Dimensionless Numbers Reveal Distinct Regimes in the Structure and Dynamics of Pedestrian Crowds

Des nombres sans dimension révèlent plusieurs régimes en termes de structure et d'organisation des foules piétonnes

Jakob Cordes (1, 2) , Andreas Schadschneider (1) , Alexandre Nicolas (3, 4)

1 Institut für Theoretische Physik [Köln]
2 FZJ - Forschungszentrum Jülich GmbH | Centre de recherche de Jülich | Jülich Research Centre
3 ILM - Institut Lumière Matière [Villeurbanne]
4 CNRS - Centre National de la Recherche Scientifique

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. Using an extensive dataset, we show that these delineate regimes that are characterized by distinct structural signatures, best probed in terms of distances at low Avoidance number and times-to-collision at low Intrusion number. These findings prompt a perturbative expansion of the agent-based dynamics; the generic models thus obtained perform well in (and only in) the regime in which they were derived.

Mots clés: pedestrian crowds; modeling; dimensionless numbers; collision avoidance

Domaines: Mécanique statistique [cond-mat.stat-mech]; Physique et Société [physics.soc-ph]

Jakob Cordes, Andreas Schadschneider, Alexandre Nicolas. Dimensionless Numbers Reveal Distinct Regimes in the Structure and Dynamics of Pedestrian Crowds. PNAS Nexus, In press, 3 (4), pgae120. ⟨10.1093/pnasnexus/pgae120⟩. ⟨hal-04169676v3⟩