Statistical fluctuations in pedestrian evacuation times and the effect of social contagion

Mathematical models of pedestrian evacuation and the associated simulation software have become essential tools for the assessment of the safety of public facilities and buildings. While a variety of models are now available, their calibration and test against empirical data are generally restricted to global, averaged quantities, the statistics compiled from the time series of individual escapes (" microscopic " statistics) measured in recent experiments are thus overlooked. In the same spirit, much research has primarily focused on the average global evacuation time, whereas the whole distribution of evacuation times over some set of realizations should matter. In the present paper we propose and discuss the validity of a simple relation between this distribution and the " microscopic " statistics, which is theoretically valid in the absence of correlations. To this purpose, we develop a minimal cellular automaton, with novel features that afford a semi-quantitative reproduction of the experimental " microscopic " statistics. We then introduce a process of social contagion of impatient behavior in the model and show that the simple relation under test may dramatically fail at high contagion strengths, the latter being responsible for the emergence of strong correlations in the system. We conclude with comments on the potential practical relevance for safety science of calculations based on " microscopic " statistics

A counterintuitive way to speed up pedestrian and granular bottleneck flows prone to clogging: can 'more' escape faster?

Dense granular flows through constrictions, as well as competitivepedestrian evacuations, are hindered by a propensity to form clogs. We use simulations of model pedestrians and experiments with granular disks to explore an original strategy to speed up these flows, which consists in including contact-averse entities in the assembly. On the basis of a minimal cellular automaton and a continuous agent-based model for pedestrian evacuation dynamics, we find that the inclusion of polite pedestrians amid a given competitive crowd fails to reduce the evacuation time when the constriction (the doorway) is acceptably large. This is not surprising, because adding agents makes the crowd larger. In contrast, when the door is so narrow that it can accommodate at most one or two agents at a time, our strategy succeeds in substantially curbing long-lived clogs and speeding up the evacuation. A similar eect is seen experimentally in a vibrated two-dimensional hopper flow with an opening narrower than 3 disk diameters. Indeed, by adding to the initial collection of neutral disks a large fraction of magnetic ones, interacting repulsively, we observe a shortening of the time intervals between successive egresses of neutral disks, as reflected by the study of their probability distribution. On a more qualitative note, our study suggests that the much discussed analogy between pedestrian flows and granular flows could be extended to some behavioural traits of individualpedestrians.Fil: Nicolas, Alexandre. Université Paris Sud; Francia. Centre National de la Recherche Scientifique; Francia. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Ibáñez, Santiago Agustín. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Universidad Nacional de Río Negro. Sede Andina; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Kuperman, Marcelo Nestor. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Universidad Nacional de Río Negro. Sede Andina; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Bouzat, Sebastian. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Universidad Nacional de Río Negro. Sede Andina; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Sexually transmitted infections and the marriage problem

87.23.Ge Dynamics of social systems, 87.23.Cc Population dynamics and ecological pattern formation,

Transport properties of melanosomes along microtubules interpreted by a tug-of-war model with loose mechanical coupling.

In this work, we explored theoretically the transport of organelles driven along microtubules by molecular motors of opposed polarities using a stochastic model that considers a Langevin dynamics for the cargo, independent cargo-motor linkers and stepping motion for the motors. It has been recently proposed that the stiffness of the motor plays an important role when multiple motors collectively transport a cargo. Therefore, we considered in our model the recently reported values for the stiffness of the cargo-motor linker determined in living cells (∼0.01 pN/nm,) which is significantly lower than the motor stiffness obtained in in vitro assays and used in previous studies. Our model could reproduce the multimodal velocity distributions and typical trajectory characteristics including the properties of the reversions in the overall direction of motion observed during melanosome transport along microtubules in Xenopus laevis melanophores. Moreover, we explored the contribution of the different motility states of the cargo-motor system to the different modes of the velocity distributions and could identify the microscopic mechanisms of transport leading to trajectories compatible with those observed in living cells. Finally, by changing the attachment and detachment rates, the model could reproduce the different velocity distributions observed during melanosome transport along microtubules in Xenopus laevis melanophores stimulated for aggregation and dispersion. Our analysis suggests that active tug-of-war processes with loose mechanical coupling can account for several aspects of cargo transport along microtubules in living cells

SURVIVAL AND EXTINCTION IN THE REPLICATOR MODEL: DYNAMICS AND STATISTICS

We study the multi-species replicator model with linear fitness and random fitness matrices of various classes. By means of numerical resolution of the replicator equations, we determine the survival probability of a species in terms of its average interaction with the rest of the system. The role of the interaction pattern of the ecosystem in defining survival and extinction probabilities is emphasized.Replicator dynamics, ecosystem models, survival strategy

Des fluctuations statistiques et de l'effet de la contagion sociale dans évacuations piétonnes

International audienceMathematical models of pedestrian evacuation and the associated simulation software have become essential tools for the assessment of the safety of public facilities and buildings. While a variety of models are now available, their calibration and test against empirical data are generally restricted to global, averaged quantities; the statistics compiled from the time series of individual escapes (" microscopic " statistics) measured in recent experiments are thus overlooked. In the same spirit, much research has primarily focused on the average global evacuation time, whereas the whole distribution of evacuation times over some set of realizations should matter. In the present paper we propose and discuss the validity of a simple relation between this distribution and the " microscopic " statistics, which is theoretically valid in the absence of correlations. To this purpose, we develop a minimal cellular automaton, with novel features that afford a semi-quantitative reproduction of the experimental " microscopic " statistics. We then introduce a process of social contagion of impatient behavior in the model and show that the simple relation under test may dramatically fail at high contagion strengths, the latter being responsible for the emergence of strong correlations in the system. We conclude with comments on the potential practical relevance for safety science of calculations based on " microscopic " statistics.Les modèles mathématiques d'évacuation piétonne et les logiciels de simulations qui en dérivent sont devenus des outils incontournables pour l'évaluation de la sécurité des établissements recevant du public. Divers modèles sont désormais disponibles, mais leur calibration / validation contre des données empiriques se limite généralement à l'étude de quantités globales et moyennées; ne sont donc pas prises en compte les statistiques issues des séries temporelles des sorties individuelles de piétons (statistiques "microscopiques") mesurées au cours d'expériences récentes. Dans le même ordre d'idées, c'est le temps d'évacuation globale moyen qui a été au cœur de la plupart des travaux, alors que l'intégralité de la distribution des temps d'évacuation, sur un espace de réalisations incontrôlé, devrait avoir de l'importance. Dans cet article, nous proposons une relation simple entre cette distribution et les statistiques "microscopiques", rigoureusement valide en l'absence de corrélations, et nous discutons sa validité dans un cadre plus général. À cette fin, nous développons un automate cellulaire minimaliste, comprenant des traits nouveaux qui permettent de capturer semi-quantitativement les statistiques "microscopiques" déterminées expérimentalement. Nous introduisons ensuite un procédé de contagion sociale des comportements impatients dans le modèle et montrons qu'il peut conduire à la violation de la relation simple proposée, à fortes intensités de contagion, cette dernière étant alors responsable de l'émergence de fortes corrélations dans le système. En guise de conclusion, nous abordons la possible portée pratique pour les sciences de la sécurité de nos calculs fondés sur les statistiques "microscopiques"

Une manière contre-intuitive d'accélérer les écoulements piétons et granulaires à travers une constriction donnant lieu à des blocages: Plus de monde peut-il évacuer plus rapidement ?

International audienceDense granular flows through constrictions, as well as competitive pedestrian evacuations, are hindered by a propensity to form clogs. We usesimulations of model pedestrians and experiments with granular disks to explore an original strategy to speed up these flows, which consists in including contact-averse entities in the assembly. On the basis of a minimal cellular automaton and a continuous agent-based model for pedestrian evacuation dynamics, we find that the inclusion of polite pedestrians amid a given competitive crowd fails to reduce the evacuation time when the constriction (the doorway) is acceptably large. This is not surprising, because adding agents makes the crowd larger. In contrast, when the door is so narrow that it can accommodate at most one or two agents at a time, our strategy succeeds in substantially curbing long-lived clogs and speeding up the evacuation. A similar effect is seen experimentally in a vibrated two-dimensional hopper flow with an opening narrower than 3 disk diameters. Indeed, by adding to the initial collection of neutral disks a large fraction of magnetic ones, interacting repulsively, we observe a shortening of the time intervals between successive egresses of neutral disks, as reflected by the study of their probability distribution. On a more qualitative note, our study suggests that the much discussed analogy between pedestrian flows and granular flows could be extended to some behavioural traits of individual pedestrians