EULER–LAGRANGE CORRESPONDENCE OF GENERALIZED BURGERS CELLULAR AUTOMATON

Junta Matsukidaira () and Katsuhiro Nishinari ()
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Junta Matsukidaira: Department of Applied Mathematics and Informatics, Ryukoku University, Otsu, Shiga 520-2194, Japan
Katsuhiro Nishinari: Department of Applied Mathematics and Informatics, Ryukoku University, Otsu, Shiga 520-2194, Japan

International Journal of Modern Physics C (IJMPC), 2004, vol. 15, issue 04, 507-515

Abstract: Recently, we have proposed aEuler–Lagrange transformationfor cellular automata (CA) by developing new transformation formulas. Applying this method to the Burgers CA (BCA), we have succeeded in obtaining the Lagrange representation of the BCA. In this paper, we apply this method to multi-value generalized Burgers CA (GBCA) which include the Fukui–Ishibashi model and the quick-start model associated with traffic flow. As a result, we have succeeded in clarifying the Euler–Lagrange correspondence of these models. It turns out moreover that the GBCA can naturally be considered as a simple model of a multi-lane traffic flow.

Keywords: Euler–Lagrange correspondence; ultra-discrete; cellular automaton; traffic flow model (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1142/S0129183104005917

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