Künstliche Randbedingungen und Algebraische Äquivalenzen in der Elastizitätstheorie

In dieser Arbeit werden zwei Aspekte bei Randwertproblemen der linearen Elastizitätstheorie untersucht: die Approximation von Lösungen auf unbeschränkten Gebieten und die Änderung von Symmetrieklassen unter speziellen Transformationen. Ausgangspunkt der Dissertation ist das von Specovius-Neugebauer und Nazarov in "Artificial boundary conditions for Petrovsky systems of second order in exterior domains and in other domains of conical type"(Math. Meth. Appl. Sci, 2004; 27) eingeführte Verfahren zur Untersuchung von Petrovsky-Systemen zweiter Ordnung in Außenraumgebieten und Gebieten mit konischen Ausgängen mit Hilfe der Methode der künstlichen Randbedingungen. Dabei werden für die Ermittlung von Lösungen der Randwertprobleme die unbeschränkten Gebiete durch das Abschneiden mit einer Kugel beschränkt, und es wird eine künstliche Randbedingung konstruiert, um die Lösung des Problems möglichst gut zu approximieren. Das Verfahren wird dahingehend verändert, dass das abschneidende Gebiet ein Polyeder ist, da es für die Lösung des Approximationsproblems mit üblichen Finite-Element-Diskretisierungen von Vorteil sei, wenn das zu triangulierende Gebiet einen polygonalen Rand besitzt. Zu Beginn der Arbeit werden die wichtigsten funktionalanalytischen Begriffe und Ergebnisse der Theorie elliptischer Differentialoperatoren vorgestellt. Danach folgt der Hauptteil der Arbeit, der sich in drei Bereiche untergliedert. Als erstes wird für abschneidende Polyedergebiete eine formale Konstruktion der künstlichen Randbedingungen angegeben. Danach folgt der Nachweis der Existenz und Eindeutigkeit der Lösung des approximativen Randwertproblems auf dem abgeschnittenen Gebiet und im Anschluss wird eine Abschätzung für den resultierenden Abschneidefehler geliefert. An die theoretischen Ausführungen schließt sich die Betrachtung von Anwendungsbereiche an. Hier werden ebene Rissprobleme und Polarisationsmatrizen dreidimensionaler Außenraumprobleme der Elastizitätstheorie erläutert. Der letzte Abschnitt behandelt den zweiten Aspekt der Arbeit, den Bereich der Algebraischen Äquivalenzen. Hier geht es um die Transformation von Symmetrieklassen, um die Kenntnis der Fundamentallösung der Elastizitätsprobleme für transversalisotrope Medien auch für Medien zu nutzen, die nicht von transversalisotroper Struktur sind. Eine allgemeine Darstellung aller Klassen konnte hier nicht geliefert werden. Als Beispiel für das Vorgehen wird eine Klasse von orthotropen Medien im dreidimensionalen Fall angegeben, die sich auf den Fall der Transversalisotropie reduzieren lässt.

Solution of the time dependent Dirac-Fock-Slater equation for many-electron collisions systems using a time window method

We present a new scheme to solve the time dependent Dirac-Fock-Slater equation (TDDFS) for heavy many electron ion-atom collision systems. Up to now time independent self consistent molecular orbitals have been used to expand the time dependent wavefunction and rather complicated potential coupling matrix elements have been neglected. Our idea is to minimize the potential coupling by using the time dependent electronic density to generate molecular basis functions. We present the first results for 16 MeV S{^16+} on Ar.

Select-divide-and-conquer method for large-scale configuration interaction

A select-divide-and-conquer variational method to approximate configuration interaction (CI) is presented. Given an orthonormal set made up of occupied orbitals (Hartree-Fock or similar) and suitable correlation orbitals (natural or localized orbitals), a large N-electron target space S is split into subspaces S0,S1,S2,...,SR. S0, of dimension d0, contains all configurations K with attributes (energy contributions, etc.) above thresholds T0={T0egy, T0etc.}; the CI coefficients in S0 remain always free to vary. S1 accommodates KS with attributes above T1≤T0. An eigenproblem of dimension d0+d1 for S0+S 1 is solved first, after which the last d1 rows and columns are contracted into a single row and column, thus freezing the last d1 CI coefficients hereinafter. The process is repeated with successive Sj(j≥2) chosen so that corresponding CI matrices fit random access memory (RAM). Davidson's eigensolver is used R times. The final energy eigenvalue (lowest or excited one) is always above the corresponding exact eigenvalue in S. Threshold values {Tj;j=0, 1, 2,...,R} regulate accuracy; for large-dimensional S, high accuracy requires S 0+S1 to be solved outside RAM. From there on, however, usually a few Davidson iterations in RAM are needed for each step, so that Hamiltonian matrix-element evaluation becomes rate determining. One μhartree accuracy is achieved for an eigenproblem of order 24 × 106, involving 1.2 × 1012 nonzero matrix elements, and 8.4×109 Slater determinants

A combined BIE-FE method for the Stokes equations

A numerical algorithm for the biharmonic equation in domains with piecewise smooth boundaries is presented. It is intended for problems describing the Stokes flow in the situations where one has corners or cusps formed by parts of the domain boundary and, due to the nature of the boundary conditions on these parts of the boundary, these regions have a global effect on the shape of the whole domain and hence have to be resolved with sufficient accuracy. The algorithm combines the boundary integral equation method for the main part of the flow domain and the finite-element method which is used to resolve the corner/cusp regions. Two parts of the solution are matched along a numerical ‘internal interface’ or, as a variant, two interfaces, and they are determined simultaneously by inverting a combined matrix in the course of iterations. The algorithm is illustrated by considering the flow configuration of ‘curtain coating’, a flow where a sheet of liquid impinges onto a moving solid substrate, which is particularly sensitive to what happens in the corner region formed, physically, by the free surface and the solid boundary. The ‘moving contact line problem’ is addressed in the framework of an earlier developed interface formation model which treats the dynamic contact angle as part of the solution, as opposed to it being a prescribed function of the contact line speed, as in the so-called ‘slip models’. Keywords: Dynamic contact angle; finite elements; free surface flows; hybrid numerical technique; Stokes equations.

The point source method for inverse scattering in the time domain

Many recent inverse scattering techniques have been designed for single frequency scattered fields in the frequency domain. In practice, however, the data is collected in the time domain. Frequency domain inverse scattering algorithms obviously apply to time-harmonic scattering, or nearly time-harmonic scattering, through application of the Fourier transform. Fourier transform techniques can also be applied to non-time-harmonic scattering from pulses. Our goal here is twofold: first, to establish conditions on the time-dependent waves that provide a correspondence between time domain and frequency domain inverse scattering via Fourier transforms without recourse to the conventional limiting amplitude principle; secondly, we apply the analysis in the first part of this work toward the extension of a particular scattering technique, namely the point source method, to scattering from the requisite pulses. Numerical examples illustrate the method and suggest that reconstructions from admissible pulses deliver superior reconstructions compared to straight averaging of multi-frequency data. Copyright (C) 2006 John Wiley & Sons, Ltd.

Remote gas detection and quantitative analysis from infrared emission spectra obtained by Fourier transform infrared spectroscopy

Techniques for obtaining quantitative values of the temperatures and concentrations of remote hot gaseous effluents from their measured passive emission spectra have been examined in laboratory experiments. The high sensitivity of the spectrometer in the vicinity of the 2397 cm-1 band head region of CO2 has allowed the gas temperature to be calculated from the relative intensity of the observed rotational lines. The spatial distribution of the CO2 in a methane flame has been reconstructed tomographically using a matrix inversion technique. The spectrometer has been calibrated against a black body source at different temperatures and a self absorption correction has been applied to the data avoiding the need to measure the transmission directly. Reconstruction artifacts have been reduced by applying a smoothing routine to the inversion matrix.

Influence-matrix diagnostic of a data assimilation system

The influence matrix is used in ordinary least-squares applications for monitoring statistical multiple-regression analyses. Concepts related to the influence matrix provide diagnostics on the influence of individual data on the analysis - the analysis change that would occur by leaving one observation out, and the effective information content (degrees of freedom for signal) in any sub-set of the analysed data. In this paper, the corresponding concepts have been derived in the context of linear statistical data assimilation in numerical weather prediction. An approximate method to compute the diagonal elements of the influence matrix (the self-sensitivities) has been developed for a large-dimension variational data assimilation system (the four-dimensional variational system of the European Centre for Medium-Range Weather Forecasts). Results show that, in the boreal spring 2003 operational system, 15% of the global influence is due to the assimilated observations in any one analysis, and the complementary 85% is the influence of the prior (background) information, a short-range forecast containing information from earlier assimilated observations. About 25% of the observational information is currently provided by surface-based observing systems, and 75% by satellite systems. Low-influence data points usually occur in data-rich areas, while high-influence data points are in data-sparse areas or in dynamically active regions. Background-error correlations also play an important role: high correlation diminishes the observation influence and amplifies the importance of the surrounding real and pseudo observations (prior information in observation space). Incorrect specifications of background and observation-error covariance matrices can be identified, interpreted and better understood by the use of influence-matrix diagnostics for the variety of observation types and observed variables used in the data assimilation system. Copyright © 2004 Royal Meteorological Society

Automatic internal calibration in liquid chromatography/Fourier transform ion cyclotron resonance mass spectrometry of protein digests

Accurately measured peptide masses can be used for large-scale protein identification from bacterial whole-cell digests as an alternative to tandem mass spectrometry (MS/MS) provided mass measurement errors of a few parts-per-million (ppm) are obtained. Fourier transform ion cyclotron resonance (FTICR) mass spectrometry (MS) routinely achieves such mass accuracy either with internal calibration or by regulating the charge in the analyzer cell. We have developed a novel and automated method for internal calibration of liquid chromatography (LC)/FTICR data from whole-cell digests using peptides in the sample identified by concurrent MS/MS together with ambient polydimethyl-cyclosiloxanes as internal calibrants in the mass spectra. The method reduced mass measurement error from 4.3 +/- 3.7 ppm to 0.3 +/- 2.3 ppm in an E. coli LC/FTICR dataset of 1000 MS and MS/MS spectra and is applicable to all analyses of complex protein digests by FTICRMS. Copyright (c) 2006 John Wiley & Sons, Ltd.

A method of synthesis of silicious inorganic ordered materials (MCM-41-SBA-1) employing polyacrylic acid-C(n)TAB-TEOS nanoassemblies

In this work we describe the synthesis of a variety of MCM-41 type hexagonal and SBA-1 type cubic mesostructures and mesoporous silicious materials employing a novel synthesis concept based on polyacrylic acid (Pac)-C(n)TAB complexes as backbones of the developing structures. The ordered porosity of the solids was established by XRD and TEM techniques. The synthesis concept makes use of Pac-C(n)TAB nanoassemblies as a preformed scaffold, formed by the gradual increase of pH. On this starting matrix the inorganic precursor species SiO2 precipitate via hydrolysis of TEOS under the influence of increasing pH. The molecular weight (MW) of Pac, as well as the length of carbon chain in C,TAB, determine the physical and structural characteristics of the obtained materials. Longer chain surfactants (C(16)TAB) lead to the formation of hexagonal phase, while shorter chain surfactants (C(14)TAB, C(12)TAB) favor the SBA-1 phase. Lower MW of Pac (approximate to2000) leads to better-organized structures compared to higher MW ( 450,000), which leads to worm-like mesostructures. Cell parameters and pore size increase with increasing polyelectrolyte and/or surfactant chain, while at the same time SEM photography reveals that the particle size decreases. Conductivity experiments provide some insight into the proposed self-assembling pathway. (C) 2003 Elsevier Inc. All rights reserved.

Impact damage characterisation of thermoplastic matrix composites using transmission transient thermography

In this work, IR thermography is used as a non-destructive tool for impact damage characterisation on thermoplastic E-glass/polypropylene composites for automotive applications. The aim of this experimentation was to compare impact resistance and to characterise damage patterns of different laminates, in order to provide indications for their use in components. Two E-glass/polypropylene composites, commingled ®Twintex (with three different weave structures: directional, balanced and 3-D) and random reinforced GMT, were in particular characterised. Directional and balanced Twintex were also coupled in a number of hybrid configurations with GMT to evaluate the possible use of GMT/Twintex hybrids in high-energy absorption components. The laminates were impacted using a falling weight tower, with impact energies ranging from 15 J to penetration. Using IR thermography during cooling down following a long pulse (3 s), impact damaged areas were characterised and the influence of weave structure on damage patterns was studied. IR thermography offered good accuracy for laminates with thickness not exceeding 3.5 mm: this appears to be a limit for the direct use of this method on components, where more refined signal treatment would probably be needed for impact damage characterisation.

A method of weighting indicators in building energy efficiency assessment

This paper identifies the indicators of energy efficiency assessment in residential building in China through a wide literature review. Indicators are derived from three main sources: 1) The existing building assessment methods; 2)The existing Chinese standards and technology codes in building energy efficiency; 3)Academia research. As a result, we proposed an indicator list by refining the indicators in the above sources. Identified indicators are weighted by the group analytic hierarchy process (AHP) method. Group AHP method is implemented following key steps: Step 1: Experienced experts are selected to form a group; Step 2: A survey is implemented to collect the individual judgments on the importance of indicators in the group; Step 3: Members’ judgments are synthesized to the group judgments; Step 4: Indicators are weighted by AHP on the group judgments; Step 5: Investigation of consistency estimation shows that the consistency of the judgment matrix is accepted. We believe that the weighted indicators in this paper will provide important references to building energy efficiency assessment.

Development of a liquid chromatographic time-of-flight mass spectrometric method for the determination of unlabelled and deuterium-labelled alpha-tocopherol in blood components

A method is described for the analysis of deuterated and undeuterated alpha-tocopherol in blood components using liquid chromatography coupled to an orthogonal acceleration time-of-flight (TOF) mass spectrometer. Optimal ionisation conditions for undeuterated (d0) and tri- and hexadeuterated (d3 or d6) alpha-tocopherol standards were found with negative ion mode electrospray ionisation. Each species produced an isotopically resolved single ion of exact mass. Calibration curves of pure standards were linear in the range tested (0-1.5 muM, 0-15 pmol injected). For quantification of d0 and d6 in blood components following a standard solvent extraction, a stable-isotope-labelled internal standard (d3-alpha-tocopherol) was employed. To counter matrix ion suppression effects, standard response curves were generated following identical solvent extraction procedures to those of the samples. Within-day and between-day precision were determined for quantification of d0- and d6-labelled alpha-tocopherol in each blood component and both averaged 3-10%. Accuracy was assessed by comparison with a standard high-performance liquid chromatography (HPLC) method, achieving good correlation (r(2) = 0.94), and by spiking with known concentrations of alpha-tocopherol (98% accuracy). Limits of detection and quantification were determined to be 5 and 50 fmol injected, respectively. The assay was used to measure the appearance and disappearance of deuterium-labelled alpha-tocopherol in human blood components following deuterium-labelled (d6) RRR-alpha-tocopheryl acetate ingestion. The new LC/TOFMS method was found to be sensitive, required small sample volumes, was reproducible and robust, and was capable of high throughput when large numbers of samples were generated. Copyright (C) 2003 John Wiley Sons, Ltd.

Absorption of isoflavones in humans: effects of food matrix and processing

If soy isoflavones are to be effective in preventing or treating a range of diseases, they must be bioavailable, and thus understanding factors which may alter their bioavailability needs to be elucidated. However, to date there is little information on whether the pharmacokinetic profile following ingestion of a defined dose is influenced by the food matrix in which the isoflavone is given or by the processing method used. Three different foods (cookies, chocolate bars and juice) were prepared, and their isoflavone contents were determined. We compared the urinary and serum concentrations of daidzein, genistein and equol following the consumption of three different foods, each of which contained 50 mg of isoflavones. After the technological processing of the different test foods, differences in aglycone levels were observed. The plasma levels of the isoflavone precursor daidzein were not altered by food matrix. Urinary daidzein recovery was similar for all three foods ingested with total urinary output of 33-34% of ingested dose. Peak genistein concentrations were attained in serum earlier following consumption of a liquid matrix rather than a solid matrix, although there was a lower total urinary recovery of genistein following ingestion of juice than that of the two other foods. (c) 2006 Elsevier Inc. All rights reserved.

Characterisation of blends based on hydroxyethylcellulose and maleic acid-alt-methyl vinyl ether

Hydrophilic polymeric films based on blends of hydroxyethylcellulose and maleic acid-co-methyl vinyl ether were produced by casting from aqueous solutions. The physicochemical properties of the blends have been assessed using Fourier transform infrared spectroscopy, thermal gravimetric analysis, differential scanning calorimetry, dielectric spectroscopy, etc. The pristine films exhibit complete miscibility due to the formation of intermacromolecular hydrogen bonding. The thermal treatment of the blend films leads to cross-linking via intermacromolecular esterification and anhydride formation. The cross-linked materials are able to swell in water and their swelling degree can be easily controlled by temperature and thermal treatment time. The formation of the crosslinks is apparent in the dynamic properties of the blends as observed through the mechanical relaxation and dielectric relaxation spectra. The dielectric characteristics of the material are influenced by the effects of change in the local structure of the blend on the ionic conduction processes and the rate of dipolar relaxation. Separation of these processes is attempted using the dielectric modulus method. Significant deviations from a simple additive rule of mixing on the activation energy are observed consistent with hydrogen bonding and crosslinking of the matrix. This paper indicates a method for the creation of films with good mechanical and physical characteristics by exposing the blends to a relatively mild thermal treatment.

Finding the smallest eigenvalue by the inverse Monte Carlo method with refinement

Finding the smallest eigenvalue of a given square matrix A of order n is computationally very intensive problem. The most popular method for this problem is the Inverse Power Method which uses LU-decomposition and forward and backward solving of the factored system at every iteration step. An alternative to this method is the Resolvent Monte Carlo method which uses representation of the resolvent matrix [I -qA](-m) as a series and then performs Monte Carlo iterations (random walks) on the elements of the matrix. This leads to great savings in computations, but the method has many restrictions and a very slow convergence. In this paper we propose a method that includes fast Monte Carlo procedure for finding the inverse matrix, refinement procedure to improve approximation of the inverse if necessary, and Monte Carlo power iterations to compute the smallest eigenvalue. We provide not only theoretical estimations about accuracy and convergence but also results from numerical tests performed on a number of test matrices.