Transport enhancement and efficiency optimization in two heat reservoir ratchets

doi:10.1088/1674-1056/21/5/050502

Abstract We study a Brownian motor moving in a sawtooth potential in the presence of an external driving force and two heat reservoirs. Based on the corresponding Fokker--Planck equation, the analytical expressions of the current and efficiency in the quasi-steady-state limit are obtained. The effects of temperature difference and the amplitude of the external driving force on the current and efficiency are discussed, respectively. The following is our findings. (i) The current increases with both $\delta$ and A. In other words, $\delta$ and A enhance the transport of the Brownian motor. (ii) The competition between the temperature difference and the amplitude of the external driving force can lead to efficiency optimization. The efficiency is a peaked function of temperature, i.e., $\delta$>0 and a lower amplitude value of the external driving force is necessary for efficiency optimization. (iii) The efficiency increases with $\delta$, and decreases with A. $\delta$ and A play opposite roles with respect to the efficiency, which indicates that δ enhances the efficiency of energy transformation while A weakens it.

Keywords: temperature difference sawtooth potential current and efficiency

Received: 04 November 2011
Revised: 27 April 2012
Accepted manuscript online:

PACS:	05.40.-a	(Fluctuation phenomena, random processes, noise, and Brownian motion)
	05.70.-a	(Thermodynamics)
	87.10.-e	(General theory and mathematical aspects)

Fund: Project supported by the Natural Science Foundation of Yunnan Province, China (Grant No. 2010CD031) and the Key Project of Research Fund of Education Department of Yunnan Province, China (Grant No. 2001Z011).

Cite this article:

Zeng Chun-Hua(曾春华) and Wang Hua(王华) Transport enhancement and efficiency optimization in two heat reservoir ratchets 2012 Chin. Phys. B 21 050502

[1]	Hänggi P and Marchesoni F 2009 Rev. Mod. Phys. 81 387
[2]	J黮icher F, Ajdari A and Prost J 1997 Rev. Mod. Phys. 69 1269
[3]	Reimann P 2002 Phys. Rep. 361 57
[4]	Li J H, Luczka J and Hänggi P 2001 Phys. Rev. E 64 011113
[5]	Kettner C 2000 Phys. Rev. E 61 312
[6]	Savel'ev S, Misko V, Marchesoni F and Nori F 2005 Phys. Rev. B 71 214303
[7]	Lutz C, Kollmann M and Bechinger C 2004 Phys. Rev. Lett. 93 026001
[8]	Gommers R, Denisov S and Renzoni F 2006 Phys. Rev. Lett. 96 240604
[9]	Matthias S and Muller F 2003 Nature 424 53
[10]	Li J H and Huang Z Q 1998 Phys. Rev. E 57 3917.
[11]	Cao L and Wu D J 2000 Phys. Rev. E 62 7478
[12]	Cao L and Wu D J 2001 Phys. Lett. A 291 371
[13]	Zeng C H, Wang H and Wang H T 2011 Chin. Phys. B 20 050502
[14]	Zeng C H and Wang H 2011 Commun. Theor. Phys. 52 615
[15]	Krishnan R, Roy S and Jayannavar A M 2005 J. Stat. Mech. 4 P04012
[16]	Krishnan R, Chacko J, Sahoo M and Jayannavar A M 2006 J. Stat. Mech. 6 P06017
[17]	Mateos J L 2000 Phys. Rev. Lett. 84 258
[18]	Luczka J, Bartussek R and Hanggi P 1995 Europhys. Lett. 31 431
[19]	Faucheux L P, Bourdieu L S, Kaplan P D and Libchaber A J 1995 Phys. Rev. Lett. 74 1504
[20]	Dan D, Mahato M C and Jayannavar A M 1999 Phys. Rev. E 60 6421
[21]	Ai B Q, Wang L Q and Liu L G 2007 Chaos, Solitons Fract. 34 1265
[22]	Reimann P, Bartussek R, Haussler R and Hänggi P 1994 Phys. Lett. A 215 26
[23]	Doering C R, Horsthemke W and Riordan J 1994 Phys. Rev. Lett. 72 2984
[24]	Luczka J, Bartussek R and Hänggi P 1995 Europhys. Lett. 31 431
[25]	Zeng C, Gong A and Tian Y 2010 Physica A 389 1971
[26]	Ai B Q and Liu L G 2006 Phys. Rev. E 74 051114
[27]	Ai B Q, Xie H Z and Liu L G 2007 Phys. Rev. E 75 061126
[28]	Lin M and Zhang M L 2011 Acta Phys. Sin. 60 020501 (in Chinese)
[29]	Liu B, Yan S W and Geng Y Z 2011 Acta Phys. Sin. 60 128702 (in Chinese)
[30]	Liu S J, Wang Q, Liu B, Yan S W and Fumihiko S 2011 Acta Phys. Sin. 60 128703 (in Chinese)
[31]	Zhang L Y, Jin G X and Cao L 2011 Acta Phys. Sin. 60 044207
[32]	Leng Y G 2011 Acta Phys. Sin. 60 020503 (in Chinese)
[33]	Sekimoto K 1997 J. Phys. Soc. Jpn. 66 1234
[34]	Sekimoto K 1997 J. Phys. Soc. Jpn. 66 6335
[35]	Parrondo J M R, Blanco J M, Cao F J and Brito R 1998 Europhys. Lett. 43 248
[36]	Ai B Q, Liu G T, Xie H Z, Wen D H, Wang X J, Chen W and Liu L G 2004 Chaos 14 957
[37]	Magnasco M O 1993 Phys. Rev. Lett. 71 1477
[38]	Kamegawa H, Hondou T and Takagi F 1998 Phys. Rev. Lett. 80 5251
[39]	Krishnan R, Mahato M and Jayannavar M 2004 Phys. Rev. E 70 021102
[40]	Sumithra K and Sintes T 2001 Physica A 297 1
[41]	Ai B Q, Wang X J, Liu G T, Wen D H, Xie H Z, Chen W and Liu L G 2003 Phys. Rev. E 68 061105
[42]	Ai B Q, Wang L Q and Liu L G 2005 Phys. Rev. E 72 031101
[43]	Oster G and Wang H 2002 Molecular Motors (Weinheim:Wiley-VCH) pp. 207--228
[44]	Gardiner C W 1990 Handbook of Stochastic Methods (2nd ed.) (Berlin:Springer-Verlag)
[45]	Risken H 1984 The Fokker--Planck Equation (Berlin:Springer-Verlag)
[46]	Parrondo J M R and De Cisneros B J 2002 Appl. Phys. A 75 179

[1]	Uniformity principle of temperature difference field in heat transfer optimization Xue-Tao Cheng(程雪涛), Xin-Gang Liang(梁新刚). Chin. Phys. B, 2019, 28(6): 064402.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Transport enhancement and efficiency optimization in two heat reservoir ratchets

Cite this article:

Online attention