Global Analysis of the Flows of Fluids with Pressure-Dependent Viscosities

 To describe the flows of fluids over a wide range of pressures, it is necessary to take into account the fact that the viscosity of the fluid depends on the pressure. That the viscosity depends on the pressure has been verified by numerous careful experiments. While the existence of solutions local-in-time to the equations governing the flows of such fluids are available for small, special data and rather unrealistic dependence of the viscosity on the pressure, no global existence results are in place. Our interest here is to establish the existence of weak solutions for spatially periodic three-dimensional flows that are global in time, for a large class of physically meaningful viscosity-pressure relationships. (Accepted May 1, 2002) Published online November 15, 2002 Communicated by S. S. ANTMAN     

Five-Membered 2,3-Dioxo Heterocycles: XLVI. Reaction of 5-Aryl-4-quinoxalinyl-2,3-dihydrofuran-2,3-diones with Aldehydes and Ketones. Molecular and Crystalline Structure of 5-(3-p-Tolylquinoxalin-2-yl)-4H-1,3-dioxine- 2-spiro-2'-adamantan-4-one

Aroyl(quinoxalinyl)ketenes generated by thermolysis of 5-aryl-4-(3-arylquinoxalin-2-yl)-2,3-di-hydrofuran-2,3-diones act as dienes in [4 + 2]-cycloaddition at the carbonyl group of aldehydes and ketones to afford 2-substituted 6-aryl-5-(3-arylquinoxalin-2-yl)-4H-1,3-dioxin-4-ones. The structure of 5-(3-p-tolylquino-xalin-2-yl)-4H-1,3-dioxine-2-spiro-2'-adamantan-4-one was proved by X-ray analysis.     

Structures and Stability of Complexes of E(C6F5)3 (E = B,Al, Ga,In) with Acetonitrile

Complexes formed by interaction of E(C₆F₅)₃ (E = B, Al, Ga, In) with excess of acetonitrile (AN) were structurally characterized. Quantum chemical computations indicate that for Al(C₆F₅)₃ and In(C₆F₅)₃ the formation of a complex of 1:2 composition is more advantageous than for B(C₆F₅)₃ and Ga(C₆F₅)₃, in line with experimental observations. Formation of the solvate [Al(C₆F₅)₃ · 2AN] · AN is in agreement with predicted thermodynamic instability of [Al(C₆F₅)₃ · 3AN]. Tensimetry study of B(C₆F₅)₃ · CH₃CN reveals its stability in the solid state up to 197 °C. With the temperature increase, the complex undergoes irreversible thermal decomposition with pentafluorobenzene formation.     

Torsion of cylindrically anisotropic nano/microtubes from seven-constant tetragonal crystals. Poynting’s effect

In the paper presented, we continue the research in the elastic properties of seven-constant tetragonal crystals and nano/microtubes. Our previous study concerned tension of this type of structures, and here we are dealing with their torsion, Poynting’s effect or axial extension under torsion with no tensile force, and torsional stiffness. It is demonstrated that there exists inverse Poynting’s effect: the tubes experience torsion under tension without applying a torque.     

Donor-acceptor complexes of borazines

Donor-acceptor complexes of borazine (BZ) and its substituted derivatives with Lewis acids (A = MCl(3), MBr(3); M = B, Al, Ga) and Lewis bases (D = NH(3), Py) have been theoretically studied at the B3LYP/TZVP level of theory. The calculations showed that complexes with Lewis bases only are unstable with respect to dissociation into their components, while complexes with Lewis acids only (such as aluminum and gallium trihalides) are stable. It was shown that formation of ternary D→BZ→A complexes may be achieved by subsequent introduction of the Lewis acid (acceptor A) and the Lewis base (donor D) to borazine. The nature of substituents in the borazine ring, their number, and position were shown to have only minor influence on the stability of ternary D→BZ→A complexes due to the compensation effect. Much weaker acceptor properties of borazine are explained in terms of large endothermic pyramidalization energy of the boron center in the borazine ring. In contrast to borazine, binary complexes of the isoelectronic benzene were predicted to be weakly bound even in the case of very strong Lewis acids; ternary DA complexes of benzene were predicted to be unbound. The donor-acceptor complex formation was predicted to significantly reduce both the endothermicity (by 70-95 kJ mol(-1)) and the activation energy (by 40-70 kJ mol(-1)) for the borazine hydrogenation. Thus, activation of the borazine ring by Lewis acids may be a facile way for the hydrogenation of borazines and polyborazines.     

Guided modes of integrated optical guides. A mathematical study

A waveguide in integrated optics is defined by its refractiveindex. The guide is assumed to be invariant in the propagationdirection while in the transverse direction it is supposed tobe a compact perturbation of an unbounded stratified medium.We are interested in the modes guided by this device, whichare waves with a transverse energy confined in a neighbourhoodof the perturbation. Our goal is to analyse the existence of such guided modes. Underthe assumptions of weak guidance the problem reduces to a two-dimensionaleigenvalue problem for a scalar field. The associated operatoris unbounded, selfadjoint, and bounded from below. Its spectrumconsists of the discrete spectrum corresponding to the guidedmodes and of the essential spectrum corresponding to the radiationmodes. We present existence results of guided modes and an asymptoticstudy at high frequencies, which shows that contrarily to thecase of optical fibers, the number of guided modes can remainbounded. The major tools are the min-max principle and comparisonof results between different eigenvalue problems. The originalityof the present study lies in the stratified character of theunbounded reference medium.