Data completion for the Stokes system

This Note is concerned with the severely ill-posed Cauchy–Stokes problem. This inverse problem is rephrased into an optimization one: An energy-like error functional is introduced. We prove that the optimality condition of the first order is equivalent to solving an interfacial equation which turns out to be a Cauchy–Steklov–Poincaré operator. Numerical trials highlight the efficiency of the present method. To cite this article: A. Ben Abda et al., C. R. Mecanique 337 (2009).     

On limit motions of a system of control moment gyros with intrinsic dissipation in a homogeneous gravitational field

We study the limit motions of a free rigid body bearing n two-degree-of-freedom control moment gyros with dissipation in the gyro gimbal suspension axes. We show that, in the absence of dynamic symmetry, the limit motions of the system are only steady rotations at a constant angular velocity. In the case of dynamic symmetry, the gyros can be arranged so that, in addition to steady rotations, the system exhibits limit motions that are regular precessions.     

Problème de Dirichlet pour une équation de Monge-Ampère réelle elliptique dégénérée en dimension

RÉSUMÉ. On considère dans un ouvert borné de , à bord régulier, le problème de Dirichlet

où , est positive et s'annule sur un ensemble fini de points de . On démontre alors sous certaines hypothèses sur et si est assez petit, que le problème (1) possède une solution convexe unique .

ABSTRACT. We consider in a bounded open set of , with regular boundary, the Dirichlet problem

where , is positive and vanishes on , a finite set of points in . We prove, under some hypothesis on and if is sufficiently small, that the problem (1) has a unique convex solution .

     

Structure, thermal, and infrared analyses of [NH3(CH2)3NH3]2[Ni(HP2O7)2(H2O)2] ? 4H2O

[NH₃(CH₂)₃NH₃]₂[Ni(HP₂O₇)₂(H₂O)₂] 4H₂O (NiDAP) is a new diphosphate of transition metallic and organic cations obtained from a mixture of H₄P₂O₇, 2NiCO₃ Ni(OH)₂ 4H₂O and NH₂(CH₂)₃NH₂ in a 1:1/6:1 molar ratio. This mixed organo-mineral compound crystallizes in the triclinic system, P¯, with the unit cell dimensions: a = 7.3678(3)~Å, b = 7.8018(5)Å, c = 11.1958(7)Å, = 76.914(4), = 81.052(4), = 85.46(1), V = 618.57(6)ų and Z = 1. The crystal structure of NiDAP consists of a complex anion, [Ni(HP₂O₇)₂(H₂O)₂]^4– and a diammoniumpropane cation. The complex anion is built up from two neutral water molecules (OW1) and two diphosphosphoric anions coordinated to Ni(II) in a bidentate chelating manner. (OW1) molecules link anionic complexes, [Ni(HP₂O₇)₂(H₂O)₂]^4– to create a thick bidimensional layers parallel to the (a, b) plane. These layers are interconnected in three dimensions through hydrogen bonds established between organic cations, the remaining water molecules OW2, OW3, and some external oxygen atoms of the anionic complex arrays. NiDAP was also characterized by IR spectroscopy, TG-DTA, and DSC analyses.     

Microemulsion breakdown by pervaporation technique: effect of the alkyl chain length of n-alkanol, a cosurfactant of the microemulsion

Two sets of microemulsions, cyclohexane- and water-rich ones, were prepared with the following n-alkanols as cosurfactants: n-propanol, n-butanol, n-pentanol, and n-hexanol. The results showed the influence of the alkyl chain length of the n-alkanol on the permselectivity properties of the pervaporation technique in the breakdown of the microemulsions. The variations of the total flux rate J and the enrichment factor beta were in parallel with the effect of the cosurfactant on the swelling extent of the PDMS membrane.