Showing papers by "École normale supérieure de Cachan published in 1993"
TL;DR: In this paper, it was shown that ue → u0 in a smooth bounded simply connected domain is a minimizer for Ee onH====== g====== 1>>\s, where u0 is identified.
Abstract: LetΩ ⊂ ℝ2 be a smooth bounded simply connected domain. Consider the functional
$$E_\varepsilon (u) = \frac{1}{2}\int\limits_\Omega {\left| {
abla u} \right|^2 + \frac{1}{{4\varepsilon ^2 }}} \int\limits_\Omega {(|u|^2 - 1)^2 } $$
on the classH
g
1
={u eH
1(Ω; ℂ);u=g on ∂Ω} whereg:∂Ω∂ → ℂ is a prescribed smooth map with ¦g¦=1 on ∂Ω∂ and deg(g, ∂Ω)=0. Let uu
e be a minimizer for Ee onH
g
1
. We prove that ue → u0 in
$$C^{1,\alpha } (\bar \Omega )$$
as e → 0, where u0 is identified. Moreover
$$\left\| {u_\varepsilon - u_0 } \right\|_{L^\infty } \leqslant C\varepsilon ^2 $$
.
341 citations
TL;DR: In this article, it was shown that a weakly harmonic map from a compact riemannian manifold to a stationary harmonic map is smooth in the special case that the manifold is a sphere.
Abstract: LetM andN be compact riemannian manifolds, andu a stationary harmonic map fromM toN. We prove thatH
n−2
(Σ)=0, wheren=dimM and Σ is the singular set ofu. This is a generalization of a result of C. Evans [7], where this is proved in the special caseN is a sphere. We also prove that, ifu is a weakly harmonic map inW
1,n
(M, N), thenu is smooth. This extends results of F. Helein for the casen=2, or the caseN is a sphere ([9], [10]).
231 citations
TL;DR: In this paper, the asymptotic behavior of solutions as t → ∞ for coupled matrix Riccati equations occurring in open-loop linear-quadratic Nash games is studied.
49 citations
TL;DR: The in vitro proliferation capacity of the cells immobilized in the calcium alginate beads was investigated and showed that chondrocytes are able to grow and to divide for several days inside the beads; in parallel an increase in protein contents was also measured.
42 citations
TL;DR: In this article, a brief survey of the main nonelliptic Schrodinger equations known by the authors, with emphasis on water waves, is made, and a theory is developed for the Cauchy problem for selected examples, based on linear estimates which are strongly related to the dispersion relation of the problem.
Abstract: Nonelliptic Schrodinger equations are defined as multidimensional nonlinear dispersive wave equations whose linear part in the space variables is not an elliptic equation. These equations arise in a natural fashion in several contexts in physics and fluid mechanics. The aim of this paper is twofold. First, a brief survey is made of the main nonelliptic Schrodinger equations known by the authors, with emphasis on water waves. Second, a theory is developed for the Cauchy problem for selected examples. The method is based on linear estimates which are strongly related to the dispersion relation of the problem.
41 citations
28 citations
TL;DR: In this article, the authors propose a procedure to include the constraints of manufacturing in the dimensioning and the tolerancing of a workpiece in order to obtain a part model in medium dimensions.
25 citations
Patent•
03 Nov 1993TL;DR: In this paper, a linear actuator with a mobile assembly moving relative to a stator in a traveling direction is described, and the assembly includes an excitation winding and an armature comprising pole pieces and permanent magnets.
Abstract: A device for a linear actuator, including a mobile assembly moving relative to a stator in a traveling direction. The assembly includes an excitation winding and an armature comprising pole pieces and permanent magnets. The stator is a simple guide tube defining the path of the mobile assembly, and may be made from a profiled ferromagnetic material, with holes extending through two walls thereof to define stator poles in two rows mutually longitudinally offset by a half pitch.
21 citations
01 Jul 1993-Precision Engineering-journal of The International Societies for Precision Engineering and Nanotechnology
TL;DR: In this paper, a theoretical model for sphere is fitted to a set of sampled surface points using the least-squares criterion, and an analysis is conducted of various errors involved during the steps leading to the identification of the sphere and location of its center.
Abstract: Probe calibration on a coordinate measuring machine is dependent on the accuracy with which the center of a reference sphere can be located. In this article, a theoretical model for sphere is fitted to a set of sampled surface points using the least-squares criterion. An analysis is conducted of various errors involved during the steps leading to the identification of the sphere and location of its center. The errors include those associated with surface accessibility for sampling, points sampling strategies, optimization algorithm, and probe diameter versus reference sphere diameter. Inferences are drawn regarding the relative influence of these errors, and a calibration strategy is proposed as a function of sampled points, optimization algorithm, and the geometric surface involved.
21 citations
01 Jun 1993
TL;DR: This paper presents a mitigation strategy which aims to maintain the inverter synchronized on the induction machine during short supply interruptions and allows an automatic soft restart right after the power system recovery.
Abstract: Recent developments in power electronics technology have led to a significant market penetration of adjustable speed drives (ASDs), which are economical, reliable and highly flexible in their use. However, ASDs are particularly sensitive to short supply interruptions from the distribution network. These events may result in the total disconnection of the specific ASD load, thereby causing loss of revenue for the user. It may cause a loss of production capacity and may also incur significant restart costs depending on the specific industrial process in which the ASD is used. This paper presents a mitigation strategy which aims to maintain the inverter synchronized on the induction machine during short supply interruptions. This mitigation strategy allows an automatic soft restart right after the power system recovery. This technique has been validated using numerical simulations. >
20 citations
TL;DR: In this article, the authors proposed to optimize pole arcs which have a highly significant importance on the permeance wave ofvernier reluctance motors (VR.Ms) to obtain a high base speed, therefore a high power.
Abstract: To maximize their performances. It is profitable to supply vernier reluctance motors (V.R.Ms.) with square wave current, but the converter has to switch this current successively into each inductive phase. This raises problems at high speeds. To obtain a high base speed, therefore a high power, we proposed to optimize pole arcs which have a highly significant importance on the permeance wave of V.R.Ms. The variation range of the angles is restricted by certain conditions, but within these limits optimization is possible. All dimensional parameters were taken into account and used to calculate average torque in linear as well as in saturated mode. We neglected the Influence of mutual coupling between phases and this hypothesis was Justified by results obtained through measurements. Though we used a model with linearized segments to minimize the number of parameters, the same method can be applied to other more accurate models. A V.R.M. with 6–4 structure was designed and realized ; it allowed vali...
TL;DR: In this article, the authors studied the standing wave solutions to some generalization of the system iφt+Δφ= -div(|∇ψ|2∇ ψ), Δψ=φ.
24 May 1993
TL;DR: An approach called process ascending generation (PAG) to generate sequences of operations for a given machining feature is presented and a forward-chaining rule-based strategy is used to implement the PAG concept in Prolog language.
Abstract: An approach called process ascending generation (PAG) to generate sequences of operations for a given machining feature is presented. The PAG determines the sequences of operations for a given feature, starting from its finished state and, by successive steps, leading up to its raw state. The object modeling problem is solved for some machining features and for an object database called Cutting Tool Chart (CTC). The CTC is a new concept used to model the abilities of the cutting tools to perform a machining feature. A forward-chaining rule-based strategy is used to implement the PAG concept in Prolog language. All of those aspects are implemented on CAD-CAM software, which is constituted by an object oriented database (OODB) and an integrated AI language. >
TL;DR: In this article, a surface is interpolated between data derived from 3-D metrology and limit surfaces are computed that bound a region of space containing the known data and the most probable interpolation of the missing data of the surface.
15 Dec 1993
TL;DR: A new phase current commutation strategy is proposed in order to reduce the torque ripple and to improve the dynamic performances of the nonlinear position control.
Abstract: In order to maximize the torque/current ratio, the phase currents of the switched reluctance motor (SRM) are controlled with regard to the rotor position. Unfortunately, during the commutation of the currents from one supply phase to another, torque ripples are naturally created. The authors show that the two combined effects of the phase commutation and of the sampling spoil the dynamic performances of the nonlinear position control. Nevertheless, with regard to todays technology, the sampling period cannot be reduced. Thus, a new phase current commutation strategy is proposed in order to reduce the torque ripple and to improve the dynamic performances of the nonlinear position control. >
TL;DR: In this paper, the authors present the control of a low cost and robust technology of mechatronic sensors composed of a double metallic multi-layered tuning-fork resonator, and controlled by two bimorphic piezoelectric ceramic transducers.
TL;DR: In this paper, a real-time control structure of production cells within realtime production management functions is presented, and an executable production scenario is conceived according to the production management rules.
Abstract: Between the steps of operation release and process control of the production activity control, no re-evaluation of the production organization is undertaken. However, the production organization can be technically optimized or modified. This level of production management is difficult to achieve, essentially because several fields come into play. It becomes apparent, however, that it is essential to integrate production management and production cell control in order to obtain advanced production systems which are more ‘reactive’ to technical and economic perturbations. In this paper, a contribution to the resolution of this problems is presented and the following ideas are introduced: 1. a control structure of production cells within “real-time production management functions”, 2. a control strategy of the cells by “scenario de production” (production scenario). First of all, the functions of this control structure are described and then the principles of its generic utilization for the control of a complex production system are given. An executable production scenario is conceived according to the production management rules, the data and know-how of the fabricators also play a role. The last section of this paper describes, using an industrial example in the field of sub-contracted machining, the construction of such a scenario.
TL;DR: In this article, the authors prove the existence of a smooth solution of the equation of evolution of harmonic maps if the initial data lies in a compact subset of the upper hemisphere of an ellispoid.
Abstract: This paper is concerned with the evolution of harmonic maps from an open set Ω of ℝm into an n-dimensionnal ellipsoid
$$N = \left\{ {u = (u_I ,u_{II} ) \in \mathbb{R}^n \times \mathbb{R}/u_I^2 + \frac{{u_{II}^2 }}{{a^2 }} = 1} \right\}$$
where a ∈ (0, 1] We prove the existence of a smooth solution of the equation of evolution of harmonic maps if the initial data lies in a compact subset of the upper hemisphere of an ellispoid.