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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.
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Keywords:
- direct transport /
- time-shift corrugated channels
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[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
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[15] 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]
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[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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[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] Zheng Z G 2004 Spatiotemporal Dynamics and Collective Behaviors in Coupled Nonlinear Systems (Beijing: Higher Education Press) (in Chinese) [郑志刚 2004 耦合非线性系统的时空动力学与合作行为 (北京: 高等教育出版社)]
[15] 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]
[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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