分数阶非对称耦合系统在对称周期势中的定向输运

屠浙; 赖莉; 罗懋康

doi:10.7498/aps.63.120503

摘要

在没有外力且周期势对称的情况下，对非对称耦合粒子链的运动，以具备更强刻画能力的分数阶微积分理论建立了分数阶模型，对其定向输运现象进行针对性研究，采用分数阶差分法进行数值求解并分析系统参数对定向输运速度的影响. 相应仿真表明，分数阶非对称耦合系统在没有外力和噪声驱动的情况下仍能产生定向输运，且输运速度随阶数的增大而增大；当阶数固定时，粒子链平均速度随耦合强度和势垒高度非单调变化；当系统存在噪声时，粒子链平均速度出现了广义随机共振现象，且通过调节其他参数，可使得系统对噪声免疫甚至使噪声促进定向输运.

关键词:

Abstract

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.

Keywords:

作者及机构信息

1.
四川大学数学学院, 成都 610065;

2.
四川大学空天科学与工程学院, 成都 610065

基金项目: 国家自然科学基金（批准号：11171238）资助的课题.

Authors and contacts

1.
College of Mathematics, Sichuan University, Chengdu 610065, China;

2.
College of Aerospace Science and Engineering, Sichuan University, Chengdu 610065, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11171238).

参考文献

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[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 62 030502]
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施引文献

[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 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 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 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 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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