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The mathematical modeling of crowds is complicated by the fact that crowds possess the behavioral ability to develop and adapt moving strategies in response to the context. For example, in emergency situations, people tend to alter their…

Numerical Analysis · Mathematics 2024-11-21 Daewa Kim , Demetrio Labate , Kamrun Mily , Annalisa Quaini

We study the evacuation dynamics of a crowd evacuating from a complex geometry in the presence of a fire as well as of a slowly spreading smoke curtain. The crowd is composed of two kinds of individuals: those who know the layout of the…

Physics and Society · Physics 2018-06-11 Omar Richardson , Andrei Jalba , Adrian Muntean

Identifying and quantifying factors influencing human decision making remains an outstanding challenge, impacting the performance and predictability of social and technological systems. In many cases, system failures are traced to human…

In this chapter, we discuss the mathematical modeling of egressing pedestrians in an unknown environment with multiple exits. We investigate different control problems to enhance the evacuation time of a crowd of agents, by few informed…

Optimization and Control · Mathematics 2021-08-30 Giacomo Albi , Federica Ferrarese , Chiara Segala

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

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

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

Computational models of collective behavior in birds has allowed us to infer interaction rules directly from experimental data. Using a generic form of these rules we explore the collective behavior and emergent dynamics of a simulated…

Adaptation and Self-Organizing Systems · Physics 2012-07-24 Michael Small , Xiaoke Xu

Security is an important topic in our contemporary world, and the ability to automate the detection of any events of interest that can take place in a crowd is of great interest to a population. We hypothesize that the detection of events…

Computer Vision and Pattern Recognition · Computer Science 2023-12-12 Matheus Schreiner Homrich da Silva , Paulo Brossard de Souza Pinto Neto , Rodolfo Migon Favaretto , Soraia Raupp Musse

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

In this paper, we deal with a size-variable group of pedestrians moving in a unknown confined environment and searching for an exit. Pedestrian dynamics are simulated by means of a recently introduced microscopic (agent-based) model,…

Physics and Society · Physics 2019-06-28 Emiliano Cristiani , Daniele Peri

Pedestrian dynamics is an interdisciplinary field of research. Psychologists, sociologists, traffic engineers, physicists, mathematicians and computer scientists all strive to understand the dynamics of a moving crowd. In principle,…

Artificial Intelligence · Computer Science 2019-07-24 Benedikt Kleinmeier , Benedikt Zönnchen , Marion Gödel , Gerta Köster

Collective motion of large human crowds often depends on their density. In extreme cases like heavy metal concerts and Black Friday sales events, motion is dominated by physical interactions instead of conventional social norms. Here, we…

Physics and Society · Physics 2016-11-30 Arianna Bottinelli , David T. J. Sumpter , Jesse L. Silverberg

In this paper we devise a microscopic (agent-based) mathematical model for reproducing crowd behaviour in a specific scenario: a number of pedestrians, consisting of numerous social groups, flow along a corridor until a gate located at the…

Dynamical Systems · Mathematics 2022-07-19 Giuseppe G. Amaro , Emiliano Cristiani , Marta Menci

People often help others who are in trouble, especially in emergency evacuation situations. For instance, during the 2005 London bombings, it was reported that evacuees helped injured persons to escape the place of danger. In terms of game…

Physics and Society · Physics 2020-06-26 Jaeyoung Kwak , Michael H Lees , Wentong Cai , Marcus EH Ong

Impulse propagation in crowds is a phenomenon that is crucial for understanding collective dynamics, but has been scarcely addressed so far. Therefore, we have carried out experiments in which persons standing in a crowd are pushed forward…

Physics and Society · Physics 2025-03-26 Sina Feldmann , Juliane Adrian , Maik Boltes

Many biological phenomena such as locomotion, circadian cycles, and breathing are rhythmic in nature and can be modeled as rhythmic dynamical systems. Dynamical systems modeling often involves neglecting certain characteristics of a…

Dynamical Systems · Mathematics 2016-01-20 M. Mert Ankaralı , Shahin Sefati , Manu S. Madhav , Andrew Long , Amy J. Bastian , Noah J. Cowan

The conjugated forces model (CFM) capable of reproducing bypassing behaviour is proposed and adopted to simulate pedestrian evacuation. Primarily, the concept of collision and evading and surpassing behaviour is particularly defined to…

Physics and Society · Physics 2019-05-21 Xiaolu Jia , Hao Yue , Dongliang He

We adapt the social force model of crowd dynamics to capture the evacuation during a zombie outbreak from an academic building. Individuals navigate the building, opening doors, and evacuate to the nearest exit. Zombies chase the uninfected…

Physics and Society · Physics 2024-12-10 Sydney Balkovitz , Alyssa Croco , Jake Garda , Maggie Hatch , Franklyn Paul , Lauren Vu , Tristan West , Gavin Buxton

In this paper, we investigate disparities in pedestrian crossing behaviors within static and dynamic crowds through experimental analysis. First, qualitative trajectory observations revealed significant behavioral differences in static and…

Physics and Society · Physics 2025-06-19 Jinghui Wang , Yajuan Jiang , Xiaoying Zhang , Fangwei Deng , Wei Lv
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