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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.
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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 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 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 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 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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