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Based on the fractional calculus theory, in the absence of external driving force, the fractional transport model of asymmetric coupling particle chain in symmetric periodic potential is established. Using the method of fractional difference, the model is solved numerically and the influences of the various system parameters on directional transport velocity are discussed. Numerical results show that in the case without external force and noise-driven, the fractional asymmetric coupling system can still generate directional transport, and the transport velocity increases as fractional order increases. When the fractional order is fixed, the average velocity of the particle chain varies non-monotonically with coupling strength and barrier height. In the case with noise, the generalized stochastic resonance phenomenon occurs. Besides, we can make the noise not affect the system or even promote directional transport by adjusting other parameters.
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Keywords:
- fractional system /
- asymmetric coupling /
- directional transport /
- generalized stochastic resonance
[1] Fendrik A J, Romanelli L, Reale M V 2012 Phys. Rev. E 85 041149
[2] Zheng Z G 2004 Spantiotemporal 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]
[3] Guérin T, Prost J, Martin P 2010 Current Opinnion in Cell Biology 22 14
[4] Chen H B, Zheng Z G 2012 J. Univ. Shanghai Sci. Technol. 34 6 (in Chinese) [陈宏斌, 郑志刚 2012 上海理工大学学报 34 6]
[5] Savel E S, Marchesoni F, Nori F 2003 Phys. Rev. Lett. 91 10601
[6] Veigel C, Schmidt C F 2011 Nat. Rev. Mol. Cel. Biol. 12 163
[7] Lipowsky R, Klumpp S, Nieuwenhuizen T M 2001 Phys. Rev. Lett. 87 108101
[8] Downton M T, Zuckermann M J, Craig E M, Plischke M, Linke H 2006 Phys. Rev. E 73 011909
[9] Roostalu J, Hetrich C, Bieling P, Telley I A, Schiebel E, Surrey T 2011 Science 332 94
[10] Porto M, Urbakh M, Klafter J 2000 Phys. Rev. Lett. 84 6058
[11] Zheng Z G, Hu G, Hu B 2001 Phys. Rev. Lett. 86 2273
[12] Bao J D 2012 Introduction to Anomalous Statistics Dynamics (Beijing: Science Press) p196 (in Chinese) [包景东 2012 反常统计动力学导论 (北京: 科学出版社) 第196页]
[13] Liu F, Anh V V, Turner I, Zhuang P 2003 J. Appl. Math. Comp. 13 233
[14] Bai W S M, Peng H, Tu Z, Ma H 2012 Acta Phys. Sin. 61 210501 (in Chinese) [白文斯密, 彭皓, 屠浙, 马洪 2012 物理学报 61 210501]
[15] Benson D A, Wheatcraft S W, Meerschaert M M 2000 Water Resour. Res. 36 1403
[16] Tu Z, Peng H, Wang F, Ma H 2013 Acta Phys. Sin. 62 030502 (in Chinese) [屠浙, 彭皓, 王飞, 马洪 2013 物理学报 62 030502]
[17] Lai L, Zhou X X, Ma H, Luo M K 2013 Acta Phys. Sin. 62 150502 (in Chinese) [赖莉, 周薛雪, 马洪, 罗懋康 2013 物理学报 62 150502]
[18] Zhang L, Deng K, Luo M K 2012 Chin. Phys. B 21 090505
[19] Wang F, Deng C, Tu Z, Ma H 2013 Acta Phys. Sin. 62 040501 (in Chinese) [王飞, 邓翠, 屠浙, 马洪 2013 物理学报 62 040501]
[20] 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]
[21] Oldham K B, Spanier J 1974 The Fractional Calculus (New York: Academic Press)
[22] Podlubny I 1998 Fractional Differential Equation (San Diego: Academic Press)
[23] Petrás I 2011 Fractional-Order Nonlinear Systerms Modeling, Analysis and Simulation (1st Ed.) (Beijing: Higher Education Press) p19
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[1] Fendrik A J, Romanelli L, Reale M V 2012 Phys. Rev. E 85 041149
[2] Zheng Z G 2004 Spantiotemporal 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]
[3] Guérin T, Prost J, Martin P 2010 Current Opinnion in Cell Biology 22 14
[4] Chen H B, Zheng Z G 2012 J. Univ. Shanghai Sci. Technol. 34 6 (in Chinese) [陈宏斌, 郑志刚 2012 上海理工大学学报 34 6]
[5] Savel E S, Marchesoni F, Nori F 2003 Phys. Rev. Lett. 91 10601
[6] Veigel C, Schmidt C F 2011 Nat. Rev. Mol. Cel. Biol. 12 163
[7] Lipowsky R, Klumpp S, Nieuwenhuizen T M 2001 Phys. Rev. Lett. 87 108101
[8] Downton M T, Zuckermann M J, Craig E M, Plischke M, Linke H 2006 Phys. Rev. E 73 011909
[9] Roostalu J, Hetrich C, Bieling P, Telley I A, Schiebel E, Surrey T 2011 Science 332 94
[10] Porto M, Urbakh M, Klafter J 2000 Phys. Rev. Lett. 84 6058
[11] Zheng Z G, Hu G, Hu B 2001 Phys. Rev. Lett. 86 2273
[12] Bao J D 2012 Introduction to Anomalous Statistics Dynamics (Beijing: Science Press) p196 (in Chinese) [包景东 2012 反常统计动力学导论 (北京: 科学出版社) 第196页]
[13] Liu F, Anh V V, Turner I, Zhuang P 2003 J. Appl. Math. Comp. 13 233
[14] Bai W S M, Peng H, Tu Z, Ma H 2012 Acta Phys. Sin. 61 210501 (in Chinese) [白文斯密, 彭皓, 屠浙, 马洪 2012 物理学报 61 210501]
[15] Benson D A, Wheatcraft S W, Meerschaert M M 2000 Water Resour. Res. 36 1403
[16] Tu Z, Peng H, Wang F, Ma H 2013 Acta Phys. Sin. 62 030502 (in Chinese) [屠浙, 彭皓, 王飞, 马洪 2013 物理学报 62 030502]
[17] Lai L, Zhou X X, Ma H, Luo M K 2013 Acta Phys. Sin. 62 150502 (in Chinese) [赖莉, 周薛雪, 马洪, 罗懋康 2013 物理学报 62 150502]
[18] Zhang L, Deng K, Luo M K 2012 Chin. Phys. B 21 090505
[19] Wang F, Deng C, Tu Z, Ma H 2013 Acta Phys. Sin. 62 040501 (in Chinese) [王飞, 邓翠, 屠浙, 马洪 2013 物理学报 62 040501]
[20] 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]
[21] Oldham K B, Spanier J 1974 The Fractional Calculus (New York: Academic Press)
[22] Podlubny I 1998 Fractional Differential Equation (San Diego: Academic Press)
[23] Petrás I 2011 Fractional-Order Nonlinear Systerms Modeling, Analysis and Simulation (1st Ed.) (Beijing: Higher Education Press) p19
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