Multiscale Modeling of Pedestrian Dynamics

Cristiani, Emiliano; Piccoli, Benedetto; Tosin, Andrea

doi:10.1007/978-3-319-06620-2

Cited by 200 publications

(227 citation statements)

References 8 publications

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“…[3,14]. Finally, our results are valid in the presence of certain non-local interactions, that may arise in applications such as surface tension [34], defects in metal crystals (dislocations) [20,26], pedestrian dynamics [8,18] and swarming [5].…”

Section: Introductionmentioning

confidence: 59%

From continuum mechanics to SPH particle systems and back: Systematic derivation and convergence

et al. 2017

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In this paper, we derive from the principle of least action the equation of motion for a continuous medium with regularized density field in the context of measures. The eventual equation of motion depends on the order in which regularization and the principle of least action are applied. We obtain two different equations, whose discrete counterparts coincide with the scheme used traditionally in the Smoothed Particle Hydrodynamics (SPH) numerical method [27], and with the equation treated by Di Lisio et al. in [9], respectively. Additionally, we prove the convergence in the Wasserstein distance of the corresponding measure-valued evolutions, moreover providing the order of convergence of the SPH method. The convergence holds for a general class of force fields, including external and internal conservative forces, friction and non-local interactions. The proof of convergence is illustrated numerically by means of one and two-dimensional examples.

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Section: Introductionmentioning

confidence: 59%

From continuum mechanics to SPH particle systems and back: Systematic derivation and convergence

et al. 2017

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“…The interest comes from both its connections with open scientific challenges related to the development of complex behaviors and pattern formation in nonequilibrium systems [1], as well as from its relevance to the design and safety of infrastructures [2]. Connections with statistical physics [3] and fluid dynamics descriptions [4] have been used to develop models capable of reproducing some of the features observed in crowd phenomenology [5][6][7]. From a macroscopic point of view, it is no surprise that crowds may be described, at least qualitatively, by means of fluidlike continuity equations for the local crowd density [7].…”

Section: Introductionmentioning

confidence: 99%

Fluctuations around mean walking behaviors in diluted pedestrian flows

et al. 2017

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Understanding and modeling the dynamics of pedestrian crowds can help with designing and increasing the safety of civil facilities. A key feature of crowds is its intrinsic stochasticity, appearing even under very diluted conditions, due to the variability in individual behaviours. Individual stochasticity becomes even more important under densely crowded conditions, since it can be nonlinearly magnified and may lead to potentially dangerous collective behaviours. To understand quantitatively crowd stochasticity, we study the real-life dynamics of a large ensemble of pedestrians walking undisturbed, and we perform a statistical analysis of the fully-resolved pedestrian trajectories obtained by a year-long high-resolution measurement campaign. Our measurements have been carried out in a corridor of the Eindhoven University of Technology via a combination of Microsoft Kinect TM 3D-range sensor and automatic headtracking algorithms. The temporal homogeneity of our large database of trajectories allows us to robustly define and separate average walking behaviours from fluctuations parallel and orthogonal with respect to the average walking path. Fluctuations include rare events when individuals suddenly change their minds and invert their walking direction. Such tendency to invert direction has been poorly studied so far even if it may have important implications on the functioning and safety of facilities. We propose a novel model for the dynamics of undisturbed pedestrians, based on stochastic differential equations, that provides a good agreement with our experimental observations, including the occurrence of rare events.

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“…For scenarios characterized by large numbers of individuals, both upscaling and meanfield theory could be convenient strategies to control the high computational effort required by reproducing the pedestrian flow in extended environments, as provided by the relative literature, see for relevant examples Bellomo and Dogbé (2008), Colombo and Rosini (1567), Coscia and Canavesio (2008), Cristiani et al (2014), Hughes (2002) and references therein. However, these approaches would cause the loss of the characterization of the single pedestrians, i.e., in particular of the individual gazing direction and environmental awareness (which, as already explained, are key features of our model).…”

Section: Discussionmentioning

confidence: 99%

“…However, living entities, such as cells, human crowds or swarms, are not passively prone to the Newtonian laws of inertia, as they are able to actively develop behavioral strategies which depend both on intrinsic stimuli and on the interaction with the external environment. For instance, a pedestrian, at least when he/she is not running too quick, can decide to stop and change direction of motion: intelligence can be in fact regarded also as the ability of an individual to actively control his/her body and therefore his/her movement, see also Cristiani et al (2014). These concepts allow to neglect the inertial term in Eq.…”

Section: Pedestrian Dynamicsmentioning

confidence: 97%

A discrete mathematical model for the dynamics of a crowd of gazing pedestrians with and without an evolving environmental awareness

Colombi

Scianna

Alaia³

2016

Comp. Appl. Math.

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In this article, we present a microscopic-discrete mathematical model describing crowd dynamics in no panic conditions. More specifically, pedestrians are set to move in order to reach a target destination and their movement is influenced by both behavioral strategies and physical forces. Behavioral strategies include individual desire to remain sufficiently far from structural elements (walls and obstacles) and from other walkers, while physical forces account for interpersonal collisions. The resulting pedestrian behavior emerges therefore from non-local, anisotropic and short/long-range interactions. Relevant improvements of our mathematical model with respect to similar microscopic-discrete approaches present in the literature are: (i) each pedestrian has his/her own dynamic gazing direction, which is regarded to as an independent degree of freedom and (ii) each walker is allowed to take dynamic strategic decisions according to his/her environmental awareness, which increases due to new information acquired on the surrounding space through their visual region. The resulting mathematical modeling environment is then applied to specific scenarios that, although simplified, resemble real-word situations. In particular, we focus on pedestrian flow in twodimensional buildings with several structural elements (i.e., corridors, divisors and columns, and exit doors). The noticeable heterogeneity of possible applications demonstrates the potential of our mathematical model in addressing different engineering problems, allowing for optimization issues as well.Communicated by Eduardo Souza de Cursi.

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Multiscale Modeling of Pedestrian Dynamics

Cited by 200 publications

References 8 publications

From continuum mechanics to SPH particle systems and back: Systematic derivation and convergence

From continuum mechanics to SPH particle systems and back: Systematic derivation and convergence

Fluctuations around mean walking behaviors in diluted pedestrian flows

A discrete mathematical model for the dynamics of a crowd of gazing pedestrians with and without an evolving environmental awareness

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