二维势场中弹性耦合粒子的定向输运研究

吴魏霞; 郑志刚

doi:10.7498/aps.62.190511

摘要

建立了二维势场中弹性耦合粒子的输运模型, 其中一维上加交流驱动及噪声, 另一维上不加驱动及噪声, 分析讨论了过阻尼情形下系统和外部参量对定向流的影响. 结果表明, 粒子可以通过相互耦合使一个方向上输入的驱动能量转化到垂直方向上, 从而使无能量输入的方向产生定向流. 适当的弹簧自由长度及耦合强度可以使定向流达到极值, 特别是当耦合强度及噪声强度固定时, 定向流会随弹簧自由长度的变化而振荡, 出现多峰现象. 研究还发现, 定向流随噪声强度的变化出现随机共振现象. 当产生定向流方向上的势的不对称度达到一定程度时会出现流反转现象.

关键词:

Abstract

A transport model of elastically coupled particles in a two-dimensional potential is investigated. Here, we propose that one dimension of the model is exerted by an AC drive and an external noise, and the other dimension by neither AC drive nor external noise. The effects of system and external parameters on the directed current under an overdamped case are discussed. The studies show that particles can transfer energy from one direction to its perpendicular direction through coupling, thereby producing a directed current. There is an optimal value of the spring free length or the coupling intensity at which the directed current can reach a maximum. For a fixed coupling intensity or noise intensity, the directed current will oscillate as the free length of spring varies, that is, multiple peaks appear. Moreover, a stochastic resonance appears in the directed current as noise intensity varies. Finally, when the degree of asymmetry of the ratchet potential achieves a maximum value, the current reversion takes place.

Keywords:

作者及机构信息

吴魏霞¹,
郑志刚²

1.
北京印刷学院基础部, 北京 102600;

2.
北京师范大学物理学系, 北京 100875

基金项目: 北京市教育委员会科技计划(批准号:KM201110015004);北京市属高等学校人才强教深化计划(批准号:PHR201108353);北京市优秀人才培养资助项目(批准号:2012D005004000005);国家自然科学基金(批准号:11075016)和高等学校博士学科点专项科研基金(批准号:20100003110007)资助的课题.

Authors and contacts

Wu Wei-Xia¹,
Zheng Zhi-Gang²

1.
Science Education Department, Beijing Institute of Graphic Communication, Beijing 102600, China;

2.
Department of Physics, Beijing Normal University, Beijing 100875, China

Funds: Project supported by the Science and Technology Project of Beijing Municipal Education Commission, China (Grant No. KM201110015004), the Funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality, China (Grant No. PHR201108353), the Foundation of cultivating talents in Beijing City, China (Grant No. 2012D005004000005), the National Natural Science Foundation of China (Grant No. 11075016), and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20100003110007).

参考文献

[1]	Schnitzer M J, Block S M 1997 Nature 388 386
[2]	Asbury C L, Fehr A N, Block S M 2003 Science 302 2130
[3]	Coy D L, Wagenbach M, Howard J 1999 J. Biol. Chem. 274 3667
[4]	Zheng Z G 2004 Spatiotemporal Dynamics and Collective Behaviors in Coupled Nonlinear Systems (Beijing: Higher Education Press) p278 (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278页]
[5]	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]
[6]	Bao J D 2009 Stochastic Simulation Method of Classic and Quantum Dissipative Sysmtem (Beijing: Science Press) p160 (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160页]
[7]	Gehlen S V, Evstigneev M, Reimann P 2009 Phys. Rev. E 79 031114
[8]	Astumian R D 1997 Science 176 917
[9]	Li W, Guo H Y, Ji Q, Zhan Y, Zhao T J 2004 Acta Phys. Sin. 53 3684 (in Chinese) [李微, 郭鸿涌, 纪青, 展永, 赵同军 2004 53 3684]
[10]	Shubeita G T, Tran S L, Xu J, Vershinin M, Cermelli S, Cotton S L, Welte M A, Gross S P 2008 Cell 135 1098
[11]	Mallik R, Petrov D, Lex S A, King S J, Gross S P 2005 Curr Biol. 15 2075
[12]	Hill D B, Plaza M J, Bonin K, Holzwarth G 2004 Eur Biophys J. 33 623
[13]	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]
[14]	Wang L F, Gao T F, Huang R Z, Zheng Y X 2013 Acta Phys. Sin. 62 070502 (in Chinese) [王莉芳, 高天附, 黄仁忠, 郑玉祥 2013 62 070502]
[15]	Zheng Z G, Liu F Z, Gao J 2003 Chin. Phys. 12 846
[16]	Zhang H W, Wen S T, Chen G R, Li Y X, Cao Z X, Li W 2012 Chin. Phys. B 21 038701
[17]	Xie P, Dou S X, Wang P Y 2004 Chin. Phys. 13 1569
[18]	Avik W G, Sanjay V K 2000 Phys. Rev. Lett. 84 5243
[19]	Bao J D, Zhuo Y Z 1998 Phys. Lett. A 239 228
[20]	Chen H B 2006 The Cooperative Transport in Deterministic Ratchets (Beijing: Beijing Normal University) [陈宏斌 2006 博士学位论文 (北京: 北京师范大学)]
[21]	Zheng Z G, Chen H B 2010 Europhys. Lett. 92 30004
[22]	Schott D H, Collins R N, Bretscher A 2002 J. Cell Biol. 156 35
[23]	Sakamoto T, Yildiz A, Selvin P R, Sellers J R 2005 Biochemistry 44 16203
[24]	Zhou C, Kurths J, Hu B 2001 Phys. Rev. Lett. 87 098101

施引文献

[1]	Schnitzer M J, Block S M 1997 Nature 388 386
[2]	Asbury C L, Fehr A N, Block S M 2003 Science 302 2130
[3]	Coy D L, Wagenbach M, Howard J 1999 J. Biol. Chem. 274 3667
[4]	Zheng Z G 2004 Spatiotemporal Dynamics and Collective Behaviors in Coupled Nonlinear Systems (Beijing: Higher Education Press) p278 (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278页]
[5]	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]
[6]	Bao J D 2009 Stochastic Simulation Method of Classic and Quantum Dissipative Sysmtem (Beijing: Science Press) p160 (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160页]
[7]	Gehlen S V, Evstigneev M, Reimann P 2009 Phys. Rev. E 79 031114
[8]	Astumian R D 1997 Science 176 917
[9]	Li W, Guo H Y, Ji Q, Zhan Y, Zhao T J 2004 Acta Phys. Sin. 53 3684 (in Chinese) [李微, 郭鸿涌, 纪青, 展永, 赵同军 2004 53 3684]
[10]	Shubeita G T, Tran S L, Xu J, Vershinin M, Cermelli S, Cotton S L, Welte M A, Gross S P 2008 Cell 135 1098
[11]	Mallik R, Petrov D, Lex S A, King S J, Gross S P 2005 Curr Biol. 15 2075
[12]	Hill D B, Plaza M J, Bonin K, Holzwarth G 2004 Eur Biophys J. 33 623
[13]	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]
[14]	Wang L F, Gao T F, Huang R Z, Zheng Y X 2013 Acta Phys. Sin. 62 070502 (in Chinese) [王莉芳, 高天附, 黄仁忠, 郑玉祥 2013 62 070502]
[15]	Zheng Z G, Liu F Z, Gao J 2003 Chin. Phys. 12 846
[16]	Zhang H W, Wen S T, Chen G R, Li Y X, Cao Z X, Li W 2012 Chin. Phys. B 21 038701
[17]	Xie P, Dou S X, Wang P Y 2004 Chin. Phys. 13 1569
[18]	Avik W G, Sanjay V K 2000 Phys. Rev. Lett. 84 5243
[19]	Bao J D, Zhuo Y Z 1998 Phys. Lett. A 239 228
[20]	Chen H B 2006 The Cooperative Transport in Deterministic Ratchets (Beijing: Beijing Normal University) [陈宏斌 2006 博士学位论文 (北京: 北京师范大学)]
[21]	Zheng Z G, Chen H B 2010 Europhys. Lett. 92 30004
[22]	Schott D H, Collins R N, Bretscher A 2002 J. Cell Biol. 156 35
[23]	Sakamoto T, Yildiz A, Selvin P R, Sellers J R 2005 Biochemistry 44 16203
[24]	Zhou C, Kurths J, Hu B 2001 Phys. Rev. Lett. 87 098101

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