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Facilitated asymmetric exclusion.

Alan Gabel1, P L Krapivsky, S Redner

  • 1Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA.

Physical Review Letters
|January 15, 2011
PubMed
Summary
This summary is machine-generated.

We introduce facilitated asymmetric exclusion processes where particles move when pushed. An unexpected discontinuity in rarefaction waves was observed, differing from typical shock waves in these systems.

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Area of Science:

  • Statistical mechanics
  • Non-equilibrium systems
  • Theoretical physics

Background:

  • Asymmetric exclusion processes (AEPs) are fundamental models in statistical mechanics.
  • Understanding particle dynamics and emergent phenomena in driven systems is crucial.
  • Facilitated transport mechanisms can alter standard exclusion process behavior.

Purpose of the Study:

  • Introduce a novel class of facilitated asymmetric exclusion processes.
  • Analyze particle dynamics, specifically how neighbor interactions influence movement.
  • Investigate the formation and characteristics of density waves (rarefaction and shock waves).

Main Methods:

  • Analytical determination of steady-state current and cluster size distribution on a ring.
  • Modeling particle hopping based on neighbor occupation and facilitation.
  • Simulation or theoretical analysis of initial density profiles (downstep and upstep).

Main Results:

  • Derived the steady-state current and cluster size distribution for the simplest facilitated AEP.
  • Observed that an initial density downstep forms a rarefaction wave with a potential jump discontinuity.
  • An initial density upstep results in a shock wave, consistent with some AEPs.

Conclusions:

  • The facilitated nature of these exclusion processes leads to unique wave phenomena.
  • A general occurrence of jump discontinuities in rarefaction waves for facilitated exclusion processes was identified.
  • These findings offer new insights into non-equilibrium statistical mechanics and transport phenomena.