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Current-density relation in the exclusion process with dynamic obstacles.

J Szavits-Nossan1, B Waclaw1,2

  • 1School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom.

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|November 20, 2020
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Summary
This summary is machine-generated.

This study explores the totally asymmetric simple exclusion process (TASEP) with dynamic obstacles. Results show a quasiparabolic current-density relation, similar to standard TASEP, arising from complex term cancellations.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Biophysics

Background:

  • The totally asymmetric simple exclusion process (TASEP) is a fundamental model in statistical mechanics.
  • Understanding particle transport with dynamic obstacles is crucial for biological processes like DNA transcription.
  • Previous mean-field approximations failed to precisely define the current-density relation in TASEP with obstacles.

Purpose of the Study:

  • To investigate the current-density relation in TASEP with dynamically binding and unbinding obstacles.
  • To elucidate the underlying mechanisms responsible for the observed current-density behavior.
  • To bridge the gap between simulation results and exact theoretical explanations.

Main Methods:

  • Extensive Monte Carlo simulations were employed to model the TASEP with dynamic obstacles.
  • Exact calculations were performed in the limits of low and high particle densities.
  • Analysis focused on the current-density relationship and its dependence on obstacle dynamics.

Main Results:

  • Monte Carlo simulations revealed a quasiparabolic current-density relation, mirroring the behavior of TASEP without obstacles.
  • The observed symmetric, quasiparabolic relation was found to result from a nontrivial cancellation of higher-order terms.
  • This cancellation mechanism is analogous to that observed in the standard TASEP.

Conclusions:

  • The presence of dynamic obstacles in TASEP does not fundamentally alter the emergent quasiparabolic current-density relationship.
  • The study provides a deeper theoretical understanding of particle transport phenomena in complex systems.
  • The findings have implications for modeling biological systems with interacting components.