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We present a strategy capable of describing basic features of the dynamics of crowds. The behaviour of the crowd is considered from a twofold perspective. We examine both the large scale behaviour of the crowd, and phenomena happening at…

Mathematical Physics · Physics 2011-08-09 Joep Evers

Ultra-dense crowds, in which physical contact between people cannot be avoided, pose major safety concerns. Nevertheless, the underlying dynamics driving their collective behaviours remain poorly understood. Existing dense crowd models,…

Physics and Society · Physics 2026-01-12 Thomas Chatagnon , Mohcine Chraibi , Julien Pettré , Armin Seyfried , Antoine Tordeux

Pedestrian crowds encompass a complex interplay of intentional movements aimed at reaching specific destinations, fluctuations due to personal and interpersonal variability, and interactions with each other and the environment. Previous…

Physics and Society · Physics 2025-03-10 Caspar A. S. Pouw , Geert G. M. van der Vleuten , Alessandro Corbetta , Federico Toschi

In this paper we systematically apply the mathematical structures by time-evolving measures developed in a previous work to the macroscopic modeling of pedestrian flows. We propose a discrete-time Eulerian model, in which the space…

Mathematical Physics · Physics 2009-07-02 Benedetto Piccoli , Andrea Tosin

People tend to walk in groups, and interactions with those groups have a significant impact on crowd behavior and pedestrian traffic dynamics. Social norms can be seen as unwritten rules regulating people interactions in social settings.…

Physics and Society · Physics 2025-10-31 Saleh Albeaik , Faisal Alsallum , Mohamad Alrished

In this paper we deal with pedestrian modeling, aiming at simulating crowd behavior in normal and emergency scenarios, including highly congested mass events. We are specifically concerned with a new agent-based, continuous-in-space,…

Adaptation and Self-Organizing Systems · Physics 2023-11-23 E. Cristiani , M. Menci , A. Malagnino , G. G. Amaro

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…

Physics and Society · Physics 2025-09-09 Cécile Appert-Rolland , Anne-Hélène Olivier , Julien Pettré

In recent years modelling crowd and evacuation dynamics has become very important, with increasing huge numbers of people gathering around the world for many reasons and events. The fact that our global population grows dramatically every…

Physics and Society · Physics 2015-01-28 Mohamed H. Dridi

Environmental, demographical and psychological factors have a demonstrated impact on risky crossing behaviour. In this work we focus on the potential influence of social factors on the considered phenomenon (i.e. group crossing decision).…

Multiagent Systems · Computer Science 2018-01-10 Andrea Gorrini , Luca Crociani , Giuseppe Vizzari , Stefania Bandini

When two pedestrians travelling in opposite directions approach one another, each must decide on which side (the left or the right) they will attempt to pass. If both make the same choice then passing can be completed with ease, while if…

Physics and Society · Physics 2016-05-19 Nickolas A. Morton , Shaun C. Hendy

As we walk towards our destinations, our trajectories are constantly influenced by the presence of obstacles and infrastructural elements: even in absence of crowding our paths are often curved. Over the last two decades pedestrian dynamics…

A spreading process can be observed when particular information, substances, or diseases spread through a population over time in social and biological systems. It is widely believed that contact interactions among individual entities play…

Physics and Society · Physics 2024-07-08 Jaeyoung Kwak , Michael H. Lees , Wentong Cai

This work presents a microscopic model to describe pedestrian flows based on the social force theory. The aim of this study is twofold: (1) developing a realistic model that can be used as a tool for designing pedestrian-friendly…

Multiagent Systems · Computer Science 2026-01-07 Péter Molnár

The collection of active agents often exhibits intriguing statistical and dynamical properties, particularly when considering human crowds. In this study, we have developed a computational model to simulate the recent experiment on real…

Statistical Mechanics · Physics 2025-01-07 Pratikshya Jena , Shradha Mishra

In order to investigate collective effects of interactions between pedestrians and attractions, this study extends the social force model. Such interactions lead pedestrians to form stable clusters around attractions, or even to rush into…

Physics and Society · Physics 2017-09-07 Jaeyoung Kwak , Hang-Hyun Jo , Tapio Luttinen , Iisakki Kosonen

Collective motion is an ubiquitous phenomenon in nature, inspiring engineers, physicists and mathematicians to develop mathematical models and bio-inspired designs. Collective motion at small to medium group sizes ($\sim$10-1000…

Machine Learning · Computer Science 2024-01-19 Utkarsh Pratiush , Arshed Nabeel , Vishwesha Guttal , Prathosh AP

The empirical relation between density and velocity of pedestrian movement is not completely analyzed, particularly with regard to the `microscopic' causes which determine the relation at medium and high densities. The simplest system for…

Physics and Society · Physics 2009-11-11 Armin Seyfried , Bernhard Steffen , Wolfram Klingsch , Maik Boltes

Pedestrian crowds can very realistically be simulated with a social force model which describes the different influences affecting individual pedestrian motion by a few simple force terms. The model is able to reproduce the emergence of…

Statistical Mechanics · Physics 2007-05-23 Dirk Helbing , Peter Molnar

This paper presents a new approach to behavioral-social dynamics of human crowds. First order models are derived based on mass conservation at the macroscopic scale, while methods of the kinetic theory are used to model the decisional…

Physics and Society · Physics 2015-01-14 Nicola Bellomo , Stefano Berrone , Livio Gibelli , Alexandre Pieri

We study an ecology-inspired model for a population of bounded size, whose dynamics is governed by random birth, death, and immigration events. Stochastic fluctuations in the number of individuals give rise to a succession of alternating…

Populations and Evolution · Quantitative Biology 2026-05-27 Lucas M. Brugevin , Damián H. Zanette