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Totally asymmetric exclusion process with site-wise dynamic disorder

Totally asymmetric exclusion process with site-wise dynamic disorder
Totally asymmetric exclusion process with site-wise dynamic disorder
We propose an extension of the totally asymmetric simple exclusion process (TASEP) in which particles hopping along a lattice can be blocked by obstacles that dynamically attach/detach from lattice sites. The model can be thought as TASEP with site-wise dynamic disorder. We consider two versions of defect dynamics: (i) defects can bind to any site, irrespective of particle occupation, (ii) defects only bind to sites which are not occupied by particles (particle-obstacle exclusion). In case (i) there is a symmetric, parabolic-like relationship between the current and particle density, as in the standard TASEP. Case (ii) leads to a skewed relationship for slow defect dynamics. We also show that the presence of defects induces particle clustering, despite the translation invariance of the system. For open boundaries the same three phases as for the standard TASEP are observed, albeit the position of phase boundaries is affected by the presence of obstacles. We develop a simple mean-field theory that captures the model’s quantitative behaviour for periodic and open boundary conditions and yields good estimates for the current-density relationship, mean cluster sizes and phase boundaries. Lastly, we discuss an application of the model to the biological process of gene transcription.
1-27
Waclaw, Bartlomiej
caa8d9c8-625a-4b49-98b5-a319cec21742
Cholewa-Waclaw, Justyna
9452d1ef-ad40-4793-831d-344eab0ae742
Greulich, Philip
65da32ad-a73a-435a-86e0-e171437430a9
Waclaw, Bartlomiej
caa8d9c8-625a-4b49-98b5-a319cec21742
Cholewa-Waclaw, Justyna
9452d1ef-ad40-4793-831d-344eab0ae742
Greulich, Philip
65da32ad-a73a-435a-86e0-e171437430a9

Waclaw, Bartlomiej, Cholewa-Waclaw, Justyna and Greulich, Philip (2019) Totally asymmetric exclusion process with site-wise dynamic disorder. Journal of Physics A, 52 (065002), 1-27, [1809.0544]. (doi:10.1088/1751-8121/aafb8a).

Record type: Article

Abstract

We propose an extension of the totally asymmetric simple exclusion process (TASEP) in which particles hopping along a lattice can be blocked by obstacles that dynamically attach/detach from lattice sites. The model can be thought as TASEP with site-wise dynamic disorder. We consider two versions of defect dynamics: (i) defects can bind to any site, irrespective of particle occupation, (ii) defects only bind to sites which are not occupied by particles (particle-obstacle exclusion). In case (i) there is a symmetric, parabolic-like relationship between the current and particle density, as in the standard TASEP. Case (ii) leads to a skewed relationship for slow defect dynamics. We also show that the presence of defects induces particle clustering, despite the translation invariance of the system. For open boundaries the same three phases as for the standard TASEP are observed, albeit the position of phase boundaries is affected by the presence of obstacles. We develop a simple mean-field theory that captures the model’s quantitative behaviour for periodic and open boundary conditions and yields good estimates for the current-density relationship, mean cluster sizes and phase boundaries. Lastly, we discuss an application of the model to the biological process of gene transcription.

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Totally asymmetric exclusion process with site-wise dynamic disorder - Accepted Manuscript
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Accepted/In Press date: 2 January 2019
e-pub ahead of print date: 2 January 2019
Published date: 21 January 2019

Identifiers

Local EPrints ID: 423459
URI: http://eprints.soton.ac.uk/id/eprint/423459
PURE UUID: 683114cc-3d5c-4df6-86f9-15d9055fddcc
ORCID for Philip Greulich: ORCID iD orcid.org/0000-0001-5247-6738

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Date deposited: 24 Sep 2018 16:30
Last modified: 02 Jan 2020 05:01

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