A roe-type Riemann solver for hyperbolic systems with relaxation based on time-dependent wave decomposition

Summary. The paper is devoted to the construction of a higher order Roe-type numerical scheme for the solution of hyperbolic systems with relaxation source terms. It is important for applications that the numerical scheme handles both stiff and non stiff source terms with the same accuracy and computational cost and that the relaxation variables are computed accurately in the stiff case. The method is based on the solution of a Riemann problem for a linear system with constant coefficients: a study of the behavior of the solutions of both the nonlinear and linearized problems as the relaxation time tends to zero enables to choose a convenient linearization such that the numerical scheme is consistent with both the hyperbolic system when the source terms are absent and the correct relaxation system when the relaxation time tends to zero. The method is applied to the study of the propagation of sound waves in a two-phase medium. The comparison between our numerical scheme, usual fractional step methods, and numerical simulation of the relaxation system shows the necessity of using the solutions of a fully coupled hyperbolic system with relaxation terms as the basis of a numerical scheme to obtain accurate solutions regardless of the stiffness. Received October 7, 1994 / Revised version received September 27, 1995     

Highly ordered metal oxide nanopatterns prepared by template-assisted chemical solution deposition

TiO₂, Al₂O₃, and ZrO₂ patterns composed of ordered nano motifs of various morphologies (i.e. perforations (craters), rings, canyons, wires, dots, or channels) with typical lateral dimensions of less than 40 nm and thickness below 15 nm are presented. Simple chemical solution deposition (CSD) of molecular inorganic precursors and commercial block copolymers was used to create patterns on several substrate surfaces (bare, hydrophobized or gold covered silicon wafers and ITO). Self-assembly during evaporation and subsequent stabilization at 500 °C leads to the various nanostructures. Compared to other techniques for surface nano patterning, the present method has the advantage of being cheap, reproducible and easy to scale up and does not require specialized equipment. The type, dimension, and organization of these motifs were assessed by AFM, FE-SEM, spectroscopic ellipsometry, and GI-SAXS and are shown to depend on the conditions of preparation. Usage as model surfaces for modelling of wetting properties and as nanoelectrode arrays were investigated.     

Low temperature raman evidence for two crystalline phases of methylcyclohexane

Comparison of the lattice mode region of the low-temperature Raman spectrum of MCH and MCH-d₁₄ under various cooling rates shows that there are two crystalline modifications. The molecular mode region frequencies however, remain invariant to cooling rate suggesting a single molecular conformation for both crystalline phases.     

1H and 13C NMR of platinum porphyrins—III. Platinum deuteroporphyrin IX dimethyl ester

¹H and ¹³C NMR spectra of the title compound are reported and peaks assigned by comparison with the free-base porphyrin. Long-range spin—spin coupling is observed between platinum and the macrocyclic protons and carbon atoms. Meso-protons are assigned from line-broadening observed for three of the peaks, possibly caused by residual coupling of these protons to the pyrrole β-protons. Allylic coupling of the pyrrole β-protons to adjacent methyl groups is also noted, and supports the tautomeric model of an 18-atom delocalisation pathway around the macrocycle. The ¹H NMR spectrum of the title compound is more concentration-dependent than that of the free-base porphyrin and probably reflects additional macrocyclic interactions via the platinum atoms.     

Limiting distributions of homogeneous functions of sample spacings for distributions approaching the uniform distribution

Summary X ₁,...,X _n are independent random variables, identically distributed over the unit interval, with common probability density function 1 + r(x)/n for all sufficiently large n, where is a positive constant, and |r(x)| <D. V ₁, ..., V _n+1 are the sample spacings generated by X ₁,..., X _n . It is shown that in many cases, the asymptotic joint distribution of homogeneous functions of V ₁,..., V _n+1 can be found directly from the asymptotic joint distribution of homogeneous functions of independent exponential random variables.Research supported by NSF Grant GP 3783.     

Conforming finite element computations applied to a spatially periodic,harmonic Navier-Stokes problem

In this paper computations in the two dimensional case of a harmonic Navier-Stokes problem with periodic boundary conditions are presented. This study of an incompressible viscous fluid leads to a non-symmetric linear problem (very low Reynolds number). Moreover unknown functions have complex values (monochromatic dynamic behaviour). Numerical treatment of the incompressibility condition is a generalization of the classical treatment of Stokes problem. A mixed formulation, where discrete pressure plays the role of Lagrange multipliers is used (Uzawa algorithm). Two conforming finite element methods are tested on different meshes. The second one uses a classical refinement in the shape function: the so-called bulb function. All computational tests show that the use of a bulb function on each element gives better results than refinement in the mesh without introducing too many degrees of freedom. Finally numerical results are compared to experimental data.     

Rotating ring-disk electrode studies of the reaction of stable radical cations with styrene and isobutyl vinyl ether

An electroanalytical technique has been utilized in a new method for the study of reactive intermediates in polymerization reactions. A ring-disk electrode system generated persistent carbocation radicals whose stability decreased in the order: 1,3,6,8-tetraphenylpyrene (TPP), rubrene (Ru), 9,10-diphenylanthracene (DPA), and 9,10-dimethylanthracene (DMA). Radical cations from these parent compounds flowed to a collecting ring which was controlled potentiostatically to reduce unreacted cations. When styrene or isobytyl vinyl ether was added to the solution, the concentration of carbocation radicals reaching the electrode was reduced. Current collection efficiencies N were determined as a function of rotation speed ω for each monomer concentration. Plots of N^?1 as ω^?1 in the absence of monomer show no dependence on ω (indicative of stable intermediates), but a linear dependence is found with each concentration of monomer. This indicates a first-order dependence on radical cation concentration. The rate constants show a trend in cation reactivities which is in agreement with that obtained by other methods. This technique, however, extends the range of investigation to a much shorter time scale.     

Synthesis, crystal structure and reactivity of uranium(IV) complexes with p-tert-butylcalix[4]arene ligands

Reactions of UCl4 with 25,27-dimethoxy-5,11,17,23-tetra-tert-butylcalix[4]arene (H2Me2calix) in THF or pyridine at 80 degrees C gave [UCl2(Me2calix)L2] [L = THF (1) or pyridine (2)]. Similar treatment of U(acac)(4) (acac = MeCOCHCOMe) with H2Me2calix in THF or pyridine afforded [U(acac)2(Me2calix)] (3). The bis-calixarene compound [U(Me2calix)(H2calix)] (4) was obtained by reaction of U(OTf)4 or U(OTf)3 with H2Me2calix in pyridine at 110 degrees C. Treatment of UCl4 with H2Me2calix in pyridine at 110 degrees C gave [Mepy][UCl2(Hcalix)(py)2] (5) resulting from demethylation and acid cleavage of the methoxy groups of the calixarene ligand of 2. Adventitious traces of air were responsible for the formation of [Hpy][Mepy]4[{UCl(calix)}3(mu3-O)][UCl6] (6) during the reaction of UCl4 and H2Me2calix, and of [{U(Me2calix)(mu3-O)LiCl(THF)}2] (7) during the reaction of 2 with tBuLi. The X-ray crystal structures of 1.2THF, 2.2py, 3.0.25L (L = THF and py), 4.2py, 5, 6.3py and 7.THF have been determined.