We present a Godunov type numerical scheme for a class of scalar conservation laws with nonlocal flux arising for example in traffic flow modeling. The scheme delivers more accurate solutions than the widely used Lax-Friedrichs type scheme and also allows to show well-posedness of the model. In a second step, we consider the extension of the non-local traffic flow model to road networks by defining appropriate conditions at junctions. Based on the proposed numerical scheme we show some properties of the approximate solution and provide several numerical examples.[-]

We will present in this talk a mathematical model for a mixture composed by solid particles immersed in a viscous liquid. In a dense regime (high concentration of solid particles), the lubrication effects are predominant in the dynamics. Our goal is to study mathematically a minimal effective model, based on compressible Navier-Stokes equations, which take into account lubrication effects via a singular dissipation term. We will also consider the regime where the viscosity of the interstitial fluid tends to 0.[-]

This minicourse aims at providing tentative explanations of some specific phenomena observed in the motion of crowds, or more generally collections of living entities. The first lecture shall focus on the so-called Stop and Go Waves, which sometimes spontaneously emerge and persist in crowds in motion. We shall present a general class of dynamical systems which are likely to exhibit this type of instabilities, and emphasize the critical role of two basic ingredients: the asymmetry of interactions, and any sort of delay in the transmission of information through the network of entities. The second lecture will address the Capacity Drop Phenomenon (decrease of the flux though a bottleneck when the upstream density becomes too high), and the more paradoxical Faster is Slower Effect (in some regimes, attempts to go quicker may slow down the overall process). We shall in particular detail how an accurate description of the relative position of entities (at the microscopic level) is crucial to recover and understand those effects.[-]

The talk summarize the empirical state of knowledge on bottleneck flow and introduces an approach to describe crowd disasters. The approach combines quantities well known in natural sciences with concepts of social psychology. It allows to describe crowds at bottlenecks in case of exceptional (life-threatening) or normal circumstances.
On the basis of empirical data, the influence of the spatial structure of the boundaries (width and length of the bottleneck) and the motivation of pedestrians on flow and density will be presented. The phenomenon of clogging and its effects on the flow will be discussed in connection with congestion, rewards, motivation and pushing. Positive effects of pillars in front of bottlenecks are critically questioned by recent experiments. Results of two experiments including questionnaire studies connect flow and density with factors of social psychology like rewards, social norms, expectations or fairness.[-]