An energy-consistent depth-averaged Euler system: derivation and properties

In this paper, we present an original derivation process of a non-hydrostatic shallow water-type model which aims at approximating the incompressible Euler and Navier-Stokes systems with free surface. The closure relations are obtained by aminimal energy constraint instead of an asymptotic expansion. The model slightly differs from thewell-known Green-Naghdi model and is confronted with stationary andanalytical solutions of the Euler system corresponding to rotationalflows. At the end of the paper, we givetime-dependent analytical solutions for the Euler system that are alsoanalytical solutions for the proposed model but that are not solutionsof the Green-Naghdi model. We also give and compare analytical solutions of thetwo non-hydrostatic shallow water models

Data Assimilation for hyperbolic conservation laws. A Luenberger observer approach based on a kinetic description

Developing robust data assimilation methods for hyperbolic conservation laws is a challenging subject. Those PDEs indeed show no dissipation effects and the input of additional information in the model equations may introduce errors that propagate and create shocks. We propose a new approach based on the kinetic description of the conservation law. A kinetic equation is a first order partial differential equation in which the advection velocity is a free variable. In certain cases, it is possible to prove that the nonlinear conservation law is equivalent to a linear kinetic equation. Hence, data assimilation is carried out at the kinetic level, using a Luenberger observer also known as the nudging strategy in data assimilation. Assimilation then resumes to the handling of a BGK type equation. The advantage of this framework is that we deal with a single "linear" equation instead of a nonlinear system and it is easy to recover the macroscopic variables. The study is divided into several steps and essentially based on functional analysis techniques. First we prove the convergence of the model towards the data in case of complete observations in space and time. Second, we analyze the case of partial and noisy observations. To conclude, we validate our method with numerical results on Burgers equation and emphasize the advantages of this method with the more complex Saint-Venant system

U.N. Sovereign Immunity: Using the Haitian Experience to Transition from Absolute to Qualified Immunity

The United Nations (“U.N.”) has been looked at globally and historically as an international organization that has given aid to millions of people in the hopes of promoting peace and reducing human rights violations. It is no surprise then that many countries have welcomed U.N. troops with open arms in the hopes of stabilizing communities. However, instead of receiving aid, imagine receiving a deadly disease. Imagine having the nearby river that has been your only source of water for drinking, laundry, and bathing for decades turned into a waste dump. It is from that river turned waste dump that you—and hundreds of thousands of other innocent people—have now contracted cholera. This was the reality for thousands of Haitian citizens who now continue to suffer from cholera due to a U.N. base’s negligent disposal of its troops’ waste into a river the Haitian citizens depended on for survival. Despite being responsible for the cholera epidemic now plaguing Haiti—a third world country with too few resources struggling to support its citizens—the U.N. has failed to not only properly respond to the outbreak, but also to accept legal responsibility. This Note discusses different options to bring about financial, legal, and actual relief to the victims of the cholera outbreak in Haiti. It reviews the failed attempts of Haitian victims to hold the U.N. legally accountable for its actions and seeks to answer the following question: in what ways can relief be achieved, if at all, in the human rights realm

A multilayer Saint-Venant system with mass exchanges for Shallow Water flows. Derivation and numerical validation

The standard multilayer Saint-Venant system consists in introducing fluid layers that are advected by the interfacial velocities. As a consequence there is no mass exchanges between these layers and each layer is described by its height and its average velocity. Here we introduce another multilayer system with mass exchanges between the neighborhing layers where the unknowns are a total height of water and an average velocity per layer. We derive it from Navier-Stokes system with an hydrostatic pressure and prove energy and hyperbolicity properties of the model. We also give a kinetic interpretation leading to effective numerical schemes with positivity and energy properties. Numerical tests show the versatility of the approach and its ability to compute recirculation cases with wind forcing.Comment: Submitted to M2A

Du cens à la parité : la conquête électorale féminine pour le droit de vote selon l'exemple de la France

Depuis toujours, les femmes se battent pour accéder à la responsabilité politique. De la Révolution française à nos jours, nombreuses sont les raisons qui ont été invoquées pour empêcher la conquête de ce droit élémentaire. Aux causes d'origine historique, religieuse et sociologique, dont il est difficile d'apprécier la portée relative, s'ajoutent des raisons d'ordre pratique, tenant à la difficulté de concilier vie professionnelle, vie familiale et activité politique. Certes, depuis quelques années et sous la pression populaire des mouvements féministes en Angleterre et en France, les partis politiques ont adopté, à des degrés divers, une stratégie volontariste pour faire de la place aux femmes parmi leurs candidats : détermination d'un taux de candidatures féminines ou bien constitution de listes paritaires. Cependant, au vu des résultats en termes statistiques, ces mesures demeurent insuffisantes : les femmes sont aujourd'hui encore sous-représentées dans les assemblées et les gouvernements. Il apparaît alors que seule une modification constitutionnelle sera de nature à ouvrir la voie à des dispositions législatives accordant une place propre aux femmes dans la vie publique.Women have always struggled to be politically enfranchised. From the French Revolution to modern times, many reasons have been concocted to deprive them of conquering this fundamental right. In addition to historic, religious and sociological reasons, there are also practical ones issuing from the vicissitudes of daily living .family life, professional commitments and political activities. Nonetheless, in recent years owing to pressure from feminist groups in England and France, political parties have to varying degrees adopted voluntary strategies for making more room for women candidates, female candidate quotas or parity list makeups. Despite all this, hard-figure statistical results show that these measures remain insufficient and women are still under-represented in assemblies and governments. It hence appears that a constitutional amendment alone would open the way to legislative provisions providing women with a specific place in public life