We consider a system of weakly coupled singularly perturbed convection-diffusion equations with multiple scales. Based on sharp estimates for first order derivatives, Linß [T. Linß, Computing 79 (2007) 23–32.] analyzed the upwind finite-difference method on a Shishkin mesh. We derive such sharp bounds for second order derivatives which show that the coupling generates additional weak layers. Finally, we prove the first robust convergence result for the Galerkin finite element method for this class of problems on modified Shishkin meshes introducing a mesh grading to cope with the weak layers. Numerical experiments support our theory.

Gescannte und vektorisierte technische Zeichnungen werden automatisch unter Nutzung eines Netzes von Modellen in eine hochwertige Datenstruktur migriert. Die Modelle beschreiben die Inhalte der Zeichnungen hierarchisch und deklarativ. Modelle für einzelne Bestandteile der Zeichnungen können paarweise unabhängig entwickelt werden. Dadurch werden auch sehr komplexe Zeichnungsklassen wie Elektroleitungsnetze oder Gebäudepläne zugänglich. Die Modelle verwendet der neue, sogenannte Y-Algorithmus: Hypothesen über die Deutung lokaler Zeichnungsinhalte werden hierarchisch generiert. Treten bei der Nutzung konkurrierender Modelle Konflikte auf, werden diese protokolliert. Mittels des Konfliktbegriffes können konsistente Interpretationen einer kompletten Zeichnung abstrakt definiert und während der Analyse einer konkreten Zeichnung bestimmt werden. Ein wahrscheinlichkeitsbasiertes Gütemaß bewertet jede dieser alternativen, globalen Interpretationen. Das Suchen einer bzgl. dieses Maßes optimalen Interpretation ist ein NP-hartes Problem. Ein Branch and Bound-Algorithmus stellt die adäquate Lösung dar.

We address the excitation of quantum breathers in small nonlinear networks of two and three degrees of freedom, in order to study their properties. The invariance under permutation of two sites of these networks substitutes the translation invariance that is present in nonlinear lattices, where (classical) discrete breathers are time periodic space localized solutions of the underlying classical equations of motion. We do a systematic analysis of the spectrum and eigenstates of such small systems, characterizing quantum breather states by their tunnelling rate (energy splitting), site correlations, fluctuations of the number of quanta, and entanglement. We observe how these properties are reflected in the time evolution of initially localized excitations. Quantum breathers manifest as pairs of nearly degenerate eigenstates that show strong site correlation of quanta, and are characterized by a strong excitation of quanta on one site of the network which perform slow coherent tunnelling motion from one site to another. They enhance the fluctuations of quanta, and are the least entangled states among the group of eigenstates in the same range of the energy spectrum. We use our analysis methods to consider the excitation of quantum breathers in a cell of two coupled Josephson junctions, and study their properties as compared with those in the previous cases. We describe how quantum breathers could be experimentally observed by employing the already developed techniques for quantum information processing with Josephson junctions.

A detailed and comprehensive description of the state of the art in the field of flood forecasting opens this work. Advantages and shortcomings of currently available methods are identified and discussed. Amongst others, one important aspect considers the most exigent weak point of today’s forecasting systems: The representation of all the fundamentally different event specific patterns of flood formation with one single set of model parameters. The study exemplarily proposes an alternative for overcoming this restriction by taking into account the different process characteristics of flood events via a dynamic parameterisation strategy. Other fundamental shortcomings in current approaches especially restrict the potential for real time flash flood forecasting, namely the considerable computational requirements together with the rather cumbersome operation of reliable physically based hydrologic models. The new PAI-OFF methodology (Process Modelling and Artificial Intelligence for Online Flood Forecasting) considers these problems and offers a way out of the general dilemma. It combines the reliability and predictive power of physically based, hydrologic models with the operational advantages of artificial intelligence. These operational advantages feature extremely low computation times, absolute robustness and straightforward operation. Such qualities easily allow for predicting flash floods in small catchments taking into account precipitation forecasts, whilst extremely basic computational requirements open the way for online Monte Carlo analysis of the forecast uncertainty. The study encompasses a detailed analysis of hydrological modeling and a problem specific artificial intelligence approach in the form of artificial neural networks, which build the PAI-OFF methodology. Herein, the synthesis of process modelling and artificial neural networks is achieved by a special training procedure. It optimizes the network according to the patterns of possible catchment reaction to rainstorms. This information is provided by means of a physically based catchment model, thus freeing the artificial neural network from its constriction to the range of observed data – the classical reason for unsatisfactory predictive power of netbased approaches. Instead, the PAI-OFF-net learns to portray the dominant process controls of flood formation in the considered catchment, allowing for a reliable predictive performance. The work ends with an exemplary forecasting of the 2002 flood in a 1700 km² East German watershed.

In der Arbeit wird ein Ansatz zur Verwaltung von Lernmaterialien in einem semistrukturierten Datenbanksystem vorgestellt. Der Ansatz zeichnet sich durch die Wiederverwendung einmal gespeicherter Lernmaterialien aus

Hochsch., Diplomarbeit--Wismar, 2006.

Zugl.: Dresden, Techn. Univ., Diss., 2009

Die Chemnitzer Linux-Tage sind eine Veranstaltung rund um das Thema Open Source. Im Jahr 2011 wurden 102 Vorträge und Workshops gehalten. Der Band enthält ausführliche Beiträge zu 12 Hauptvorträgen sowie Zusammenfassungen zu 78 weiteren Vorträgen. / The "Chemnitz Linux Days" is a conference that deals with Linux and Open Source Software. In 2011 102 talks and workshops were given. This volume contains papers of 12 main lectures and 78 abstracts (in german).

Universiẗat, Diss., 2006--Saarbrücken.

Zugl.: Ilmenau, Techn. Univ., Diss., 2008