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Totally asymmetric simple exclusion process on a periodic lattice with Langmuir kinetics depending on the occupancy of the forward neighboring site

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Abstract

We generalize the totally asymmetric simple exclusion process with Langmuir kinetics on a periodic lattice. In the extended model, the rates of attachment and detachment depend on the occupancy of the forward neighboring site. Using a mean-field theory, we obtain the analytical expression of the density profile in the steady state and the relaxation dynamics in our model. We verify their accuracy by comparing the results with Monte Carlo simulations.

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References

  1. C.T. MacDonald, J.H. Gibbs, A.C. Pipkin, Biopolymers 6, 1 (1968)

    Article  Google Scholar 

  2. B. Derrida, M.R. Evans, V. Hakim, V. Pasquier, J. Phys. A: Math. Gen. 26, 1493 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  3. A.B. Kolomeisky, G.M. Schütz, E.B. Kolomeisky, J.P. Straley, J. Phys. A: Math. Gen. 31, 6911 (1998)

    Article  ADS  Google Scholar 

  4. T. Sasamoto, J. Phys. A: Math. Gen. 32, 7109 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  5. R.A. Blythe, M.R. Evans, J. Phys. A: Math. Theor. 40, R333 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  6. A. Schadschneider, D. Chowdhury, K. Nishinari, Stochastic Transport in Complex Systems: From Molecules to Vehicles (Elsevier Science, 2010)

  7. D. Yanagisawa, Y. Suma, A. Tomoeda, A. Miura, K. Ohtsuka, K. Nishinari, Transp. Res. Part C 37, 238 (2013)

    Article  Google Scholar 

  8. A. Parmeggiani, T. Franosch, E. Frey, Phys. Rev. Lett. 90, 086601 (2003)

    Article  ADS  Google Scholar 

  9. M.R. Evans, R. Juhász, L. Santen, Phys. Rev. E 68, 026117 (2003)

    Article  ADS  Google Scholar 

  10. A. Parmeggiani, T. Franosch, E. Frey, Phys. Rev. E 70, 046101 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  11. K. Nishinari, Y. Okada, A. Schadschneider, D. Chowdhury, Phys. Rev. Lett. 95, 118101 (2005)

    Article  ADS  Google Scholar 

  12. T. Mitsudo, H. Hayakawa, J. Phys. A: Math. Gen. 39, 15073 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  13. T. Ezaki, K. Nishinari, J. Phys. A: Math. Theor. 45, 185002 (2012)

    Article  ADS  Google Scholar 

  14. I. Neri, N. Kern, A. Parmeggiani, Phys. Rev. Lett. 110, 098102 (2013)

    Article  ADS  Google Scholar 

  15. I. Neri, N. Kern, A. Parmeggiani, New J. Phys. 15, 085005 (2013)

    Article  ADS  Google Scholar 

  16. I. Dhiman, A.K. Gupta, Europhys. Lett. 107, 20007 (2014)

    Article  ADS  Google Scholar 

  17. H.D. Vuijk, R. Rens, M. Vahabi, F.C. MacKintosh, A. Sharma, Phys. Rev. E 91, 032143 (2015)

    Article  ADS  Google Scholar 

  18. J. Sato, K. Nishinari, Phys. Rev. E 93, 042113 (2016)

    Article  ADS  Google Scholar 

  19. S. Ichiki, J. Sato, K. Nishinari, J. Phys. Soc. Jpn 85, 044001 (2016)

    Article  ADS  Google Scholar 

  20. W. Knospe, L. Santen, A. Schadschneider, M. Schreckenberg, J. Phys. A: Math. Gen. 35, 3369 (2002)

    Article  ADS  MathSciNet  Google Scholar 

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Correspondence to Shingo Ichiki.

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Ichiki, S., Sato, J. & Nishinari, K. Totally asymmetric simple exclusion process on a periodic lattice with Langmuir kinetics depending on the occupancy of the forward neighboring site. Eur. Phys. J. B 89, 135 (2016). https://doi.org/10.1140/epjb/e2016-70192-5

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  • DOI: https://doi.org/10.1140/epjb/e2016-70192-5

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