实值max-plus粒子系统三维基本图析的解析推导

中文摘要 AI 辅助

我们研究有限周期晶格上的实值max-plus粒子系统。其三维基本图将平均流与两个密度相关联：守恒粒子密度和由局部状态函数定义的第二个密度。我们证明，对于所有状态值在[0,1]内的任意初始数据，偏离该图的偏差趋于零。证明使用了两个非负局部量及其演化关系。对于所有状态值在[0,1]内的有理初始数据，轨道最终是周期的，且基本图关系在周期轨道上精确成立。

英文摘要

We study a real-valued max-plus particle system on a finite periodic lattice. Its three-dimensional fundamental diagram relates the mean flow to two densities: the conserved particle density and a second density defined by a local state function. We prove that the deviation from the diagram tends to zero for arbitrary initial data with all state values in [0,1]. The proof uses two nonnegative local quantities and their evolution relations. For rational initial data with all state values in $[0,1]$, the orbit is eventually periodic, and the fundamental-diagram relation holds exactly on the periodic orbit.

发表机构

• Faculty of Fundamental Science and Engineering, Waseda University（早稻田大学基础科学与工程学院）
• Faculty of Advanced Science and Technology, Ryukoku University（龙谷大学先进科学技术学部）
• Faculty of Information Design, Heisei International University（平成国际大学信息设计学部）

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