122,382 research outputs found
Trudinger-Moser Inequalities with the Exact Growth Condition in R<sup>N</sup> and Applications
No full textIn a recent paper [19], the authors obtained a sharp version of the Trudinger-Moser inequality in the whole space R2, giving necessary and sufficient conditions for the boundedness and the compactness of general nonlinear functionals in W 1, 2(R2). We complete this study showing that an analogue of the result in [19] holds in arbitrary dimensions N ≥2. We also provide an application to the study of the existence of ground state solutions for quasilinear elliptic equations in RN
Adams' Inequality with the Exact Growth Condition in R4
No full textAdams' inequality is an extension of the Trudinger-Moser inequality to the case when the Sobolev space considered has more than one derivative. The goal of this paper is to give the optimal growth rate of the exponential-type function in Adams' inequality when the problem is considered in the whole space R4
Higher order Adams' inequality with the exact growth condition
No full textAdams' inequality is the complete generalization of the TrudingerâMoser inequality to the case of Sobolev spaces involving higher order derivatives. The failure of the original form of the sharp inequality when the problem is considered on the whole space (Formula presented.) served as a motivation to investigate in the direction of a refined sharp inequality, the so-called Adams' inequality with the exact growth condition. Due to the difficulties arising in the higher order case from the lack of direct symmetrization techniques, this refined result is known to hold on first- and second-order Sobolev spaces only. We extend the validity of Adams' inequality with the exact growth to higher order Sobolev spaces
Space Quasi-Periodic Steady Euler Flows Close to the Inviscid Couette Flow
No full textWe prove the existence of steady space quasi-periodic stream functions, solutions for the Euler equation in a vorticity-stream function formulation in the two dimensional channel R×[-1,1]. These solutions bifurcate from a prescribed shear equilibrium near the Couette flow, whose profile induces finitely many modes of oscillations in the horizontal direction for the linearized problem. Using a Nash–Moser implicit function iterative scheme, near such equilibrium we construct small amplitude, space reversible stream functions, slightly deforming the linear solutions and retaining the horizontal quasi-periodic structure. These solutions exist for most values of the parameters characterizing the shear equilibrium. As a by-product, the streamlines of the nonlinear flow exhibit Kelvin’s cat eye-like trajectories arising from the finitely many stagnation lines of the shear equilibrium
Remarks on the blowup criteria for Oldroyd models
No full textAbstractWe provide a new method to prove and improve the Chemin–Masmoudi criterion for viscoelastic systems of Oldroyd type in [J.Y. Chemin, N. Masmoudi, About lifespan of regular solutions of equations related to viscoelastic fluids, SIAM J. Math. Anal. 33 (1) (2001) 84–112] in two space dimensions. Our method is much easier than the one based on the well-known losing a priori estimate and is expected to be easily adopted to other problems involving the losing a priori estimate
Global existence of weak solutions to some micro-macro models
No full textOn montre l'existence globale de solutions faibles à certains modèles micro-macro. En particulier on étudie le modèle FENE (le cas des ressorts) et le modèle de Doi (le cas des barres rigides). La preuve est basée sur la propagation de la compacité. Pour citer cet article : P.-L. Lions, N. Masmoudi, C. R. Acad. Sci. Paris, Ser. I 345 (2007).We prove the global existence of weak solutions for the co-rotational FENE dumbbell model and the Doi model also called the Rod model. The proof is based on propagation of compactness, namely if we take a sequence of weak solutions which converges weakly and such that the initial data converges strongly then the weak limit is also a solution. To cite this article: P.-L. Lions, N. Masmoudi, C. R. Acad. Sci. Paris, Ser. I 345 (2007).ou
Investigation on the effects of laser power and scanning speed on polypropylene diode transmission welds
No full textDiode laser transmission welding was well established as a leading technique for industrial applications of joining plastics. The weld soundness of plastics depends on several variables like the non-isothermal crystallization, the germs growth rate, the dimensions of the heat-affected zone induced by recrystallization. Firstly, this paper proves the reliability of a numerical model based on the finite difference method at calculating the soundness variables for diode laser welding of polypropylene thermoplastic polymer. The numerical model was validated by microscopy observation of experimental polypropylene welds. Then a parametric study on the effects of the laser power and welding speed on the weld soundness variables is presented through a number of plots of the main process variables against time. The overall investigation gives a detailed picture of the influence of laser power and welding speed on the weld soundness from a microstructure point of view
Présence de Walter Benjamin (Entretien)
No full textDufour-El Maleh Marie-Cécile, Masmoudi Abdelouhed. Présence de Walter Benjamin (Entretien). In: Horizons Maghrébins - Le droit à la mémoire, N°28-29, 1995. Juan Goytisolo : trajectoires. pp. 214-219
FEA-Assisted steady-state modelling of a spoke type IPM machine with enhanced flux weakening capability
No full textInterior permanent magnet (IPM) machines with spoke-type design are possible candidates for various applications, including vehicle traction. One of their drawback is the high demagnetizing current required in the flux weakening region to let the motor achieve high speeds. This problem can be mitigated by equipping the motor with a mechanical devices consisting of mobile rotor yokes. These move radially by centrifugal force so as to reduce the air-gap flux at high speed with no need for demagnetizing current injection. This paper addresses the problem of modeling such IPM motor to study its steady-state behavior under different operating conditions, both in the full-flux and in the flux-weakening region of the speed range. The approach uses a limited set of non-linear finite element analysis to characterize the dependency of motor flux linkages on the stator currents and rotor position. Interpolating functions are then obtained to mathematically capture this dependency and plug it into the steady-state electromechanical equations of the motor. The effectiveness and accuracy of the method are assessed through on-load measurements taken on the modelled motor both in low and high speed operation
Fast Computation Method for Stator Winding Skin-Effect Additional Losses in Synchronous Machines with Open Slots and Arbitrary Rotor Geometry
No full textLarge medium-voltage electric machine stators are usually equipped with form wound coils made of flat conductors (strands) and embedded in open (rectangular) slots. Air-gap magnetic flux lines can enter the slot and, sweeping the strands placed nearest the slot opening, induce eddy currents in them. Such eddy currents cause additional losses which can be much higher than usual skin-effect and proximity losses. In order to avoid dangerous overheating and hot spots, the additional losses in question need to be carefully predicted in the design stage. Time-stepping finite-element analysis (TSFEA) can be used for the purpose, which however implies a large computational burden and requires the machine geometry to be modeled in detail. This article proposes alternative methods based on time-harmonic finite-element analysis (THFEA) simulations performed on highly simplified machine models and with no need to take rotor motion into account. The proposed methods are shown to produce very accurate results, compared to TSFEA, but with very significant time and computational savings
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