CHARACTERIZING THE HYDRODYNAMICS OF HIGH DENSITY CROWDS

Abstract

The derivation of a hydrodynamic model for a certain physical system is normally done by utilizing symmetry arguments and first principles. The model is then validated through experimental observations. Such a classical process has been successful in characterizing a wide range of systems in physics and engineering, but not in complex sciences. To overcome these challenges, scientists have made use of the major advancements in video tracking technologies and sensors used in experiments to quantitatively characterize human crowd systems. The combination of such innovations with statistical learning techniques such as Non-Linear Regression and Neural Networks has facilitated the inference of the system's governing partial differential equations (PDEs) solely from time series data collected at different spatial points. Recently, influential work such as PDE-Find has proposed sparse regression techniques to infer the PDEs from spatiotemporal data. This approach determines the most prominent components in an equation via Penalized Linear Regression Methods and balances between accuracy and complexity.

In this thesis, we derive a hydrodynamic model for the collective behavior of runners in a marathon using the sparse regression approach. The motion is made up of millions of runners heading toward the start line guided by staff members who are performing a regular cycle of walks and stops. The motion is thus perfectly polarized with orientational fluctuations repressed. Furthermore, the runners' response to the staff's excitation causes the propagation of hybrid density and velocity waves spanning the entire system where the attenuation is small and the propagation is a longitudinal wave. Modeling the slow dynamics of the crowd's flow is beneficial in providing recommendations for crowd management to avoid hazardous and momentous events in marathons.