On a free boundary problem for the Reynolds equation derived from the Stokes system with Tresca boundary conditions

The asymptotic behaviour of a Stokes flow with Tresca free boundary friction conditions when one dimension of the fluid domain tends to zero is studied. A specific Reynolds equation associated with variational inequalities is obtained and uniqueness is proved.     

Study of the reactione + e −→K + K − in the energy range1350 \leqq \sqrt s \leqq 2400 MeV

Thee ⁺ e ^?→K ⁺ K ^? cross section has been measured from about 750 events in the energy interval \(1350 \leqq \sqrt s \leqq 2400 MeV\) with the DM2 detector at DCI. TheK ^± form factor |F _F ^±| cannot be explained by the ρ, ω, ? and ρ′(1600). An additional resonant amplitude at 1650 MeV has to be added as suggested by a previous experiment.     

Radiative decay ofJ/ψ into γ π+ π−

The radiative decayJ/ψ → γ π⁺ π^? has been studied using the 8.6 millionJ/ψ produced in the DM2 experiment at the DCIe ⁺e^? storage rings at Orsay. The π⁺ π^? mass spectrum shows a cleanf ₂ (1270) signal, and the possible presence of two other states at thef ₂ (1720) andf ₄ (2030) masses. For thef ₂ (1270), the branching ratio BR(J/ψ →γf)xBR(f→π⁺ π^?) is measured to be (7.50±0.30±1.12)×10^?4, and the spin analysis prefers theJ=2 assignment, with helicity parametersx=0.83±0.06 andy=0.01±0.06. The existence of higher mass states is discussed.     

Non-planar smoulder propagation governed by diffusion

The steady propagation of a thin smouldering front in a half-spacehas been considered. A suitable coordinate transformation hasallowed the region near the leading edge of the front to beexamined for both a maintained planar surface and with surfacecollapse due to material shrinkage. The change in the oxidizerconcentration for a small increment in the propagation speedfor large time and surface collapse has been determined. Theinfluence of two types of nonlinear diffusion on the shape ofthe smouldering front has been found; other cases can be dealtwith in a similar manner.     

Effets d'anisotropie par homogénéisation dans un problème à frontière libre

The Elrod–Adams model is a pressure–saturation formulation which takes into account cavitation phenomena in thin fluid films mechanics. We study the asymptotic behavior of the model, using the two-scale convergence technique, in devices such as journal bearings. Interest is highly motivated by the roughness effects of the surfaces. Anisotropic effects appear on the coefficients, which is usual, but also on the saturation function, since various saturation functions appear through the homogenization process. To cite this article: G. Bayada et al., C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

Algorithme de Neumann–Dirichlet pour des problèmes de contact unilatéral : Résultat de convergenceNeumann–Dirichlet algorithm for unilateral contact problems: Convergence results

In this Note, we propose and we prove the convergence of a Neumann–Dirichlet algorithm in order to approximate a Signorini problem between two elastic bodies. The idea is to retain the natural interface between the two bodies as numerical interface for the domain decomposition and to replace the Dirichlet problem in [4] by a variational inequality. To cite this article: G. Bayada et al., C. R. Acad. Sci. Paris, Ser. I 335 (2002) 381–386.     

KMgF3:Ni2+晶体的占位、局部结构、吸收光谱和顺磁g因子的统一解释

利用完全对角化方法和强场耦合方案,采用半自洽场(semi-SCF)自由Ni2+的d轨道模型和Ni2+-6X-(x=F,Cl,Br,I)络合物的μ-κ-α模型研究,建立了含有过渡族金属离子的晶体的局域结构与吸收光谱和顺磁g因子之间的定量关系,对KMgF3:Ni2+晶体的占位、局域结构、吸收光谱和顺磁g因子作出了统一解释,预测了KMgF3:Ni2+晶体的光谱精细结构.所得理论计算结果与实验值符合得很好.     

The L.P.D.E.M., a mixed finite difference method for elliptic problems

Summary A mixed finite difference method is analyzed for solving certain elliptic problems. This method, called L.P.D.E.M. (Locally exact Partial Differential Equation Method) was initially proposed in the frame of hydrodynamic lubrication. Convergence is obtained. Relations between this scheme and homogenization theory are also discussed. For a one-dimensional elliptic equation with no zero-order term and in conservative form, this method is an exact one. Some numerical results will also be given.     

Mathematical analysis of some new Reynolds‐rod elastohydrodynamic models

In this paper, some new elastohydrodynamic Reynolds‐rod models are posed to obtain the existence of solution (the lubricant pressure and the elastic rod displacement). More precisely, a sign restriction on fluid pressure for cavitation modelling and different unilateral conditions on the rod displacement associated with a rigid structure coating are formulated in terms of coupled variational inequalities. The particular hinged or clamped boundary conditions on the rod displacement require different techniques to prove the existence of solution. Besides nearly linear coupled problems, two non‐linear rod problems including curvature effects are analysed. Mainly, regularity results and L^∞ estimates for the solution of variational inequalities and fixed‐point theorems lead to the existence results for the various coupled models. Copyright © 2001 John Wiley & Sons, Ltd.