The Incompressible Euler Limit of the Boltzmann Equation with Accommodation Boundary Condition

The convergence of solutions of the incompressible Navier-Stokes equations set in a domain with boundary to solutions of the Euler equations in the large Reynolds number limit is a challenging open problem both in 2 and 3 space dimensions. In particular it is distinct from the question of existence in the large of a smooth solution of the initial-boundary value problem for the Euler equations. The present paper proposes three results in that direction. First, if the solutions of the Navier-Stokes equations satisfy a slip boundary condition with vanishing slip coefficient in the large Reynolds number limit, we show by an energy method that they converge to the classical solution of the Euler equations on its time interval of existence. Next we show that the incompressible Navier-Stokes limit of the Boltzmann equation with Maxwell's accommodation condition at the boundary is governed by the Navier-Stokes equations with slip boundary condition, and we express the slip coefficient at the fluid level in terms of the accommodation parameter at the kinetic level. This second result is formal, in the style of [Bardos-Golse-Levermore, J. Stat. Phys. 63 (1991), 323-344]. Finally, we establish the incompressible Euler limit of the Boltzmann equation set in a domain with boundary with Maxwell's accommodation condition assuming that the accommodation parameter is small enough in terms of the Knudsen number. Our proof uses the relative entropy method following closely the analysis in [L. Saint-Raymond, Arch. Ration. Mech. Anal. 166 (2003), 47-80] in the case of the 3-torus, except for the boundary terms, which require special treatment.Comment: 40 page

Entropy production and multiple equilibria: the case of the ice-albedo feedback

Nonlinear feedbacks in the Earth System provide mechanisms that can prove very useful in understanding complex dynamics with relatively simple concepts. For example, the temperature and the ice cover of the planet are linked in a positive feedback which gives birth to multiple equilibria for some values of the solar constant: fully ice-covered Earth, ice-free Earth and an intermediate unstable solution. In this study, we show an analogy between a classical dynamical system approach to this problem and a Maximum Entropy Production (MEP) principle view, and we suggest a glimpse on how to reconcile MEP with the time evolution of a variable. It enables us in particular to resolve the question of the stability of the entropy production maxima. We also compare the surface heat flux obtained with MEP and with the bulk-aerodynamic formula.Comment: 29 pages, 12 figure

Prise en charge, commitment ou scène énonciative

Cet article, partant d'une réflexion sur la notion de prise en charge et, dans une moindre mesure, de commitment propose une approche alternative reposant sur la notion de scène énonciative

Verbes préfixés et intensité en français et en russe

Cet article est consacré à l'étude d'une série de verbes préfixés en français et en russe que l'on peut considérer comme des manifestations particulières de la notion d'intensité, prise ici dans le sens que donne le Petit Robert à l'adjectif " intense " : " qui dépasse la mesure ordinaire "

Phase transitions and marginal ensemble equivalence for freely evolving flows on a rotating sphere

The large-scale circulation of planetary atmospheres like that of the Earth is traditionally thought of in a dynamical framework. Here, we apply the statistical mechanics theory of turbulent flows to a simplified model of the global atmosphere, the quasi-geostrophic model, leading to non-trivial equilibria. Depending on a few global parameters, the structure of the flow may be either a solid-body rotation (zonal flow) or a dipole. A second order phase transition occurs between these two phases, with associated spontaneous symmetry-breaking in the dipole phase. This model allows us to go beyond the general theory of marginal ensemble equivalence through the notion of Goldstone modes.Comment: 7 pages, 3 figures; accepted for publication in Physical Review

Photoferroelectric oxides

Giant photovoltaic effect due to bulk photovoltaic effect observed in multiferroic BiFeO3 thin films has triggered a renewed interest on photoferroelectric materials for photovoltaic applications. Tremendous advance has been done to improve power conversion efficiency (up to up to 8.1%) in photoferroelectrics via absorption increase using narrow bandgap ferroelectrics. Other strategies, as it is the more efficient use of ferroelectric internal electric field, are ongoing. Moreover, as a by-product, several progress have been also achieved on photostriction that is the photo-induced deformation phenomenon. Here, we review ongoing and promising routes to improve ferroelectrics photoresponse

La réduplication du nom et de l'adjectif en khmer

Cet article traite de la réduplication en khmer contemporain. Nous chercherons à montrer que, loin de constituer un domaine isolé dont pourrait traiter en termes d'iconicité, la réduplication en khmer peut être décrite en termes d'opérations intervenant dans la construction de la valeur référentielle de l'énoncé. Plus précisément, la réduplication correspond à une pluralisation qualitative en dehors de toute détermination quantitative