Journal ArticleDOI
First-order macroscopic modelling of human crowd dynamics
Vincenzo Coscia,C. Canavesio +1 more
TLDR
In this paper, the authors deal with the mathematical modelling of crowd dynamics within the framework of continuum mechanics, using the mass conservation equation closed by phenomenological models linking the local velocity to density and density gradients.Abstract:
This paper deals with the mathematical modelling of crowd dynamics within the framework of continuum mechanics. The method uses the mass conservation equation closed by phenomenological models linking the local velocity to density and density gradients. The closures take into account movement in more than one space dimension, presence of obstacles, pedestrian strategies, and modelling of panic conditions. Numerical simulations of the initial-boundary value problems visualize the ability of the models to predict several interesting phenomena related to the complex system under consideration.read more
Citations
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Journal ArticleDOI
On a mean field game approach modeling congestion and aversion in pedestrian crowds
TL;DR: In this paper, a new class of pedestrian crowd models based on the mean field games theory introduced by Lasry and Lions in 2006 is presented, which considers smart pedestrians who rationally interact and anticipate the future.
Journal ArticleDOI
On the modelling crowd dynamics from scaling to hyperbolic macroscopic models
Nicola Bellomo,Christian Dogbe +1 more
TL;DR: This paper is devoted to scaling and related representation problems, then the macroscopic scale is selected and a variety of models are proposed according to different approximations of the pedestrian strategies and interactions, and a qualitative analysis of the models is conducted with the aim of analyzing their properties.
Journal ArticleDOI
A macroscopic crowd motion model of gradient flow type
TL;DR: In this article, a simple model to handle the flow of people in emergency evacuation situations is considered: at every point x, the velocity U(x) that individuals at x would like to realize is given, yet, the incompressibility constraint prevents this velocity field to be realized and the actual velocity is the projected one onto the set of admissible velocities.
Journal ArticleDOI
Multiscale modeling of granular flows with application to crowd dynamics
TL;DR: A new multiscale modeling technique relies on a recently introduced measure-theoretic approach, which allows one to manage the microscopic and the macroscopic scale under a unique framework and in the resulting coupled model the two scales coexist and share information.
Posted Content
A macroscopic crowd motion model of gradient flow type
TL;DR: In this paper, a simple model to handle the flow of people in emergency evacuation situations is considered: at every point x, the velocity U(x) that individuals at x would like to realize is given, yet, the incompressibility constraint prevents this velocity field to be realized and the actual velocity is the projected one onto the set of admissible velocities.
References
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Journal ArticleDOI
Simulating dynamical features of escape panic
TL;DR: A model of pedestrian behaviour is used to investigate the mechanisms of panic and jamming by uncoordinated motion in crowds, and an optimal strategy for escape from a smoke-filled room is found, involving a mixture of individualistic behaviour and collective ‘herding’ instinct.
Journal Article
On kinetic waves, II . A theory of traffic flow on long crowded roads
M J Lighthill,G B Whitham +1 more
TL;DR: In this paper, a functional relationship between flow and concentration for traffic on crowded arterial roads has been postulated for some time, and has experimental backing, from which a theory of the propagation of changes in traffic distribution along these roads may be deduced.
Journal ArticleDOI
On kinematic waves II. A theory of traffic flow on long crowded roads
TL;DR: The theory of kinematic waves is applied to the problem of estimating how a ‘hump’, or region of increased concentration, will move along a crowded main road, and is applicable principally to traffic behaviour over a long stretch of road.
Journal ArticleDOI
Traffic and related self-driven many-particle systems
Dirk Helbing,Dirk Helbing +1 more
TL;DR: This article considers the empirical data and then reviews the main approaches to modeling pedestrian and vehicle traffic, including microscopic (particle-based), mesoscopic (gas-kinetic), and macroscopic (fluid-dynamic) models.
Journal ArticleDOI
Emergent Behavior in Flocks
Felipe Cucker,Steve Smale +1 more
TL;DR: The main result shows that when beta<1/2 convergence of the flock to a common velocity is guaranteed, while for betages1/ 2 convergence is guaranteed under some condition on the initial positions and velocities of the birds only.