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.
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References
MacDonald, C.T., Gibbs, J.H., Pipkin, A.C.: Kinetics of biopolymerization on nucleic acid templates. Biopolymers 6(1), 1–5 (1968)
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)
Schadschneider, A., Chowdhury, D., Nishinari, K., Santen, L.: Stochastic Transport in Complex Systems. Elsevier, Amsterdam/Oxford (2010)
Wolfram, S.: Cellular Automata and Complexity: Collected Papers. Westview Press, Boulder (1994)
Parmeggiani, A., Franosch, T., Frey, E.: Phase coexistence in driven one-dimensional transport. Phys. Rev. Lett. 90(8), 086601 (2003)
Evans, M.R., Juhász, R., Santen, L.: Shock formation in an exclusion process with creation and annihilation. Phys. Rev. E 68(2), 026117 (2003)
Parmeggiani, A., Franosch, T., Frey, E.: Totally asymmetric simple exclusion process with Langmuir kinetics. Phys. Rev. E 70(4), 046101 (2004)
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)
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)
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)
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)
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)
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)
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)
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)
Acknowlgement
We are grateful to Jun Sato for kind cooperation in checking this paper. This work was financially supported by JSPS KAKENHI Grant Number 15K17583.
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Yanagisawa, D., Ichiki, S. (2016). Totally Asymmetric Simple Exclusion Process on an Open Lattice with Langmuir Kinetics Depending on the Occupancy of the Forward Neighboring Site. In: El Yacoubi, S., Wąs, J., Bandini, S. (eds) Cellular Automata. ACRI 2016. Lecture Notes in Computer Science(), vol 9863. Springer, Cham. https://doi.org/10.1007/978-3-319-44365-2_40
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DOI: https://doi.org/10.1007/978-3-319-44365-2_40
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