Coexistence of shocks and rarefaction fans: complex phase diagram of a simple hyperbolic particle system

Marton Balazs, Attila László Nagy, Balint Toth, István Tóth

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This paper investigates the non-equilibrium hydrodynamic behavior of a simple totally asymmetric interacting particle system of particles, antiparticles and holes on Z. Rigorous hydrodynamic results apply to our model with a hydrodynamic flux that is exactly calculated and shown to change convexity in some region of the model parameters. We then characterize the entropy solutions of the hydrodynamic equation with step initial condition in this scenario which include various mixtures of rarefaction fans and shock waves. We highlight how the phase diagram of the model changes by varying the model parameters.
Original languageEnglish
Pages (from-to)115-125
Number of pages11
JournalJournal of Statistical Physics
Issue number1
Early online date24 Aug 2016
Publication statusPublished - Oct 2016



  • Asymmetric particle system
  • hydrodynamic equation
  • non-equilibrium behavior
  • non-convex flux
  • Riemann problem
  • shock
  • rarefaction fan

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