Giving particles legs: How balance recovery may drive emergent collective dynamics in ultra-dense crowds

Ultra-dense crowds, in which physical contact between individuals cannot be avoided, pose major safety concerns. Nevertheless, the underlying dynamics driving their collective behaviours remain poorly understood. Existing dense crowd models, mostly two-dimensional and contact-based, overlook biomechanical mechanisms that govern human balance motion. In this study, we introduce a minimal two-level pedestrian model that couples upper body and legs dynamics, allowing us to capture how individuals continuously lose and recover balance under physical contact. This coupling generates emergent collective behaviours, such as self‑organised waves and large‑scale rotational motion, which prior modelling attempts failed to achieve. The model bridges basic individual biomechanical concepts and crowd-scale dynamics, offering a new interpretable framework for understanding collective dynamics in ultra-dense crowds.