Max-plus analysis on some binary particle systems

Details Max-plus analysis on some binary particle systems Max-plus analysis on some binary particle systems

2010-12-22

arxiv.org/abs/1012.4887v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

24 pages, 5 figures, submitted to J. Phys. A

Scientific paper

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.

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