The solvolysis oftrans-[Co(4-Mepy)4Cl2]ClO4 in water: acetonitrile and water: dioxan mixtures

Summary The solvolysis of the title complex is slower in 0 to 70% v/v aqueous dioxan than in aqueous acetonitrile at 40, 45, 50 and 55° C, a fact that is attributed to the higher basicity and ionizing power of the latter solvent mixtures. The observed non-linearity for logk (solvolysis) versus 1/D plots was interpreted in terms of the relative stability of ground and transition state species. The calculated Gibbs free energy for transfer of the species in the transition state is consistent with the extreme stretching of the chlorinecobalt bond, a result which confirms the interchange dissociative mechanismI _d for the complex under study.     

Solvent effects on the initial and transition states upon solvolysis oftrans-dichlorotetra(4-ethylpyridine) cobalt(III) perchlorate in water +t-butanol mixtures

Summary The solvolysis of the title complex was investigated in water and in water +t-butanol mixtures in the 40 to 55°C range. The activation thermodynamic parameters were calculated and the extrema observed for H and S were compared with data obtained from the measured physical properties of the same solvent mixtures. The ethyl substituent in the pyridine rings manifests its effect on the activation entropy values and on the relatively low activation energies compared with the respective values obtained previously from the solvolysis oftrans-[Co(4-MePy)₄Cl₂]⁺ in the same media. The free energies of transfer of the cation were calculated in the ground and transition states. In the ground state, the ethyl and methyl substituents in the pyridine rings provide the complex cation with nearly equal stabilities. However, the effect of solvent on the cation stability is more pronounced in the transition state for the ethyl substituent.     

Mega three-photon absorption cross-section enhancement in pseudoisocyanine J-aggregates

Herein we report an extraordinary three-photon absorption cross-section (sigma'3) enhancement in J-aggregates supramolecular systems. The much higher value of sigma'3 in PIC J-aggregate (2.5 x 10(-71) cm6 s2 ph(-2)) compared to typical values obtained in organic molecules (10(-80) cm6 s2 ph(-2)) is attributed to the strong molecular transition dipole moment coupling in the supramolecular assembly. Three-photon absorption of PIC J-aggregates and monomer aqueous solutions were measured using the well known open aperture Z-scan technique pumping with a 25 ps pulse laser-OPG system at 1720 nm. This novel result opens new expectations for applications of supramolecular systems in bioimaging and medicine.     

The influence of solvent structure on the solvolysis oftrans-dichlorotetra (4-ethylpyridine) cobalt(III) perchlorate

Summary The solvolysis oftrans-[Co(4-Etpy)₄Cl₂]ClO₄, was followed spectrophotometrically in water/isopropanol at different temperatures. The activation energy varied nonlinearly with the mole fraction of the co-solvent, ₂. The plot of logk versus D _s ^–1 was also non-linear. These features were attributed to the differential solvation of the initial and transition states. On plotting H versus S, the points fall very close to straight line. The isokinetic temperature was found to be 334K, indicating that the solvolysis reaction is controlled by S and not H. The change in H and S with the mole fraction of the cosolvent shows extrema at the composition range where changes in solvent structure occur. The influence of the solvent structure on the complex ion in the transition state dominates over that in the initial state, where –G _t ⁰ [Co(4-Etpy)₄Cl]²⁺>–G _t ⁰ [Co(4-Etpy)₄Cl₂]⁺.     

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 estimates of the balanced gyro drift and the accuracy of the magnus formula

We construct efficient estimates of the balanced gyro drift due to nutation oscillations. We show that, for oscillation amplitudes not exceeding one degree and for amajority of gyromotions, the relative error in the drift rate calculations on the basis of the obtained estimates does not exceed tenths of one percent. The numerical results show that the accuracy of the Magnus formula is not worse than predicted by these estimates.     

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 .

     

A control type method for solving the Cauchy–Stokes problem

In this work, we propose an approximate optimal control formulation of the Cauchy problem for the Stokes system. Here the problem is converted into an optimization one. In order to handle the instability of the solution of this ill-posed problem, a regularization technique is developed. We add a term in the least square function which happens to vanish while the algorithm converges. The efficiency of the proposed method is illustrated by numerical experiments.