arXiv subjects

Cécile Appert-Rolland

Publications and source records attributed to Cécile Appert-Rolland.

At least 19 recordsLinked to original sources

arXiv2025

Modelling vehicle and pedestrian collective dynamics: Challenges and advances

In our urbanised societies, the management and regulation of traffic and pedestrian flows is of considerable interest for public safety, economic development, and the conservation of the environment. However, modelling and controlling the collective dynamics of vehicles and pedestrians raises several challenges. Not only are the individual entities self-propelled and hard to describe, but their complex nonlinear physical and social interactions makes the multi-agent problem of crowd and traffic flow even more involved. In this chapter, we purport to review the suitability and limitations of classical modelling approaches through four examples of collective behaviour: stop-and-go waves in traffic flow, lane formation, long-term avoidance behaviour, and load balancing in pedestrian dynamics. While stop-and-go dynamics and lane formation can both be addressed by basic reactive models (at least to some extent), the latter two require anticipation and/or coordination at the level of the group. The results highlight the limitations of classical force-based models, but also the need for long-term anticipation mechanisms and multiscale modelling approaches. In response, we review new developments and modelling concepts.

physics.soc-ph↗

arXiv2025

Properties of pedestrians walking in line without density constraint

This article deals with the experimental study of pedestrian behaviours in some situations of one-dimensional traffic. Participants were pre-organized in a line, and asked to walk either in a straight line with a fast or slow leader, or to form a circle. The originality of our experimental protocol compared to previous ones on similar situations, is to have left the condition of density free. While the observed density results from individual decisions in the line case, both density and velocity have to be collectively chosen in the case of circle formation. Our major findings are the following. In the case of circle formations, we observe that the resulting velocity is very stable among realizations, as if collective decision was playing the role of an average. For line flows with a slow leader, the same operating point close to the jamming transition is chosen as in previous experiments where it was not velocity but density that was imposed. In the less constrained line experiments, although participants could choose comfortable headways, they rather stick to short headways requiring a faster adaption - a fact that could come from a "social pressure from behind" and had previously only been observed at high densities. This could be due to the uncertainty and individual responsibility that stem in less constrained situations. Our results open new avenues for future research, as they show that the walking values preferred by humans in following tasks depend on more factors than previously considered.

physics.soc-ph↗

arXiv2024

Eliminating Bias in Pedestrian Density Estimation: A Voronoi Cell Perspective

For pedestrians moving without spatial constraints, extensive research has been devoted to develop methods of density estimation. In this paper we present a new approach based on Voronoi cells, offering a means to estimate density for individuals in small, unbounded pedestrian groups. A thorough evaluation of existing methods, encompassing both Lagrangian and Eulerian approaches employed in similar contexts, reveals notable limitations. Specifically, these methods turn out to be ill-defined for realistic density estimation along a pedestrian's trajectory, exhibiting systematic biases and fluctuations that depend on the choice of parameters. There is thus a need for a parameter-independent method to eliminate this bias. We propose a modification of the widely used Voronoi-cell based density estimate to accommodate pedestrian groups, irrespective of their size. The advantages of this modified Voronoi method are that it is an instantaneous method that requires only knowledge of the pedestrians' positions at a give time, does not depend on the choice of parameter values, gives us a realistic estimate of density in an individual's neighborhood, and has appropriate physical meaning for both small and large human crowds in a wide variety of situations. We conclude with general remarks about the meaning of density measurements for small groups of pedestrians.

physics.soc-ph↗

arXiv2024

Modeling of obstacle avoidance by a dense crowd as a Mean-Field Game

In this paper we use a minimal model based on Mean-Field Games (a mathematical framework apt to describe situations where a large number of agents compete strategically) to simulate the scenario where a static dense human crowd is crossed by a cylindrical intruder. After a brief explanation of the mathematics behind it, we compare our model directly against the empirical data collected during a controlled experiment replicating the aforementioned situation. We then summarize the features that make the model adhere so well to the experiment and clarify the anticipation time in this framework.

physics.soc-ph↗

arXiv2024

Mean-Field Games Modeling of Anticipation in Dense Crowds

Understanding and modeling pedestrian dynamics in dense crowds is a complex yet essential aspect of crowd management and urban planning. In this work, we investigate the dynamics of a dense crowd crossed by a cylindrical intruder using a Mean-Field Game (MFG) model. By incorporating a discount factor to account for pedestrians' limited anticipation and information processing, we examine the model's ability to simulate two distinct experimental configurations: pedestrians facing the obstacle and pedestrians giving their back to the intruder. Through a comprehensive comparison with experimental data, we demonstrate that the MFG model effectively captures essential crowd behaviors, including anticipatory motion and collision avoidance.

physics.soc-ph↗

arXiv2024

Discounted Mean-Field Game model of a dense static crowd with variable information crossed by an intruder

It was demonstrated in [Bonnemain et al., Phys. Rev. E 107, 024612 (2023)] that the anticipation pattern displayed by a dense crowd crossed by an intruder can be successfully described by a minimal Mean-Field Games model. However, experiments show that changes in the pedestrian knowledge significantly modify the dynamics of the crowd. Here, we show that the addition of a single parameter, the discount factor $γ$, which gives a lower weight to events distant in time, is sufficient to observe the whole variety of behaviors observed in the experiments. We present a comparison between the discounted MFG and the experimental data, also providing new analytic results and insight about how the introduction of $γ$ modifies the model.

physics.soc-ph↗

arXiv2022

Methods of density estimation for pedestrians moving in small groups without a spatial boundary

For a group of pedestrians without any spatial boundaries, the methods of density estimation is a wide area of research. Besides, there is a specific difficulty when the density along one given pedestrian trajectory is needed in order to plot an `individual-based' fundamental diagram. We illustrate why several methods become ill-defined in this case. We then turn to the widely used Voronoi-cell based density estimate. We show that for a typical situation of crossing flows of pedestrians, Voronoi method has to be adapted to the small sample size. We conclude with general remarks about the meaning of density measurements in such context.

physics.soc-ph↗

arXiv2022

Pedestrians in static crowds are not grains, but game players

The local navigation of pedestrians amid a crowd is generally believed to involve no anticipation beyond (at best) the avoidance of the most imminent collisions. We show that current models rooted in this belief fail to reproduce some key features experimentally evidenced when a dense static crowd is crossed by an intruder. We identify the missing ingredient as the pedestrians' ability to plan their motion well beyond the next interaction, whence they may accept to move towards denser regions for a short time. To account for this effect, we introduce a minimal model based on mean-field game theory, which proves remarkably successful in replicating the aforementioned observations as well as other daily-life situations involving collective behaviour in dense crowds, such as partial metro boarding. This demonstrates the ability of game approaches to capture the anticipatory effects at play in operational crowd dynamics.

physics.soc-ph↗

arXiv2021

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

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.

physics.soc-ph↗

arXiv2018

Mechanical response of dense pedestrian crowds to the crossing of intruders

The increasing number of mass events involving large crowds calls for a better understanding of the dynamics of dense crowds. Inquiring into the possibility of a mechanical description of these dynamics, we experimentally study the crossing of dense static crowds by a cylindrical intruder, a mechanical test which is classical for granular matter. The analysis of our experiments reveals robust features in the crowds' response, comprising both similarities and discrepancies with the response of granular media. Common features include the presence of a depleted region behind the intruder and the short-range character of the perturbation. On the other hand, unlike grains, pedestrians anticipate the intruder's passage by moving much before contact and their displacements are mostly lateral, hence not aligned with the forces exerted by the intruder. Similar conclusions are reached when the intruder is not a cylinder, but a single crossing pedestrian. Thus, our work shows that pedestrian interactions even at high densities (3 to 6 ped/m 2) do not reduce to mechanical ones. More generally, the avoidance strategies evidenced by our findings question the incautious use of force models for dense crowds.

physics.soc-ph↗

arXiv2018

Experimental Study of Collective Pedestrian Dynamics

We report on two series of experiments, conducted in the frame of two different collaborations designed to study how pedestrians adapt their trajectories and velocities in groups or crowds. Strong emphasis is put on the motivations for the chosen protocols and the experimental implementation. The first series deals with pattern formation, interactions between pedestrians, and decision-making in pedestrian groups at low to medium densities. In particular, we show how pedestrians adapt their headways in single-file motion depending on the (prescribed) leader's velocity. The second series of experiments focuses on static crowds at higher densities, a situation that can be critical in real life and in which the pedestrians' choices of motion are strongly constrained sterically. More precisely, we study the crowd's response to its crossing by a pedestrian or a cylindrical obstacle of 74cm in diameter. In the latter case, for a moderately dense crowd, we observe displacements that quickly decay with the minimal distance to the obstacle, over a lengthscale of the order of the meter.

physics.soc-ph↗

arXiv2017

Zone clearance in an infinite TASEP with a step initial condition

The TASEP is a paradigmatic model of out-of-equilibrium statistical physics, for which many quantities have been computed, either exactly or by approximate methods. In this work we study two new kinds of observables that have some relevance in biological or traffic models. They represent the probability for a given clearance zone of the lattice to be empty (for the first time) at a given time, starting from a step density profile. Exact expressions are obtained for single-time quantities, while more involved history-dependent observables are studied by Monte Carlo simulation, and partially predicted by a phenomenological approach.

cond-mat.stat-mech↗

arXiv2016

Non-equilibrium fluctuations of a semi-flexible filament driven by active cross-linkers

The cytoskeleton is an inhomogeneous network of semi-flexible filaments, which are involved in a wide variety of active biological processes. Although the cytoskeletal filaments can be very stiff and embedded in a dense and cross-linked network, it has been shown that, in cells, they typically exhibit significant bending on all length scales. In this work we propose a model of a semi-flexible filament deformed by different types of cross-linkers for which one can compute and investigate the bending spectrum. Our model allows to couple the evolution of the deformation of the semi-flexible polymer with the stochastic dynamics of linkers which exert transversal forces onto the filament. We observe a $q^{-2}$ dependence of the bending spectrum for some biologically relevant parameters and in a certain range of wavenumbers $q$. However, generically, the spatially localized forcing and the non-thermal dynamics both introduce deviations from the thermal-like $q^{-2}$ spectrum.

physics.bio-ph↗

arXiv2016

Spontaneous pulsing states in an active particle system

We study a two-lane two-species exclusion process inspired by Lin et al. (C. Lin et al. J. Stat. Mech., 2011), that exhibits a non-equilibrium pulsing phase. Particles move on two parallel one-dimensional tracks, with one open and one reflecting boundary. The particle type defines the hopping direction. When only particles hopping towards the open end are allowed to change lane, the system exhibits a phase transition from a low density phase to a pulsing phase depending on the ratio between particle injection and type-changing rate. This phase transition can be observed in the stochastic model as well as in a mean-field description. In the low density phase, the density profile can be predicted analytically. The pulsing phase is characterised by a fast filling of the system and - once filled - by a slowly backwards moving front separating a decreasing dense region and an expanding low density region. The hopping of the front on the discrete lattice is found to create density oscillations, both, in time and space. By means of a stability analysis we can predict the structure of the dense region during the emptying process, characterised by exponentially damped perturbations, both at the open end and near the moving front.

cond-mat.stat-mech↗

arXiv2015

Two dimensional outflows for cellular automata with shuffle updates

In this paper, we explore the two-dimensional behavior of cellular automata with shuffle updates. As a test case, we consider the evacuation of a square room by pedestrians modeled by a cellular automaton model with a static floor field. Shuffle updates are characterized by a variable associated to each particle and called phase, that can be interpreted as the phase in the step cycle in the frame of pedestrian flows. Here we also introduce a dynamics for these phases, in order to modify the properties of the model. We investigate in particular the crossover between low- and high-density regimes that occurs when the density of pedestrians increases, the dependency of the outflow in the strength of the floor field, and the shape of the queue in front of the exit. Eventually we discuss the relevance of these results for pedestrians.

nlin.CG↗

arXiv2014

Time-delayed Follow-the-Leader model for pedestrians walking in line

We use the results of a pedestrian tracking experiment to identify a follow-the-leader model for pedestrians walking-in-line. We demonstrate the existence of a time-delay between a subject's response and the predecessor's corresponding behavior. This time-delay induces an instability which can be damped out by a suitable relaxation. By comparisons with the experimental data, we show that the model reproduces well the emergence of large-scale structures such as congestions waves. The resulting model can be used either for modeling pedestrian queuing behavior or can be incorporated into bi-dimensional models of pedestrian traffic. Acknowledgements: This work has been supported by the french 'Agence Nationale pour la Recherche (ANR)' in the frame of the contract "Pedigree" (ANR-08-SYSC-015-01). JH acknowledges support of the ANR and the Institut de Math{é}matiques de Toulouse, where he conducted this research. AJ acknowledges support of the ANR and of the Laboratoire de physique t A c orique in Orsay where she conducted this research. PD is on leave from CNRS, Institut de Mat A c matiques de Toulouse, France.

physics.soc-ph↗

arXiv2014

Fluctuation effects in bidirectional cargo transport

We discuss a theoretical model for bidirectional cargo transport in biological cells, which is driven by teams of molecular motors and subject to thermal fluctuations. The model describes explicitly the directed motion of the molecular motors on the filament. The motor-cargo coupling is implemented via linear springs. By means of extensive Monte Carlo simulations we show that the model describes the experimentally observed regimes of anomalous diffusion, i.e. subdiffusive behavior at short times followed by superdiffusion at intermediate times. The model results indicate that subdiffuse regime is induced by thermal fluctuations while the superdiffusive motion is generated by correlations of the motors' activity. We also tested the efficiency of bidirectional cargo transport in crowded areas by measuring its ability to pass barriers with increased viscosity. Our results show a remarkable gain of efficiency for high viscosities.

physics.bio-ph↗

arXiv2014

Stochastic modeling of cargo transport by teams of molecular motors

Many different types of cellular cargos are transported bidirectionally along microtubules by teams of molecular motors. The motion of this cargo-motors system has been experimentally characterized in vivo as processive with rather persistent directionality. Different theoretical approaches have been suggested in order to explore the origin of this kind of motion. An effective theoretical approach, introduced by Müller et al., describes the cargo dynamics as a tug-of-war between different kinds of motors. An alternative approach has been suggested recently by Kunwar et al., who considered the coupling between motor and cargo in more detail. Based on this framework we introduce a model considering single motor positions which we propagate in continuous time. Furthermore, we analyze the possible influence of the discrete time update schemes used in previous publications on the system's dynamic.

physics.bio-ph↗