Showing papers by "École normale supérieure de Cachan published in 1995"

Vortices for a variational problem related to superconductivity

Abstract: We study minimizers of Ginzburg-Landau functional, which depend on a parameter ϵ. These functional appear in superconductivity and two dimensional abelian Higgs models. We study the asymptotic limit, as ϵ → 0, of minimizers and show that the limiting configuration has vortices, which have topological degree one.

Feedback Stabilization of Nonlinear Systems: Sufficient Conditions and Lyapunov and Input-output Techniques

Abstract: This lecture is devoted to the survey of some recent results on feedback stabilization of nonlinear systems. This text can be seen as a prolongation of the overview written by E. Sontag in 1990 [83] in several directions where progress has been made. It consists of three parts: The first part is devoted to sufficient conditions on the stabilization problem by means of discontinuous or time-varying state or output feedback. In the second part, we present some techniques for explicitly designing these feedbacks by using Lyapunov’s method. This introduces us with the notion of assignable Lyapunov function and leads us to concentrate our attention on systems having some special recurrent structure. The third part presents some techniques for designing feedback based on L ∞ stability properties. This last section also addresses robustness through a small gain theorem.

Unicité et minimalité des solutions d'une équation de Ginzburg-Landau

Abstract: Resume On etudie les solutions de l’equation −∆u + u(u2 − 1) = 0, ou u est element de H l o c 1 ( ℝ n ) . On montre que la solution f ( x 1 , … , x n ) = t h ( x 1 2 ) minimise l’energie parmi les fonctions tendant vers −1 lorsque x1 tend vers −∞ et vers +1 lorsque x1 tend vers +∞. De plus, on prouve que toute solution de l’equation qui tend vers 1 lorsque |x| tend vers +∞ est constante egale a 1 sur ℝn.

A regularity result for critical points of conformally invariant functionals

Abstract: Let Ω be an open set inR 2 andI be a conformally invariant functional defined onH 1(Ω,R d ). Letu be a critical point ofI. We show that, ifu is apriori assumed to be bounded, thenu is smooth in Ω, up to ∂Ω (ifu |δΩ is smooth). This is a partial (positive) answer to a conjecture of S. Hildebrandt [13]. As an application, we establish a regularity result for weak solutions to the equation of surfaces of prescribed mean curvature in a three-dimensional compact riemannian manifold.

Analyse des possibilités de fonctionnement en régime des désexcitation des moteurs à aimants permanents

Abstract: Cet article traite de l'extension de la plage de vitesse des moteurs (ou alternateurs) a excitation par aimants permanents et alimentes par convertisseur electronique. La tension et le courant sont limites en amplitude par l'alimentation electronique. L'objectif est d'obtenir une puissance proche de celle correspondant au regime de base sur une plage de vitesse etendue. Ceci necessite une reduction de flux d'entrefer ou «desexitation» au dela de la vitesse de base. Une analyse parametrique des caracteristiques du moteur est effectuee pour mettre en evidence l'influence de la reaction d'induit et de la saillance magnetique. Nous montrons qu'il existe une condition ideale pour obtenir une plage de fonctionnement a puissance constante theoriquement illimitee. La saillance magnetique permet d'accroitre le facteur de puissance surtout lorsque L d > L q . Les principales hypotheses de cette etude sont l'absence de saturation, des f.e.m. et des courants sinusoidaux et une induction spatiale sinusoidale dans l'entrefer. Enfin, nous effectuons un bilan des structures de rotors permettant un fonctionnement en regime de desexcitation

Solvent effect on the excited state behaviour of donor—acceptor-substituted biaryls

Abstract: The fluorescence properties of two biaryl donor-acceptor compounds (4-dimethylamino-4′-cyanobiphenyl (DMACNB) and 4-dimethyl-anilino-1-cyanonaphthalene (DMACNN)) were compared in solvents of different polarity. Low temperature, steady state spectra were also studied in non-polar and polar media. The transient Stokes shifts measured with 30 ps excitation in 1-propanol and 1-hexanol at room temperature show that the charge transfer process is controlled by the dynamics of solvation. A large decrease in the radiative rate constant as a function of the solvent polarity and as a function of time in 1-hexanol solution was observed for DMACNN, whereas this effect was not significant in the case of DMACNB. These differences have been related to the larger steric hindrance to coplanarity in the phenylnaphthalene derivative with respect to that in the substituted biphenyl.

Fifty Years of Maurice Allais’ Economic Writings: Seeds for Renewal in Contemporary Economic Thought

Abstract: Until he discovered the situation in the United States of 1933, Maurice Allais has been fascinated by history, even in his youth, as well as by physics and mechanics a little later. But the trip was to dramatically change the focus of the young man’s interest. He had recently graduated first in his class from the Ecole Polytechnique, one of the most competitive engineering schools in France, originally founded by Napoleon to educate an elite of engineers and scientists. To the young engineer, who had little training in economics, it seemed impossible that responsible men and women in charge of the American economy had let things deteriorate to the point he could observe when looking around on the American streets. The only explanation he could see was that these men and women did not know enough about economics. This conclusion made the field attractive to Maurice Allais: there was something to be searched for, some ‘truths’ indeed to be discovered! The fact that these potential discoveries could help improve society made the challenge still more attractive, because young Maurice had been the son of a family of very modest means.

Algorithme de contraintes actives et contact unilatéral sans frottement

Abstract: We propose a method to take into account the unilateral contact problem based on an active set algorithm. This algorithm is developed inside the computation Code Aster. We first present a short bibliography on the subject. Then we develop the unilateral contact problem, the associated model and some theorems of uniqueness and convergence. The Kuhn Tucker theorem is then discussed in the context of minimization with constraints. The algorithm is presented by mean of a theoretical algorithm on which we demonstrate a convergence property and a computational algorithm with a discussion on the method. The validation of the obtained results is made by comparing the numerical results to analytical ones on a Hertz like problem. The last part is dedicated to the description of an industrial case with an elastoplastic law.

Méthode semi-numérique de pré-dimensionnement des machines à aimants permanents et à bobinage global

Abstract: Les machines electriques peuvent etre caracterisees par une echelle globale relative a l'enroulement induit et une echelle locale relative aux dimensions dentaires. Dans les structures synchrones a bobinage global excitees par des aimants fractiones, le rapport caracteristique des deux echelles precitees est tres superieur a l'unite. L'etude parametrique complete de la machine utilisant un couplage fort, s'avere particulierement lourd et complexe. Dans cet article, nous proposons une methode de pre-dimensionnement simple, rapide et qui prend en compte differentes limitations ou contraintes telles que la desaimantation, l'echauffement, l'encombrement etc. Cette methode, basee sur un modele cellulaire et se limitant au regime lineaire, combine un calcul numerique de champ par la methode des elements finis 2D et une approximation semianalytique des contraintes. Tout d'abord, le formalisme des performances intrinseques ainsi que les modeles relatifs aux contraintes sont presentes. L'influence de certains parametres sur les performances limites et optimales de la machine est ensuite analysee. Enfin, les resultats numeriques obtenus sont confrontes aux essais effectues sur un banc d'essai compose d'une machine cylindrique a aimants ferrites

Flow control in a failure-prone multi-machine manufacturing system

Abstract: The problem of computing optimal production rates for a multimachine multiproduct manufacturing system subject to machine failure is considered. The inventory balance equation is represented by a discrete-time flow model with Markovian jumps to take into account machine breakdown. When defining quadratic cost functions, the associated optimal control problem leads to a set of strongly coupled Riccati-like equations. A necessary and sufficient condition for the existence of a positive semidefinite solution for such equations is given. By verifying a simple matrix inequality, it is shown that such solution exists and can be obtained as a limit of a monotonic sequence. This leads to a straightforward numerical algorithm for the computation of the solution. In this way the optimal production rates for each product type can be determined. An example involving 9 machines and 6 product types is given to illustrate the proposed approach.

A decision-based approach: application to the automatic design of process planning

Abstract: The notion of centre of decision presented in this article defines a conceptual and generic model enabling us to represent and use expert knowledge. It is suitable when the problem to be solved can be broken down into a sum of interdependent subproblems. Actions can be planned progressively and previous decisions can he modified by a backtrack mechanism. This principle is iterative. The structure is made up of many independent rules and an action plan. The customization of the application is possible even if the software evolves with future updates. This model has been applied in the LURPA-TOUR software which is a computer-aided process planning system for rotational parts.

Pollution imagery by optical interferometry: application to SO(2) gas.

Abstract: The interferometric correlation method can provide a simple and inexpensive solution for pollution imagery, especially in the case of a spatially localized gaseous cloud. We describe herein a general method for designing an interferometric correlator for the analysis of any pollutant gas that has regularly distributed absorption spectral lines. We also present a setup using a birefringent interferometer in front of a simplified camera formed by a plano–convex lens and a linear CCD sensor; this demonstrates the monitoring of SO2 gas. Results from the laboratory simulation show the feasibility of this method. Outdoor measurements permit determination of the required conditions for on-site real-time measurement.

Active shielding of eddy current sensors: a method to focus the magnetic field in order to improve lateral resolution and coupling coefficient

Abstract: We present an original method called ‘active shielding’, which provides improved eddy current sensor performance, mainly in terms of the coupling coefficient with the target, distance range and spatial resolution. The method is derived from the theory of electrical images. Initially, the basic principles of such sensor are highlighted. Then we present the method applied to the design of a cup sensor. We finally discuss the effects of active shielding based on the use of active elements to modify the distribution of the magnetic field in the sensing region of the sensor. The advantages of this method are demonstrated with examples: the coupling coefficient and the spatial resolution are improved whereas the distance range is not modified.

Complexity and Strategic Decision Under Uncertainty. How can we Adapt the Theory

Abstract: Experience shows that those who try to apply the most accepted mathematical theory of decision under uncertainty in a prescriptive way, will encounter situations where this technique will be firmly rejected by those responsible for taking the decision, whether it concerns an individual, a company director for example, or a group, such as a Board of Directors or a technical study group. The opinion expressed by those involved in such cases, is that such things as utility functions in a risky universe do not exist, whatever name you might give them. The same opinion believes that we cannot completely rely on well-defined probabilities, once again, whatever the name given to them may be and whatever the technique used to define their distribution in the situation envisaged. It means, finally, that to retain the expected utility criterion constitutes neither a convincing procedure for choosing between several projects or multifaceted (and therefore multidimensional) strategies, nor a way of escaping from the inadequacies of the utilities and probabilities mentioned above.

Triplet excited-state characterization and determination of the photoionization mechanism of the antitumoral drug pazelliptine

Abstract: The triplet properties of the excited triplet state of pazelliptine (PZE), an antitumoral drug derived from ellipticine, were investigated in dioxane, ethanol and buffer aqueous solutions using the laser flash photolysis technique. The triplet absorption spectra and the kinetic parameters associated with the excited state decay were quite similar in the different solvents. 3 PZE reacted with unexcited PZE in deaerated solutions ( k = 6 × 10 10 M −1 s −1 ) and was quenched by oxygen ( k ≈ 2 × 10 7 s −1 ). The extinction coefficients of the triplet transition were estimated and used to calculate the singlet-triplet intersystem crossing quantum yields of about 5%. A biphotonic ionization of PZE in buffer aqueous solution has been demonstrated in a previous work. This process was also observed in ethanol but not in dioxane. Mixed yttrium aluminum garnet laser harmonics (355 nm + 532 nm) and delayed-pulse experiments were carried out in order to determine the intermediate excited state involved in this photoionization process. The results indicate that pazelliptine radical cation and e − s are formed via a consecutive two-photon absoprtion in which the first excited singlet state is the only intermediate.

Evaluation criteria: a method to represent and compute technological knowledge in CAPP

Abstract: The complexity of research in CAPP is, on the one hand, about the knowledge formalization of the machining expert (knowledge based on scientific models but also on experience) and, on the other hand, about the use of this knowledge to obtain a system of CAPP for general machining (knowledge valuation). The authors' method is based on three tools which allows them to: represent the process plans, describe the knowledge of a machining expert, and imagine process plans. A study of the finished part allows one to conceive many anterior stages of the workpiece and, by successive iterations to obtain raw shapes. This way, technological criteria translate machining expert knowledge, and compute and eliminate non-viable solutions step by step. The graph of representation of process plans, finally obtained, has only a few technologically viable process plans. A global evaluation can then be executed (cost study for example). In this paper, the authors develop the evaluation criteria and the construction of the graph to avoid a combinatorial explosion. The authors' experimental software LURPA-TOUR uses this method on a IBM RISC 6000 computer for turning parts.

On the undecidability of deadlock detection in families of nets

Abstract: In this paper, we are interested in modelization of some aspects of massively parallel computers built by connecting together copies of a unique given pattern. Thus, a natural and important question arises. Is it possible to verify that a property holds, not for one given configuration, but for all the configurations that can be constructed? Of course, the difficulty comes from the fact that the number of distinct configurations is infinite. We focus in this paper on the deadlock problem: can we verify that any net, constructed by connecting an arbitrary number of copies of the pattern, is deadlock free? As in a great number of models, the semantics of the pattern and thus the semantics of a net are given by finite transition systems. The main result of this paper proves that the deadlock problem is surprisingly undecidable.

Almost periodicity for the nonlinear cubic Schrödinger equation

Abstract: For initial data inH 2 we prove that the periodic solutions in space to the nonlinear cubic Schrodinger equation are almost periodic in time.

Complexity, the Concept of Uncertainty and Bounded Rationality of Man

Abstract: Our Societies become more complex everyday, particularly in the economic sphere. This is due not only to technology, but also to organizational needs in every social cell, from government services down to the individual. Everyday even the ordinary person is becoming more aware of the necessary links between today’s societies across the world, and feels that human behavior must be adapted to this new situation. This law of emerging “Complexity-Conscience” has long been known [Teilhard de Chardin, 1959]. One can also see, in our societies, that our decisions and actions are prepared and applied under a very strong uncertainty.