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Based on the research on transport phenomenon of fractional Brownian motor, a systematic parameter (i.e. symmetry parameter) which describes the asymmetry of the periodic potential field is introduced, and the influences of the symmetry parameter and the memory parameter (i.e. the fractional order) on the transport behavior are also investigated. The numerical results show that the combined effect of fractional order and symmetry parameter can result in the reverse flow of Brownian particle's transport, and the fractional order corresponding to the maximal averaged velocity is irrelevant to the frequency of the external periodic force, but it will still increase monotonically as the symmetry parameter increases.
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Keywords:
- fractional Brownian motor /
- memorable medium /
- asymmetry /
- directed transport
[1] Hänggi P, Marchesoni F 2009 Rev. Mod. Phys. 81 387
[2] Smoluchowski M V 1912 Physik. Z. 13 1069
[3] Feynman R P, Leighton R B, Sands M 1963 The Feynman Lectures on Physics (Boston: Addison-Wesley) p46
[4] Fendrik A J, Romanelli L 2012 Phys. Rev. E 85 041149
[5] Zheng Z G 2004 Spatiotemporal Dynamics and Collective Behaviors in Coupled Nonlinear Systems (Beijing: Higher Education Press) pp279-286 (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) 第279–286页]
[6] Qian M, Wang Y, Zhang X J 2003 Chin. Phys. Lett. 20 810
[7] Astumian R, Bier M 1994 Phys. Rev. Lett. 72 1766
[8] Reimann P 2002 Phys. Rep. 361 57
[9] Ai B Q, He Y F, Zhong W R 2010 Phys. Rev. E 82 061102
[10] Yang M C, Ripoll M 2013 Phys. Rev. E 87 062110
[11] Simon M S, Sancho J M, Lindenberg K 2013 Phys. Rev. E 88 062105
[12] Gao T F, Zheng Z G, Chen J C 2013 Chin. Phys. B 22 080502
[13] Bhat D, Gopalakrishnan M 2013 Phys. Rev. E 88 042702
[14] Liu F, Anh V V, Turner I, Zhuang P 2003 J. Appl. Math. Comput. 13 233
[15] Zhang L, Deng K, Luo M K 2012 Chin. Phys. B 21 090505
[16] Goychuk I, Kharchenko V 2012 Phys. Rev. E 85 051131
[17] Ernst D, Hellmann M, Kohler J, Weiss M 2012 Soft Matter 8 4886
[18] 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]
[19] Oldham K B, Spanier J 1974 The Fractional Calculus (New York: Academic Press) pp198-216
[20] Kou S C, Xie X S 2004 Phys. Rev. Lett. 93 180603
[21] Gao S L, Zhong S C, Wei K, Ma H 2012 Acta Phys. Sin. 61 100502 (in Chinese) [高仕龙, 钟苏川, 韦鹍, 马洪 2012 物理学报 61 100502]
[22] Podlubny I 1999 Fractional Differential Equations (San Diego: Academic Press) pp78-81
[23] Samko S G, Kilbas A A, Marichev O I 1993 Fractional Integrals and Derivatives Theory and Applications (New York: Gordon and Breach Science Publisher Inc.) pp321-344
[24] He Y F, Ai B Q 2010 Phys. Rev. E 81 021110
[25] 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]
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[1] Hänggi P, Marchesoni F 2009 Rev. Mod. Phys. 81 387
[2] Smoluchowski M V 1912 Physik. Z. 13 1069
[3] Feynman R P, Leighton R B, Sands M 1963 The Feynman Lectures on Physics (Boston: Addison-Wesley) p46
[4] Fendrik A J, Romanelli L 2012 Phys. Rev. E 85 041149
[5] Zheng Z G 2004 Spatiotemporal Dynamics and Collective Behaviors in Coupled Nonlinear Systems (Beijing: Higher Education Press) pp279-286 (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) 第279–286页]
[6] Qian M, Wang Y, Zhang X J 2003 Chin. Phys. Lett. 20 810
[7] Astumian R, Bier M 1994 Phys. Rev. Lett. 72 1766
[8] Reimann P 2002 Phys. Rep. 361 57
[9] Ai B Q, He Y F, Zhong W R 2010 Phys. Rev. E 82 061102
[10] Yang M C, Ripoll M 2013 Phys. Rev. E 87 062110
[11] Simon M S, Sancho J M, Lindenberg K 2013 Phys. Rev. E 88 062105
[12] Gao T F, Zheng Z G, Chen J C 2013 Chin. Phys. B 22 080502
[13] Bhat D, Gopalakrishnan M 2013 Phys. Rev. E 88 042702
[14] Liu F, Anh V V, Turner I, Zhuang P 2003 J. Appl. Math. Comput. 13 233
[15] Zhang L, Deng K, Luo M K 2012 Chin. Phys. B 21 090505
[16] Goychuk I, Kharchenko V 2012 Phys. Rev. E 85 051131
[17] Ernst D, Hellmann M, Kohler J, Weiss M 2012 Soft Matter 8 4886
[18] 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]
[19] Oldham K B, Spanier J 1974 The Fractional Calculus (New York: Academic Press) pp198-216
[20] Kou S C, Xie X S 2004 Phys. Rev. Lett. 93 180603
[21] Gao S L, Zhong S C, Wei K, Ma H 2012 Acta Phys. Sin. 61 100502 (in Chinese) [高仕龙, 钟苏川, 韦鹍, 马洪 2012 物理学报 61 100502]
[22] Podlubny I 1999 Fractional Differential Equations (San Diego: Academic Press) pp78-81
[23] Samko S G, Kilbas A A, Marichev O I 1993 Fractional Integrals and Derivatives Theory and Applications (New York: Gordon and Breach Science Publisher Inc.) pp321-344
[24] He Y F, Ai B Q 2010 Phys. Rev. E 81 021110
[25] 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]
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