A finite volume scheme for nonlinear parabolic equations derived from one-dimensional local dirichlet problems

In this paper, we propose a new method to compute the numerical flux of a finite volume scheme, used for the approximation of the solution of the nonlinear partial differential equation u_t+div(qf(u))−ΔΦ(u)=0 in a 1D, 2D or 3D domain. The function Φ is supposed to be strictly increasing, but some values s such that Φ′(s)=0 can exist. The method is based on the solution, at each interface between two control volumes, of the nonlinear elliptic two point boundary value problem (qf(υ)+(Φ(υ))′)′=0 with Dirichlet boundary conditions given by the values of the discrete approximation in both control volumes. We prove the existence of a solution to this two point boundary value problem. We show that the expression for the numerical flux can be yielded without referring to this solution. Furthermore, we prove that the so designed finite volume scheme has the expected stability properties and that its solution converges to the weak solution of the continuous problem. Numerical results show the increase of accuracy due to the use of this scheme, compared to some other schemes.     

Moment relationships for queues with Poisson input

This paper presents new relationships between the higher-order moments of the FIFO and LIFO disciplines. These relationships hold over a class of queueing models that includeM/G/1 queues with exceptional first service,M/G/1 queues with server vacations, andM/G/1 priority models. The results also generalize to a class of service disciplines that includes FIFO and LIFO as special cases.     

The Effect of Assembled Amphiphiles on Catalytic Reactions in Aqueous Media

Micelle-forming amphiphiles can promote catalyzed reactions in aqueous media. An example is the asymmetric hydrogenation of amino acid precursors. In comparison to the most common solvent methanol, the hydrogenation in water leads to a decrease of activity and a decrease of enantioselectivity, but, by adding a small amount of a surfactant (20 mol %), the activity increased to a value similar to methanol and the enantioselectivity increased sometimes to values higher than in methanol. A disadvantagous consequence of the use of surfactants is the more difficult phase separation within the work up of the reaction mixture because of the detergent effect of the amphiphile. Another problem is the recycling of the catalyst. To solve both these problems, we developed two methods: (i) the use of polymerized and polymeric amphiphiles in a membrane reactor and (ii) an immobilization of amphiphiles on an inorganic support. The precondition for the realization of these concepts is a leaching-free embedding of the catalytic rhodium complex in the macromolecular amphiphilic layer. Advantages and disadvantages of these methods will be discussed.     

A detailed analysis of vibrational excitations in x-ray photoelectron spectra of adsorbed small hydrocarbons

The vibrational fine structure of x-ray photoelectron (XP) spectra of a number of different small hydrocarbon molecules and reaction intermediates adsorbed on Pt(111) and Ni(111) has been investigated in detail. The data for methyl, methylidyne, acetylene, and ethylene can consistently be analyzed within the linear coupling model. The S factor, i.e., the intensity ratio of the first vibrationally excited to the adiabatic transition, is obtained to be 0.17+/-0.02 per C-H bond; for the deuterated species a value of 0.23+/-0.02 is obtained. Therefore, the vibrational fine structure can be used for fingerprinting in the analysis of XP spectra and for identifying unknown reaction intermediates. From the data, Deltar, the change of the minimum in the potential energy curve upon core ionization, is calculated within the linear coupling model using a first order correction. For all adsorbates, including the deuterated ones, a value of Deltar=0.060+/-0.004 A is obtained. Furthermore, from the binding energy of the adiabatic peak and from the energy of the vibrational excitation in the ionic final state some information on the adsorbate/substrate bond and the adsorption site can be derived.     

A site-selective in situ study of CO adsorption and desorption on Pt(355)

Using time-dependent high-resolution x-ray photoelectron spectroscopy at BESSY II, the adsorption and desorption processes of CO on stepped Pt(355) = Pt[5(111) x (111)] were investigated. From a quantitative analysis of C 1s data, the distribution of CO on the various adsorption sites can be determined continuously during adsorption and desorption. These unique data show that the terrace sites are only occupied when the step sites are almost saturated, even at temperatures as low as 130 K. The coverage-dependent occupation of on-top and bridge adsorption sites on the (111) terraces of Pt(355) is found to differ from that on Pt(111), which is attributed to the finite width of the terraces and changes in adsorbate-adsorbate interactions. In particular, no long-range order of the adsorbate layer could be observed by low-energy electron diffraction. Further details are derived from sticking coefficient measurements using the method devised by King and Wells [Proc. R. Soc. London, Ser. A 339, 245 (1974)] and temperature-programmed desorption. The CO saturation coverage is found to be slightly smaller on the stepped surface as compared to that on Pt(111). The initial sticking coefficient has the same high value of 0.91 for both surfaces.     

Tensored polynomial models

The theme of the present paper is to introduce and study two different versions of tensor products of functional models, one over the underlying field and the other over the corresponding algebra of polynomials, as well as related models based on the Kronecker product of polynomial matrices. In the process, we study the Sylvester equation and its reduction to a polynomial matrix equation. We analyse the relation between the two tensor products and use this to elucidate the role of the Anderson-Jury generalized Bezoutians in this context.     

CO/Alkene Copolymers as a Promising Class of Biocompatible Materials, 1. Examination of the In Vitro Toxicity

Novel 1,4‐polyketones were synthesized by a Pd^II catalyzed copolymerization reaction from cheap technical monomers. The spectrum of mechanical properties ranges from highly crystalline, hard materials to thermoplastic, soft elastomers. The hydrophilicity of the surface is adjustable from nonpolar to highly polar by a proper choice of the α‐olefin component. This control of polymer properties is a basis for the development of new biocompatible materials. The results of standardized as well as more specific in vitro tests clearly demonstrate the nontoxicity of the investigated copolymers.

Polyketone synthesis.     

A routine method for the determination of the TVOC content in wallcoverings using headspace gas-chromatography

A method for the fast routine analysis of the total content of volatile organic compounds in wallcoverings and paper products was developed, using headspace gas-chromatography for quantification. 57 wallcoverings of different types were investigated. Typical components were toluene, methyl-ethyl ketone, methyl-iso-butyl ketone, n-butyl acetate and iso-butyl acetate, all compounds being used as industrial solvents. The TVOC concentrations are calculated in toluene-carbon equivalents and ranged from 0.31 g/g to 1789 g/g with an average value of 123.22 g/g and a median of 20.37 g/g. To obtain an estimation of VOC-concentrations in indoor air, 10 selected wallcoverings were also analyzed in a 1 m³ climate test chamber. A correlation between headspace data and chamber concentrations could not be observed, which might be a result of increased analytical uncertainties at low emission rates under chamber conditions.