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Dynamic instability transitions in one-dimensional driven diffusive flow with nonlocal hopping.

Meesoon Ha1, Hyunggyu Park, Marcel den Nijs

  • 1Department of Physics, Chonbuk National University, Jeonju 561-756, Korea.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 7, 2007
PubMed
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This study reveals how nonlocal hopping drives phase transitions in driven stochastic flow systems. It identifies conditions for second-order and first-order transitions into an empty-road phase, driven by cluster dynamics.

Area of Science:

  • Statistical Mechanics
  • Complex Systems
  • Nonlinear Dynamics

Background:

  • One-dimensional driven stochastic flow models exhibit complex phase behaviors.
  • Competing local and nonlocal hopping events introduce instabilities.
  • Nonlocal interactions can lead to significant particle clustering.

Purpose of the Study:

  • To investigate the phase transition from a populated to an empty-road (ER) phase in a driven stochastic flow system.
  • To analyze the role of nonlocal hopping and particle clustering in this transition.
  • To determine the order of the phase transition under different control regimes.

Main Methods:

  • Implementation within the asymmetric exclusion process framework.
  • Numerical simulations to observe system dynamics and phase transitions.

Related Experiment Videos

  • Analysis of cluster dynamics and their influence on scaling properties.

    • Main Results:

    • Nonlocal skids promote strong clustering in the stationary populated phase.
    • The transition to the ER phase is second order when the entry point reservoir controls current.
    • The transition is first order when the bulk controls current, driven by cluster drift velocity reversal.

    Conclusions:

    • Cluster dynamics are crucial for driving phase transitions and determining scaling properties.
    • The order of the phase transition depends on the dominant control mechanism (reservoir vs. bulk).
    • Analytic current, linear density vanishing, and uncorrelated noise fluctuations characterize the critical line.