The Euler Limit of the Navier‐Stokes Equations, and Rotating Fluids with Boundary

In this paper we study the convergence of weak solutions of the Navier-Stokes equations in some particular domains, with different horizontal and vertical viscosities, when they go to zero with different speeds. The difficulty here comes from the Dirichlet boundary conditions. Precisely we show that if the ratio of the vertical viscosity to the horizontal viscosity also goes to zero, then the solutions converge to the solution of the Euler system. We study the same limit for rotating fluids with Rossby number also going to zero. (Accepted March 20, 1997)     

On a general approach to the formal cohomology of quadratic Poisson structures

We propose a general approach to the formal Poisson cohomology of r-matrix induced quadratic structures, we apply this device to compute the cohomology of structure 2 of the Dufour-Haraki classification, and provide complete results also for the cohomology of structure 7.     

Friction and wear behaviour of cp Ti and Ti6Al4V following nitric acid passivation

Nitric acid passivation increases the thickness of the TiO₂ passive film formed at the cp Ti and Ti6Al4V surface. The TiO₂ oxide, which has a lubricating nature, reduces the wear rate. A linear ball-on-disc friction test has been carried out at room temperature in ambient air, NaCl 3% and Ringer's solutions, with a sliding velocity of 4 mm s⁻¹ and a normal load of 1 N. Friction coefficient curves obtained from ball-on-disc wear test, as well as following the optical microscopy observation of ball trace, indicated the presence of periodic phenomenon. One period can be divided into four stages. This can be clearly seen for cp Ti (accommodation stage, creation of wear particles, adherence of particles layer on the alumina ball and ejection of this layer). In order to confirm this observation and understand the chemical interfacial phenomena, open circuit potential (OCP) measurements were carried out in the same time of friction tests.     

Extension of the variance function of a steep exponential family

Let F={P(m,F); mM_F} be a multidimensional steep natural exponential family parameterized by its domain of the means M_F and let V_F(m) be its variance function. This paper studies the boundary behaviour of V_F. Necessary and sufficient conditions on a point of ∂M_F are given so that V_F admits a continuous extension to the point . It is also shown that the existence of implies the existence of a limit distribution concentrated on an exposed face of containing . The relation between and is established and some illustrating examples are given.     

A double microbeam MEMS ohmic switch for RF-applications with low actuation voltage

In this paper, we propose the design of an ohmic contact RF microswitch with low voltage actuation, where the upper and lower microplates are displaceable. We develop a mathematical model for the RF microswitch made up of two electrostatically actuated microplates; each microplate is attached to the end of a microcantilever. We assume that the microbeams are flexible and that the microplates are rigid. The electrostatic force applied between the two microplates is a nonlinear function of the displacements and applied voltage. We formulate and solve the static and eigenvalue problems associated with the proposed microsystem. We also examine the dynamic behavior of the microswitch by calculating the limit-cycle solutions. We discretize the equations of motion by considering the first few dominant modes in the microsystem dynamics. We show that only two modes are sufficient to accurately simulate the response of the microsystem under DC and harmonic AC voltages. We demonstrate that the resulting static pull-in voltage and switching time are reduced by 30 and 45%, respectively, as compared to those of a single microbeam-microplate RF-microswitch. Finally, we investigate the global stability of the microswitch using different excitation conditions.     

Synthesis and Structure of Bis(3-dimethylammonium-1-propyne)pentachlorobismuthate(III) (C<Subscript>5</Subscript>H<Subscript>10</Subscript>N)<Subscript>2</Subscript>BiCl<Subscript>5</Subscript>

Abstract  

The synthesis and crystal structure are given for the bis(3-dimethylammonium-1-propyne)pentachlorobismuthate(III) salt. An X-ray investigation has shown that the title compound crystallizes at 298 K in a centrosymmetric monoclinic system, space group C2/c with the following lattice parameters a = 12.6215(4) ?, b = 18.9228(5) ?, c = 8.3134(2) ?, β = 104.100(2)°, V = 1925.70(9) ?³. The structure was solved from 7,716 independent reflections with R ₁ = 0.0457 and wR ₂ = 0.0906, and refined with 85 parameters. The structure consists of disordered 3-dimethylammonium-1-propyne, C₅H₉NH⁺ cations and polynuclear anions in which slightly distorted (BiCl₅)²⁻ anions, sharing an apex are interconnected in chains. These chains are themselves interconnected by means of N–H···Cl originating from the C₅H₉NH⁺ entities, forming a three-dimensional network.     

Global existence of weak solutions to the FENE dumbbell model of polymeric flows

Systems coupling fluids and polymers are of great interest in many branches of sciences. One of the most classical models to describe them is the FENE (Finite Extensible Nonlinear Elastic) dumbbell model. We prove global existence of weak solutions to the FENE dumbbell model of polymeric flows. The main difficulty is the passage to the limit in a nonlinear term that has no obvious compactness properties. The proof uses many weak convergence techniques. In particular it is based on the control of the propagation of strong convergence of some well chosen quantity by studying a transport equation for its defect measure. In addition, this quantity controls a rescaled defect measure of the gradient of the velocity.     

The Topological Gradient Method: From Optimal Design to Image Processing

The aim of this article is to review and extend the applications of the topological gradient to major image processing problems. We briefly review the topological gradient, and then present its application to the crack localization problem, which can be solved using the Dirichlet to Neumann approach. A very natural application of this technique in image processing is the inpainting problem, which can be solved by identifying the optimal location of the missing edges. Edge detection is of extreme importance, as edges convey essential information in a picture. A second natural application is then the image reconstruction. A class of image reconstruction problems is considered that includes restoration, demosaicing, segmentation and super-resolution. These problems are studied using a unified theoretical framework which is based on the topological gradient method. This tool is able to find the localization and orientation of the edges for blurred, low sampled, partially masked, noisy images. We review existing algorithms and propose new ones. The performance of our approach is compared with conventional image reconstruction processes.     

A multiobjective stochastic program for hospital bed planning

In this paper, we study hospital bed capacity management for a set of existing hospitals when the demand for beds is random. We propose a multiobjective stochastic program model to assign beds to hospital departments. We consider three objective functions to be minimized, which are the cost of creation and management of new beds and the number of nurses and physicians working in these hospitals, subject to demand satisfaction of three kinds of health-care specialities. A certainty equivalent program was derived based on a mixture between the chance constrained approach, the recourse approach and the goal programming approach. Empirical results using real data from 157 Tunisian national hospitals are reported.     

From the Boltzmann Equations¶to the Equations of¶Incompressible Fluid Mechanics, II

We consider here the problem of deriving rigorously from renormalized solutions of Boltzmann's equation, globally in time, for general initial conditions and without any additional assumption, solutions of Stokes' equations (together with the strong Boussinesq relation). We also obtain similar results for Euler equations where, however, we need to make an assumption on the high velocities of the solutions of Boltzmann's equation.