Heterogeneity-induced lane and band formation in self-driven particle systems

Khelfa, Basma; Korbmacher, Raphael; Schadschneider, Andreas; Tordeux, Antoine

doi:10.48550/arxiv.2110.05874

Cited by 3 publications

(3 citation statements)

References 58 publications

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“…Self-organized spatial patterns have been observed when two groups cross each other. In counterflow, the formation of stable lanes is regularly reported in both human experiments [3,36,[40][41][42][43][44] and numerical simulations [45][46][47][48][49][50][51][52][53][54][55][56][57], in which alternating lanes of pedestrian traffic are aligned with the walking directions of the two groups (180°apart). A jamming transition can occur above a critical flow density [47,51,54,55].…”

Section: Introductionmentioning

confidence: 86%

Analysis of emergent patterns in crossing flows of pedestrians reveals an invariant of `stripe' formation in human data

Mullick¹,

Fontaine²,

Appert-Rolland³

et al. 2021

Preprint

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When two streams of pedestrians cross at an angle, striped patterns spontaneously emerge as a result of local pedestrian interactions. This clear case of self-organized pattern formation remains to be elucidated. In counterflows, with a crossing angle of 180°, alternating lanes of traffic are commonly observed moving in opposite directions, whereas in crossing flows at an angle of 90°, diagonal stripes have been reported. Naka (1977) hypothesized that stripe orientation is perpendicular to the bisector of the crossing angle. However, studies of crossing flows at acute and obtuse angles remain underdeveloped. We tested the bisector hypothesis in experiments on small groups (18-19 participants each) crossing at seven angles (30°intervals), and analyzed the geometric properties of stripes. We present two novel computational methods for analyzing striped patterns in pedestrian data: (i) an edge-cutting algorithm, which detects the dynamic formation of stripes and allows us to measure local properties of individual stripes; and (ii) a pattern-matching technique, based on the Gabor function, which allows us to estimate global properties (orientation and wavelength) of the striped pattern at a time T . We find an invariant property: stripes in the two groups are parallel and perpendicular to the bisector at all crossing angles. In contrast, other properties depend on the crossing angle: stripe spacing (wavelength), stripe size (number of pedestrians per stripe), and crossing time all decrease as the crossing angle increases from 30°to 180°, whereas the number of stripes increases with crossing angle. We also observe that the width of individual stripes is dynamically squeezed as the two groups cross each other. The findings thus support the bisector hypothesis at a wide range of crossing angles, although the theoretical reasons for this invariant remain unclear. The present results provide empirical constraints on theoretical studies and computational models of crossing flows.

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Section: Introductionmentioning

confidence: 86%

Analysis of emergent patterns in crossing flows of pedestrians reveals an invariant of `stripe' formation in human data

Mullick¹,

Fontaine²,

Appert-Rolland³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Mathematical modeling of pedestrian dynamics has a practical benefit in civil engineering [23,26,27] for example in the design of complex architectures, e.g., stadiums, city centers, and shopping malls, or for the management of large public events like festivals, concerts, pilgrimages, or manifestations [10]. Capturing both, the individual and collective behaviors in pedestrian dynamics, is rather complex [2,7].…”

Section: Introductionmentioning

confidence: 99%

Gradient-based parameter calibration of an anisotropic interaction model for pedestrian dynamics

Zhomart

Totzeck

2023

Eur. J. Appl. Math

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We propose an extension of the anisotropic interaction model which allows for collision avoidance in pairwise interactions by a rotation of forces (Totzeck (2020) Kinet. Relat. Models13(6), 1219–1242.) by including the agents’ body size. The influence of the body size on the self-organisation of the agents in channel and crossing scenarios as well as the fundamental diagram is studied. Since the model is stated as a coupled system of ordinary differential equations, we are able to give a rigorous well-posedness analysis. Then we state a parameter calibration problem that involves data from real experiments. We prove the existence of a minimiser and derive the corresponding first-order optimality conditions. With the help of these conditions, we propose a gradient descent algorithm based on mini-batches of the data set. We employ the proposed algorithm to fit the parameter of the collision avoidance and the strength parameters of the interaction forces to given real data from experiments. The results underpin the feasibility of the method.

show abstract

“…Mathematical modelling of pedestrian dynamics is of practical benefit in civil engineering [23,26,27] for example in the design of complex architectures, e.g., stadiums, city centers, shopping malls, or for the management of large public events like festivals, concerts, pilgrimages, or manifestations [10]. Capturing both, the individual and collective behaviours in pedestrian dynamics, is rather complex [2,7].…”

Section: Introductionmentioning

confidence: 99%

Gradient-based parameter calibration of an anisotropic interaction model for pedestrian dynamics

Zhomart¹,

Totzeck²

2022

Preprint

View full text Add to dashboard Cite

We propose an extension of the anisotropic interaction model which allows for collision avoidance in pairwise interactions by a rotation of forces [34] by including the agents' body size. The influence of the body size on the self-organization of the agents in channel and crossing scenarios as well as the fundamental diagram is studied. Since the model is stated as a coupled system of ordinary differential equations, we are able to give a rigorous well-posedness analysis. Then we state a parameter calibration problem that involves data from real experiments. We prove the existence of a minimizer and derive the corresponding first-order optimality conditions. With the help of these conditions we propose a gradient descent algorithm based on mini-batches of the data set. We employ the proposed algorithm to fit the parameter of the collision avoidance and the strength parameters of the interaction forces to given real data from experiments. The results underpin the feasibility of the method.

show abstract

Heterogeneity-induced lane and band formation in self-driven particle systems

Cited by 3 publications

References 58 publications

Analysis of emergent patterns in crossing flows of pedestrians reveals an invariant of `stripe' formation in human data

Analysis of emergent patterns in crossing flows of pedestrians reveals an invariant of `stripe' formation in human data

Gradient-based parameter calibration of an anisotropic interaction model for pedestrian dynamics

Gradient-based parameter calibration of an anisotropic interaction model for pedestrian dynamics

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