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Related Experiment Videos

Queuing transitions in the asymmetric simple exclusion process.

Meesoon Ha1, Jussi Timonen, Marcel den Nijs

  • 1Department of Physics, University of Washington, P.O. Box 351560, Seattle, WA 98195-1560, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 20, 2003
PubMed
Summary

This study numerically confirms a dynamic queuing phase transition in a channel flow model. Above the transition, queues exhibit power-law density profiles, suggesting universal scaling properties for traffic jams.

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David Thouless (1934-2019).

Science (New York, N.Y.)·2019

Area of Science:

  • Statistical Mechanics
  • Complex Systems
  • Non-equilibrium Physics

Background:

  • Stochastic driven flow in channels is often modeled using the asymmetric simple exclusion process.
  • Understanding phase transitions and queue dynamics is crucial for analyzing traffic jams and system behavior.

Purpose of the Study:

  • To numerically confirm the existence of a dynamic queuing phase transition.
  • To establish the scaling properties of queues below and above this transition.
  • To investigate the universality of the observed scaling exponent.

Main Methods:

  • Numerical simulations of the asymmetric simple exclusion process.
  • Analysis of queue length and density profiles.
  • Heuristic arguments for universality.

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Main Results:

  • A dynamic queuing phase transition occurs at a nonzero obstruction strength.
  • Below the transition, queue length scales linearly with system size (macroscopic jam).
  • Above the transition, density profiles follow a power law, rho ~ x^(-1/3), with nu=1/3.
  • Fast bonds lead to depletion queues with exponents near 0.63(3).

Conclusions:

  • The exponent nu=1/3 for density profiles is likely universal and independent of the underlying dynamic exponent.
  • The findings have implications for interface faceting and polymer localization near defects.