Max-plus analysis on some binary particle systems
Exactly Solvable and Integrable Systems
2015-05-20 v1 Cellular Automata and Lattice Gases
Pattern Formation and Solitons
Abstract
We concern with a special class of binary cellular automata, i.e., the so-called particle cellular automata (PCA) in the present paper. We first propose max-plus expressions to PCA of 4 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.
Keywords
Cite
@article{arxiv.1012.4887,
title = {Max-plus analysis on some binary particle systems},
author = {Daisuke Takahashi and Junta Matsukidaira and Hiroaki Hara and Bao-Feng Feng},
journal= {arXiv preprint arXiv:1012.4887},
year = {2015}
}
Comments
24 pages, 5 figures, submitted to J. Phys. A