Analytical properties of ultradiscrete Burgers equation and rule-184 cellular automaton

Katsuhiro Nishinari, Daisuke Takahashi

    Research output: Contribution to journalArticle

    91 Citations (Scopus)

    Abstract

    In this paper, we propose an ultradiscrete Burgers equation of which all the variables are discrete. The equation is derived from a discrete Burgers equation under an ultradiscrete limit and reduces to an ultradiscrete diffusion equation through the Cole-Hopf transformation. Moreover, it becomes a cellular automaton (CA) under appropriate conditions and is identical to rule-184 CA in a specific case. We show shock wave solutions and asymptotic behaviours of the CA exactly via the diffusion equation. Finally, we propose a particle model expressed by the CA and discuss a mean flux of particles.

    Original languageEnglish
    Pages (from-to)5439-5450
    Number of pages12
    JournalJournal of Physics A: Mathematical and General
    Volume31
    Issue number24
    DOIs
    Publication statusPublished - 1998 Jun 19

    Fingerprint

    Burger equation
    cellular automata
    Cellular automata
    Burgers Equation
    Cellular Automata
    Diffusion equation
    Cole-Hopf Transformation
    Discrete Equations
    Shock Waves
    Shock waves
    shock waves
    Asymptotic Behavior
    Fluxes

    ASJC Scopus subject areas

    • Physics and Astronomy(all)
    • Statistical and Nonlinear Physics
    • Mathematical Physics

    Cite this

    Analytical properties of ultradiscrete Burgers equation and rule-184 cellular automaton. / Nishinari, Katsuhiro; Takahashi, Daisuke.

    In: Journal of Physics A: Mathematical and General, Vol. 31, No. 24, 19.06.1998, p. 5439-5450.

    Research output: Contribution to journalArticle

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