Dans ce travail de thèse, il s'agit essentiellement de déterminer les propriétés mécaniques et physiques linéaires effectives des composites dans lesquels l'interface entre deux phases n'est pas lisse mais très rugueuse. Une approche efficace pour surmonter les difficultés provenant de la présence de rugosités d'interface consiste d'abord à homogénéiser une zone d'interface rugueuse comme une interphase équivalente par une analyse asymptotique et ensuite à appliquer des schémas micromécaniques pour estimer les propriétés effectives en tenant en compte de la présence de l'interphase équivalente. L'objectif principal de ce travail est de développer cette approche dans un cadre général où la surface autour de laquelle l'interface oscille périodiquement et rapidement peut être courbée et les phénomènes physiques concernés peuvent être couplés. Pour atteindre cet objectif, la conduction thermique est premièrement étudiée comme un prototype des phénomènes de transport non couplés pour élaborer dans un cadre simple les éléments essentiels de notre approche. Cette étude, préliminaire mais très utile au vu de l'importance des phénomènes de transport, montre que des résultats généraux et compacts peuvent s'obtenir quand l'interface est ondulée dans une seule direction et que des méthodes numériques sont en général nécessaires dans le cas où l'interface oscille suivant deux directions. L'approche développée et les résultats obtenus pour la conduction thermique sont étendus d'abord à l'élasticité linéaire et ensuite aux phénomènes physiques linéaires couplés tels que la thermoélectricité et la piézoélectricité. Dans ces cas plus complexes, des résultats généraux sont obtenus pour les composites stratifiés avec les interfaces ondulées dans une seule direction et des méthodes numériques sont élaborées pour les composites dans lesquels les interfaces oscillent suivant deux directions / This work is essentially concerned with determining the effective linear mechanical and physical properties of composites in which the interface between two phases is not smooth but very rough. An efficient approach to overcome the difficulties arising from the presence of interfacial roughness is first to homogenize a rough interface zone as an equivalent interphase by an asymptotic analysis and then to apply micromechanical schemes to estimation of the effective properties while accounting for the equivalent interphase. The present work aims mainly to develop this approach in a general situation where the surface around which an interface oscillates periodically and quickly can be curved and the physical phenomena involved can be coupled. To achieve this goal, thermal conduction is first studied as a prototype of transport phenomena so as to elaborate key elements of our approach in a simple situation. This study,even preliminary but very useful in view of the importance of transport phenomena, shows that general and compact results can be obtained when the interface is corrugated in only one direction and that numerical methods are generally required when an interface is curved along two directions. The approach developed and the results obtained for thermal conduction are extended first to linear elasticity and then to linear coupled physical phenomena such as thermoelectricity and piezoelectricity. In these more complex cases, general results are obtained for composite laminates with interfaces oscillating in only one direction, and numerical methods are elaborated for composites in which the interfaces oscillate in two directions

This thesis is deals with the nerve fibre layer in the colour ophthalmology images of retina. The thesis describes how can we use finding of nerve fibre layer and how was it solved in the past. In the thesis are proposed the methods that are based on processing and scoring frequency spectrums of individual sample of retina. At first here are described the methods of detection on the artificial generated samples that just simulate the nerve fibre layer. Then the thesis concentrates on processing of real images of retina. Because of the bloodstream, that depreciates processing at real images, are all surveyed samples are chosen manually. Except detection the nerve fibre layer itself, the thesis also deals with determination of direction their dissemination.

Master´s thesis is focused to analyse the acoustic and electomagnetic emission signals. These signals generate external power applied on the material. This power put there plastic deformation and create cracks. Spectral analyse show that signals are non-stationary. Wavelet transformation was used to spectral analyse which informate about time-frequence vaules of the signal.

Main issue of this master´s thesis deals with high-frequency pulsations caused by cavitating hydraulic components (in this case nozzle and throttle valve). In first measurement on the nozzle was not a high-frequency sensor set in the way, so the evaluation was incorrect. After re-setting of the way was the nozzle measured again and the pulsations were evaluated correct this time. During the last measurement was the sensor located behind the throttle valve, which was with gradual opening and cavitation treatment measured. Resulting dependencies worked out on time dependence. A special mathematical method, Fourier transformation, was used. It transformed pressure amplitudes into frequency dependence. Evaluation of dependecies is the basic step for frequency band assesment, in which the cavitation on particular components happens.

The main target of this master’s thesis is to focus on methods of analysis of vibration signals in electric machines. To get know the basic principles of the diagnostics methods, is important to clarify origin of the vibration signals and the impact they have. The selected methods were tested practically by measurement on electric machines. Measured data were processed in program LabVIEW. In this thesis were created programs which actually can be aplicated for complete vibrodiagnostics of electric machines in particular induction motors. The basic evaluation of vibration are the RMS value, Crest factor, time course and power spectrum. Results of this thesis are used to demonstrate how quickly and effectively can be vibration signals from electric machines evaluated.

An der Schnittstelle zwischen Elektrofahrzeug und dem Niederspannungsnetz nimmt die Ladesäule eine Schlüsselposition beim Ausbau von intelligenten Stromnetzen in Synergie mit der Elektromobilität ein. Durch die Entwicklung einer frequenzselektiven Stromregelung des Wechselrichters der Ladesäule wurde die Reduktion der Netzrückwirkung bei hoher Ladeleistung ermöglicht und zusätzliche Netzdienstleistungen wie Netzstützung, Phasenschieberbetrieb, Netzsymmetrierung und Oberschwingungskompensation für eine aktive Verbesserung der Netzspannungsqualität realisiert. Ein neues Verfahren zur Optimierung der Phasenregelung erzielte eine höhere Effizienz der Kompensation der Oberschwingungen der Netzspannung. Diese Funktionen wurden an einem Prototyp der intelligenten Ladesäule in einem Inselnetz praktisch erforscht.

In dieser Arbeit befassen wir uns mit einer Reihe von entscheidenden Schritten, um die unpolarisierten Helizitäts- und Trasversitäts-Parton-Verteilungsfunktionen der Nukleonen im Rahmen der Gitter-QCD zu bewerten. Diskretisierungsartefakte werden unter Verwendung eines N_f=2+1+1 Eichensembles von Fermionen mit verdrillter Wilson-Masse untersucht, die bei einer Pionenmasse von ungefähr M=37 MeV simuliert werden. Die unpolarisierten und Helizitäts Partonverteilungsfunktionen weisen eine nicht vernachlässigbare Abhängigkeit vom Gitterabstand auf, und die Kontinuumsextrapolation ergibt eine bessere Übereinstimmung mit Phänomenologie. Die direkte Berechnung der Fourier-Transformation mit diskreten Gitterdaten kann Artefakte verursachen. Daher arbeiten wir mit einer neuen datengesteuerten Methode, die auf Gauß-Prozess-Regression basiert, die sogenannte Bayes-Gauß-Fourier-Transformation, um die Einschränkungen der diskreten Fourier-Transformation zu überwinden. Wir sind der Meinung, dass dieser datengesteuerte Ansatz die durch die Diskretisierung der Fourier-Transformation eingeführten Artefakte drastisch reduzieren kann, jedoch ist der endgültige Effekt auf die Lichtkegel-PDFs gering. Darüber hinaus präsentieren wir die Ergebnisse der ersten ab initio Berechnung der individuellen up, down und strange unpolarisierten, Helizitäts- und Transversitäts-Partonverteilungsfunktionen für das Proton. Die Analyse wird an einem durch N_f=2+1+1 verdrillten Kleeblatt-verbesserten Fermionen-Ensemble durchgeführt, das bei einer Pionenmasse von 260 MeV simuliert wird. Wir verwenden den hierarchischen Sondierungsalgorithmus, um die unzusammenhängenden Quarkschleifen auszuwerten. Dadurch erhalten wir Ergebnisse ungleich Null für den unbegundenen isoskalaren Beitrag und die strange Quark-Matrixelemente. / In this work, we address a number of crucial steps in order to evaluate the nucleon unpolarized helicity and trasversity parton distribution functions within the framework of lattice QCD. Discretization artifacts are investigated using an N_f=2+1+1 gauge ensemble of Wilson twisted mass fermions simulated at a pion mass of approximately M=370 MeV. The unpolarized and helicity parton distribution functions show a non-negligible dependence on the lattice spacing, with the continuum extrapolation producing a better agreement with phenomenology. The direct computation of the Fourier transform using discrete lattice data may introduce artifacts and we, therefore, use a new data-driven method based on Gaussian process regression, the so-called Bayes-Gauss Fourier transform to overcome the limitations of the discrete Fourier transform. We find that this data-driven approach can drastically reduce the artifacts introduced by the discretization of the Fourier transform, however, the final effect on the light-cone PDFs is small. Furthermore, we present results of the first ab initio calculation of the individual up, down, and strange unpolarized, helicity, and transversity parton distribution functions for the proton. The analysis is performed on an N_f=2+1+1 twisted mass clover-improved fermion ensemble simulated at a pion mass of 260 MeV. We employ the hierarchical probing algorithm to evaluate the disconnected quark loops, allowing us to obtain non-zero results for the disconnected isoscalar contribution and the strange quark matrix elements.

The computation of the Coulomb potentials and forces in charged particle systems under 3d-periodic boundary conditions is possible in an efficient way by utilizing the Ewald summation formulas and applying the fast Fourier transform (FFT). In this paper we consider the particle-particle NFFT (P2NFFT) approach, which is based on the fast Fourier transform for nonequispaced data (NFFT) and compare the error behaviors regarding different window functions, which are used in order to approximate the given continuous charge distribution by a mesh based charge density. Typically B-splines are applied in the scope of particle mesh methods, as for instance within the well-known particle-particle particle-mesh (P3M) algorithm. The publicly available P2NFFT algorithm allows the application of an oversampled FFT as well as the usage of different window functions. We consider for the first time also an approximation by Bessel functions and show how the resulting root mean square errors in the forces can be predicted precisely and efficiently. The results show that, if the parameters are tuned appropriately, the Bessel window function is in many cases even the better choice in terms of computational costs. Moreover, the results indicate that it is often advantageous in terms of efficiency to spend some oversampling within the NFFT while using a window function with a smaller support.

Fahrbahnunebenheiten und Gleislagestörungen können als Repräsentanten schwach stationärer Prozesse aufgefasst werden. Die Beschreibung der Qualitätsklassen von Fahrwegen erfolgt konventionell über die Spektraldichte (Leistungsdichte). Ausgehend von der Spektraldichte-Beschreibung wird die Generierung synthetischer Fahrwegstörungen für die numerische Simulation von Fahrzeugen als Mehrkörpersystem mit den Mitteln der Fourieranalyse und mit Hilfe von Wavelets untersucht. / Road unevenness and track irregularities can be considered as realisations of weakly stationary stochastic processes. A description of track quality levels is given by the (power)spectral density of the related process. Here, the synthesis of track irregularities for a given spectral density using fourier series and wavelets is considered.

By the help of several examples the interactive work with the ClassPad330 is considered. The student can solve difficult exercises of practical applications step by step using the symbolic calculation and the graphic possibilities of the calculator. Sometimes several fields of mathematics are combined to solve a problem. Let us consider the ClassPad330 (with the actual operating system OS 03.03) and discuss on some new exercises in analysis, e.g. solving a linear differential equation by the help of the Laplace transformation and using the inverse Laplace transformation or considering the Fourier transformation in discrete time (the Fast Fourier Transformation FFT and the inverse FFT). We use the FFT- and IFFT-function to study periodic signals, if we only have a sequence generated by sampling the time signal. We know several ways to get a solution. The techniques for studying practical applications fall into the following three categories: analytic, graphic and numeric. We can use the Classpad software in the handheld or in the PC (ClassPad emulator version of the handheld).