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Iftimie D.,Camille Jordan Institute | Sueur F.,University Pierre and Marie Curie
Archive for Rational Mechanics and Analysis | Year: 2011

We tackle the issue of the inviscid limit of the incompressible Navier-Stokes equations when the Navier slip-with-friction conditions are prescribed on impermeable boundaries. We justify an asymptotic expansion which involves a weak amplitude boundary layer, with the same thickness as in Prandtl's theory and a linear behavior. This analysis holds for general regular domains, in both dimensions two and three. © 2010 Springer-Verlag.

Ernst A.,Karolinska Institutet | Alkass K.,Karolinska Institutet | Bernard S.,Camille Jordan Institute | Salehpour M.,Uppsala University | And 5 more authors.
Cell | Year: 2014

In most mammals, neurons are added throughout life in the hippocampus and olfactory bulb. One area where neuroblasts that give rise to adult-born neurons are generated is the lateral ventricle wall of the brain. We show, using histological and carbon-14 dating approaches, that in adult humans new neurons integrate in the striatum, which is adjacent to this neurogenic niche. The neuronal turnover in the striatum appears restricted to interneurons, and postnatally generated striatal neurons are preferentially depleted in patients with Huntington's disease. Our findings demonstrate a unique pattern of neurogenesis in the adult human brain. © 2014 Elsevier Inc.

Clarke F.,Camille Jordan Institute
Annual Reviews in Control | Year: 2011

We study the controllability and stability of control systems that are nonlinear, and for which, for whatever reason, linearization fails. We begin by motivating the need for two seemingly exotic tools: nonsmooth control-Lyapunov functions, and discontinuous feedbacks. With the aid of nonsmooth analysis, we build a theory around these tools. We proceed to apply it in various contexts, focusing principally on the design of discontinuous stabilizing feedbacks. © 2010 Elsevier Ltd. All rights reserved.

Kasraoui A.,Camille Jordan Institute
European Journal of Combinatorics | Year: 2010

We put recent results on the symmetry of the joint distribution of the numbers of crossings and nestings of two edges over matchings, set partitions and linked partitions in the larger context of enumeration of increasing and decreasing sequences of length 2 in fillings of moon polyominoes. © 2009 Elsevier Ltd. All rights reserved.

Filbet F.,Camille Jordan Institute
Multiscale Modeling and Simulation | Year: 2012

In this paper we present several numerical results performed with a fully deterministic scheme to discretize the Boltzmann equation of rarefied gas dynamics in a bounded domain for multiscale problems. Periodic, specular reflection and diffusive boundary conditions are discussed and investigated numerically. The collision operator is treated by a Fourier approximation of the collision integral, which guarantees spectral accuracy in velocity with a computational cost of MN log(N), where N is the number of degrees of freedom in velocity space andM represents the number of discrete angles of the collision kernel. This algorithm is coupled with a second order finite volume scheme in space and a time discretization allowing us to deal for rarefied regimes as well as their hydrodynamic limit. Our numerical results show that the proposed approach significantly improves the near-wall nonstationary flow accuracy of standard numerical methods over a wide range of Knudsen numbers, in particular when the solution to the Boltzmann equation is close to the local equilibrium and for slow motion flows. © 2012 Society for Industrial and Applied Mathematics.

Le Roux D.Y.,Camille Jordan Institute
Journal of Computational Physics | Year: 2012

For most of the discretization schemes, the numerical approximation of shallow-water models is a delicate problem. Indeed, the coupling between the momentum and the continuity equations usually leads to the appearance of spurious solutions and to anomalous dissipation/dispersion in the representation of the fast (Poincaré) and slow (Rossby) waves. In order to understand these difficulties and to select appropriate spatial discretization schemes, Fourier/dispersion analyses and the study of the null space of the associated discretized problems have proven beneficial. However, the cause of spurious oscillations and reduced convergence rates, that have been detected for most of mixed-order finite element shallow-water formulations, in simulating classical problems of geophysical fluid dynamics, is still an open question. The aim of the present study is to show that when spurious inertial solutions are present, they are mainly responsible for the aforementioned problems. Further, a criterion is found which determines the existence and the number of spurious inertial solutions. As it is delicate to cure spurious inertial modes, a class of possible discretization schemes is proposed, that is not affected by such spurious solutions. © 2012 Elsevier Inc.

Brandolese L.,Camille Jordan Institute
Communications in Mathematical Physics | Year: 2014

We unify a few of the best known results on wave breaking for the Camassa-Holm equation (by R. Camassa, A. Constantin, J. Escher, L. Holm, J. Hyman and others) in a single theorem: a sufficient condition for the breakdown is that {Mathematical expression} is strictly negative in at least one point {Mathematical expression}. Such blowup criterion looks more natural than the previous ones, as the condition on the initial data is purely local in the space variable. Our method relies on the introduction of two families of Lyapunov functions. Contrary to McKean's necessary and sufficient condition for blowup, our approach applies to other equations that are not integrable: we illustrate this fact by establishing new local-in-space blowup criteria for an equation modeling nonlinear dispersive waves in elastic rods. © 2014 Springer-Verlag Berlin Heidelberg.

Filbet F.,Camille Jordan Institute | Jin S.,University of Wisconsin - Madison
Journal of Computational Physics | Year: 2010

In this paper, we propose a general time-discrete framework to design asymptotic-preserving schemes for initial value problem of the Boltzmann kinetic and related equations. Numerically solving these equations are challenging due to the nonlinear stiff collision (source) terms induced by small mean free or relaxation time. We propose to penalize the nonlinear collision term by a BGK-type relaxation term, which can be solved explicitly even if discretized implicitly in time. Moreover, the BGK-type relaxation operator helps to drive the density distribution toward the local Maxwellian, thus naturally imposes an asymptotic-preserving scheme in the Euler limit. The scheme so designed does not need any nonlinear iterative solver or the use of Wild Sum. It is uniformly stable in terms of the (possibly small) Knudsen number, and can capture the macroscopic fluid dynamic (Euler) limit even if the small scale determined by the Knudsen number is not numerically resolved. It is also consistent to the compressible Navier-Stokes equations if the viscosity and heat conductivity are numerically resolved. The method is applicable to many other related problems, such as hyperbolic systems with stiff relaxation, and high order parabolic equations. © 2010 Elsevier Inc.

Nadeau P.,Camille Jordan Institute
Journal of Combinatorial Theory. Series A | Year: 2013

In this work we continue our study of Fully Packed Loop (FPL) configurations in a triangle. These are certain subgraphs on a triangular subset of Z2, which first arose in the study of the usual FPL configurations on a square grid. We show that, in a special case, the enumeration of these FPLs in a triangle is given by Littlewood-Richardson coefficients. The proof consists of a bijection with Knutson-Tao puzzles. © 2013 Elsevier Inc.

Nadeau P.,Camille Jordan Institute
Journal of Combinatorial Theory. Series A | Year: 2013

Fully Packed Loop configurations (FPLs) are certain configurations on the square grid, naturally refined according to certain link patterns. If A X is the number of FPLs with link pattern X, the Razumov-Stroganov correspondence provides relations between numbers A X relative to a given grid size. In another line of research, if X ∪ p denotes X with p additional nested arches, then A X ∪p was shown to be polynomial in p: the proof gives rise to certain configurations of FPLs in a triangle (TFPLs).In this work we investigate these TFPL configurations and their relation to FPLs. We prove certain properties of TFPLs, and enumerate them under special boundary conditions. From this study we deduce a class of linear relations, conjectured by Thapper, between quantities A X relative to different grid sizes, relations which thus differ from the Razumov-Stroganov ones. © 2013 Elsevier Inc.

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