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

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Cellular Automata (ACRI 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9863))

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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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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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Authors and Affiliations

  1. Research Center for Advanced Science and Technology, The University of Tokyo, 4-6-1, Komaba, Meguro-ku, Tokyo, 153-8904, Japan

    Daichi Yanagisawa

  2. Department of Advanced Interdisciplinary Studies, School of Engineering, The University of Tokyo, 4-6-1, Komaba, Meguro-ku, Tokyo, 153-8904, Japan

    Shingo Ichiki

Authors
  1. Daichi Yanagisawa
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  2. Shingo Ichiki
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Correspondence to Daichi Yanagisawa .

Editor information

Editors and Affiliations

  1. University of Perpignan, Perpignan, France

    Samira El Yacoubi

  2. AGH University of Science and Techn, Kraków, Poland

    Jaroslaw Wąs

  3. Department of Computer Science, University of Milano-Bicocca, Milan, Italy

    Stefania Bandini

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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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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-44364-5

  • Online ISBN: 978-3-319-44365-2

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