214 research outputs found

    Volcan islandais Eyjafjöll : mais où vont les particules ?

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    International audienceNous entendions ce matin à la radio qu'il devait y avoir une erreur dans les modèles mathématiques, puisque les vols d'essais menés par plusieurs compagnies aériennes semblent avoir laissé les moteurs dans un état intact. Nous allons essayer de décrypter cette affirmation

    Viscoplastic Free-Surface Flows: The Herschel-Bulkley Case

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    International audienceIn this paper, we will describe consistent numerical methods for power-law viscoplastic free-surface flows. From the rheological viewpoint, associated models are of Herschel-Bulkley type, which is a generalization of the Bingham model. On the one hand, Bingham model is the simplest model when it comes to describe viscoplasticity. On the other hand, power-law model is a natural extension of a rate-of-shear dependant viscosity, as opposed to the canical case of the (often) constant viscosity used in the Navier-Stokes equations. After describing a shallow-water asymptotics of a 3D Navier-Stokes-Herschel-Bulkley model with free surface, we will end up with a model which has various mathematical difficulties. We will show how to handle optimization problems arising from the variational inequalities associated to the model, as well as their coupling with finite-volume discretization. Several numerical tests will be shown, including a comparison with an analytic solution, to confirm the well balanced property and the ability to cope with the various rheological regimes associated with the Herschel-Bulkley constitutive law. See : http://www.iccfd.org/iccfd7/assets/pdf/papers/ICCFD7-3302_paper.pd

    Efficient numerical schemes for viscoplastic avalanches. Part 2: the 2D case

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    This paper deals with the numerical resolution of a shallow water viscoplastic flow model. Viscoplastic materials are characterized by the existence of a yield stress: below a certain critical threshold in the imposed stress, there is no deformation and the material behaves like a rigid solid, but when that yield value is exceeded, the material flows like a fluid. In the context of avalanches, it means that after going down a slope, the material can stop and its free surface has a non-trivial shape, as opposed to the case of water (Newtonian fluid). The model involves variational inequalities associated with the yield threshold: finite volume schemes are used together with duality methods (namely Augmented Lagrangian and Bermúdez–Moreno) to discretize the problem. To be able to accurately simulate the stopping behavior of the avalanche, new schemes need to be designed, involving the classical notion of well-balancing. In the present context, it needs to be extended to take into account the viscoplastic nature of the material as well as general bottoms with wet/dry fronts which are encountered in geophysical geometries. Here we derive such schemes in 2D as the follow up of the companion paper treating the 1D case. Numerical tests include in particular a generalized 2D benchmark for Bingham codes (the Bingham–Couette flow with two non-zero boundary conditions on the velocity) and a simulation of the avalanche path of Taconnaz in Chamonix—Mont-Blanc to show the usability of these schemes on real topographies from digital elevation models (DEM)

    On the entropy of rectifiable and stratified measures

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    We summarize some results of geometric measure theory concerning rectifiable sets and measures. Combined with the entropic chain rule for disintegrations (Vigneaux, 2021), they account for some properties of the entropy of rectifiable measures with respect to the Hausdorff measure first studied by (Koliander et al., 2016). Then we present some recent work on stratified measures, which are convex combinations of rectifiable measures. These generalize discrete-continuous mixtures and may have a singular continuous part. Their entropy obeys a chain rule, whose conditional term is an average of the entropies of the rectifiable measures involved. We state an asymptotic equipartition property (AEP) for stratified measures that shows concentration on strata of a few "typical dimensions" and that links the conditional term of the chain rule to the volume growth of typical sequences in each stratum.Comment: To appear in the proceedings of Geometric Science of Information (GSI2023

    Algunes lleis fonètiques catalanes no observades fins ara

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    Algunes lleis fonètiques catalanes no observades fins ara

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