Change of criticality in a prototypical thermoacoustic system

In this paper, we report on the existence of the phenomenon of change of criticality in a horizontal Rijke tube, a prototypical thermoacoustic system. In the experiments, the phenomenon is shown to occur as the criticality of the Hopf bifurcation changes with varying air flow rates in the system. The dynamics of a nonlinear system exhibiting Hopf bifurcation can be described using a Stuart-Landau equation (SLE) in the vicinity of the bifurcation point. The criticality of Hopf bifurcations can be determined by the Landau constant of the Stuart-Landau equation, which represents the effect of nonlinearities in the system. We propose an SLE to model the bifurcations seen in the horizontal Rijke tube. We identify a rescaled version of Strouhal number as the Landau constant, which determines the criticality of the bifurcation in the present study

Particle methods for pedestrian flow models: from microscopic to non-local continuum models

A hierarchy of models for pedestrian flow is numerically investigated using particle methods. It includes microscopic models based on interacting particle system coupled to an eikonal equation, hydrodynamic models using equations for density and mean velocity, nonlocal continuum equations for the density and diffusive Hughes equations. Particle methods are used on all levels of the hierarchy. Numerical test cases are investigated by comparing the above models

On a three dimensional vision based collision avoidance model

International audienceThis paper presents a three dimensional collision avoidance approach for aerial vehicles inspired by coordinated behaviors in biological groups. The proposed strategy aims to enable a group of vehicles to converge to a common destination point avoiding collisions with each other and with moving obstacles in their environment. The interaction rules lead the agents to adapt their velocity vectors through a modification of the relative bearing angle and the relative elevation. Moreover the model satisfies the limited field of view constraints resulting from individual perception sensitivity. From the proposed individual based model, a mean-field kinetic model is derived. Simulations are performed to show the effectiveness of the proposed model

Mathematical models and methods for crowd dynamics control

In this survey we consider mathematical models and methods recently developedto control crowd dynamics, with particular emphasis on egressing pedestrians.We focus on two control strategies: The first one consists in using specialagents, called leaders, to steer the crowd towards the desired direction.Leaders can be either hidden in the crowd or recognizable as such. Thisstrategy heavily relies on the power of the social influence (herding effect),namely the natural tendency of people to follow group mates in situations ofemergency or doubt. The second one consists in modify the surroundingenvironment by adding in the walking area multiple obstacles optimally placedand shaped. The aim of the obstacles is to naturally force people to behave asdesired. Both control strategies discussed in this paper aim at reducing asmuch as possible the intervention on the crowd. Ideally the natural behavior ofpeople is kept, and people do not even realize they are being led by anexternal intelligence. Mathematical models are discussed at different scales ofobservation, showing how macroscopic (fluid-dynamic) models can be derived bymesoscopic (kinetic) models which, in turn, can be derived by microscopic(agent-based) models