Max-min-plus expressions for one-dimensional particle cellular automata obtained from a fundamental diagram

Takazumi Okumura, Junta Matsukidaira, Daisuke Takahashi

    Research output: Contribution to journalArticle

    1 Citation (Scopus)

    Abstract

    We study one-dimensional neighborhood-five conservative cellular automata (CA), referred to as particle cellular automata five (particle CA5). We show that evolution equations for particle CA5s that belong to certain types can be obtained in the form of max-min-plus expressions from a fundamental diagram. The obtained equations are transformed into other max-min-plus expressions by ultradiscrete Cole-Hopf transformations, which enable us to analyze the asymptotic behaviors of general solutions. The equations in the Lagrange representation, which describe particle motion, are also presented, which can also be obtained from a fundamental diagram. Finally, we discuss the generalization to a one-dimensional conservative neighborhood-n CA, i.e., particle CAn.

    Original languageEnglish
    Article number295101
    JournalJournal of Physics A: Mathematical and Theoretical
    Volume46
    Issue number29
    DOIs
    Publication statusPublished - 2013 Jul 26

    Fingerprint

    Fundamental Diagram
    cellular automata
    Cellular automata
    Min-max
    Cellular Automata
    diagrams
    Cole-Hopf Transformation
    particle motion
    General Solution
    Lagrange
    Evolution Equation
    Asymptotic Behavior
    Motion

    ASJC Scopus subject areas

    • Mathematical Physics
    • Physics and Astronomy(all)
    • Statistical and Nonlinear Physics
    • Modelling and Simulation
    • Statistics and Probability

    Cite this

    Max-min-plus expressions for one-dimensional particle cellular automata obtained from a fundamental diagram. / Okumura, Takazumi; Matsukidaira, Junta; Takahashi, Daisuke.

    In: Journal of Physics A: Mathematical and Theoretical, Vol. 46, No. 29, 295101, 26.07.2013.

    Research output: Contribution to journalArticle

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