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温度反馈控制棘轮的最优控制

刘天宇 曹佳慧 刘艳艳 高天附 郑志刚

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温度反馈控制棘轮的最优控制

刘天宇, 曹佳慧, 刘艳艳, 高天附, 郑志刚

Optimal control of temperature feedback control ratchets

Liu Tian-Yu, Cao Jia-Hui, Liu Yan-Yan, Gao Tian-Fu, Zheng Zhi-Gang
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  • 基于Cao的误差棘轮模型, 通过引入温度因子进一步对反馈棘轮实施控制. 本文详细讨论了温度因子、温度相位差和温度频率对耦合布朗粒子定向输运的影响. 研究发现, 温度因子并不总是减小温度反馈棘轮的定向输运, 这意味着在一定条件下温度因子还可以增强反馈棘轮的定向输运. 此外, 在小温度振幅范围内耦合粒子的质心平均速度和Pe数随温度频率的变化都呈多峰结构. 这一结果表明, 合适的温度变化频率能够使反馈棘轮的定向输运获得多次的增强. 本文所得结论不仅能够启发实验上通过选取合适的温度反馈信息来优化布朗棘轮的定向输运, 还可为实验上的数据分析与处理特别是误差分析提供理论参考.
    Biomolecular motors are macromolecules of enzyme proteins that convert chemical energy into mechanical energy. Experimental studies have shown that the directed movement of the biomolecular motor fully participates in the material transport process in the cell. Theoretically, the directed movement of biomolecular motors can be studied by the ratchet model. However, in most of feedback control ratchet models, none of the influences of external factors on experimental manipulation is considered, especially the inevitable random error, systematic error and human error in the experiment. Therefore, in order to further study the influences of error factors on feedback control ratchets, Cao's research group (Feito M, Cao F J 2007 Eur. Phys. J. B 59 63) pioneered the idea of error probability and discussed the transport behavior of feedback ratchets in the presence of error probability.Based on Cao's error ratchet model, in this paper the temperature factor in introduced to further control the feedback ratchets, and the directed transport characteristics of the coupled Brownian particles in the temperature feedback ratchets are studied. The effects of temperature factor, phase difference and temperature frequency on the directed transport of coupled Brownian particles are discussed in detail. It is found that the temperature factor does not always reduce the directed transport of Brownian particles. There is a minimum value which means that the temperature factor can enhance the directed transport of the feedback ratchets within a certain change interval. In addition, in a small temperature amplitude range, the directed transport of the coupled particles exhibits a multi-peak structure with the change of temperature frequency. It is means that the appropriate temperature change frequency can enhance the directed transport of the feedback ratchets multiple times. The conclusions obtained in this paper can not only inspire experimental selection of appropriate temperature feedback information to optimize the directed transport of the Brownian ratchets, but also provide theoretical references for analyzing and processing the experimental data, especially error analysis.
      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) 、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.
      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), 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).
    [1]

    舒咬根, 欧阳钟灿 2007 物理 36 735Google Scholar

    Shu Y G, Ouyang Z C 2007 Physics 36 735Google Scholar

    [2]

    Xie P 2010 Int. J. Biol. Sci 6 665

    [3]

    Oster G, Wang H 2003 Trends Cell Biol 13 114Google Scholar

    [4]

    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)

    [5]

    Palmigiano A, Santaniello F, Cerutti A, Penkov D, Purushothama D 2018 Sci. Rep. 8 3198Google Scholar

    [6]

    Linke H 2002 Appl. Phys. A 75 167Google Scholar

    [7]

    van den Heuvel M G L, Dekker C 2007 Science 317 333Google Scholar

    [8]

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

    [9]

    Doering C R 1995 Nuovo Cimento 17 685Google Scholar

    [10]

    Astumian R D, Bier M 1994 Phys. Rev. Lett. 72 1766Google Scholar

    [11]

    Gao T F, Chen J C 2009 J. Phys. A: Math. Theor. 42 065002Google Scholar

    [12]

    Reimann P 2002 Phys. Rep. 361 57Google Scholar

    [13]

    Rosalie L W, Fabrice M K P 2016 Physica A 460 326Google Scholar

    [14]

    Pawel R, Felix M 2010 Phys. Rev. E 81 061120Google Scholar

    [15]

    Feito M, Cao F J 2006 Phys. Rev. E 74 041109Google Scholar

    [16]

    范黎明, 吕明涛, 黄仁忠, 高天附, 郑志刚 2017 物理学报 66 010501Google Scholar

    Fan L M, Lv M T, Gao T F, Huang R Z, Zheng Z G 2017 Acta. Phys. Sin. 66 010501Google Scholar

    [17]

    Feito M, Cao F J 2007 Phys. Rev. E 76 061113Google Scholar

    [18]

    Feito M, Cao F J 2008 Physica A 387 4553Google Scholar

    [19]

    Wang H Y, Bao J D 2007 Physica A 374 33Google Scholar

    [20]

    Feito M, Baltanas J P, Cao F J 2009 Phys. Rev. E 80 031128Google Scholar

    [21]

    Rousselet J, Salome L, Ajdari A, Prost J 1994 Nature 370 446Google Scholar

    [22]

    Feito M, Cao F J 2007 Eur. Phys. J. B 59 63Google Scholar

    [23]

    Dan D, Jayannavarar A M, Menon G I 2003 Physica A 318 40Google Scholar

    [24]

    王莉芳, 高天附, 黄仁忠, 郑玉祥 2013 物理学报 62 070502Google Scholar

    Wang L F, Gao T F, Huang R Z, Zheng Y X 2013 Acta. Phys. Sin. 62 070502Google Scholar

    [25]

    Li C P, Chen H B, Zheng Z G 2017 Front. Phys. 12 120507Google Scholar

    [26]

    Cao F J, Feito M, Touchette H 2007 Physica A 388 113

    [27]

    Zheng Z G, Cross M C, Hu G 2002 Phys. Rev. Lett. 89 154102Google Scholar

    [28]

    Mateos J L 2004 Fluctuation Noise Lett 4 161Google Scholar

    [29]

    Lindner B, Schimanasky-Geier L 2002 Phys. Rev. Lett. 89 230602Google Scholar

    [30]

    Wang H Y, Bao J D 2005 Physica A 357 373Google Scholar

  • 图 1  (a) 质心平均速度$\left\langle {{V_{{\rm{cm}}}}} \right\rangle $, (b) 质心扩散系数$ {D_{{\text{eff}}}} $和 (c) $ Pe $数随温度相位差$ \theta $的变化曲线, 其中$ \omega = 0.1{\text{π}} $, $A = $$ 1.0$, $ {T_0} = 0.7 $

    Fig. 1.  Curves of (a) the center-of-mass mean velocity $\left\langle {{V_{{\rm{cm}}}}} \right\rangle $, (b) the center-of-mass diffusion coefficient $ {D_{{\text{eff}}}} $ and (c) $ Pe $ number varying with the phase different of temperature $ \theta $, where $ \omega = 0.1{\text{π}} $, $ A = 1.0 $, $ {T_0} = 0.7 $.

    图 2  (a) 质心平均速度$\left\langle {{V_{{\rm{cm}}}}} \right\rangle $, (b) 质心扩散系数$ {D_{{\text{eff}}}} $和 (c) $ Pe $数随临界温度$ {T_{\text{C}}} $的变化曲线, 其中$ \omega = 0.1{\text{π}} $, $A = $$ 1.0$, $ \theta = 0.2{\text{π}} $

    Fig. 2.  Curves of (a) the center-of-mass mean velocity $\left\langle {{V_{{\rm{cm}}}}} \right\rangle $, (b) the center-of-mass diffusion coefficient $ {D_{{\text{eff}}}} $ and (c) $ Pe $ number varying with the critical temperature ${T_{\rm{C}}}$, where $ \omega = 0.1{\text{π}} $, $ A = 1.0 $, $ \theta = 0.2{\text{π}} $.

    图 3  (a) 质心平均速度$\left\langle {{V_{{\rm{cm}}}}} \right\rangle $, (b) 质心扩散系数$ {D_{{\text{eff}}}} $和 (c) $ Pe $数随温度频率$ \omega $的变化曲线, 其中$ {T_0} = 0.7 $, $\theta = $$ 0.2{\text{π}}$, $ {\alpha _i} = 0.8 $

    Fig. 3.  Curve of (a) the center-of-mass mean velocity $\left\langle {{V_{{\rm{cm}}}}} \right\rangle $, (b) the center-of-mass diffusion coefficient $ {D_{{\text{eff}}}} $ and (c) $ Pe $ number varying with the temperature frequency $ \omega $, where $ {T_0} = 0.7 $, $ \theta = 0.2{\text{π}} $, $ {\alpha _i} = 0.8 $.

  • [1]

    舒咬根, 欧阳钟灿 2007 物理 36 735Google Scholar

    Shu Y G, Ouyang Z C 2007 Physics 36 735Google Scholar

    [2]

    Xie P 2010 Int. J. Biol. Sci 6 665

    [3]

    Oster G, Wang H 2003 Trends Cell Biol 13 114Google Scholar

    [4]

    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)

    [5]

    Palmigiano A, Santaniello F, Cerutti A, Penkov D, Purushothama D 2018 Sci. Rep. 8 3198Google Scholar

    [6]

    Linke H 2002 Appl. Phys. A 75 167Google Scholar

    [7]

    van den Heuvel M G L, Dekker C 2007 Science 317 333Google Scholar

    [8]

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

    [9]

    Doering C R 1995 Nuovo Cimento 17 685Google Scholar

    [10]

    Astumian R D, Bier M 1994 Phys. Rev. Lett. 72 1766Google Scholar

    [11]

    Gao T F, Chen J C 2009 J. Phys. A: Math. Theor. 42 065002Google Scholar

    [12]

    Reimann P 2002 Phys. Rep. 361 57Google Scholar

    [13]

    Rosalie L W, Fabrice M K P 2016 Physica A 460 326Google Scholar

    [14]

    Pawel R, Felix M 2010 Phys. Rev. E 81 061120Google Scholar

    [15]

    Feito M, Cao F J 2006 Phys. Rev. E 74 041109Google Scholar

    [16]

    范黎明, 吕明涛, 黄仁忠, 高天附, 郑志刚 2017 物理学报 66 010501Google Scholar

    Fan L M, Lv M T, Gao T F, Huang R Z, Zheng Z G 2017 Acta. Phys. Sin. 66 010501Google Scholar

    [17]

    Feito M, Cao F J 2007 Phys. Rev. E 76 061113Google Scholar

    [18]

    Feito M, Cao F J 2008 Physica A 387 4553Google Scholar

    [19]

    Wang H Y, Bao J D 2007 Physica A 374 33Google Scholar

    [20]

    Feito M, Baltanas J P, Cao F J 2009 Phys. Rev. E 80 031128Google Scholar

    [21]

    Rousselet J, Salome L, Ajdari A, Prost J 1994 Nature 370 446Google Scholar

    [22]

    Feito M, Cao F J 2007 Eur. Phys. J. B 59 63Google Scholar

    [23]

    Dan D, Jayannavarar A M, Menon G I 2003 Physica A 318 40Google Scholar

    [24]

    王莉芳, 高天附, 黄仁忠, 郑玉祥 2013 物理学报 62 070502Google Scholar

    Wang L F, Gao T F, Huang R Z, Zheng Y X 2013 Acta. Phys. Sin. 62 070502Google Scholar

    [25]

    Li C P, Chen H B, Zheng Z G 2017 Front. Phys. 12 120507Google Scholar

    [26]

    Cao F J, Feito M, Touchette H 2007 Physica A 388 113

    [27]

    Zheng Z G, Cross M C, Hu G 2002 Phys. Rev. Lett. 89 154102Google Scholar

    [28]

    Mateos J L 2004 Fluctuation Noise Lett 4 161Google Scholar

    [29]

    Lindner B, Schimanasky-Geier L 2002 Phys. Rev. Lett. 89 230602Google Scholar

    [30]

    Wang H Y, Bao J D 2005 Physica A 357 373Google Scholar

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出版历程
  • 收稿日期:  2021-03-17
  • 修回日期:  2021-05-20
  • 上网日期:  2021-09-18
  • 刊出日期:  2021-10-05

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