非对称耦合粒子链在棘齿势中的确定性定向输运

季袁冬; 屠浙; 赖莉; 罗懋康

doi:10.7498/aps.64.070501

摘要

针对不受外力和噪声驱动的非对称耦合粒子链在棘齿势中的运动, 建立了相应的数学模型, 并对其确定性定向输运现象进行研究. 仿真结果表明: 在粒子间的非对称耦合和具有空间反演非对称的棘齿势的共同作用下, 粒子链能够产生定向输运现象, 并在适当参数条件下还能形成反向定向流; 粒子链平均速度关于耦合系数、势垒高度、弹簧自由长度等系统参数分别都存在广义共振现象, 即存在最佳参数使得定向输运速度达到最大; 在其他参数固定的情况下, 粒子链平均速度关于弹簧自由长度变化的曲线具有近似反对称的特点, 并存在广义多峰共振现象.

关键词:

Abstract

In the absence of external force and noise, a deterministic transport model for asymmetrically coupled nonlinear oscillators in a ratchet potential is established. By numerical simulation, both directed current and reversely directed current can be obtained by selecting appropriate parameters. The complex dependences of current velocity on the model parameters are discussed. It is observed that the average velocity of the particle chain varies non-monotonically with coupling strength and potential height, indicating a generalized resonance phenomenon. When the other parameters are fixed, the speed curve which is dependent on spring free length has a roughly inverse symmetry, and there also exists a generalized multi-peak resonance.

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)和电子信息控制重点实验室项目(批准号: 2013035) 资助的课题.

Authors and contacts

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

2.
School of Aeronautics and Astronautics, Sichuan University, Chengdu 610065, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11171238), and the Foundation of Science and Technology on Electronic Information Control Laboratory, China (Grant No. 2013035).

参考文献

[1]	Fendrik A J, Romanelli L, Reale M V 2012 Phys. Rev. E 85 041149
[2]	Zhang H W, Wen S T, Chen G R, Li Y X, Cao Z X, Li W 2012 Chin. Phys. B 21 038701
[3]	Zhao A K, Zhang H W, Liu Y X 2010 Chin. Phys. B 19 110506
[4]	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]
[5]	Zheng Z G 2004 Spantiotemporal Dynamics and Collective Behaviors in Coupled Nonlinear Systems (Beijing:Higher Education Press) p279, 292 (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, 292页]
[6]	Chen H B, Zheng Z G 2012 J. Univ.Shanghai for Science and Technology 34 6 (in Chinese) [陈宏斌, 郑志刚 2012 上海理工大学学报 34 6]
[7]	Tu Z, Lai L, Luo M K 2014 Acta Phys. Sin. 63 120503 (in Chinese) [屠浙, 赖莉, 罗懋康 2014 物理学报 63 120503]
[8]	Guérin T, Prost J, Martin P 2010 Current Opinnion in Cell Biology 22 14
[9]	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]
[10]	Savel E S, Marchesoni F, Nori F 2003 Phys. Rev. Lett. 91 10601
[11]	Veigel C, Schmidt C F 2011 Nat. Rev. Mol. Cel. Biol. 12 163
[12]	Lipowsky R, Klumpp S, Nieuwenhuizen T M 2001 Phys. Rev. Lett. 87 108101
[13]	Roostalu J, Hetrich C, Bieling P, Telley I A, Schiebel E, Surrey T 2011 Science 332 94
[14]	Downton M T, Zuckermann M J, Craig E M, Plischke M, Linke H 2006 Phys. Rev. E 73 011909
[15]	Beeg J, Klumpp S, Dimova R, Gracia R S, Unger E, Lipowsky R 2008 Biophys. J. 94 532

施引文献

[1]	Fendrik A J, Romanelli L, Reale M V 2012 Phys. Rev. E 85 041149
[2]	Zhang H W, Wen S T, Chen G R, Li Y X, Cao Z X, Li W 2012 Chin. Phys. B 21 038701
[3]	Zhao A K, Zhang H W, Liu Y X 2010 Chin. Phys. B 19 110506
[4]	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]
[5]	Zheng Z G 2004 Spantiotemporal Dynamics and Collective Behaviors in Coupled Nonlinear Systems (Beijing:Higher Education Press) p279, 292 (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, 292页]
[6]	Chen H B, Zheng Z G 2012 J. Univ.Shanghai for Science and Technology 34 6 (in Chinese) [陈宏斌, 郑志刚 2012 上海理工大学学报 34 6]
[7]	Tu Z, Lai L, Luo M K 2014 Acta Phys. Sin. 63 120503 (in Chinese) [屠浙, 赖莉, 罗懋康 2014 物理学报 63 120503]
[8]	Guérin T, Prost J, Martin P 2010 Current Opinnion in Cell Biology 22 14
[9]	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]
[10]	Savel E S, Marchesoni F, Nori F 2003 Phys. Rev. Lett. 91 10601
[11]	Veigel C, Schmidt C F 2011 Nat. Rev. Mol. Cel. Biol. 12 163
[12]	Lipowsky R, Klumpp S, Nieuwenhuizen T M 2001 Phys. Rev. Lett. 87 108101
[13]	Roostalu J, Hetrich C, Bieling P, Telley I A, Schiebel E, Surrey T 2011 Science 332 94
[14]	Downton M T, Zuckermann M J, Craig E M, Plischke M, Linke H 2006 Phys. Rev. E 73 011909
[15]	Beeg J, Klumpp S, Dimova R, Gracia R S, Unger E, Lipowsky R 2008 Biophys. J. 94 532

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