Polarised crowd in motion: insights into statistical and dynamical behavior.

The collection of active agents often exhibits intriguing statistical and dynamical properties, particularly when considering human crowds. In this study, we have developed a computational model to simulate the recent experiment on real marathon races by Bain et al. (Science 363:46-49, 2019). Our primary goal is to investigate the impact of race staff on crowd dynamics. By comparing simulated races with and without the presence of race staff, our study reveals that the local velocity and density of participants display a wave pattern akin to real races for both the cases. The observed traveling wave in the crowd consistently propagates at a constant speed, regardless of the system size under consideration. The participants' dynamics in the longitudinal direction primarily contribute to velocity fluctuations, while fluctuations in the transverse direction are suppressed. In the absence of race staff, density and velocity fluctuations weaken without significantly affecting other statistical and dynamic characteristics of the crowd. Through this research, we aim to deepen our understanding of crowd motion, providing insights that can inform the development of effective crowd management strategies and contribute to the successful control of such events.