Experiments with pedestrians revealed that the geometry of the domain, as well as the incentive of pedestrians to reach a target as fast as possible have a strong influence on the overall dynamics. In this paper, we propose and validate different mathematical models at the micro- and macroscopic levels to study the influence of both effects. We calibrate the models with experimental data and compare the results at the micro- as well as macroscopic levels. Our numerical simulations reproduce qualitative experimental features on both levels, and indicate how geometry and motivation level influence the observed pedestrian density. Furthermore, we discuss the dynamics of solutions for different modeling approaches and comment on the analysis of the respective equations.

中文翻译：

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走廊拥挤和推挤的微观和宏观建模

对行人的实验表明，该区域的几何形状以及行人尽可能快地达到目标的动机对整体动力学有很大影响。在本文中，我们在微观和宏观层面提出并验证了不同的数学模型，以研究这两种效应的影响。我们用实验数据校准模型，并比较微观和宏观水平的结果。我们的数值模拟在两个级别上都再现了定性的实验特征，并指出了几何形状和动机级别如何影响观察到的行人密度。此外，我们讨论了针对不同建模方法的解决方案的动力学问题，并对有关各个方程的分析进行了评论。