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Coexistence of Shocks and Rarefaction Fans: Complex Phase Diagram of a Simple Hyperbolic Particle System

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Abstract

This paper investigates the non-equilibrium hydrodynamic behavior of a simple totally asymmetric interacting particle system of particles, antiparticles and holes on \(\mathbb {Z}\). 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.

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Acknowledgments

Márton Balázs and Bálint Tóth acknowledge support from the Grants OTKA K100473 and OTKA K109684. B. T. also thanks support from the Leverhulme International Network Grant “Laplacians, Random Walks and Quantum Spin Systems”. We are indebted to an anonymous referee whose detailed and helpful comments greatly improved the exposition of the paper.

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Authors and Affiliations

  1. School of Mathematics, University of Bristol, Bristol, UK

    Márton Balázs & Bálint Tóth

  2. Institute of Mathematics, Budapest University of Technology and Economics, Budapest, Hungary

    Attila László Nagy & István Tóth

  3. MTA-BME Stochastics Research Group and Rényi Institute Budapest, Budapest, Hungary

    Bálint Tóth

Authors
  1. Márton Balázs
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  2. Attila László Nagy
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  3. Bálint Tóth
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  4. István Tóth
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Correspondence to Attila László Nagy.

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Balázs, M., Nagy, A.L., Tóth, B. et al. Coexistence of Shocks and Rarefaction Fans: Complex Phase Diagram of a Simple Hyperbolic Particle System. J Stat Phys 165, 115–125 (2016). https://doi.org/10.1007/s10955-016-1600-2

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  • DOI: https://doi.org/10.1007/s10955-016-1600-2

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