Generalized discrete and ultradiscrete Burgers equations derived through the correlated random walk
Generalized discrete and ultradiscrete Burgers equations derived through the correlated random walk
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通过相关随机游走导出广义离散和超离散 Burgers 方程
DOI：
10.1080/10236198.2023.2172969
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发表时间：
2023
影响因子：
1.1
通讯作者：
Watanabe Sennosuke
中科院分区：
文献类型：
--
作者：
Fukuda Akiko;Segawa Etsuo;Watanabe Sennosuke
相关随机游走被称为众所周知的随机游走的推广。在本研究中，我们提出了与相关随机游走相对应的广义离散伯格斯方程可以通过科尔-霍普夫变换为广义离散扩散方程来获得。通过应用超离散化技术，可以获得广义超离散扩散方程、超离散 Cole-Hopf 变换和超离散 Burgers 方程的变体。此外，这项研究表明，由此产生的超离散 Burgers 方程产生的元胞自动机可以解释为具有车流可控性的交通流模型。
The correlated random walk is known as a generalization of the well-known random walk. In this study, we present that a generalized discrete Burgers equation corresponding to the correlated random walk can be obtained through a Cole–Hopf transformation to a generalized discrete diffusion equation. By applying a technique called ultradiscretization, the generalized ultradiscrete diffusion equation, the ultradiscrete Cole–Hopf transformation, and a variant of the ultradiscrete Burgers equation are obtained. Additionally, this study shows that the resulting ultradiscrete Burgers equation yields cellular automata that can be interpreted as a traffic flow model with controllability of vehicle flow.
与噪声 Burgers 方程相关的随机元胞自动机
DOI：
10.1016/s0378-4371(98)00299-4
发表时间：
1998
影响因子：
3.3
作者：
H. Emmerich;B. Kahng
通讯作者：
B. Kahng