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Royer J.,Institute Of Mathematiques Of Toulouse
Annales Henri Poincare | Year: 2015

We prove exponential decay for the solution of the Schrödinger equation on a dissipative waveguide. The absorption is effective everywhere on the boundary, but the geometric control condition is not satisfied. The proof relies on separation of variables and the Riesz basis property for the eigenfunctions of the transverse operator. The case where the absorption index takes negative values is also discussed. © 2014, Springer Basel.

Apkarian P.,ONERA | Dao M.N.,Hanoi National University of Education | Noll D.,Institute Of Mathematiques Of Toulouse
IEEE Transactions on Automatic Control | Year: 2015

We present a new approach to parametric robust controller design, where we compute controllers of arbitrary order and structure which minimize the worst-case H∞ norm over a pre-specified set of uncertain parameters. At the core of our method is a nonsmooth minimization method tailored to functions which are semi-infinite minima of smooth functions. A rich test bench and a more detailed example illustrate the potential of the technique, which can deal with complex problems involving multiple possibly repeated uncertain parameters. © 2015 IEEE.

Ervedoza S.,Institute Of Mathematiques Of Toulouse | Hillairet M.,University of Paris Dauphine | Lacave C.,University Paris Diderot
Communications in Mathematical Physics | Year: 2014

In this article, we study the long-time behavior of solutions of the two-dimensional fluid-rigid disk problem. The motion of the fluid is modeled by the two-dimensional Navier-Stokes equations, and the disk moves under the influence of the forces exerted by the viscous fluid. We first derive L p-L q decay estimates for the linearized equations and compute the first term in the asymptotic expansion of the solutions of the linearized equations. We then apply these computations to derive time-decay estimates for the solutions to the full Navier-Stokes fluid-rigid disk system. © 2014 Springer-Verlag Berlin Heidelberg.

Dimarco G.,University of Ferrara | Mieussens L.,Institute Of Mathematiques Of Bordeaux | Rispoli V.,Institute Of Mathematiques Of Toulouse
Journal of Computational Physics | Year: 2014

In this work we present an efficient strategy to deal with plasma physics simulations in which localized departures from thermodynamical equilibrium are present. The method is based on the introduction of intermediate regions which allows smooth transitions between kinetic and fluid zones. In this paper we extend Domain Decomposition techniques, obtained through dynamic coupling and buffer zones, to the study of plasmas and, moreover, we combine them with Asymptotic Preserving and Asymptotically Accurate strategies for the time integration. We use a hybrid scheme in which both kinetic and fluid descriptions are considered and coupled together while the kinetic model is solved by asymptotic preserving and accurate methods, in order to guarantee high efficiency and accuracy in all regimes. The numerical scheme is validated and its performances are analyzed by numerical simulations. © 2014 Elsevier Inc.

Mestre O.,Institute Of Mathematiques Of Toulouse | Gruber C.,Zentralanstalt fur Meteorologie und Geodynamik | Prieur C.M.,Joseph Fourier University | Caussinus H.,University Paul Sabatier | Jourdain S.,Direction de la Climatologie
Journal of Applied Meteorology and Climatology | Year: 2011

One major concern of climate change is the possible rise of temperature extreme events, in terms of occurrence and intensity. To study this phenomenon, reliable daily series are required, for instance to compute dailybased indices: high-order quantiles, annual extrema, number of days exceeding thresholds, and so on. Because observed series are likely to be affected by changes in the measurement conditions, adapted homogenization procedures are required. Although a very large number of procedures have been proposed for adjustment of observed series at amonthly time scale, fewhave been proposed for adjustment of daily temperature series. This article proposes a newadjustmentmethod for temperature series at a daily time scale. This method, called spline daily homogenization (SPLIDHOM), relies on an indirect nonlinear regression method. Estimation of the regression functions is performed by cubic smoothing splines. This method is able to adjust the mean of the series aswell as high-order quantiles andmoments of the series. When usingwell-correlated series, SPLIDHOM improves the results of two widely usedmethods, as a result of an optimal selection of the smoothing parameter. Applications to the Toulouse, France, temperature series are shown as a real example. © 2011 American Meteorological Society.

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