12 research outputs found
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
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
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
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
Free/Congested Two-Phase Model from Weak Solutions to Multi-Dimensional Compressible Navier-Stokes Equations
We approximate a two--phase model by the compressible Navier-Stokes equations
with a singular pressure term. Up to a subsequence, these solutions are shown
to converge to a global weak solution of the compressible system with the
congestion constraint studied for instance by P.L. Lions and N. Masmoudi [
Annales I.H.P., 1999]. The paper is an extension of the previous result
obtained in one-dimensional setting by D. Bresch et al. [ C. R. Acad. Sciences
Paris, 2014] to the multi-dimensional case with heterogeneous barrier for the
density
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
Asymptotic problems and numerical schemes for traffic flows with unilateral constraints describing the formation of jams
International audienceWe discuss numerical strategies to deal with PDE systems describing traffic flows, taking into account a density threshold, which restricts the vehicles density in the situation of congestion. These models are obtained through asymptotic arguments. Hence, we are interested in the simulation of approached models that contain stiff terms and large speeds of propagation. We design schemes intended to apply with relaxed stability conditions
A dynamic network loading model for anisotropic and congested pedestrian flows
A macroscopic loading model for multi-directional, time-varying and congested pedestrian flows is proposed in this paper. Walkable space is represented by a network of streams that are each associated with an area in which they interact. To describe this interaction, a stream-based pedestrian fundamental diagram is used that relates density and walking speed in multi-directional flow. The proposed model is applied to two different case studies. The explicit modeling of anisotropy in walking speed is shown to significantly improve the ability of the model to reproduce empirically observed walking time distributions. Moreover, the obtained model parametrization is in excellent agreement with the literature