameters on the motion of coupled particles. According to the numerical value, the memory effect of system has a significant influence on the motion of coupled particles, in addition, the current reversal which does not exist in a non-memorable system appears, this is an abnormal phenomenon. What is more in this research we find that there appears the generalized resonance in the system mean velocity as the spring constant and the fractional order are varied, and the generalized stochastic resonance will appear with noise intensity changing.-
Keywords:
- fractional Frenkel-Kontorova model /
- memorable medium /
- stochastic resonance /
- current reversal
[1] Hänggi P, Marchesoni F 2009 Rev. Mod. Phys. 81 387
[2] Qian M, Wang Y, Zhang X J 2003 Chin. Phys. Lett. 20 810
[3] Ai B Q, He Y F 2010 J. Chem. Phys. 132 094504
[4] Wang H Y, Bao J D 2004 Physica A 337 13
[5] Csahók Z, Family F, Vicsek T 1997 Phys. Rev. E 55 5179
[6] Ai B Q, He Y F, Zhong W R 2011 Phys. Rev. E 83 051106
[7] Kumar K V, Ramaswamy S, Rao M 2008 Phys. Rev. E 77 020102
[8] Gehlen S V, Evstigneev M, Reimann P 2009 Phys. Rev. E 79 031114
[9] Fendrik A J, Romanelli L 2012 Phys. Rev. E 85 041149
[10] Zheng Z G 2004 Spatiotemporal Dynamics and Collective Behaviors in Coupled Nonlinear Systems (Beijing: Higher Education Press) p279 (in Chinese) [郑志刚 2004 耦合非线性系统的时空动力学与合作行为 (北京: 高等教育出版社) 第279页]
[11] Vadakkepatt A, Dong Y L, Lichter S, Martini A 2011 Phys. Rev. E 84 066311
[12] Nishikawa M, Takagi H, Shibata T, Iwane A H, Yanagida T 2008 Phys. Rev. Lett. 101 128103
[13] Campás O, Kafri Y, Zeldovich K B, Casademunt J, Joanny J F 2006 Phys. Rev. Lett. 97 038101
[14] Liu F, Anh V V, Turner I, Zhuang P 2003 J. Appl. Math. Comp. 13 233
[15] de Andrade M F, Lenzi E K, Evangelista L R, Mendes R S, Malacarne L C 2005 Phys. Lett. A 347 160
[16] Braun O M, Kivshar Y S 2004 The Frenkel-Kontorova Model: Concepts, Methods and Application (New York: Springer)
[17] Han X Q, Jiang H, Shi Y R, Liu Y X, Sun J H, Chen J M, Duan W S 2011 Acta Phys. Sin. 60 116801 (in Chinese) [韩秀琴, 姜虹, 石玉仁, 刘妍秀, 孙建华, 陈建敏, 段文山 2011 物理学报 60 116801]
[18] Bao J D 2009 Random Simulation Method of Classical and Quantum Dissipation System (Beijing: Science Press) p80 (in Chinese) [包景东 2009经典和量子耗散系统的随机模拟方法(北京: 科学出版社)第80页]
[19] Oldham K B, Spanier J 1974 The Fractional Calculus (New York: Academic Press)
[20] Kou S C, Xie X S 2004 Phys. Rev. Lett. 93 180603
[21] Gao S L, Zhong S C, Wei K, Ma H 2012 Acta Phys. Sin. 61 100502 (in Chinese) [高仕龙, 钟苏川, 韦鹍, 马洪 2012 物理学报 61 100502]
[22] Podlubny I 1999 Fractional Differential Equations (San Diegop, CA: Academic Press)
[23] Samko S G, Kilbas A A, Marichev O I 1993 Fractional Integrals and Derivatives Theory and Applications (New York: Gordon and Breach Science Publisher)
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[1] Hänggi P, Marchesoni F 2009 Rev. Mod. Phys. 81 387
[2] Qian M, Wang Y, Zhang X J 2003 Chin. Phys. Lett. 20 810
[3] Ai B Q, He Y F 2010 J. Chem. Phys. 132 094504
[4] Wang H Y, Bao J D 2004 Physica A 337 13
[5] Csahók Z, Family F, Vicsek T 1997 Phys. Rev. E 55 5179
[6] Ai B Q, He Y F, Zhong W R 2011 Phys. Rev. E 83 051106
[7] Kumar K V, Ramaswamy S, Rao M 2008 Phys. Rev. E 77 020102
[8] Gehlen S V, Evstigneev M, Reimann P 2009 Phys. Rev. E 79 031114
[9] Fendrik A J, Romanelli L 2012 Phys. Rev. E 85 041149
[10] Zheng Z G 2004 Spatiotemporal Dynamics and Collective Behaviors in Coupled Nonlinear Systems (Beijing: Higher Education Press) p279 (in Chinese) [郑志刚 2004 耦合非线性系统的时空动力学与合作行为 (北京: 高等教育出版社) 第279页]
[11] Vadakkepatt A, Dong Y L, Lichter S, Martini A 2011 Phys. Rev. E 84 066311
[12] Nishikawa M, Takagi H, Shibata T, Iwane A H, Yanagida T 2008 Phys. Rev. Lett. 101 128103
[13] Campás O, Kafri Y, Zeldovich K B, Casademunt J, Joanny J F 2006 Phys. Rev. Lett. 97 038101
[14] Liu F, Anh V V, Turner I, Zhuang P 2003 J. Appl. Math. Comp. 13 233
[15] de Andrade M F, Lenzi E K, Evangelista L R, Mendes R S, Malacarne L C 2005 Phys. Lett. A 347 160
[16] Braun O M, Kivshar Y S 2004 The Frenkel-Kontorova Model: Concepts, Methods and Application (New York: Springer)
[17] Han X Q, Jiang H, Shi Y R, Liu Y X, Sun J H, Chen J M, Duan W S 2011 Acta Phys. Sin. 60 116801 (in Chinese) [韩秀琴, 姜虹, 石玉仁, 刘妍秀, 孙建华, 陈建敏, 段文山 2011 物理学报 60 116801]
[18] Bao J D 2009 Random Simulation Method of Classical and Quantum Dissipation System (Beijing: Science Press) p80 (in Chinese) [包景东 2009经典和量子耗散系统的随机模拟方法(北京: 科学出版社)第80页]
[19] Oldham K B, Spanier J 1974 The Fractional Calculus (New York: Academic Press)
[20] Kou S C, Xie X S 2004 Phys. Rev. Lett. 93 180603
[21] Gao S L, Zhong S C, Wei K, Ma H 2012 Acta Phys. Sin. 61 100502 (in Chinese) [高仕龙, 钟苏川, 韦鹍, 马洪 2012 物理学报 61 100502]
[22] Podlubny I 1999 Fractional Differential Equations (San Diegop, CA: Academic Press)
[23] Samko S G, Kilbas A A, Marichev O I 1993 Fractional Integrals and Derivatives Theory and Applications (New York: Gordon and Breach Science Publisher)
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