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二维非对称周期时移波状通道中的粒子定向输运问题

谢天婷 邓科 罗懋康

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二维非对称周期时移波状通道中的粒子定向输运问题

谢天婷, 邓科, 罗懋康

Direct transport of particles in two-dimensional asymmetric periodic time-shift corrugated channel

Xie Tian-Ting, Deng Ke, Luo Mao-Kang
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  • 目前大部分关于通道中粒子的输运问题是在静态边界的情形下研究的,但时变通道中的粒子输运问题的研究显然具有重要价值和意义. 为此,本文讨论了二维非对称周期时移波状通道中的粒子定向输运问题,详细分析了该模型的输运机理,利用数值仿真讨论了输运速度与通道参数和噪声强度的关系. 研究发现,通道沿延伸方向的非对称周期时移会使粒子位置分布在通道横截方向上表现出非对称性,粒子总体在通道延伸方向会表现出定向输运流. 定向流平均速度与通道对称参数成正比例关系,随通道宽度的增加而递减,随通道空间频率及时间频率变化均会出现广义共振现象;随着噪声强度的增加,定向流速度会先增大后减小,即适当的噪声可以增强系统的输运行为.
    Studies on direct transport of particles not only attribute to understand many processes in the fields of biology, physics, chemistry, etc., but also to provide suitable methods to artificially control particles and micro-devices. In recent decades, direct transport in channels has aroused the interest of an increasing number of researchers. However, the current researches on direct transports in channels mainly focus on static boundary situations. Considering the fact that the time-variable channels exist widely in reality, the corresponding studies in time-variable channels are of distinct value and significance. Therefore, in this paper, direct transport of particles in two-dimensional (2D) asymmetric periodic time-shift corrugated channel is discussed. Firstly, the corresponding Langevin equation describing the motion of particles in a 2D time-shift corrugated channel is established. The channel discussed here is periodic and symmetric in space but follows a periodic and asymmetric time-shift law. Secondly, the transport mechanism and properties of the above model are analyzed by numerical simulation. The average velocity of particles is chosen to evaluate the transport performance. The relationships between the average velocity and typical systematic parameters are discussed in detail. According to the research, the transport mechanism is analyzed as follows. The asymmetric shift of the channel along the longitudinal direction will cause the distribution disparity of particles along the section direction, which can influence the bound effect of the channel on the motion of particles. Specifically, higher concentration of the particles along the section direction implies weaker bound effect of the channel walls, and vice versa. As a result, the particles exhibit different diffusive behaviors along the positive and negative longitudinal directions, thus inducing a direct current. By investigating the relationships between the average velocity and typical systematic parameters, the conclusions are derived as follows. 1) The average current velocity is proportional to the asymmetric degree of channel since increasing asymmetric degree can increase the bound effect disparity, and thus promoting the direct transport behavior. 2) Higher temporal frequency can increase the directional impetus number in a certain period of time, but makes the distribution of particles more concentrated simultaneously. The competition between these two effects leads to generalized resonance transport behavior as the temporal frequency varies. 3) Wider channels allow particles to diffuse freely in larger space. Therefore, as the channel width increases, the bound effect is weakened and the direct transport is hindered, resulting in a decline in average velocity of particles. 4) The average current velocity exhibits generalized resonance behavior as the spatial frequency varies, which is caused by the competition between the diffusion scale of particle and the spatial period of channel. 5) With the growth of the noise intensity, the current velocity will first increase and then decrease, which means that adding proper noise to the system can enhance the direct transport phenomenon.
      通信作者: 罗懋康, makaluo@scu.edu.cn
    • 基金项目: 国家自然科学基金青年科学基金(批准号:11301361)资助的课题.
      Corresponding author: Luo Mao-Kang, makaluo@scu.edu.cn
    • Funds: Project supported by the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 11301361).
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    Locatelli E, Baldovin F, Orlandini E, Pierrno M 2015 Phys. Rev. E 91 022109

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    Ai B Q, Shao Z G, Zhong W R {2012 J. Chem. Phys. 137 174101

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    Reguera D, Rubi J M 2001 Phys. Rev. E 64 061106

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    Reguera D, Schmid G, Burada P S, Rubi J M, Reimann P, Hanggi P 2006 Phys. Rev. Lett. 96 130603

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    Malgaretti P, Pagonabarraga I, Rubi J M 2013 J. Chem. Phys. 138 194906

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    Ai B Q, Wu J C 2014 J. Chem. Phys. 140 094103

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    Fleishman D, Filippov A E, Urbakh M 2004 Phys. Rev. E 69 011908

    [30]

    Popov V L, Filippov A E 2008 Phys. Rev. E 77 021114

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    Ai B Q 2009 J. Chem. Phys. 131 054111

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    Ding H, Jiang H J, Hou Z H 2015 J. Chem. Phys. 143 244119

    [33]

    Brenk M, Bungartz H J, Mehl M, Muntean I L, Neckel T, Weinzierl T 2008 SIAM Conference on Computational Science and Engineering Costa Mesa, CA February 19-23, 2007 p2777

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    Duke T A J, Austin R H {1998 Phys. Rev. Lett. 80 1552

    [35]

    Derenyi I, Astumian R D 1998 Phys. Rev. E 58 7781

  • [1]

    Reimann P 2002 Phys. Rep. 361 57

    [2]

    Astumian R D 1997 Science 276 917

    [3]

    Parrondo J M R, De Cisneros B J 2002 Appl. Phys. A 75 179

    [4]

    Astumian R D, Hanggi P {2002 Physics. Today 55 33

    [5]

    Ai B Q, He Y F, Zhong W R 2011 Phys. Rev. E 83 051106

    [6]

    Zhang H W, Wen S T, Zhang H T, Li Y X, Chen G R 2012 Chin. Phys. B 21 078701

    [7]

    Gao T F, Liu F S, Chen J C 2012 Chin. Phys. B 21 020502

    [8]

    Hanggi P, Marchesoni F 2009 Rev. Mod. Phys. 81 387

    [9]

    Li F G, Xie H Z, Liu X M, Ai B Q 2015 Chaos 25 033110

    [10]

    Wu J C, Chen Q, Wang R, Ai B Q 2015 Physica A 428 273

    [11]

    Jung P, Kissner J G, Hanggi P 1996 Phys. Rev. Lett. 76 3436

    [12]

    Flach S, Yevtushenko O, Zolotaryuk Y 2000 Phys. Rev. Lett. 84 11

    [13]

    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]

    [14]

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    [15]

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    [16]

    Ai B Q, He Y F 2010 J. Chem. Phys. 132 094504

    [17]

    Ai B Q, He Y F, Zhong W R 2010 Phys. Rev. E 82 061102

    [18]

    Zwanzig R 1992 J. Chem. Phys. 97 3587

    [19]

    Berezhkovskii A M, Dagdug L, Bezrukov S M 2015 J. Chem. Phys. 142 134101

    [20]

    Wang X L, Drazer G 2015 J. Chem. Phys. 142 154114

    [21]

    Alvarez-Ramirez J, Dagdug L, Inzunza L 2014 Physica A 410 319

    [22]

    Chen Q, Ai B Q, Xiong J W 2014 Chaos 24 033119

    [23]

    Locatelli E, Baldovin F, Orlandini E, Pierrno M 2015 Phys. Rev. E 91 022109

    [24]

    Ai B Q, Shao Z G, Zhong W R {2012 J. Chem. Phys. 137 174101

    [25]

    Reguera D, Rubi J M 2001 Phys. Rev. E 64 061106

    [26]

    Reguera D, Schmid G, Burada P S, Rubi J M, Reimann P, Hanggi P 2006 Phys. Rev. Lett. 96 130603

    [27]

    Malgaretti P, Pagonabarraga I, Rubi J M 2013 J. Chem. Phys. 138 194906

    [28]

    Ai B Q, Wu J C 2014 J. Chem. Phys. 140 094103

    [29]

    Fleishman D, Filippov A E, Urbakh M 2004 Phys. Rev. E 69 011908

    [30]

    Popov V L, Filippov A E 2008 Phys. Rev. E 77 021114

    [31]

    Ai B Q 2009 J. Chem. Phys. 131 054111

    [32]

    Ding H, Jiang H J, Hou Z H 2015 J. Chem. Phys. 143 244119

    [33]

    Brenk M, Bungartz H J, Mehl M, Muntean I L, Neckel T, Weinzierl T 2008 SIAM Conference on Computational Science and Engineering Costa Mesa, CA February 19-23, 2007 p2777

    [34]

    Duke T A J, Austin R H {1998 Phys. Rev. Lett. 80 1552

    [35]

    Derenyi I, Astumian R D 1998 Phys. Rev. E 58 7781

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出版历程
  • 收稿日期:  2016-04-17
  • 修回日期:  2016-05-28
  • 刊出日期:  2016-08-05

二维非对称周期时移波状通道中的粒子定向输运问题

  • 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
  • 通信作者: 罗懋康, makaluo@scu.edu.cn
    基金项目: 国家自然科学基金青年科学基金(批准号:11301361)资助的课题.

摘要: 目前大部分关于通道中粒子的输运问题是在静态边界的情形下研究的,但时变通道中的粒子输运问题的研究显然具有重要价值和意义. 为此,本文讨论了二维非对称周期时移波状通道中的粒子定向输运问题,详细分析了该模型的输运机理,利用数值仿真讨论了输运速度与通道参数和噪声强度的关系. 研究发现,通道沿延伸方向的非对称周期时移会使粒子位置分布在通道横截方向上表现出非对称性,粒子总体在通道延伸方向会表现出定向输运流. 定向流平均速度与通道对称参数成正比例关系,随通道宽度的增加而递减,随通道空间频率及时间频率变化均会出现广义共振现象;随着噪声强度的增加,定向流速度会先增大后减小,即适当的噪声可以增强系统的输运行为.

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