非保守力作用下二维耦合布朗粒子的定向输运

刘艳艳; 孙佳明; 范黎明; 高天附; 郑志刚

doi:10.7498/aps.72.20221741

摘要

本文主要研究二维耦合布朗粒子在非保守外力作用下的定向输运问题. 研究发现, 非保守外力有促进二维耦合棘轮定向输运的效果. 同时, 在保守力(弹簧弹力)和非保守外力的相互协作与竞争中耦合布朗粒子的反向输运能够获得增强. 特别地, 随着弹簧原长或弹性系数的改变, 二维耦合布朗粒子的定向运动都能够产生反向, 这意味着耦合作用能够诱导二维布朗棘轮流反转的产生. 实验上, 通过选取不同种类的外力(保守力及非保守力), 能够对二维耦合布朗粒子的分离技术提供新的方案.

关键词:

Abstract

In recent years, biomolecular motors have received widespread attention. Biomolecular motors are biological macromolecules that convert chemical energy into mechanical energy. The biomolecular motor is only a few tens of nanometers in size. According to Brownian theory of motion, people have constructed different types of Brownian ratchet models, such as rocking ratchets and closed-loop control ratchets. In previous studies, the directional transportation of Brownian ratchet is affected by conservative forces. These conservative forces include constant force, elastic force or harmonic force. However, whether the ratchet system can produce directional motion under the action of non-conservative forces is still rarely studied. Owing to the complex environment in the organism, for the studies of two-dimensional systems, the transport behavior of molecular motor has not been fully explained. Therefore, it is more practical to study the transport of Brownian particles in a two-dimensional ratchet potential.The directional transport of two-dimensional Brownian particles subjected to conservative forces and non-conservative forces are studied in this work. It is found that the non-conservative external force has the effect of promoting the directional transport of coupling ratchets. With the change of the free length of the spring and spring coefficient, the average velocity of the coupled particles can be reversed. This means that the coupling effect can induce the inversion of two-dimensional Brownian ratchets. At the same time, the reverse transportation of coupled particles is enhanced under the interaction effect of conservative forces (spring elasticity) and non-conservative external forces. By choosing different kinds of external forces (conserved and non-conserved), in the experiment, it is possible to provide new method of separating two-dimensional coupled Brownian particles.

Keywords:

作者及机构信息

1.
沈阳师范大学物理科学与技术学院, 沈阳　110034

2.
华侨大学信息科学与工程学院, 厦门　361021

通信作者: 高天附, tianfugao@synu.edu.cn ; 郑志刚, zgzheng@hqu.edu.cn

基金项目: 国家自然科学基金(批准号:11875135, 11347003)、辽宁省高等学校基本科研项目(批准号: LJKMZ20221478)、沈阳师范大学高层次人才支持计划和沈阳师范大学研究生教育教学改革研究一般项目(批准号: YJSJG320210100) 资助的课题

Authors and contacts

1.
College of Physical Science and Technology, Shenyang Normal University, Shenyang 110034, China

2.
College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China

Corresponding author: Gao Tian-Fu, tianfugao@synu.edu.cn ; Zheng Zhi-Gang, zgzheng@hqu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11875135, 11347003), Basic Scientific Research Project of Colleges in Liaoning Province, China (Grant No. LJKMZ20221478), the High-level Talent Support Program of Shenyang Normal University, China, and the Postgraduate Education Reform Project of Shenyang Normal University, China (Grant No. YJSJG320210100).

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参考文献

[1]	舒咬根, 欧阳钟灿 2007 自然杂志 5 249 Google Scholar Shu Y G, Ouyang Z C 2007 Chin. J. Nat. 5 249 Google Scholar
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施引文献

图 1 二维棘轮外势$ V(x, y) $的结构示意图

Fig. 1. The schematic diagram of two-dimensional ratchet potential $ V(x, y) $.

下载: 全尺寸图片幻灯片

图 2 非保守外力$ {F_x} $和$ {F_y} $的结构示意图, 非保守力参量$ a = 0.4 $

Fig. 2. The schematic diagram of non-conservative forces $ {F_x} $ and $ {F_y} $, where non-conservative force parameter $ a = 0.4 $.

下载: 全尺寸图片幻灯片

图 3 不同弹簧原长$ L $下平均速度$ \left\langle {{V_x}} \right\rangle $随非保守力参数$ a $的变化曲线, 其中$ D = 0.1 $, $ k = 2 $

Fig. 3. The curves of the mean velocity $ \left\langle {{V_x}} \right\rangle $ varying with the non-conservative force parameter $ a $ under different original length of the spring L, where $ D = 0.1 $, $ k = 2 $.

下载: 全尺寸图片幻灯片

图 4 非保守力$ {F_x} $随参数$ a $的变化曲线

Fig. 4. The curve of the non-conservative force $ {F_x} $ varying with the parameter $ a $.

下载: 全尺寸图片幻灯片

图 5 不同噪声强度$ D $下平均速度$ \left\langle {{V_x}} \right\rangle $随弹簧原长$ L $的变化曲线, 其中$ a = 0.4 $, $ k = 2 $

Fig. 5. The curves of the mean velocity $ \left\langle {{V_x}} \right\rangle $ varying with the original length of the spring $ L $ under different noise intensity $ D $, where $ a = 0.4 $, $ k = 2 $.

下载: 全尺寸图片幻灯片

图 6 耦合粒子的位置随时间演化图像, 其中$ a = 0.4 $, $ k = 2 $, $ L = 3.5 $, $ D = 0.1 $

Fig. 6. Trajectories for the coupled particles as a function of time, where $ a = 0.4 $, $ k = 2 $, $ L = 3.5 $, $ D = 0.1 $.

下载: 全尺寸图片幻灯片

图 7 不同耦合强度下平均速度$ \left\langle {{V_x}} \right\rangle $随热噪声$ D $的变化曲线, 其中$ a = 0.4 $, $ L = 1 $

Fig. 7. The curves of the mean velocity $ \left\langle {{V_x}} \right\rangle $ varying with the noise $ D $ under different coupling strength, where $ a = 0.4 $, $ L = 1 $.

下载: 全尺寸图片幻灯片

图 8 不同非保守外力参量$ a $下平均速度$ \left\langle {{V_x}} \right\rangle $随弹性系数$ k $的变化曲线, 其中$ D = 0.1 $, $ L = 1 $

Fig. 8. The curves of the mean velocity $ \left\langle {{V_x}} \right\rangle $ varying with the spring coefficient $ k $ under different non-conservative force parameter $ a $, where $ D = 0.1 $, $ L = 1 $.

下载: 全尺寸图片幻灯片

图 9 耦合粒子的位置随时间演化图像, 其中$ a = 0.3 $, $ k = 0.3 $, $ L = 1 $, $ D = 0.1 $

Fig. 9. Trajectories for the coupled particles as a function of time, where $ a = 0.3 $, $ k = 0.3 $, $ L = 1 $, $ D = 0.1 $.

下载: 全尺寸图片幻灯片

[1]	舒咬根, 欧阳钟灿 2007 自然杂志 5 249 Google Scholar Shu Y G, Ouyang Z C 2007 Chin. J. Nat. 5 249 Google Scholar
[2]	舒咬根, 欧阳钟灿 2007 物理 10 735 Google Scholar Shu Y G, Ouyang Z C 2007 Physics 10 735 Google Scholar
[3]	国家自然科学基金委员会, 中国科学院 2020 中国学科发展战略·软凝聚态物理学(下) (北京: 科学出版社) 第1037页 National Natural Science Foundation of China, Chinese Academy of Sciences 2020 Chinese Subject Development Strategy · Soft Condensed Matter Physics (Part 2) (Beijing: Science Press) p1037 (in Chinese)
[4]	Wu J, Zhou J, Ai B 2016 Physica A 462 864 Google Scholar
[5]	耿轶钊, 晏世伟 2016 物理学进展 36 157 Google Scholar Geng Y Z, Yan S W 2016 Prog. Phys. 36 157 Google Scholar
[6]	卓益忠, 赵同军, 展永 2000 物理 12 712 Google Scholar Zhuo Y Z, Zhao T J, Zhan Y 2000 Physics 12 712 Google Scholar
[7]	舒咬根 2004 博士学位论文 (厦门: 厦门大学) Shu Y G 2004 Ph. D. Dissertation (Xiamen: Xiamen University) (in Chinese)
[8]	刘芳 2011 硕士学位论文 (秦皇岛: 燕山大学) Liu F 2011 M. S. Thesis (Qinhuangdao: Yanshan University) (in Chinese)
[9]	Van den Heuvel M G L, Dekker C 2007 Science 317 333 Google Scholar
[10]	Bartussek R, Hänggi P, Kissner J G 1994 Eur. Phys. Lett. 28 459 Google Scholar
[11]	Zhang H W, Wen S T, Zhang H T, Li Y X, Chen G R 2012 Chin. Phys. B 21 078701 Google Scholar
[12]	Bao J D, Zhuo Y Z 1998 Phys. Lett. A 239 228 Google Scholar
[13]	Doering C R 1995 Il Nuovo Cimento D 17 685 Google Scholar
[14]	Bartussek R, Reimann P, Hänggi P 1996 Phys. Rev. Lett. 76 1166 Google Scholar
[15]	Gao T F, Chen J C 2009 J. Phys. A: Math. Theor. 42 065002 Google Scholar
[16]	吴魏霞, 郑志刚 2013 物理学报 62 135 Google Scholar Wu W X, Zheng Z G 2013 Acta Phys. Sin. 62 135 Google Scholar
[17]	吴魏霞, 宋艳丽, 韩英荣 2015 物理学报 64 17 Google Scholar Wu W X, Song Y L, Han Y R 2015 Acta Phys. Sin. 64 17 Google Scholar
[18]	谢天婷, 邓科, 罗懋康. 2016 物理学报 65 7 Google Scholar Xie T T, Deng K, Luo M K 2016 Acta Phys. Sin. 65 7 Google Scholar
[19]	刘红梅, 汪瑜 2014 物理通报 10 129 Google Scholar
[20]	马文蔚 2008 物理学(上册) 第五版 (北京: 高等教育出版社) 第75页
[21]	Tomé T 2010 Phys. Rev. E 82 021120 Google Scholar
[22]	Tomé T 2006 Braz. J. Phys. 36 1285 Google Scholar
[23]	Ai B Q, Chen Q Y, He Y F, Li F G, Zhong W R 2013 Phys. Rev. E 88 062129 Google Scholar
[24]	Li C P, Chen H B, Zheng Z G 2017 Front. Phys. 12 1 Google Scholar
[25]	Romanczuk P, Müller F, Schimansky-Geier L 2010 Phys. Rev. E 81 061120 Google Scholar
[26]	Wang H Y, Bao J D 2007 Physica A 374 33 Google Scholar
[27]	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 Google Scholar
[28]	Hill D B, Plaza M J, Bonin K, Holzwarth G 2004 Eur. Biophys. J 33 623 Google Scholar
[29]	Mallik R, Petrov D, Lex S A, King S J, Gross S P 2005 Curr. Biol. 15 2075 Google Scholar
[30]	Bao J D 2001 Phys. Rev. E 63 061112 Google Scholar
[31]	Ai B 2017 Phys. Rev. E 96 012131 Google Scholar
[32]	Luo Y H, Zeng C H, Ai B Q 2020 Phys. Rev. E 102 042114 Google Scholar
[33]	He Y F, Ai B Q, Dai C X 2020 Phys. Rev. Lett. 124 075001 Google Scholar

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非保守力作用下二维耦合布朗粒子的定向输运