Self-Organized Hydrodynamics with congestion and path formation in crowds

A continuum model for self-organized dynamics is numerically investigated. The model describes systems of particles subject to alignment interaction and short-range repulsion. It consists of a non-conservative hyperbolic system for the density and velocity orientation. Short-range repulsion is included through a singular pressure which becomes infinite at the jamming density. The singular limit of infinite pressure stiffness leads to phase transitions from compressible to incompressible dynamics. The paper proposes an Asymptotic-Preserving scheme which takes care of the singular pressure while preventing the breakdown of the CFL stability condition near congestion. It relies on a relaxation approximation of the system and an elliptic formulation of the pressure equation. Numerical simulations of impinging clusters show the efficiency of the scheme to treat congestions. A two-fluid variant of the model provides a model of path formation in crowds

Macroscopic models of collective motion and self-organization

International audienceIn this paper, we review recent developments on the derivation and properties of macroscopic models of collective motion and self-organization. The starting point is a model of self-propelled particles interacting with its neighbors through alignment. We successively derive a mean-field model and its hydrodynamic limit. The resulting macroscopic model is the Self-Organized Hydrodynamics (SOH). We review the available existence results and known properties of the SOH model and discuss it in view of its possible extensions to other kinds of collective motion

Finite Volume approximations of the Euler system with variable congestion

We are interested in the numerical simulations of the Euler system with variable congestion encoded by a singular pressure. This model describes for instance the macroscopic motion of a crowd with individual congestion preferences. We propose an asymptotic preserving (AP) scheme based on a conservative formulation of the system in terms of density, momentum and density fraction. A second order accuracy version of the scheme is also presented. We validate the scheme on one-dimensional test-cases and extended here to higher order accuracy. We finally carry out two dimensional numerical simulations and show that the model exhibit typical crowd dynamics

A Comprehensive Study on Pedestrians' Evacuation

Human beings face threats because of unexpected happenings, which can be avoided through an adequate crisis evacuation plan, which is vital to stop wound and demise as its negative results. Consequently, different typical evacuation pedestrians have been created. Moreover, through applied research, these models for various applications, reproductions, and conditions have been examined to present an operational model. Furthermore, new models have been developed to cooperate with system evacuation in residential places in case of unexpected events. This research has taken into account an inclusive and a 'systematic survey of pedestrian evacuation' to demonstrate models methods by focusing on the applications' features, techniques, implications, and after that gather them under various types, for example, classical models, hybridized models, and generic model. The current analysis assists scholars in this field of study to write their forthcoming papers about it, which can suggest a novel structure to recent typical intelligent reproduction with novel features

Transport of congestion in two-phase compressible/incompressible flows

We study the existence of weak solutions to the two-phase fluid model with congestion constraint. The model encompasses the flow in the uncongested regime (compressible) and the congested one (incompressible) with the free boundary separating the two phases. The congested regime appears when the density in the uncongested regime achieves a threshold value that describes the comfort zone of individuals. This quantity is prescribed initially and transported along with the flow. We prove that this system can be approximated by the fully compressible Navier–Stokes system with a singular pressure, supplemented with transport equation for the congestion density. We also present the application of this approximation for the purposes of numerical simulations in the one-dimensional domain

Anticipation decides on lane formation in pedestrian counterflow -- a simulation study

Human crowds base most of their behavioral decisions upon anticipated states of their walking environment. We explore a minimal version of a lattice model to study lanes formation in pedestrian counterflow. Using the concept of horizon depth, our simulation results suggest that the anticipation effect together with the presence of a small background noise play an important role in promoting collective behaviors in a counterflow setup. These ingredients facilitate the formation of seemingly stable lanes and ensure the ergodicity of the system

Mean-Field-Type Games in Engineering

A mean-field-type game is a game in which the instantaneous payoffs and/or the state dynamics functions involve not only the state and the action profile but also the joint distributions of state-action pairs. This article presents some engineering applications of mean-field-type games including road traffic networks, multi-level building evacuation, millimeter wave wireless communications, distributed power networks, virus spread over networks, virtual machine resource management in cloud networks, synchronization of oscillators, energy-efficient buildings, online meeting and mobile crowdsensing.Comment: 84 pages, 24 figures, 183 references. to appear in AIMS 201

Singular limit of a Navier–Stokes system leading to a free/congested zones two-phase model

The aim of this work is to justify mathematically the derivation of a viscous free/congested zones two-phase model from the isentropic compressible Navier-Stokes equations with a singular pressure playing the role of a barrier