A robust nonconforming -element

Finite element methods for some elliptic fourth order singular perturbation problems are discussed. We show that if such problems are discretized by the nonconforming Morley method, in a regime close to second order elliptic equations, then the error deteriorates. In fact, a counterexample is given to show that the Morley method diverges for the reduced second order equation. As an alternative to the Morley element we propose to use a nonconforming -element which is -conforming. We show that the new finite element method converges in the energy norm uniformly in the perturbation parameter.

     

Determination of alkylmercury compounds in fish tissue with an atomic absorption spectrometer used as a specific gas chromatographic detector

Atomic absorption spectrometry is used as a specific gas chromatography detector in the determination of alkylmercury compounds in fish. An electrical furnace “cracks” the organic mercury molecules in the Chromatographic effluent. An extraction procedure has been developed which improves the precision of the method. The detection limit is 0.3 ppm of mercury for 0.5-g samples.     

Donor-acceptor pair spectra in 6H and 4H SiC doped with nitrogen and aluminium

We investigated the low temperature luminescence spectra of 6H and 4H SiC doped with nitrogen and aluminium. The investigation involved photoluminescence spectra, time-resolved cathodoluminescence spectra and decay measurements. From the observation of (i) a detailed line structure in the photoluminescence spectra, (ii) a narrowing of the bands in the time-resolved spectra with increasing delay time and (iii) a non-exponential decay, it is concluded that the spectra characteristic for material doped with N and Al are due to donor-acceptor pair recombination. From the decay measurements the parameter W_max in the relation describing the transition probability of the pairs is estimated to be 3x10⁵ s^-1. It is further concluded, that the spectra of both polytypes involve two zero-phonon bands and their phonon replicas. We show that an interpretation in terms of N as the donor and Al as the acceptor is compatible with existing information about these impurities. Comparison of the spectral data with other information suggests that the existence of two zero-phonon bands is due to the difference in ionization energy between N donors on “hexagonal” and “cubic” sites respectively.     

Analysis of Mesoscopic Structured 2-Propanol/Water Mixtures Using Pressure Perturbation Calorimetry and Molecular Dynamic Simulation

In this paper we demonstrate the application of pressure perturbation calorimetry (PPC) to the characterization of 2-propanol/water mixtures. PPC of different 2-propanol/water mixtures provides two useful measurements: (i) the change in heat (ΔQ); and (ii) the \( \left[ {\delta \bar{C}_{p} /\delta p} \right]_{T} \) value. The results demonstrate that the ΔQ values of the mixtures deviate from that expected for a random mixture, with a maximum at ~20–25 mol% 2-propanol. This coincides with the concentration at which molecular dynamics (MD) simulations show a maximum deviation from random distribution, and also the point at which alcohol–alcohol hydrogen bonds become dominant over alcohol–water hydrogen bonds. Furthermore, the \( \left[ {\delta \bar{C}_{p} /\delta p} \right]_{T} \) value showed transitions at 2.5 mol% 2-propanol and at approximately 14 mol% 2-propanol. Below 2.5 mol% 2-propanol the values of \( \left[ {\delta \bar{C}_{p} /\delta p} \right]_{T} \) are negative; this is indicative of the presence of isolated 2-propanol molecules surrounded by water molecules. Above 2.5 mol% 2-propanol \( \left[ {\delta \bar{C}_{p} /\delta p} \right]_{T} \) rises, reaching a maximum at ~14 mol% corresponding to a point where mixed alcohol–water networks are thought to dominate. The values and trends identified by PPC show excellent agreement not only with those obtained from MD simulations but also with results in the literature derived using viscometry, THz spectroscopy, NMR and neutron diffraction.     

Catalysis as a resonance effect, V. Factors that determine the isokinetic temperature in catalytic reactions

When describing isokinetic effects by the model of selective energy transfer by resonance, it is sometimes found that the frequency of the forcing oscillator is quite different to that of the reacting molecule,i.e.‘resonance’ is not a very good concept to use. By noting that the two frequencies thus found are related to each other as the ratios of small integers,e.g. 4∶3, this dilemma is resolved. The investigation covers formic acid decomposition, homogeneous ligand displacement reactions of Ni(DMSO)₆ ²⁺ and the dissociation of CO₂ on metal surfaces. Dedicated to Professor Pál Tétényi on the occasion of his 70th birthday     

Finite element differential forms

A differential form is a field which assigns to each point of a domain an alternating multilinear form on its tangent space. The exterior derivative operation, which maps differential forms to differential forms of the next higher order, unifies the basic first order differential operators of calculus, and is a building block for a great variety of differential equations. When discretizing such differential equations by finite element methods, stable discretization depends on the development of spaces of finite element differential forms. As revealed recently through the finite element exterior calculus, for each order of differential form, there are two natural families of finite element subspaces associated to a simplicial triangulation. In the case of forms of order zero, which are simply functions, these two families reduce to one, which is simply the well-known family of Lagrange finite element subspaces of the first order Sobolev space. For forms of degree 1 and of degree n − 1 (where n is the space dimension), we obtain two natural families of finite element subspaces, unifying many of the known mixed finite element spaces developed over the last decades. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

WELL-CONDITIONED FRAMES FOR HIGH ORDER FINITE ELEMENT METHODS

The purpose of this paper is to discuss representations of high order C⁰finite element spaces on simplicial meshes in any dimension.When computing with high order piecewise polynomials the conditioning of the basis is likely to be important.The main result of this paper is a construction of representations by frames such that the associated L²condition number is bounded independently of the polynomial degree.To our knowledge,such a representation has not been presented earlier.The main tools we will use for the construction is the bubble transform,introduced previously in[1],and properties of Jacobi polynomials on simplexes in higher dimensions.We also include a brief discussion of preconditioned iterative methods for the finite element systems in the setting of representations by frames.     

Synthesis of thin Cr3Se4 films from modulated elemental reactants via two amorphous intermediates: a detailed examination of the reaction mechanism

The reaction of Cr/Se multilayers when they are annealed occurs in two steps: interdiffusion of the single layers to an amorphous Cr-Se alloy and crystallization of Cr3Se4. Both reaction steps were characterized using various techniques. At approximately 300 degrees C the layers have interdiffused completely to form a homogeneous amorphous Cr-Se alloy. Short-range order in the alloy was probed with X-ray absorption spectroscopy (XAS) and, according to the results of this, is already very similar to Cr3Se4, which crystallizes around 500 degrees C. Crystallization occurs at a well-defined temperature, whereas crystallite growth proceeds in the whole temperature interval above the crystallization temperature and is not finished at 660 degrees C. The reaction yields a polycrystalline thin film of Cr3Se4 in a preferred orientation exhibiting a (00l) texture. In Cr-rich samples amorphous Cr is present as a by-product. A Cr-Se/Se multilayer was observed as an intermediate in the interdiffusion of some Cr-rich samples which is stable between 200 and 250 degrees C.     

Forward mortality and other vital rates — Are they the way forward?

This paper presents a comparative study of stochastic interest and stochastic mortality showing that, despite a virtual similarity, the two concepts are fundamentally different. The notion of forward mortality rate, fetched from finance and now the latest thing in actuarial science, is predicted to soon go out of fashion. Trying it on, it does not fill the measurements of a well-made theoretical concept: there is an element of arbitrariness in its very definition, it disobeys certain self-evident parity requirements, and it fails to generalize to more complex models. It is concluded that forward rate modeling, while passable in the context of interest, is not the way forward in the context of mortality and more general life history analysis.