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

Takazumi Okumura, Junta Matsukidaira, Daisuke Takahashi

研究成果査読

1 被引用数 (Scopus)

抄録

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.

本文言語English
論文番号295101
ジャーナルJournal of Physics A: Mathematical and Theoretical
46
29
DOI
出版ステータスPublished - 2013 7 26

ASJC Scopus subject areas

  • 統計物理学および非線形物理学
  • 統計学および確率
  • モデリングとシミュレーション
  • 数理物理学
  • 物理学および天文学(全般)

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