The role of fluctuations and interactions in pedestrian...
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Fluctuations in the undisturbed dynamics: Langevin-like model Based on the observed statistics we drew an analogy between undisturbed pedestrians (i.e. the diluted dynamics) and active Brownian particles and constructed a generalized Langevin model (1) that takes into account geometric restrictions, pedestrians’ destination and turningback events [1,2]. Interactions and outlook Quantitative stochastic model for the undisturbed, i.e. diluted regime as (1) are a first step toward quantitative models for entire crowds. The analysis of binary interactions, ongoing for our train station data (Fig. 5), is the next step in this direction. The role of fluctuations and interactions in pedestrian dynamics A. Corbetta*, C. Lee, J. Meeusen, R. Benzi, A. Muntean and F. Toschi Department of Applied Physics, Turbulence and Vortex Dynamics Figure 4: Comparison between the modeled and the measured dynamics in case of the corridor in Fig. 2A. (left) Probability distribution function of longitudinal velocities. (right) Number of pedestrians observed between two successive (rare) inversion events (roughly 1 in 450 on average, Poisson distributed). Figure 1: Real-life pedestrian tracking at Eindhoven train station. Raw data, as depth maps, is collected via grids of Microsoft KinectTM overhead sensors. Ad hoc algorithms are used to identify pedestrians that are tracked with Particle Tracking Velocimetry (PTV) techniques. 10 −5 10 −4 10 −3 10 −2 10 −1 10 0 10 1 −3 −2 −1 0 1 2 3 4 5 w τ [m/s] Metaforum Station LONGITUDINAL Figure 2: Probability distribution functions of (longitudinal) velocities of pedestrians walking undisturbed by others. Measurements from two locations are compared: A. corridor at Eindhoven university of Technology; B. Train station (cf. Fig. 1). In both cases rare turnback events emerge (negative velocities) Stable velocity states ˙ u =4↵u(u 2 - u 2 p )+ σ x ˙ w 10 −6 10 −5 10 −4 10 −3 10 −2 10 −1 10 0 10 1 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5 w τ [m/s] measurements simulations 10 −3 10 −2 10 −1 0 200 400 600 800 1000 1200 1400 N i measurements exponential E [N i ] = 450 simulations y-distance before bypass y-distance at bypass *Contacts: [email protected] http://corbetta.phys.tue.nl/ A. B. (1) Figure 3: A Langevin model with a double-well velocity potential (1) enables frequent small fluctuations (S) and large, although rare, velocity leaps (L) to negative velocities, i.e. turningback events. (L) (L) (S) Figure 5: Binary avoidance interactions are measured considering the variation of transversal (lateral) distance before and at the mutual by pass. References: [1] A.Corbetta et al., 2016, Fluctuations around mean walking behaviours in diluted pedestrian flows, submitted, arXiv:1610.07429 [2] A.Corbetta, 2016, Phd. Thesis, Multiscale pedestrian dynamics: physical analysis, modeling and applications [3] A.Corbetta et. al, 2014, High Statistics Measurements of Pedestrian Dynamics. Transportation Research Procedia 2, 96-104 Pedestrian dynamics The dynamics of pedestrian crowds is a relevant topic for the design and safety of civil infrastructures and furthermore a fascinating subject deeply connected with many scientific disciplines, including statistical physics and fluid dynamics. Even in simple geometries, individuals always display, in addition to average behaviors, small fluctuations and, more rarely, large “anomalous” deviations. High statistics measurements We expect observation of the crowds with very high statistics to reveal the signature of both frequent and rare fluctuations . To this aim, back in 2013 we started several year-long experimental campaigns in real-life settings. Performing 24/7 continuous pedestrian tracking via ad hoc technologies in different locations, we collected an unprecedentedly large database of human trajectories (~10M) [1-3]. Δy A B
Transcript of The role of fluctuations and interactions in pedestrian...
Fluctuations in the undisturbed dynamics:Langevin-like modelBased on the observed statistics we drew an analogy between undisturbed pedestrians (i.e. the diluted dynamics) and active Brownian particles and constructed a generalized Langevinmodel (1) that takes into account geometric restrictions, pedestrians’ destination and turningback events [1,2].
Interactions and outlookQuantitative stochastic model for the undisturbed, i.e. diluted regime as (1) are a first step toward quantitative models for entire crowds. The analysis of binary interactions, ongoing for our train station data (Fig. 5), is the next step in this direction.
The role of fluctuations and interactions in pedestrian dynamics
A. Corbetta*, C. Lee, J. Meeusen, R. Benzi, A. Muntean and F. Toschi
Department of Applied Physics, Turbulence and Vortex Dynamics
Figure 4: Comparison between the modeled and the measured dynamics in case of the corridor in Fig. 2A. (left) Probability distribution function of longitudinal velocities. (right) Number of pedestrians observed between two successive (rare) inversion events (roughly 1 in 450 on average, Poisson distributed).
Figure 1: Real-life pedestrian tracking at Eindhoven train station. Raw data, as depth maps, is collected via grids of Microsoft KinectTM overhead sensors. Ad hoc algorithms are used to identify pedestrians that are tracked with Particle Tracking Velocimetry (PTV) techniques.
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Figure 2: Probability distribution functions of (longitudinal) velocities of pedestrians walking undisturbed by others. Measurements from two locations are compared: A. corridor at Eindhoven university of Technology; B. Train station (cf. Fig. 1). In both cases rare turnback events emerge (negative velocities)
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*Contacts:[email protected]://corbetta.phys.tue.nl/
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Figure 3: A Langevin model with a double-well velocity potential (1) enables frequent small fluctuations (S) and large, although rare, velocity leaps (L) to negative velocities, i.e. turningback events.
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Figure 5: Binary avoidance interactions are measured considering the variation of transversal (lateral) distance before and at the mutual by pass.
References:[1] A.Corbetta et al., 2016, Fluctuations around mean walking behavioursin diluted pedestrian flows, submitted, arXiv:1610.07429[2] A.Corbetta, 2016, Phd. Thesis, Multiscale pedestrian dynamics: physical analysis, modeling and applications [3] A.Corbetta et. al, 2014, High Statistics Measurements of Pedestrian Dynamics. Transportation Research Procedia 2, 96-104
Pedestrian dynamicsThe dynamics of pedestrian crowds is a relevant topic for
the design and safety of civil infrastructures and furthermore a fascinating subject deeply connected with many scientific disciplines, including statistical physics and fluid dynamics.
Even in simple geometries, individuals always display, in addition to average behaviors, small fluctuations and, more rarely, large “anomalous” deviations.
High statistics measurementsWe expect observation of the crowds with very high statistics to reveal the signature of both frequent and rare fluctuations. To this aim, back in 2013 we started several year-long experimental campaigns in real-life settings. Performing 24/7 continuous pedestrian tracking via ad hoc technologies in different locations, we collected an unprecedentedly large database of human trajectories (~10M) [1-3].
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