## Crowd Behavior Dynamics: Entropic Path–Integral Model (906)

Citations: | 1 - 1 self |

### BibTeX

@MISC{Ivancevic906crowdbehavior,

author = {Vladimir G. Ivancevic and Darryn J. Reid and Eugene V. Aidman},

title = {Crowd Behavior Dynamics: Entropic Path–Integral Model},

year = {906}

}

### OpenURL

### Abstract

We propose an entropic geometrical model of crowd behavior dynamics (with dissipative crowd kinematics), using Feynman action–amplitude formalism that operates on three synergetic levels: macro, meso and micro. The intent is to explain the dynamics of crowds simultaneously and consistently across these three levels, in order to characterize their geometrical properties particularly with respect to behavior regimes and the state changes between them. Its most natural statistical descriptor (order parameter) is crowd entropy S that satisfies the Prigogine’s extended second law of thermodynamics, ∂tS ≥ 0 (for any nonisolated multi-component system). Qualitative similarities and superpositions between individual and crowd configuration manifolds motivate our claim that goal-directed crowd movement operates under entropy conservation, ∂tS = 0, while naturally chaotic crowd dynamics operates under (monotonically) increasing entropy function, ∂tS> 0. Between these two distinct topological phases lies a phase transition with a chaotic inter-phase. Both inertial crowd dynamics and its dissipative kinematics represent diffusion processes on the crowd manifold governed by the Ricci flow.

### Citations

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Citation Context ... differentiably deformed into one another, that is if they are diffeomorphic. Thus by topology change the ‘loss of diffeomorphicity’ is meant [67]. In this respect, the so– called topological theorem =-=[13]-=- says that non–analyticity is the ‘shadow’ of a more fundamental phenomenon occurring in the system’s configuration manifold (in our case the CD manifold): a topology change within the family of equip... |

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Citation Context ...derivative along a geodesic and Ri jkm are the components of the Riemann curvature tensor of the CD manifold M. The relevant part of the Jacobi equation (43) is given by the tangent dynamics equation =-=[8, 5]-=- ¨J i + R i 0k0J k = 0, (i, k = 1, . . .,3n), (44) where the only non-vanishing components of the curvature tensor of the CD manifold M are R i 0k0 = ∂2 V/∂x i ∂x k . (45) The tangent dynamics equatio... |

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6 |
From crowd dynamics to crowd safety: A video-based analysis
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Citation Context ...disasters caused by the panic stampede that can occur at high pedestrian densities and which is a serious concern during mass events like soccer championship games or annual pilgrimage in Makkah (see =-=[29, 30, 31, 54]-=-). 2 Generic three–step crowd behavior dynamics In this section we propose a generic crowd behavior dynamics as a three–step process based on a general partition function formalism. Note that the numb... |