FLOW ON SWEEPING NETWORKS
FLOW ON SWEEPING NETWORKS
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DOI：
10.1137/130927061
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发表时间：
2014-01-01
影响因子：
1.6
通讯作者：
Liu, Jian-Guo
中科院分区：
文献类型：
--
作者：
Degond, Pierre;Herty, Michael;Liu, Jian-Guo
我们引入了一个元胞自动机模型和一个关于图上流的输运方程。通过切换过程来描述流的方向，其中切换概率根据相邻小区中的传输量的值动态地改变。一种动机是在一条狭小的走廊中，恐慌情况下的行人动态，在走廊的一部分，人们的传播可以是向左的，也可以是向右的。在混沌传播和平均场极限的假设下，我们得到了一个主方程和相应的平均场动力学模型和宏观模型。对稳态进行了计算和分析，并展示了多个亚稳态和磁滞的可能性。
We introduce a cellular automaton model coupled with a transport equation for flows on graphs. The direction of the flow is described by a switching process where the switching probability dynamically changes according to the value of the transported quantity in the neighboring cells. A motivation is pedestrian dynamics during panic situations in a small corridor where the propagation of people in a part of the corridor can be either left- or right-going. Under the assumptions of propagation of chaos and mean-field limit, we derive a master equation and the corresponding mean-field kinetic and macroscopic models. Steady-states are computed and analyzed and exhibit the possibility of multiple metastable states and hysteresis.