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Understanding the mechanisms behind the remote triggering of landslides by seismic waves at micro-strain amplitude is essential for quantifying seismic hazards. Granular materials provide a relevant model system to investigate landslides within the unjamming transition framework, from solid to liquid states. Furthermore, recent laboratory experiments have revealed that ultrasound-induced granular avalanches can be related to a reduction in the interparticle friction through shear acoustic lubrication of the contacts. However, investigating slip at the scale of grain contacts within an optically opaque granular medium remains a challenging issue. Here, we propose an original coupling model and numerically investigate two-dimensional dense granular flows triggered by basal acoustic waves. We model the triggering dynamics at two separated time scales – one for grain motion (milliseconds) and the other for ultrasound (10 ${\rm \mu} {\rm s}$) – relying on the computation of vibrational modes with a discrete element method through the reduction of the local friction. We show that ultrasound predominantly propagates through the strong-force chains, while the ultrasound-induced decrease of interparticle friction occurs in the weak contact forces perpendicular to the strong-force chains. This interparticle friction reduction initiates local rearrangements at the grain scale that eventually lead to a continuous flow through a percolation process at the macroscopic scale – with a delay depending on the proximity to the failure. Consistent with experiments, we show that ultrasound-induced flow appears more uniform in space than pure gravity-driven flow, indicating the role of an effective temperature by ultrasonic vibration. [ABSTRACT FROM AUTHOR]

These lecture notes address mathematical issues related to the modeling of opinion propagation on networks of the social type. Starting from the behavior of the simplest discrete linear model, we develop various standpoints and describe some extensions: stochastic interpretation, monitoring of a network, time continuous evolution problem, charismatic networks, links with discretized Partial Differential Equations, nonlinear models, inertial version and stability issues. These developments rely on basic mathematical tools, which makes them accessible at an undergraduate level. In a last section, we propose a new model of opinion propagation, where the opinion of an agent is described by a Gaussian density, and the (discrete) evolution equation is based on barycenters with respect to the Fisher metric.

Shock wave/turbulent boundary-layer interaction and flow separation may induce self-sustained large-scale oscillations on a profile at transonic Mach number. This phenomenon, known as transonic buffet, is at the origin of intense pressure fluctuations which can have detrimental effects, both in external and internal aerodynamics. The present paper describes a new experiment executed in the ONERA S3Ch transonic wind tunnel on shock oscillations over the OAT15A supercritical profile. These experiments have allowed the precise definition of the conditions for buffet onset and the characterization of the properties of the periodic motion from unsteady surface pressure measurements. The flowfield behavior has been described in great detail thanks to high-speed schlieren cinematography and surveys with a two-component laser Doppler velocimetry along with a conditional sampling technique. The first aim of this study was to provide the computational fluid dynamics community with well-documented test cases to validate advanced computing methods. Concerning the physics of the phenomenon, it is suggested that it is mediated by acoustic waves which are produced at the trailing edge and which travel on the two sides of the airfoil. Also, the experimental results strongly suggest that the phenomenon is essentially two- dimensional, even if three-dimensional effects are also detected. DOI: 10.2514/1.30190

In both continuous and discrete settings, Laplace operators appear quite commonly in the modeling of natural phenomena, in several context: diffusion, heat propagation, porous media, fluid flows through pipes, electricity.... In these contexts, the discrete Laplace operator enjoys all the properties of its continuous counterpart, in particular: self-adjointness, variational formulation, stochastic interpretation, mean value property, maximum principle, ...In a first part, we give a detailed description of the correspondence between these mathematical properties and modeling considerations, in contexts where the continuous and the discrete settings perfectly match. In a second part, we describe a pathological situation, in the context of granular crowd motion models. Accounting for the non-overlapping constraint between hard discs leads to a particular operator acting on a field of Lagrange multipliers, defined on the dual graph of the contact network. This operator is defective in a certain sense: although it is the microscopic counterpart of the macroscopic Laplace operator, this discrete operator indeed lacks some properties, in particular the maximum principle. We investigate here how this very defectivity may explain some paradoxical phenomena that are observed in crowd motions and granular materials, phenomena that are not reproduced by macroscopic models.

Residency after 40 is about 40 times tougher Some 15 years ago, I was starting to burn out on post-graduate training. I'd done three years of internal medicine and two [...]

We propose a new microscopic crowd motion model based on Game-Theoretic principles, from which we derive an Inhibition-Based model for evacuation situations. Each individual is supposed to have a desired velocity that they adapt to the behavior of neighbors that influence them. Possible adapted velocities are defined as instantaneous Nash equilibria: each individual does their best with respect to a personal objective (desired velocity), considering the behavior of the neighbors that influence them (to avoid overlapping). We address theoretical and modeling issues in various situations, in particular when each individual is influenced by all their neighbors, and in the case where the influence relations are structured in a hierarchical way. The second particular case is used to define the Inhibition-Based model.