Totally Asymmetric Simple Exclusion Process on an Open Lattice with Langmuir Kinetics Depending on the Occupancy of the Forward Neighboring Site

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9863)

Abstract

We have generalized the update rule of the Langmuir kinetics, which is attachment and detachment dynamics of particles, in the totally asymmetric simple exclusion process. The attachment and detachment rates in our extended model depend on the occupancy of the forward neighboring site. Although there are some extended models that consider the effect of the occupancy of the neighboring sites, our model is the first one that allows one to set the attachment and detachment rates independently without any restrictions.

We have performed a mean-field analysis and obtained phase diagrams and density profiles. It is elucidated that the attachment to vacant region and detachment from congested region extend the area of the phase that accompanies a shock, i.e., a domain wall, which divides the low and high density regime. Results of Monte Carlo simulations show good agreement with the mean-field density profiles, so that the validity of the phase diagrams are verified.

Keywords

Totally asymmetric simple exclusion process Langmuir kinetics Open boundary 

References

  1. 1.
    MacDonald, C.T., Gibbs, J.H., Pipkin, A.C.: Kinetics of biopolymerization on nucleic acid templates. Biopolymers 6(1), 1–5 (1968)CrossRefGoogle Scholar
  2. 2.
    Derrida, B., Evans, M.R., Hakim, V., Pasquier, V.: Exact solution of a 1D asymmetric exclusion model using a matrix formulation. J. Phys. A Math. Gen. 26(7), 1493–1517 (1993)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Schadschneider, A., Chowdhury, D., Nishinari, K., Santen, L.: Stochastic Transport in Complex Systems. Elsevier, Amsterdam/Oxford (2010)Google Scholar
  4. 4.
    Wolfram, S.: Cellular Automata and Complexity: Collected Papers. Westview Press, Boulder (1994)MATHGoogle Scholar
  5. 5.
    Parmeggiani, A., Franosch, T., Frey, E.: Phase coexistence in driven one-dimensional transport. Phys. Rev. Lett. 90(8), 086601 (2003)CrossRefGoogle Scholar
  6. 6.
    Evans, M.R., Juhász, R., Santen, L.: Shock formation in an exclusion process with creation and annihilation. Phys. Rev. E 68(2), 026117 (2003)CrossRefGoogle Scholar
  7. 7.
    Parmeggiani, A., Franosch, T., Frey, E.: Totally asymmetric simple exclusion process with Langmuir kinetics. Phys. Rev. E 70(4), 046101 (2004)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Sato, J., Nishinari, K.: Relaxation dynamics of the asymmetric simple exclusion process with Langmuir kinetics on a ring. Phys. Rev. E 93(4), 042113 (2016)CrossRefGoogle Scholar
  9. 9.
    Kruse, K., Sekimoto, K.: Growth of fingerlike protrusions driven by molecular motors. Phys. Rev. E - Stat. Nonlinear, Soft Matter Phys. 66(3), 1–5 (2002)CrossRefGoogle Scholar
  10. 10.
    Muto, E., Sakai, H., Kaseda, K.: Long-range cooperative binding of kinesin to a microtubule in the presence of ATP. J. Cell Biol. 168(5), 691–696 (2005)CrossRefGoogle Scholar
  11. 11.
    Vuijk, H.D., Rens, R., Vahabi, M., MacKintosh, F.C., Sharma, A.: Driven diffusive systems with mutually interactive Langmuir kinetics. Phys. Rev. E 91(3), 032143 (2015)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Messelink, J., Rens, R., Vahabi, M., MacKintosh, F.C., Sharma, A.: On-site residence time in a driven diffusive system: violation and recovery of a mean-field description. Phys. Rev. E 93(1), 012119 (2016)CrossRefGoogle Scholar
  13. 13.
    Ichiki, S., Sato, J., Nishinari, K.: Totally asymmetric simple exclusion process with Langmuir kinetics depending on the occupancy of the neighboring sites. J. Phys. Soc. Jpn. 85(4), 044001 (2016)CrossRefGoogle Scholar
  14. 14.
    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(5), 135 (2016)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Lighthill, M.J., Whitham, G.B.: On kinematic waves. I. Flood movement in long rivers. Proc. R. Soc. A Math. Phys. Eng. Sci. 229(1178), 281–316 (1955)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Research Center for Advanced Science and TechnologyThe University of TokyoTokyoJapan
  2. 2.Department of Advanced Interdisciplinary Studies, School of EngineeringThe University of TokyoTokyoJapan

Personalised recommendations