## 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 language | English |
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Article number | 295101 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 46 |

Issue number | 29 |

DOIs | |

Publication status | Published - 2013 Jul 26 |

## ASJC Scopus subject areas

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