空时非对称分数阶类Langevin棘齿

周兴旺; 林丽烽; 马洪; 罗懋康

doi:10.7498/aps.63.160503

摘要

研究了空时非对称分数阶类Langevin分子马达棘齿模型，其中势函数是空间对称破缺的周期势，时间非对称类Langevin噪声由Logistic映射生成，而分数阶则刻画了分子马达工作环境的非理想程度. 通过将模型转化为离散映射，即研究其整时间点情形，数值模拟了噪声的时间非对称性、势函数的空间非对称性以及分数阶对模型定向输运行为的影响. 数值模拟结果表明：噪声的时间非对称性是定向流产生的根源，而势函数的空间非对称性能够与其进行竞争与协作，并在适当的参数条件下导致定向流的逆转；分数阶仅影响定向流的大小而不改变其方向. 与经典的整数阶分子马达模型或时间非对称分数阶分子马达棘齿模型相比，该模型可以更为真实地描述分子马达的噪声整流工作机理.

关键词:

Abstract

In this paper, a spatiotemporally asymmetric fractional Langevin-like ratchet is constructed for the operation of a one-dimensional linear molecular motor subjected to both temporally asymmetric unbiased Langevin-like noise generated by the Logistic mapping and spatially asymmetric periodic potential. In this ratchet, the Langevin-like noise is used to describe fluctuations of intracellular surrounding, and the fractional order is responsible for the effect of the non-ideal intracellular surrounding. Then, by deducing the corresponding discrete mapping, dependance of ratchet effect on parameters are numerically investigated. Numerical results show that both the temporal asymmetry of noise and the spatial asymmetry of potential are crucial to the directed-transport of the ratchet, and competitive spatially asymmetric potential can even reverse the unidirected transport generated by the temporally asymmetric noise at suitable parameters.

Keywords:

作者及机构信息

1.
四川大学数学学院, 成都 610064;

2.
福建农林大学计算机与信息学院, 福州 350002

基金项目: 国家自然科学基金（批准号：11171238）和福建农林大学青年教师基金（批准号：2011XJJ23）资助的课题.

Authors and contacts

1.
College of Mathematics, Sichuan University, Chengdu 610064, China;

2.
College of Computer and Information, Fujian Agriculture and Forestry University, Fuzhou 350002, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11171238) and the Young Teacher Foundation of Fujian Agriculture and Forestry University, China (Grant No. 2011XJJ23).

参考文献

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[13]	Mainardi F 2010 Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models (London: Imperial College Press) p57
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[16]	Chew L Y, Ting C 2002 Physica A 307 275
[17]	Chialvo D R, Dykman M I, Millonas M M 1997 Phys. Rev. Lett. 78 1605
[18]	Chew L Y, Ting C 2004 Phys. Rev. E 69 031103
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[21]	Zhou X W, Lin L F, Ma H, Luo M K 2014 Acta Phys. Sin. 63 110501 (in Chinese) [周兴旺, 林丽烽, 马洪, 罗懋康 2014 63 110501]
[22]	Lipowsky R, Klumpp S 2005 Physica A 352 53
[23]	Vale R D 2003 Cell 112 467
[24]	Klibas A A, Srivastava H M, Trujillo J J 2006 Theory and Applications of Fractional Differential Equations (Amsterdam: Elsevier) p199
[25]	Bao J D 2009 Stochastic Simulation Method of Classic and Quantum Dissipative System (Beijing: Science Press) p13 (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13页]

施引文献

[1]	National Research Council (translated by Wang J F) 2013 A New Biology for the 21st Century (Beijing: Science Press) (in Chinese) [美国科学院研究理事会 (王菊芳译) 2013 二十一世纪新生物学 (北京: 科学出版社)]
[2]	Phillips R, Kondev J, Theriot J (translated by Tu Z C, Wang B L) 2012 Physical Biology of the Cell (Beijing: Science Press) p483 (in Chinese) [菲利普斯R, 康德夫J, 塞里奥特J著 (涂展春, 王伯林译) 2012 细胞的物理生物学 (北京: 科学出版社) 第483页]
[3]	Qian J, Xie P, Xue X G, Wang P Y 2009 Chin. Phys. B 18 4852
[4]	Li F Z, Jiang L C 2010 Chin. Phys. B 19 020503
[5]	Zhao A K, Zhang H W, Li Y X 2010 Chin. Phys. B 19 110506
[6]	Zhang H W, Wen S T, Chen G R, Li Y X, Cao Z X, Li W 2012 Chin. Phys. B 21 038701
[7]	Ellis R J, Minton A P 2003 Nature 425 27
[8]	Tarasov V E 2010 Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles Fields and Media (Beijing: Higher Education Press) p442
[9]	Baiwen 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]
[10]	Lin L F, Zhou X W, Ma H 2013 Acta Phys. Sin. 62 240501 (in Chinese) [林丽烽, 周兴旺, 马洪 2013 62 240501]
[11]	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]
[12]	Bao J D 2012 An Introduction to Anomalous Statistical Dynamics (Beijing: Science Press) p183 (in Chinese) [包景东 2012 反常统计动力学导论 (北京: 科学出版社) 第183页
[13]	Mainardi F 2010 Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models (London: Imperial College Press) p57
[14]	Podlubny I 1999 Fractional Differential Equations (New York: Academic Press) pp78-81
[15]	Lasota A, Mackey M 1994 Chaos Fractals and Noise: Stochastic Aspects of Dynamics (New York: Springer-Verlag) p8
[16]	Chew L Y, Ting C 2002 Physica A 307 275
[17]	Chialvo D R, Dykman M I, Millonas M M 1997 Phys. Rev. Lett. 78 1605
[18]	Chew L Y, Ting C 2004 Phys. Rev. E 69 031103
[19]	Chew L Y, Ting C, Lai C H 2005 Phys. Rev. E 72 036222
[20]	Chew L Y 2012 Phys. Rev. E 85 016212.
[21]	Zhou X W, Lin L F, Ma H, Luo M K 2014 Acta Phys. Sin. 63 110501 (in Chinese) [周兴旺, 林丽烽, 马洪, 罗懋康 2014 63 110501]
[22]	Lipowsky R, Klumpp S 2005 Physica A 352 53
[23]	Vale R D 2003 Cell 112 467
[24]	Klibas A A, Srivastava H M, Trujillo J J 2006 Theory and Applications of Fractional Differential Equations (Amsterdam: Elsevier) p199
[25]	Bao J D 2009 Stochastic Simulation Method of Classic and Quantum Dissipative System (Beijing: Science Press) p13 (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13页]

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