### Abstract

We are concerned with a special class of binary cellular automata, i.e. the so-called particle cellular automata (PCA) in this paper. We first propose max-plus expressions to PCA of four neighbors. Then, by utilizing basic operations of the max-plus algebra and appropriate transformations, PCA4-1, 4-2 and 4-3 are solved exactly and their general solutions are found in terms of max-plus expressions. Finally, we analyze the asymptotic behaviors of general solutions and prove the fundamental diagrams exactly.

Original language | English |
---|---|

Article number | 135102 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 44 |

Issue number | 13 |

DOIs | |

Publication status | Published - 2011 Apr 1 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

*Journal of Physics A: Mathematical and Theoretical*,

*44*(13), [135102]. https://doi.org/10.1088/1751-8113/44/13/135102

**Max-plus analysis on some binary particle systems.** / Takahashi, Daisuke; Matsukidaira, Junta; Hara, Hiroaki; Feng, Bao Feng.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and Theoretical*, vol. 44, no. 13, 135102. https://doi.org/10.1088/1751-8113/44/13/135102

}

TY - JOUR

T1 - Max-plus analysis on some binary particle systems

AU - Takahashi, Daisuke

AU - Matsukidaira, Junta

AU - Hara, Hiroaki

AU - Feng, Bao Feng

PY - 2011/4/1

Y1 - 2011/4/1

N2 - We are concerned with a special class of binary cellular automata, i.e. the so-called particle cellular automata (PCA) in this paper. We first propose max-plus expressions to PCA of four neighbors. Then, by utilizing basic operations of the max-plus algebra and appropriate transformations, PCA4-1, 4-2 and 4-3 are solved exactly and their general solutions are found in terms of max-plus expressions. Finally, we analyze the asymptotic behaviors of general solutions and prove the fundamental diagrams exactly.

AB - We are concerned with a special class of binary cellular automata, i.e. the so-called particle cellular automata (PCA) in this paper. We first propose max-plus expressions to PCA of four neighbors. Then, by utilizing basic operations of the max-plus algebra and appropriate transformations, PCA4-1, 4-2 and 4-3 are solved exactly and their general solutions are found in terms of max-plus expressions. Finally, we analyze the asymptotic behaviors of general solutions and prove the fundamental diagrams exactly.

UR - http://www.scopus.com/inward/record.url?scp=79952651969&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79952651969&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/44/13/135102

DO - 10.1088/1751-8113/44/13/135102

M3 - Article

AN - SCOPUS:79952651969

VL - 44

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 13

M1 - 135102

ER -