过阻尼布朗棘轮的斯托克斯效率研究
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摘要
根据随机能量理论解析得到阻尼环境中布朗粒子的概率流和斯托克斯效率,并进一步研究布朗粒子的输运性能.详细讨论了空间的不对称性、外偏置力及外势结构等对棘轮定向输运的影响.研究发现,合适的外偏置力能使棘轮的定向输运达到最强.通过调节外势的不对称性可使棘轮中粒子的运动反向,当选择合适的空间不对称性时布朗粒子的反向输运可获得最强.此外,一定条件下合适的外势高度也能增强棘轮输运,且能使粒子克服黏滞阻力的斯托克斯效率达到最大.所得结论能够启发实验上设计合适的外势及外偏置来优化布朗棘轮的定向输运性能,并为生物纳米器件的研制提供一定的理论参考.
Molecular motors in life activities of cell are known to operate efficiently. They could convert molecular-scale chemical energy into macroscopic-scale mechanical work with high efficiency. In order to acquire the transport mechanism of the molecular motor, the Brownian ratchet has been proposed to explore the property of directed transport and energy conversion. There are different kinds of Brownian ratchet models like flashing ratchets, rocking ratchets, and time-asymmetric ratchets and so on. Through investigating the performance of Brownian ratchet moving in periodic potential, the directed transport of ratchet could be explained, and the effective usage of ratchet energy for directed transport could also be improved. Recently, optimizing the transport of Brownian ratchet has aroused the interest of researchers. It is found that the viscous resistance could reinforce the directed transport of the Brownian particle in damping liquid. Meanwhile, a large number of conclusions indicate that the transport of Brownian ratchets would be enhanced if the asymmetry of the potential is changed. Those results show that the influences of the external potential and the damping force on the particle flow cannot be neglected. Hence in this paper, the effects of the potential structure and the temperature of heat bath on transport are discussed.Furthermore, how to use the ratchet energy effectively has been investigated in recent years. When the Brownian motor operates with load, the input energy is reduced. More importantly, the energy transformation efficiency defined as the ratio of the useful work done against the load to the input energy is assumed to be a zero value in the absence of load. With the help of stochastic energetic theory proposed by Sekimoto, the Stokes efficiency has been used to explore the performance of the Brownian ratchet. So far, the numerical solution has been used extensively in most theoretical investigations. Nevertheless, in our work, the Stokes efficiency is discussed analytically for explaining the mechanism of directed transport. We consider the transport performance of the Brownian ratchet described by the Fokker Planck equation which is corresponding to the Langevin equation under time-varying external force and thermal noise. Mainly,the effects of potential asymmetry, external force, height of the barrier, and intensity of the thermal noise on transport are discussed in detail. It is found that the transport direction of Brownian ratchet will be reversed under the condition of appropriate potential structures, and the probability current can reach a maximal value by changing the asymmetry of potential. It is worthwhile to point out that the performance of directed transport of the ratchet can be improved when an appropriate amplitude of the external force is applied. Meanwhile, there is an optimal value of the barrier height at which the Stokes efficiency reaches a maximal value and the directed transport of ratchet is enhanced. Through our conclusions, the ratchets of different structures could be designed for improving the transport property of Brownian motor. And the results have helpful theoretical guidance not only in the aspect of medical delivery but also in the control of nano-devices.
Molecular motors in life activities of cell are known to operate efficiently. They could convert molecular-scale chemical energy into macroscopic-scale mechanical work with high efficiency. In order to acquire the transport mechanism of the molecular motor, the Brownian ratchet has been proposed to explore the property of directed transport and energy conversion. There are different kinds of Brownian ratchet models like flashing ratchets, rocking ratchets, and time-asymmetric ratchets and so on. Through investigating the performance of Brownian ratchet moving in periodic potential, the directed transport of ratchet could be explained, and the effective usage of ratchet energy for directed transport could also be improved. Recently, optimizing the transport of Brownian ratchet has aroused the interest of researchers. It is found that the viscous resistance could reinforce the directed transport of the Brownian particle in damping liquid. Meanwhile, a large number of conclusions indicate that the transport of Brownian ratchets would be enhanced if the asymmetry of the potential is changed. Those results show that the influences of the external potential and the damping force on the particle flow cannot be neglected. Hence in this paper, the effects of the potential structure and the temperature of heat bath on transport are discussed.Furthermore, how to use the ratchet energy effectively has been investigated in recent years. When the Brownian motor operates with load, the input energy is reduced. More importantly, the energy transformation efficiency defined as the ratio of the useful work done against the load to the input energy is assumed to be a zero value in the absence of load. With the help of stochastic energetic theory proposed by Sekimoto, the Stokes efficiency has been used to explore the performance of the Brownian ratchet. So far, the numerical solution has been used extensively in most theoretical investigations. Nevertheless, in our work, the Stokes efficiency is discussed analytically for explaining the mechanism of directed transport. We consider the transport performance of the Brownian ratchet described by the Fokker Planck equation which is corresponding to the Langevin equation under time-varying external force and thermal noise. Mainly,the effects of potential asymmetry, external force, height of the barrier, and intensity of the thermal noise on transport are discussed in detail. It is found that the transport direction of Brownian ratchet will be reversed under the condition of appropriate potential structures, and the probability current can reach a maximal value by changing the asymmetry of potential. It is worthwhile to point out that the performance of directed transport of the ratchet can be improved when an appropriate amplitude of the external force is applied. Meanwhile, there is an optimal value of the barrier height at which the Stokes efficiency reaches a maximal value and the directed transport of ratchet is enhanced. Through our conclusions, the ratchets of different structures could be designed for improving the transport property of Brownian motor. And the results have helpful theoretical guidance not only in the aspect of medical delivery but also in the control of nano-devices.
引文
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[7]Gao T F,Liu F S,Chen J C 2012 Chin.Phys.B 21020502
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[9]Ai B Q,He Y F,Li F G,Zhong W R 2013 Phys.Rev.E 138 154107
[10]Fan L M,L(u|¨)M T,Huang R Z,Gao T F,Zheng Z G2017 Acta Phys.Sin.66 010501(in Chinese)[范黎明,吕明涛,黄仁忠,高天附,郑志刚2017物理学报66 010501]
[11]Sahoo M,Jayannavar A M 2017 Physica A 465 40
[12]Sekimoto K 1997 J.Phys.Soc.Jpn.66 1234
[13]Parrondo J M R,Cisneros B J D 2002 Physics A 75 179
[14]Wang H,Oster G 2002 EPL 57 134
[15]Li Y X,Wu X Z,Zhuo Y Z 2000 Physica A 286 147
[16]Chueshov I,Kuksin S 2008 Physica D 237 1352
[17]Winkler M,Abel M 2015 Phys.Rev.E 92 063002
[18]Anders M 2013 Phys.Rev.E 92 063002
[19]Sztuk E,Przekop R,Gradon L 2012 Chem.Process Eng.33 279
[20]Spiechowicz J,Luczka J,Machura L 2016 Physics 2016054038
[21]Zheng Z G,Cross M C,Hu G 2002 Phys.Rev.Lett.89154102
[22]Li C P,Han Y R,Zhan Y,Hu J J,Zhang L G,Qu J2013 Acta Phys.Sin.62 230051(in Chinese)[李晨璞,韩英荣,展永,胡金江,张礼刚,曲蛟2013物理学报62230051]
[23]Zeng C H,Wang H 2012 Chin.Phys.B 21 76
[24]Ai B Q 2004 Ph.D.Dissertation(Guangzhou:Sun Yatsen University)(in Chinese)[艾保全2004博士学位论文(广州:中山大学)]
[25]Kamegawa H,Hondou T,Takagi F 1998 Phys.Rev.Lett.80 5251
[26]Ai B Q,Xie H Z,Liao H Y,Liu L G 2006 J.Stat.Mech.50 09016
[27]Bartussek R,Hanggi P,Lindner B,Schimansky Geier L1997 Physica D 109 17
[28]Kula J,Czernik T,Luczka J 1998 Phys.Rev.Lett.801377
[29]Linke H 2002 Appl.Phys.A:Mater.Sci.Process.75167
[30]Heuvel MGLVD,Dekker C 2007 Science 317 333
[31]Braun O M,Kivshar Y S 1998 Phys.Rep.306 1
[32]Landa P S,McClintock P V E 2000 Phys.Rep.323 1
[2]Doering C R 1995 Nuovo Cimento 17 685
[3]Astumian R D,Bier M 1994 Phys.Rev.Lett.72 1766
[4]Gao T F,Chen J C 2009 J.Phys.A:Math.Theor.42065002
[5]Ai B Q,He Y F,Zhong W R 2011 Phys.Rev.E 83051106
[6]Zhang H W,Wen S T,Zhang H T,Li Y X,Chen G R2012 Chin.Phys.B 21 078701
[7]Gao T F,Liu F S,Chen J C 2012 Chin.Phys.B 21020502
[8]Zhan Y,Bao J D,Zhuo Y Z 1997 Acta Phys.Sin.461880(in Chinese)[展永,包景东,卓益忠1997物理学报46 1880]
[9]Ai B Q,He Y F,Li F G,Zhong W R 2013 Phys.Rev.E 138 154107
[10]Fan L M,L(u|¨)M T,Huang R Z,Gao T F,Zheng Z G2017 Acta Phys.Sin.66 010501(in Chinese)[范黎明,吕明涛,黄仁忠,高天附,郑志刚2017物理学报66 010501]
[11]Sahoo M,Jayannavar A M 2017 Physica A 465 40
[12]Sekimoto K 1997 J.Phys.Soc.Jpn.66 1234
[13]Parrondo J M R,Cisneros B J D 2002 Physics A 75 179
[14]Wang H,Oster G 2002 EPL 57 134
[15]Li Y X,Wu X Z,Zhuo Y Z 2000 Physica A 286 147
[16]Chueshov I,Kuksin S 2008 Physica D 237 1352
[17]Winkler M,Abel M 2015 Phys.Rev.E 92 063002
[18]Anders M 2013 Phys.Rev.E 92 063002
[19]Sztuk E,Przekop R,Gradon L 2012 Chem.Process Eng.33 279
[20]Spiechowicz J,Luczka J,Machura L 2016 Physics 2016054038
[21]Zheng Z G,Cross M C,Hu G 2002 Phys.Rev.Lett.89154102
[22]Li C P,Han Y R,Zhan Y,Hu J J,Zhang L G,Qu J2013 Acta Phys.Sin.62 230051(in Chinese)[李晨璞,韩英荣,展永,胡金江,张礼刚,曲蛟2013物理学报62230051]
[23]Zeng C H,Wang H 2012 Chin.Phys.B 21 76
[24]Ai B Q 2004 Ph.D.Dissertation(Guangzhou:Sun Yatsen University)(in Chinese)[艾保全2004博士学位论文(广州:中山大学)]
[25]Kamegawa H,Hondou T,Takagi F 1998 Phys.Rev.Lett.80 5251
[26]Ai B Q,Xie H Z,Liao H Y,Liu L G 2006 J.Stat.Mech.50 09016
[27]Bartussek R,Hanggi P,Lindner B,Schimansky Geier L1997 Physica D 109 17
[28]Kula J,Czernik T,Luczka J 1998 Phys.Rev.Lett.801377
[29]Linke H 2002 Appl.Phys.A:Mater.Sci.Process.75167
[30]Heuvel MGLVD,Dekker C 2007 Science 317 333
[31]Braun O M,Kivshar Y S 1998 Phys.Rep.306 1
[32]Landa P S,McClintock P V E 2000 Phys.Rep.323 1