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This paper presents a new approach to behavioral-social dynamics of pedestrian crowds by suitable development of methods of the kinetic theory. It is shown how heterogeneous individual behaviors can modify the collective dynamics, as well…

Physics and Society · Physics 2014-11-05 Nicola Bellomo , Livio Gibelli

This paper deals with the kinetic theory modeling of crowd dynamics with the aim of showing how the dynamics at the micro-scale is transferred to the dynamics of collective behaviors. The derivation of a new model is followed by a…

Mathematical Physics · Physics 2013-01-24 Nicola Bellomo , Abdelghani Bellouquid , Damian Knopoff

The strategic behaviour of pedestrians is largely determined by how they perceive and react to neighbouring people. This issue is addressed in this paper by a model which combines, in a time and space-dependent way, discrete and continuous…

Physics and Society · Physics 2016-06-23 Annachiara Colombi , Marco Scianna , Andrea Tosin

Dense pedestrian crowds may pose significant safety risks, yet their underlying dynamics remain insufficiently understood to reliably prevent accidents. In these environments, physical interactions and contact forces fundamentally shape the…

Physics and Society · Physics 2025-05-12 Thomas Chatagnon , Antoine Tordeux , Mohcine Chraibi

Population dynamics deals with the collective phenomena of living organisms, and it has attracted much attention since it is expected to explain how not only living organisms but also human beings have been adapted to varying environments.…

Statistical Mechanics · Physics 2019-04-23 Hideyuki Miyahara

This essay provides a critical overview of the mathematical kinetic theory of active particles, which is used to model and study collective systems consisting of interacting living entities, such as those involved in behavior and evolution.…

Physics and Society · Physics 2025-10-17 Marina Dolfin , Leone Leonida

Although the traits emerged in a mass gathering are often non-deliberative, the act of mass impulse may lead to irre- vocable crowd disasters. The two-fold increase of carnage in crowd since the past two decades has spurred significant…

Computer Vision and Pattern Recognition · Computer Science 2017-11-01 Ven Jyn Kok , Mei Kuan Lim , Chee Seng Chan

The modelling of human crowd behaviors offers many challenging questions to science in general. Specifically, the social human behavior consists of many physiological and psychological processes which are still largely unknown. To model…

Physics and Society · Physics 2023-10-17 Thi Kim Thoa Thieu , Roderick Melnik

This contribution describes efforts to model the behavior of individual pedestrians and their interactions in crowds, which generate certain kinds of self-organized patterns of motion. Moreover, this article focusses on the dynamics of…

Physics and Society · Physics 2013-09-09 Dirk Helbing , Anders Johansson

Understanding the movement behaviours of individuals and the way they react to the external world is a key component of any problem that involves the modelling of human dynamics at a physical level. In particular, it is crucial to capture…

Computer Vision and Pattern Recognition · Computer Science 2025-12-09 Gabriele Galatolo , Mirco Nanni

The availability of new data sources on human mobility is opening new avenues for investigating the interplay of social networks, human mobility and dynamical processes such as epidemic spreading. Here we analyze data on the time-resolved…

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

In animal societies as well as in human crowds, many observed collective behaviours result from self-organized processes based on local interactions among individuals. However, models of crowd dynamics are still lacking a systematic…

Physics and Society · Physics 2009-09-30 Mehdi Moussaid , Dirk Helbing , Simon Garnier , Anders Johansson , Maud Combe , Guy Theraulaz

This article is on collective phenomena in pedestrian dynamics during the assembling and dispersal phases of gatherings. To date pedestrian dynamics have been primarily studied in the natural and engineering sciences. Pedestrians are…

Physics and Society · Physics 2017-07-05 Anna Sieben , Jette Schumann , Armin Seyfried

Pedestrians are often encountered walking in the company of some social relations, rather than alone. The social groups thus formed, in variable proportions depending on the context, are not randomly organised but exhibit distinct features,…

Physics and Society · Physics 2021-07-29 Alexandre Nicolas , Fadratul Hafinaz

Interactions among living organisms, from bacteria colonies to human societies, are inherently more complex than interactions among particles and nonliving matter. Group interactions are a particularly important and widespread class,…

Physics and Society · Physics 2013-01-11 Matjaz Perc , Jesús Gómez-Gardeñes , Attila Szolnoki , Luis M. Floría , Yamir Moreno

This paper proposes a crowd dynamic macroscopic model grounded on microscopic phenomenological observations which are upscaled by means of a formal mathematical procedure. The actual applicability of the model to real world problems is…

Mathematical Physics · Physics 2016-11-07 Luca Bruno , Alessandro Corbetta , Andrea Tosin

Human crowds often bear a striking resemblance to interacting particle systems, and this has prompted many researchers to describe pedestrian dynamics in terms of interaction forces and potential energies. The correct quantitative form of…

Physics and Society · Physics 2014-12-04 Ioannis Karamouzas , Brian Skinner , Stephen J. Guy

This chapter focuses on the mathematical modelling of active particles (or agents) in crowded environments. We discuss several microscopic models found in literature and the derivation of the respective macroscopic partial differential…

Statistical Mechanics · Physics 2022-11-11 Maria Bruna , Martin Burger , Jan-Frederik Pietschmann , Marie-Therese Wolfram

In this paper, we present a computational modeling approach for the dynamics of human crowds, where the spreading of an emotion (specifically fear) has an influence on the pedestrians' behavior. Our approach is based on the methods of the…

Physics and Society · Physics 2021-02-19 Daewa Kim , Kaylie O'Connell , William Ott , Annalisa Quaini
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