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分数阶布朗马达在闪烁棘齿势中的合作输运现象

赖莉 周薛雪 马洪 罗懋康

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分数阶布朗马达在闪烁棘齿势中的合作输运现象

赖莉, 周薛雪, 马洪, 罗懋康

Transport properties of fractional coupled Brownian motors in flash ratchet potential

Lai Li, Zhou Xue-Xue, Ma Hong, Luo Mao-Kang
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  • 引入分数阶微积分理论,建立耦合分数阶布朗马达在闪烁棘齿势中的合作输运模型, 利用分数阶差分法求得模型数值解并分析了模型参数对合作定向输运性质的影响. 发现在具有记忆性的分数阶棘齿系统中, 系统阶数与粒子间耦合强度不仅可影响粒子链输运速度, 还可使粒子链出现与整数阶方向相反的定向流; 在阶数固定下, 定向输运速度将随参数(噪声强度、耦合强度、棘齿势峰值高度)变化出现广义随机共振现象.
    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.
    • 基金项目: 国家自然科学基金(批准号: 11171238)资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11171238).
    [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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    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

  • [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

计量
  • 文章访问数:  4878
  • PDF下载量:  514
  • 被引次数: 0
出版历程
  • 收稿日期:  2013-01-20
  • 修回日期:  2013-04-10
  • 刊出日期:  2013-08-05

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