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.
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U2 - 10.1088/1751-8113/44/13/135102
DO - 10.1088/1751-8113/44/13/135102
M3 - Article
AN - SCOPUS:79952651969
SN - 1751-8113
VL - 44
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
IS - 13
M1 - 135102
ER -