Extension of a combined analytical/numerical initial value problem solver for unsteady periodic flow

Here we describe analytical and numerical modifications that extend the Differential Reduced Ejector/ mixer Analysis (DREA), a combined analytical/numerical, multiple species ejector/mixing code developed for preliminary design applications, to apply to periodic unsteady flow. An unsteady periodic flow modelling capability opens a range of pertinent simulation problems including pulse detonation engines (PDE), internal combustion engine ICE applications, mixing enhancement and more fundamental fluid dynamic unsteadiness, e.g. fan instability/vortex shedding problems. Although mapping between steady and periodic forms for a scalar equation is a classical problem in applied mathematics, we will show that extension to systems of equations and, moreover, problems with complex initial conditions are more challenging. Additionally, the inherent large gradient initial condition singularities that are characteristic of mixing flows and that have greatly influenced the DREA code formulation, place considerable limitations on the use of numerical solution methods. Fortunately, using the combined analytical–numerical form of the DREA formulation, a successful formulation is developed and described. Comparison of this method with experimental measurements for jet flows with excitation shows reasonable agreement with the simulation. Other flow fields are presented to demonstrate the capabilities of the model. As such, we demonstrate that unsteady periodic effects can be included within the simple, efficient, coarse grid DREA implementation that has been the original intent of the DREA development effort, namely, to provide a viable tool where more complex and expensive models are inappropriate. Copyright © 2002 John Wiley & Sons, Ltd.     

A Lie theoretic galois theory for the spectral curves of an integrable system: I

In the study of integrable systems of ODE's arising from a Lax pair with a parameter, the constants of the motion occur as spectral curves. The specific curves depend upon the representation of the Lie algebra. In this paper a Galois theory of spectral curves is given that classifies the spectral curves from an integrable system. The spectral curves correspond to conjugacy classes of certain subgroups of the Weyl group for the Lie algebra. The theory is illustrated with the periodic Toda lattice.Partially supported by a Louisiana Education Quality Support Fund grant LEQSF (87-89)-RD-A-8     

Electrochemical reduction of Bi2Sr2Ca1Cu2O8 superconductor single crystals

Single crystals and polycrystalline pellets of the high-temperature cuprate superconductor Bi₂Sr₂Ca₁Cu₂O₈ were doped at room temperature by electrochemical reduction at > 95% Coulombic efficiency using lithium dopant ions in propylene carbonate electrolyte. Cyclic voltammetry and potential step measurements on single crystals suggest an unusual reduction mechanism, with a diffusion coefficient for Li⁺ in the c-axis direction of bulk superconductor of ca. 3 × 10⁻¹¹ cm²s⁻¹. Sintered pellets of polycrystalline powder could be doped more rapidly, with an apparent diffusion coefficient of 7 × 10⁻⁸ cm²s⁻¹. X-ray susceptibility analysis show extensive disordering occurs on heavy Li doping, with a first-order transition from a crystalline/superconducting to an amorphous/non-superconducting phase. Single, crystals of Bi₂Sr₂Ca₁Cu₂O₈ exhibited a color change on reduction from metallic gray to golden bronze. The reduced material was highly air-sensitive, forming a hydroxide surface film on exposure to ambient atmosphere.     

Self-assembly of a hydrophobic groove

Heptakis(2,6-di-O-methyl)-β-cyclodextrin interacts with 5,15-diphenylporphine to produce a 2:1 complex in dimethyl sulfoxide. This complex possesses a hydrophobic groove that circumscribes the metal binding site of the porphyrin moiety.     

Molecular dynamics study of orientational order and rotational melting in clusters of TeF6

Molecular dynamics simulations of the behavior of molecules in crystalline clusters of TeF₆ were carried out on systems of 100, 150, 250, and 350 molecules. Several diagnostic functions were applied to investigate whether rotational melting occurred before translational melting. These functions included the coefficient of rotational diffusionD _θ(T), the “orientational Lindemann index” δ_θ(T), the “orientational angular distribution function”Q(θ,T), and the “orientational pair-correlation function”g _θ(r, T). All indicators implied that rotational melting occurred before translational melting, that it began with the outermost molecules, and that its onset for smaller clusters was at lower temperatures than for larger clusters. Results also showed that the rotational transition coincided with the transition from a lower symmetry phase (monoclinic) to cubic, a phenomenon that had been noted by others to occur with some regularity for systems of globular molecules.     

Elementary operators with H∞-symbols

Let T be a c.n.u. contraction on a Hilbert spaceH and let u-(u₁,...,u_n) be an n-tuple of H(T). We calculate various joint spectra of u(T) and apply the results to study the spectral and index theories of elementary operators associated with n-tuples of the above type.Both authors have been partially supported by NSF grants.