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Local resetting in a dynamically disordered exclusion process

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  • Bhatia, Nikhil
  • Gupta, Arvind Kumar

Abstract

Inspired by the recycling process and obstruction faced by mRNA polymerase during gene transcription, we study an open, dynamically disordered, totally asymmetric simple exclusion process where particles all over the lattice locally reset to the entry site. The mean-field approximations have been employed to obtain analytical stationary-state characteristics such as density profiles, current, and phase boundaries. These results are validated by performing extensive numerical simulations. The role of hindrance-causing parameters is consolidated into a unifying parameter called the obstruction factor. The phase diagrams obtained for various choices regarding the resetting rate and the obstruction factor possess five stationary phases: three pure and two co-existing phases. Both the co-existing phases exist in a region and have localized domain walls. The quadruple and triple points in the phase diagram shift anti-diagonally with an increase in the resetting rate or the obstruction factor, expanding the region comprising the maximal-current phase. Further, potential phase transitions and the domain wall’s behavior under the influence of resetting rates and the obstruction factor have been examined. The finite-size effect has also been scrutinized on the system’s stationary-state characteristics.

Suggested Citation

  • Bhatia, Nikhil & Gupta, Arvind Kumar, 2025. "Local resetting in a dynamically disordered exclusion process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 658(C).
    • Handle: RePEc:eee:phsmap:v:658:y:2025:i:c:s0378437124007908
    DOI: 10.1016/j.physa.2024.130280
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    References listed on IDEAS

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    1. Bhatia, Nikhil & Gupta, Arvind Kumar, 2023. "Role of site-wise dynamic defects in a resource-constrained exclusion process," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    2. Kai Nagel, 1996. "Particle Hopping Models and Traffic Flow Theory," Working Papers 96-04-015, Santa Fe Institute.
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