T<scp>HE</scp> F<scp>LOW OF</scp> H<scp>UMAN</scp> C<scp>ROWDS</scp>

TLDR

Crowd motion is studied as a flowing continuum distinct from classical fluids because its agents can think, leading to nonlinear, time‑dependent equations that are conformably mappable and making the field of “thinking fluids” a promising area of research. The review aims to show how modern crowd‑motion theory could reduce the roughly 2,000 annual deaths caused by crowding accidents. The authors illustrate the theory’s use in practical contexts such as the annual Muslim Hajj, the Battle of Agincourt, and in designing barriers that paradoxically improve pedestrian flow. Because the crowd equations are mappable, many applications become analytically tractable, and the study demonstrates that strategically placed barriers can increase pedestrian throughput compared to no barriers.

Abstract

▪ Abstract The modern study of a crowd as a flowing continuum is a recent development. Distinct from a classical fluid because of the property that a crowd has the capacity to think, interesting new physical ideas are involved in its study. An appealing property of a crowd in motion is that the nonlinear, time-dependent, simultaneous equations representing a crowd are conformably mappable. This property makes many interesting applications analytically tractable. In this review examples are given in which the theory has been used to provide possible assistance in the annual Muslim Hajj, to understand the Battle of Agincourt, and, surprisingly, to locate barriers that actually increase the flow of pedestrians above that when there are no barriers present. Modern developments may help prevent some of the approximately two thousand deaths that annually occur in accidents owing to crowding.The field of crowd motion, that is, the field of “thinking fluids,” is an intriguing area of research with great promise. The field of crowd motion, that is, the field of “thinking fluids,” is an intriguing area of research with great promise.