Advertisement

International Journal of Theoretical Physics

, Volume 55, Issue 3, pp 1642–1651 | Cite as

Strong Asymmetric Coupling of Two Parallel Exclusion Processes: Effect of Unequal Injection Rates

  • Song Xiao
  • Peng Dong
  • Yingjie Zhang
  • Yanna Liu
Article

Abstract

In this letter, strong asymmetric coupling of two parallel exclusion processes: effect of unequal injection rates will be investigated. It is a generalization of the work of Xiao et al. (Phys. Lett. A 8, 374 (2009)), in which the particles only move on two lanes with rate 1 toward right. We can obtain the diverse phase diagram and density profiles of the system. The vertical cluster mean-field approach and extensively Monte Carlo simulations are used to study the system, and theoretical predictions are in excellent agreement with simulation results.

Keywords

Exclusion process Strong coupling Mean-field analysis Unequal injection rates 

Notes

Acknowledgments

Authors acknowledge the support of Item sponsored by National Natural Science Foundation (Grant No. 51568032 and 21301079).

References

  1. 1.
    Derrida, B.: Phys. Rep 65, 301 (1998)MathSciNetGoogle Scholar
  2. 2.
    Blythe, R.A., Evans, M.R.: J. Phys. A 46, R333 (2007)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    Macdonald, C.T., Gibbs, J.H.: Biopolymers 1, 6 (1968)Google Scholar
  4. 4.
    Shaw, L.B., Zia, R.K.P., Lee, K.H.: Phys. Rev. E 68, 021910 (2003)ADSCrossRefGoogle Scholar
  5. 5.
    Chou, T., Lakatos, G.: Phys. Rev. Lett 93, 198101 (2004)ADSCrossRefGoogle Scholar
  6. 6.
    Klumpp, S., Lipowsky, R.: J. Stat. Phys 113, 233 (2003)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Lipowsky, R., Klumpp, S., Nieuwenhuizen, T.: Phys. Rev. Lett 87, 108101 (2001)ADSCrossRefGoogle Scholar
  8. 8.
    Tailleur, J., Evans, M.R., Kafri, Y.: Phys. Rev. Lett 102, 118109 (2009)ADSCrossRefGoogle Scholar
  9. 9.
    Nagel, K.: Phys. Rev. E 53, 4655 (1996)ADSCrossRefGoogle Scholar
  10. 10.
    Chowdhury, D., Santen, L., Schadschneider, A.: Phys. Rep 199, 329 (2000)MathSciNetGoogle Scholar
  11. 11.
    Hahn, C.K., et al.: Appl. Phys. Lett 73, 2479 (1998)ADSCrossRefGoogle Scholar
  12. 12.
    de Gier, J., Essler, F.H.: Phys. Rev. Lett 95, 240601 (2005)ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    Popkov, V., et al.: J. Phys. A 34, L45 (2001)ADSCrossRefGoogle Scholar
  14. 14.
    Krug, J.: Phys. Rev. Lett 67, 1882 (1991)ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    Arndt, P.F., Heinzel, T., Rittenberg, V.: J. Stat. Phys 90, 783 (1998)ADSCrossRefGoogle Scholar
  16. 16.
    Evans, M.R., et al.: Phys. Rev. Lett 80, 425 (1998)ADSCrossRefGoogle Scholar
  17. 17.
    Rajewsky, N., Sasamoto, T., Speer, E.R.: Physica A 123, 279 (2000)Google Scholar
  18. 18.
    Kafri, Y., et al.: Phys. Rev. Lett 89, 035702 (2002)ADSCrossRefGoogle Scholar
  19. 19.
    Evans, M.R., et al.: Phys. Rev. Lett 74, 208 (1995)ADSCrossRefGoogle Scholar
  20. 20.
    Evans, M.R., et al.: J. Stat. Phys 80, 69 (1995)ADSCrossRefGoogle Scholar
  21. 21.
    Parmeggiani, A., Franosch, T., Frey, E.: Phys. Rev. Lett 086601, 90 (2003)Google Scholar
  22. 22.
    Nishinari, K., et al.: Phys. Rev. Lett 118101, 95 (2005)Google Scholar
  23. 23.
    Derrida, B., Evans, M.R., Hakim, V., et al.: J. Phys. A 26, 1493 (1993)ADSMathSciNetCrossRefGoogle Scholar
  24. 24.
    Derrida, B., Domany, E., Mukamel, D.: J. Stat. Phys 69, 667 (1992)ADSMathSciNetCrossRefGoogle Scholar
  25. 25.
    Popkov, V., Salerno, M.: Phys. Rev. E 69, 046103 (2004)ADSCrossRefGoogle Scholar
  26. 26.
    Lee, H.W., Popkov, V., Kim, D.: J. Phys. A 30, 8497 (1997)ADSMathSciNetCrossRefGoogle Scholar
  27. 27.
    Fouladvand, M.E., Lee, H.W.: Phys. Rev. E 60, 6465 (1999)ADSMathSciNetCrossRefGoogle Scholar
  28. 28.
    Mitsudo, T., Hayakawa, H.: J. Phys. A 38, 3087 (2005)MathSciNetCrossRefGoogle Scholar
  29. 29.
    Harris, R.J., Stinchcombe, R.B.: Physica A 354, 582 (2005)ADSCrossRefGoogle Scholar
  30. 30.
    Reichenbach, T., Franosch, T., Frey, E.: Phys. Rev. Lett 97, 050603 (2006)ADSMathSciNetCrossRefGoogle Scholar
  31. 31.
    Juhász, R.: Phys. Rev. E 021117, 76 (2007)Google Scholar
  32. 32.
    Jiang, R., Hu, M.B., Wu, Y.H., Wu, Q.S.: Phys. Rev. E 041128, 77 (2008)MathSciNetGoogle Scholar
  33. 33.
    Cai, Z.P., et al.: J. Stat. Mech. P07016 (2008)Google Scholar
  34. 34.
    Tsekouras, K., Kolomeisky, A.B.: J. Phys. A 41, 095002 (2008)ADSMathSciNetCrossRefGoogle Scholar
  35. 35.
    Popkov, V., Peschel, I.: Phys. Rev. E 64, 026126 (2001)ADSCrossRefGoogle Scholar
  36. 36.
    Pronina, E., Kolomeisky, A.B.: J. Phys. A 40, 2275 (2007)ADSMathSciNetCrossRefGoogle Scholar
  37. 37.
    Korniss, G., Schmittmann, B., Zia, R.K.P.: Europhys. Lett 45, 431 (1999)ADSCrossRefGoogle Scholar
  38. 38.
    Mettetal, J.T., Schmittmann, B., Zia, R.K.P.: Europhys. Lett 58, 653 (2002)ADSCrossRefGoogle Scholar
  39. 39.
    Georgiev, I.T., et al.: Phys. Rev. Lett 94, 115701 (2005)ADSCrossRefGoogle Scholar
  40. 40.
    Jiang, R., et al.: J. Stat. Phys 136, 73 (2009)ADSMathSciNetCrossRefGoogle Scholar
  41. 41.
    Popkov, V., Schütz, G.M.: J. Stat. Phys 112, 523 (2003)CrossRefGoogle Scholar
  42. 42.
    Pronina, E., Kolomeisky, A.B.: J. Phys. A 37, 9907 (2004)ADSMathSciNetCrossRefGoogle Scholar
  43. 43.
    Pronina, E., Kolomeisky, A.B.: Physica A 12, 372 (2006)MathSciNetGoogle Scholar
  44. 44.
    Tsekouras, K., Kolomeisky, A.B.: J. Phys. A 41, 465001 (2008)ADSMathSciNetCrossRefGoogle Scholar
  45. 45.
    Xiao, S., Liu, M., Cai, J.: Phys. Lett. A 374, 8 (2009)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Song Xiao
    • 1
  • Peng Dong
    • 1
  • Yingjie Zhang
    • 1
  • Yanna Liu
    • 2
  1. 1.Faculty of Metallurgical and Energy EngineeringKunming University of Science and TechnologyKunmingChina
  2. 2.Faculty of Chemical EngineeringKunming University of Science and TechnologyKunmingChina

Personalised recommendations