Max-plus analysis on some binary particle systems

Daisuke Takahashi; Junta Matsukidaira; Hiroaki Hara; Bao Feng Feng

doi:10.1088/1751-8113/44/13/135102

Max-plus analysis on some binary particle systems

Daisuke Takahashi^*, Junta Matsukidaira, Hiroaki Hara, Bao Feng Feng

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

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	https://doi.org/10.1088/1751-8113/44/13/135102
Publication status	Published - 2011 Apr 1
Externally published	Yes

ASJC Scopus subject areas

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

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AU - Hara, Hiroaki

AU - Feng, Bao Feng

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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.

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Max-plus analysis on some binary particle systems

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