Euler-Lagrange correspondence of ultra-discrete systems

超离散系统的欧拉-拉格朗日对应

• 批准号: 15560055
• 负责人: MATSUKIDAIRA Junta
• 金额: $ 1.22万
• 依托单位: Ryukoku University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2003
• 资助国家: 日本
• 起止时间: 2003 至 2004
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15560055/
• 关键词: solution; cellular automata; ultra-discrete system; Euler-Lagrange correspondence; セル・オートマン; Euler-Langrange対応

It is well known that Burgers cellular automaton includes Rule184 elementary cellular automaton, which is the basic traffic flow model Burgers CA is an Euler representation equation, in which variable expresses a strength of a field. Recently, Lagrange representation of Rule 184 has been found, in which variable expresses a position of particles. As this representation is expressed in a form of Max-Plus algebra, it is natural to consider the link between two representations. In the paper "Euler-Lagrange correspondence of cellular automaton for traffic-flow models, J.Matsukidaira and KNishinari, Phys.Rev.Lett.Vol.90,No.8,p088701(2003)", we have found the transformation formula between Euler representation and Lagrange representation We have been able to obtain this formula by using a new algebraic formula between Max-Plus algebra and Step function. We have also applied this method to multi-value, multi-velocity traffic flow models and have been able to obtain Euler-Lagrange correspondence of the Fukui-Ishibashi model and the quick-start model Furthermore, we have applied this method to soliton cellular automata and have succeeded to find the Euler-Lagrange correspondence of Box and Ball system. We are now preparing the paper for this result.

众所周知，Burgers元胞自动机包括Rule 184初等元胞自动机，它是基本的交通流模型Burgers CA是一个欧拉表示方程，其中变量表示场的强度。最近，已经发现了规则184的拉格朗日表示，其中变量表示粒子的位置。由于这种表示是以Max-Plus代数的形式表示的，因此很自然地要考虑两种表示之间的联系。在论文“交通流模型的元胞自动机的欧拉-拉格朗日对应，J.Matsukidaira和KNishinari，Phys.Rev.Lett.Vol.90，No.8，p088701（2003）"中，我们找到了欧拉表示和拉格朗日表示之间的转换公式，并利用Max-Plus代数和阶梯函数之间的一个新的代数公式得到了这个公式。我们还将此方法应用于多值、多速度交通流模型，得到了Fukui-Ishibashi模型和快速启动模型的Euler-Lagrange对应。此外，我们还将此方法应用于孤立子元胞自动机，成功地得到了Box和Ball系统的Euler-Lagrange对应。我们现在正在为这一结果准备论文。

项目成果

J.Matsukidaira, K.Nishinari: "Euler-Lagrange correspondence of generalized Burgers cellular automaton"J.Mod.Phys.C. 15巻4号. (2004)

J.Matsukidaira、K.Nishinari：“广义伯格元胞自动机的欧拉-拉格朗日对应”，J.Mod.Phys.C，第 15 卷，第 4 期（2004 年）

Euler–Lagrange Correspondence Of Generalized Burgers Cellular Automaton

• DOI: 10.1142/s0129183104005917
• 发表时间: 2003-11
• 期刊: International Journal of Modern Physics C
• 影响因子: 1.9
• 作者: J. Matsukidaira;K. Nishinari