论文标题
从动力学到宏观模型，然后背面
From kinetic to macroscopic models and back
论文作者
论文摘要
我们研究的动力学模型的交通流量为特征，其特征是产生向后传播波的特性。这些波可以用通常在高速公路上观察到的停留波的现象来识别。特别是，微观速度空间和动力学模型中的相互作用速率的精制建模允许在密集的交通中获得弱不稳定的向后传播波，而无需依赖非本地术语或多个可值的基本图。这些波的稳定性分析是使用Chapman-Enskog扩展进行的。这导致了BGK型模型得出的BGK型模型，该模型是跟随者或Bando模型的介质极限，其宏观极限属于二阶AW-Rascle和Zhang模型的类别。
We study kinetic models for traffic flow characterized by the property of producing backward propagating waves. These waves may be identified with the phenomenon of stop-and-go waves typically observed on highways. In particular, a refined modeling of the space of the microscopic speeds and of the interaction rate in the kinetic model allows to obtain weakly unstable backward propagating waves in dense traffic, without relying on non-local terms or multi--valued fundamental diagrams. A stability analysis of these waves is carried out using the Chapman-Enskog expansion. This leads to a BGK-type model derived as the mesoscopic limit of a Follow-The-Leader or Bando model, and its macroscopic limit belongs to the class of second-order Aw-Rascle and Zhang models.
