Pullback attractors for non-autonomous 2D-Navier–Stokes equations in some unbounded domains

In this Note we first introduce the concept of pullback asymptotic compactness. Next, we establish a result ensuring the existence of a pullback attractor for a non-autonomous dynamical system under the general assumptions of pullback asymptotic compactness and the existence of a pullback absorbing family of sets. Finally, we prove the existence of a pullback attractor for a non-autonomous 2D Navier–Stokes model in an unbounded domain, a case in which the theory of uniform attractors does not work since the non-autonomous term is quite general. To cite this article: T. Caraballo et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

The effect of buoyancy on the weight gain signal in LEC crystal growth

Crystal diameter monitoring in liquid encapsulated Czochralski (LEC) growth using the weighing method is investigated. An analytical expression for the differential weight gain signal is derived for stationary growth conditions accounting for bouyancy. For the GaAs/B₂O₃ system the buoyancy component of the signal can easily amount to 30%. The formula can be applied to determine the crystal/melt interface area, provided the radius of the part emerging from the encapsulant is known, either in advance as the seed dimension, or by separate monitoring using, e.g., conventional optical methods.     

A fixed-point equation for the high-temperature phase of discrete lattice spin systems

A fixed-point equation on an infinite-dimensional space is proposed as an alternative to the usual definition of the infinite-volume limit in discrete lattice spin systems in the high-temperature phase. It is argued heuristically that the free energy and correlation functions one obtains by solving this equation agree with the usual definitions of these quantities. A theorem is then proved that says that if a certain finite-volume condition is satisfied, then this fixed-point equation has a solution and the resulting free energy is analytic in the parameters in the Hamiltonian. For particular values of the temperature this finite-volume condition may be checked with the help of a computer. The two-dimensional Ising model is considered as a test case, and it is shown that the finite-volume condition is satisfied for0.77 _critical.     

Valence bond ground states in isotropic quantum antiferromagnets

Haldane predicted that the isotropic quantum Heisenberg spin chain is in a massive phase if the spin is integral. The first rigorous example of an isotropic model in such a phase is presented. The Hamiltonian has an exactSO(3) symmetry and is translationally invariant, but we prove the model has a unique ground state, a gap in the spectrum of the Hamiltonian immediately above the ground state and exponential decay of the correlation functions in the ground state. Models in two and higher dimension which are expected to have the same properties are also presented. For these models we construct an exact ground state, and for some of them we prove that the two-point function decays exponentially in this ground state. In all these models exact ground states are constructed by using valence bonds.Supported in part by N.S.F. Grant PHY-80-19754. Fellow of the A.P. Sloan Foundation and the Canadian Institute for Advanced ResearchN.S.F. Post-doctoral FellowSupported in part by N.S.F. Grant PHY-85-15288-A01     

Inductively coupled plasma compared with direct current arc spectrometry for analysis of minor elements in aluminium baths

A validation study was carried out in order to evaluate the efficiency of inductively coupled plasma-optical emission spectrometry (ICP-OES) for the analysis of minor elements (manganese, chromium, copper, iron, and titanium) in aluminium alloys. Aluminium casting samples were obtained by adding compressed powder compacts of each alloying element and aluminium (minitablets) to aluminum baths in a laboratory crucible furnace. Digestion of solid samples was performed using concentrated HCI and H202 35% (v/v) previous to analysis by ICP-OES without any matrix separation. This solution-based method was validated considering direct current arc spectrometry as the reference method based on direct analysis without any pretreatment of the solid samples considered. Univariate statistical procedures were carried out, for which precision <3% and trueness of the analytical results were taken into account.     

Introduction to session 2

Applied Biochemistry and Biotechnology -     

The determination of intrinsic reaction coordinates by density functional theory

The first implementation of the intrinsic reaction coordinate (IRC ) method within the density functional theory (DFT ) framework is presented. The implementation has been applied to four different types of chemical reactions represented by the isomerization process, HCN ? HNC (A); the S_N2 process, H^? + CH₄ ? CH₄ + H^? (B); the exchange process, H˙ + HX ? HX + H˙ (X ? F,Cl) (C); and the elimination process, C₂H₅Cl ? C₂H₄ + HCl (D). The present study presents for each process optimized structures and calculated harmonic vibrational frequencies for the reactant(s), the transition state, and the product(s) along with the IRC path connecting the stationary points. The calculations were carried out within the local density approximation (LDA ) as well as the LDA/NL scheme where the LDA energy expression is augmented by Perdew's and Becke's nonlocal (NL ) corrections. The LDA and LDA/NL results are compared with each other as well as the best available ab initio calculations and experimental data. For reaction (D), ab initio calculations based on MP 2 geometries and MP 4SDTQ energies have been added due to the lack of accurate published post-HF calculations on this process. A detailed discussion is provided on the efficiency of the IRC algorithms, the relative accuracy of the DFT and ab initio schemes, as well as the reaction mechanisms of the four reactions. It is concluded that the LDA/NL scheme affords the same accuracy as does the MP 4 method. The post-HF methods seem to overestimate activation energies, whereas the corresponding LDA/NL estimates are too low. The LDA activation energies are even lower than the LDA/NL counterparts. The incorporation of the IRC method into the DFT framework provides a promising and reliable tool for probing the chemical reaction path on the potential energy surfaces, even for large-size systems. IRC calculations by ab initio methods of an accuracy similar to the LDA/NL scheme, such as the MP 4 scheme, are not feasible. © John Wiley & Sons, Inc.