Linear stability for self-similar wave maps

Diese Arbeit behandelt eine Klasse von Abbildungen, genannt wave maps, vom Minkowski-Raum auf die 3-Sphäre. Solche Abbildungen genügen einer nichtlinearen Wellengleichung, für die eine selbstähnliche Lösung, genannt der Grundzustand, in geschlossener Form bekannt ist. Diese Lösung entwickelt in endlicher Zeit eine Singularität (blow-up). Numerische Untersuchungen legen nahe, dass der Grundzustand einen Attraktor für generische Anfangsdaten darstellt. In dieser Arbeit werden lineare Störungen des Grundzustands untersucht, wobei das Ziel ist, die lineare Stabilität mit analytischen Methoden zu beweisen. Die linearisierte Gleichung wird als Operatorgleichung formuliert und in zwei verschiedenen Funktionenräumen betrachtet - im Energieraum und in einem Raum, in dem die Norm mit einer höheren Energie assoziiert werden kann. Mit Methoden aus der Theorie starkstetiger, ein-parametriger Halbgruppen und durch Untersuchung des Spektralproblems kann eine Abschätzung für die zeitliche Entwicklung der Energie der Störung angegeben werden. Der Grundzustand ist linear stabil, wenn die Energie der Störung mit der Zeit abnimmt. Es wird gezeigt, dass nur eine Formulierung des Problems im höheren Energieraum zum gewünschten Ergebnis führt.This work studies a particular class of maps, called wave maps, from Minkowski space to the three-sphere. Such maps fulfill a nonlinear wave equation, for which a self-similar solution, called the ground state, is known in closed form. This solution develops a singularity in finite time (\textit{blow-up}). Numerical investigations suggest that the ground state is an attractor for generic smooth initial data. In this work linear perturbations of the ground state solution are investigated. The aim is to prove linear stability with analytic methods. We give an operator formulation of the linearized equation and consider it in two different functions spaces - in the energy space and in a higher energy space, where the norm can be associated with a higher energy. With methods from the theory of strongly continuous one-parameter semigroups and by investigation of the spectral problem an estimate for the temporal evolution of the energy of the perturbation can be found. The ground state solution is linearly stable if the energy of the perturbation decreases in time. It will be shown that only a formulation of the problem in the higher energy space leads to the intended result

Optimization of working roll cooling in hot rolling

Paper presented at the 9th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Malta, 16-18 July, 2012.The cooling of working rolls is an important process in the hot rolling technology. The optimal cooling of rolls should be designed with respect to two aspects. The first is the wearing of a roll where high temperature decreases the durability of the surface layer. The second aspect is a thermal deformation of a roll. This is critical for the shape and tolerance of flat products. Cooling at rolling mill should be designed with consideration to both aspects. Finding optimum pressure and flow rate is a difficult task. In regards to water quantity, the experience shows that the phrase “more is better” is not valid here. In other word – an increase in the amount of water can even cause a decrease in cooling intensity. Water nozzles are typically used in this case. There are many of factors which can influence the efficiency of the nozzle cooling system: Type of a nozzle, geometrical configuration (nozzle pitch, distance from the roll, orientation, number of manifolds), coolant pressure and temperature. Cooling intensity is mostly specified through Heat transfer coefficient (HTC) or heat flux (HF) distribution. Coolant flow on the rotating roll surface makes the problem complex. Surface temperature of the cylinder plays an important role in the heat transfer mechanism, especially for higher temperatures where boiling must be considered. No analytical or numerical solution of heat transfer and fluid flow for this case is known. The task can be successfully solved experimentally. An experimental bench and methodology of realistic boundary conditions determination was developed in the Heat Transfer and Fluid Flow Laboratory (HEATLAB). The strategy of optimization is based on two steps. First is investigation of present situation of work roll cooling system and second is design of a new system. Criterion of optimization is saving of cooling water with remaining or increasing of cooling intensity. Comparison of the original design and new design was done numerically, using special software and experimentally by temperature measurement of working roll after specified rolling campaign. Optimized cooling system was applied on hot flat rolling mill in voestalpine Stahl GmbH.dc201

Augmentation Methods on Monophonic Audio for Instrument Classification in Polyphonic Music

Instrument classification is one of the fields in Music Information Retrieval (MIR) that has attracted a lot of research interest. However, the majority of that is dealing with monophonic music, while efforts on polyphonic material mainly focus on predominant instrument recognition. In this paper, we propose an approach for instrument classification in polyphonic music from purely monophonic data, that involves performing data augmentation by mixing different audio segments. A variety of data augmentation techniques focusing on different sonic aspects, such as overlaying audio segments of the same genre, as well as pitch and tempo-based synchronization, are explored. We utilize Convolutional Neural Networks for the classification task, comparing shallow to deep network architectures. We further investigate the usage of a combination of the above classifiers, each trained on a single augmented dataset. An ensemble of VGG-like classifiers, trained on non-augmented, pitch-synchronized, tempo-synchronized and genre-similar excerpts, respectively, yields the best results, achieving slightly above 80% in terms of label ranking average precision (LRAP) in the IRMAS test set.ruments in over 2300 testing tracks

Observations on comatose survivors of cardiopulmonary resuscitation with generalized myoclonus

BACKGROUND: There is only limited data on improvements of critical medical care is resulting in a better outcome of comatose survivors of cardiopulmonary resuscitation (CPR) with generalized myoclonus. There is also a paucity of data on the temporal dynamics of electroenephalographic (EEG) abnormalities in these patients. METHODS: Serial EEG examinations were done in 50 comatose survivors of CPR with generalized myoclonus seen over an 8 years period. RESULTS: Generalized myoclonus occurred within 24 hours after CPR. It was associated with burst-suppression EEG (n = 42), continuous generalized epileptiform discharges (n = 5), alpha-coma-EEG (n = 52), and low amplitude (10 μV <) recording (n = 1). Except in 3 patients, these EEG-patterns were followed by another of these always nonreactive patterns within one day, mainly alpha-coma-EEG (n = 10) and continuous generalized epileptiform discharges (n = 9). Serial recordings disclosed a variety of EEG-sequences composed of these EEG-patterns, finally leading to isoelectric or flat recordings. Forty-five patients died within 2 weeks, 5 patients survived and remained in a permanent vegetative state. CONCLUSION: Generalized myoclonus in comatose survivors of CPR still implies a poor outcome despite advances in critical care medicine. Anticonvulsive drugs are usually ineffective. All postanoxic EEG-patterns are transient and followed by a variety of EEG sequences composed of different EEG patterns, each of which is recognized as an unfavourable sign. Different EEG-patterns in anoxic encephalopathy may reflect different forms of neocortical dysfunction, which occur at different stages of a dynamic process finally leading to severe neuronal loss

Stable self-similar blow up for energy subcritical wave equations

We consider the semilinear wave equation partial derivative(2)(t)psi - Delta psi = vertical bar psi vertical bar(p-1)psi for 1 0 and kappa(p) is a p-dependent constant. We prove that the blow up described by psi(T) is stable against small perturbations in the energy topology. This complements previous results by Merle and Zaag. The method of proof is quite robust and can be applied to other self-similar blow up problems as well, even in the energy supercritical case