Cordes Jakob, Schadschneider Andreas, Nicolas Alexandre
Institute of Advanced Simulation, Forschungszentrum Jülich, 52428 Jülich, Germany.
Institut für Theoretische Physik, Universität zu Köln, 50937 Köln, Germany.
PNAS Nexus. 2024 Mar 19;3(4):pgae120. doi: 10.1093/pnasnexus/pgae120. eCollection 2024 Apr.
In fluid mechanics, dimensionless numbers like the Reynolds number help classify flows. We argue that such a classification is also relevant for crowd flows by putting forward the dimensionless Intrusion and Avoidance numbers, which quantify the intrusions into the pedestrians' personal spaces and the imminency of the collisions that they face, respectively. Using an extensive dataset, we show that these numbers delineate regimes where distinct variables characterize the crowd's arrangement, namely, Euclidean distances at low Avoidance number and times-to-collision at low Intrusion number. On the basis of these findings, a perturbative expansion of the individual pedestrian dynamics is carried out around the noninteracting state, in quite general terms. Simulations confirm that this expansion performs well in its expected regime of applicability.
在流体力学中，诸如雷诺数这样的无量纲数有助于对流动进行分类。我们认为，通过提出无量纲的侵入数和避让数，这种分类对于人群流动也具有相关性，这两个数分别量化了对行人个人空间的侵入以及他们所面临碰撞的紧迫性。使用一个广泛的数据集，我们表明这些数划定了不同变量表征人群排列的区域，即在低避让数时为欧几里得距离，在低侵入数时为碰撞时间。基于这些发现，在相当一般的情况下，围绕非相互作用状态对个体行人动力学进行了微扰展开。模拟证实，这种展开在其预期的适用范围内表现良好。
