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When legs and bodies synchronize: Two-level collective dynamics in dense crowds

Thomas Chatagnon, Mohcine Chraibi, Julien Pettré, Armin Seyfried, Antoine Tordeux

TL;DR

Ultra-dense crowds involve unavoidable contact and balance-based dynamics that traditional 2D, contact-driven models struggle to explain. The authors propose a minimal two-level pedestrian model coupling an upper body to legs, with balance and unbalancing feedback and short-range repulsion, which yields density waves and chiral oscillations observed in real crowds. Simulations map a phase diagram in unbalancing rate and balance speed, revealing crystallization, density waves, chiral oscillations, and disordered regimes, with patterns robust to variations in interaction potentials. This biomechanical framework connects individual balance control to macroscopic crowd dynamics, offering interpretable insights for forecasting and mitigating hazards in ultra-dense environments.

Abstract

Ultra-dense crowds, in which physical contact between people 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 individual balance motion. In this study, we introduce a minimal two-level pedestrian model that couples upper body and legs dynamics, allowing us to capture transitions between balanced and unbalanced states at the individual scale. Whereas previous models fail to achieve it, this coupling gives rise to emergent collective behaviours observed empirically, such as self-organized waves and large-scale rotational motion within the crowd. The model bridges basic individual biomechanical concepts and macroscopic flow dynamics, offering a new framework for modelling and understanding collective motions in ultra-dense crowds.

When legs and bodies synchronize: Two-level collective dynamics in dense crowds

TL;DR

Ultra-dense crowds involve unavoidable contact and balance-based dynamics that traditional 2D, contact-driven models struggle to explain. The authors propose a minimal two-level pedestrian model coupling an upper body to legs, with balance and unbalancing feedback and short-range repulsion, which yields density waves and chiral oscillations observed in real crowds. Simulations map a phase diagram in unbalancing rate and balance speed, revealing crystallization, density waves, chiral oscillations, and disordered regimes, with patterns robust to variations in interaction potentials. This biomechanical framework connects individual balance control to macroscopic crowd dynamics, offering interpretable insights for forecasting and mitigating hazards in ultra-dense environments.

Abstract

Ultra-dense crowds, in which physical contact between people 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 individual balance motion. In this study, we introduce a minimal two-level pedestrian model that couples upper body and legs dynamics, allowing us to capture transitions between balanced and unbalanced states at the individual scale. Whereas previous models fail to achieve it, this coupling gives rise to emergent collective behaviours observed empirically, such as self-organized waves and large-scale rotational motion within the crowd. The model bridges basic individual biomechanical concepts and macroscopic flow dynamics, offering a new framework for modelling and understanding collective motions in ultra-dense crowds.
Paper Structure (9 sections, 7 equations, 6 figures, 1 table)

This paper contains 9 sections, 7 equations, 6 figures, 1 table.

Table of Contents

  1. Introduction
  2. Two-level pedestrian model
  3. Simulation results
  4. Density wave
  5. Chiral oscillation
  6. Phase diagram
  7. Discussion
  8. Acknowledgments
  9. Author contributions statement

Figures (6)

  • Figure 1: Scheme for the two-level pedestrian model. The force $\mathbf u$ acting on the upper body is an unbalancing mechanism whereby vertical displacements between the body and the legs induce instability due to the gravity. Controversially, the force $\mathbf b$ displays a balancing mechanism whereby the legs relax to the upper body to maintain the body’s upright posture.
  • Figure 2: Time evolution of pedestrian body and leg positions under the density-wave parameter setting. A diagonal density wave rapidly emerges and propagates through the system. Colour encodes pedestrian direction, and brightness indicates velocity magnitude.
  • Figure 3: System kinetic energy and velocity correlation time-series (left panel) corresponding to the sequence shown in Figure. \ref{['fig:Positions1']}, and velocity time autocorrelation function (ACF) in stationary state (left panel). The system converges to a stationary state featuring a density wave and pedestrians exhibiting periodic velocity fluctuations at high frequency.
  • Figure 4: Time evolution of pedestrian body and leg positions under the chiral-oscillation parameter setting. Pedestrians self-organize into a collective rotational motion. Color encodes pedestrian direction, and brightness represents velocity magnitude.
  • Figure 5: System kinetic energy and velocity correlation time-series (left panel) corresponding to the sequence shown in Figure. \ref{['fig:Positions2']}, and velocity time autocorrelation function (ACF) in stationary state (left panel). The system converges to a stationary state exhibiting a global collective behavior with chiral oscillations, where pedestrians display periodic velocity fluctuations at low frequency.
  • ...and 1 more figures