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Spatiotemporally asymmetric fractionalLangevin-like ratchet

Zhou Xing-Wang Lin Li-Feng Ma Hong Luo Mao-Kang

Spatiotemporally asymmetric fractionalLangevin-like ratchet

Zhou Xing-Wang, Lin Li-Feng, Ma Hong, Luo Mao-Kang
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  • 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.
    • 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).
    [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 物理学报 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 物理学报 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 物理学报 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 物理学报 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]

  • [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 物理学报 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 物理学报 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 物理学报 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 物理学报 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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    [2] Li Chen-Pu, Han Ying-Rong, Zhan Yong, Xie Ge-Ying, Hu Jin-Jiang, Zhang Li-Gang, Jia Li-Yun. The single-direction energy transition model of molecular motor based on the control of adenosine triphosphate. Acta Physica Sinica, 2013, 62(19): 190501. doi: 10.7498/aps.62.190501
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    [5] Wang Fei, Deng Cui, Tu Zhe, Ma Hong. Transport of fractional coupled Brownian motor in asymmetric periodic potential. Acta Physica Sinica, 2013, 62(4): 040501. doi: 10.7498/aps.62.040501
    [6] Ren Rui-Bin, Liu De-Hao, Wang Chuan-Yi, Luo Mao-Kang. Directed transport of fractional Brownian motor driven by a temporal asymmetry force. Acta Physica Sinica, 2015, 64(9): 090505. doi: 10.7498/aps.64.090505
    [7] Gao Shi-Long, Zhong Su-Chuan, Wei Kun, Ma Hong. Overdamped fractional Langevin equation and its stochastic resonance. Acta Physica Sinica, 2012, 61(10): 100502. doi: 10.7498/aps.61.100502
    [8] Zhong Su-Chuan, Gao Shi-Long, Wei Kun, Ma Hong. The resonant behavior of an over-damped linear fractional Langevin equation. Acta Physica Sinica, 2012, 61(17): 170501. doi: 10.7498/aps.61.170501
    [9] Lin Li-Feng, Zhou Xing-Wang, Ma Hong. Subdiffusive transport of fractional two-headed molecular motor. Acta Physica Sinica, 2013, 62(24): 240501. doi: 10.7498/aps.62.240501
    [10] Xie Tian-Ting, Zhang Lu, Wang Fei, Luo Mao-Kang. Direct transport of fractional overdamped deterministic motors in spatial symmetric potentials driven by biharmonic forces. Acta Physica Sinica, 2014, 63(23): 230503. doi: 10.7498/aps.63.230503
    [11] Ji Yuan-Dong, Tu Zhe, Lai Li, Luo Mao-Kang. Deterministic directional transport of asymmetrically coupled nonlinear oscillators in a ratchet potential. Acta Physica Sinica, 2015, 64(7): 070501. doi: 10.7498/aps.64.070501
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  • Received Date:  05 March 2014
  • Accepted Date:  25 April 2014
  • Published Online:  05 August 2014

Spatiotemporally asymmetric fractionalLangevin-like ratchet

  • 1. College of Mathematics, Sichuan University, Chengdu 610064, China;
  • 2. College of Computer and Information, Fujian Agriculture and Forestry University, Fuzhou 350002, China
Fund Project:  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).

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.

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