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Based on the fractional calculus theory, the transport model of fractional coupled Brownian motors in flashing ratchet potential is established. Using the fractional difference, the numerical solution of the model is obtained, and the directional transport properties at various parameters are investigated. Numerical results show that in fractional ratchet system, the fractional order and spring constant not only affect the transport velocity of the particles, but also reverse the current direction. Moreover, when the fractional order is fixed, the generalized stochastic resonance phenomena are observed in the mean transport velocity as the noise density, spring constant or the depth of the ratchet potential varies.
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Keywords:
- fractional Brownian motors /
- flashing ratchet potential /
- coupled directed transport /
- generalized stochastic resonance
[1] Zheng Z G 2004 Spantiotemporal Dynamics and Collective Behaviors in Coupled Nonlinear Systems (Beijing: Higher Education Press) p276 (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276页]
[2] Riemann P 2002 Phys. Rep. 361 57
[3] Kay E R, Leigh D A, Zerbetto F 2007 Angew. Chem. Int. Ed. 46 72
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[5] Souza S, Van V J, Morelle M 2006 Nature 440 651
[6] Igarashi A, Tsukamoto S, Goko H 2001 Phys. Rev. E 64 051908
[7] Wang H Y, Bao J D 2004 Physica A 337 13
[8] Wang H Y, Bao J D 2005 Physica A 357 373
[9] Ai B Q, He Y F, Zhong W R 2011 Phys. Rev. E 83 051106
[10] Chen H B, Zheng Z G 2011 Mod. Phys. Lett. B 25 1179
[11] Bao J D 2003 Phys. Lett. A 314 203
[12] Guo H Y, Li W, Ji Q, Zhan Y, Zhao T J 204 Acta Phys. Sin. 53 3684 (in Chinese) [郭鸿涌, 李微, 纪青, 展永, 赵同军 2004 物理学报 53 3684]
[13] Cheng H T, He J Z, Xiao Y L 2012 Acta Phys. Sin. 61 010502 (in Chinese) [程海涛, 何济洲, 肖宇玲 2012 物理学报 61 010502]
[14] 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]
[15] 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]
[16] Gitterman M 2005 Phys. Stat. Mech. Appl. 352 309
[17] 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]
[18] Oldham K B, Spanier J 1974 The Fractional Calculus (New York, Academic Press)
[19] 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]
[20] Podlubny I 1998 Fractional Differential Equation (San Diego: Academic Press)
[21] Petrás I 2011 Fractional-Order Nonlinear Systerms Modeling, Analysis and Simulation (1st Ed.) (Beijing: Higher Education Press) p19
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[1] Zheng Z G 2004 Spantiotemporal Dynamics and Collective Behaviors in Coupled Nonlinear Systems (Beijing: Higher Education Press) p276 (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276页]
[2] Riemann P 2002 Phys. Rep. 361 57
[3] Kay E R, Leigh D A, Zerbetto F 2007 Angew. Chem. Int. Ed. 46 72
[4] Jlicher F, Ajdari A,Prost J 1997 Rev. Mod. Phys. 69 1269
[5] Souza S, Van V J, Morelle M 2006 Nature 440 651
[6] Igarashi A, Tsukamoto S, Goko H 2001 Phys. Rev. E 64 051908
[7] Wang H Y, Bao J D 2004 Physica A 337 13
[8] Wang H Y, Bao J D 2005 Physica A 357 373
[9] Ai B Q, He Y F, Zhong W R 2011 Phys. Rev. E 83 051106
[10] Chen H B, Zheng Z G 2011 Mod. Phys. Lett. B 25 1179
[11] Bao J D 2003 Phys. Lett. A 314 203
[12] Guo H Y, Li W, Ji Q, Zhan Y, Zhao T J 204 Acta Phys. Sin. 53 3684 (in Chinese) [郭鸿涌, 李微, 纪青, 展永, 赵同军 2004 物理学报 53 3684]
[13] Cheng H T, He J Z, Xiao Y L 2012 Acta Phys. Sin. 61 010502 (in Chinese) [程海涛, 何济洲, 肖宇玲 2012 物理学报 61 010502]
[14] 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]
[15] 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]
[16] Gitterman M 2005 Phys. Stat. Mech. Appl. 352 309
[17] 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]
[18] Oldham K B, Spanier J 1974 The Fractional Calculus (New York, Academic Press)
[19] 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]
[20] Podlubny I 1998 Fractional Differential Equation (San Diego: Academic Press)
[21] Petrás I 2011 Fractional-Order Nonlinear Systerms Modeling, Analysis and Simulation (1st Ed.) (Beijing: Higher Education Press) p19
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