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

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

doi:10.1007/s10955-016-1600-2

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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Abstract

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 language	English
Pages (from-to)	115-125
Number of pages	11
Journal	Journal of Statistical Physics
Volume	165
Issue number	1
Early online date	24 Aug 2016
DOIs	https://doi.org/10.1007/s10955-016-1600-2
Publication status	Published - Oct 2016

Keywords

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

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10.1007/s10955-016-1600-2

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This is the accepted author manuscript (AAM). The final published version (version of record) is available online via Springer Verlag at DOI: 10.1007/s10955-016-1600-2. Please refer to any applicable terms of use of the publisher.
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title = "Coexistence of shocks and rarefaction fans: complex phase diagram of a simple hyperbolic particle system",

abstract = "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.",

keywords = "Asymmetric particle system, hydrodynamic equation, non-equilibrium behavior, non-convex flux, Riemann problem, shock, rarefaction fan",

author = "Marton Balazs and Nagy, {Attila L{\'a}szl{\'o}} and Balint Toth and Istv{\'a}n T{\'o}th",

year = "2016",

month = oct,

doi = "10.1007/s10955-016-1600-2",

language = "English",

volume = "165",

pages = "115--125",

journal = "Journal of Statistical Physics",

issn = "0022-4715",

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TY - JOUR

T1 - Coexistence of shocks and rarefaction fans

T2 - complex phase diagram of a simple hyperbolic particle system

AU - Balazs, Marton

AU - Nagy, Attila László

AU - Toth, Balint

AU - Tóth, István

PY - 2016/10

Y1 - 2016/10

N2 - 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.

AB - 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.

KW - Asymmetric particle system

KW - hydrodynamic equation

KW - non-equilibrium behavior

KW - non-convex flux

KW - Riemann problem

KW - shock

KW - rarefaction fan

UR - http://arxiv.org/abs/1601.02161

U2 - 10.1007/s10955-016-1600-2

DO - 10.1007/s10955-016-1600-2

M3 - Article (Academic Journal)

VL - 165

SP - 115

EP - 125

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 1

ER -

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

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Professor Balint A Toth

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

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Professor Balint A Toth

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