Ziel der vorliegenden Arbeit ist es, das Preisach-Modell bezüglich stochastischer äußerer Felder und temperaturbezogener Aspekte zu untersuchen. Das phänomenologische Preisach-Modell wird oft erfolgreich angewendet, um Systeme mit Hysterese zu beschreiben. Im ersten Teil der Arbeit wird die Antwort des Preisach-Modells auf stochastische äußere Felder untersucht. Hier liegt das Augenmerk hauptsächlich auf der Autokorrelation; sie dient dazu den Einfluss des hysteretischen Gedächtnisses zu quantifizieren. Mit analytischen Methoden wird gezeigt, dass sich ein Langzeitgedächtnis, sichtbar in der Autokorrelation der Systemantwort, entwickeln kann, selbst wenn das treibende Feld unkorreliert ist. Im Anschluss werden diese Resultate, m.H. von Simulationen, auf äußere Felder ausgeweitet, die selbst Korrelationen aufweisen können. Der zweite Teil der Arbeit befasst sich mit dem Einfluss einer endlichen Temperatur auf das Preisach-Modell. Es werden unterschiedliche Methoden besprochen, wie das Nichtgleichgewichtsmodell in seiner mikromagnetischen Interpretation mit Temperatur als Gleichgewichtseigenschaft verknüpft werden kann. Eine Formulierung wird genutzt, um die Magnetisierung von Nickelnanopartikeln in einer Fullerenmatrix zu simulieren und mit Experimenten zu vergleichen. Des Weiteren wird die Relaxationsdynamik des Gedächtnisses des Preisach-Modells bei endlichen Temperaturen untersucht. / The aim of this thesis is to investigate the Preisach model in regard to stochastically driving and temperature-related aspects. The Preisach model is a phenomenological model for systems with hysteresis which is often successfully applied. Hysteresis is a widespread phenomenon which is observed in nature and the key feature of certain technological applications. Further, it contributes to phenomena of interest in social science and economics as well. Prominent examples are the magnetization of ferromagnetic materials in an external magnetic field or the adsorption-desorption hysteresis observed in porous media. Hysteresis involves the development of a hysteresis memory, and multistability in the interrelations between external driving fields and system response. In the first part, we mainly investigate the response of Preisach hysteresis models driven by stochastic input processes with regard to autocorrelation functions to quantify the influence of the system’s memory. Using rigorous methods, it is shown that the development of a hysteresis memory is reflected in the possibility of long-time tails in the autocorrelation functions, even for uncorrelated driving fields. In the case of uncorrelated driving, these long-time tails in the autocorrelations of the system’s response are determined only by the tails of the involved densities. They will be observed if there are broad Preisach densities assigning a high weight to elementary loops of large width and narrow input densities such that rare extreme events of the input time series contribute significantly to the output for a long period of time. Afterwards, these results are extended by simulations to driving fields which themselves show correlations. It is shown that the autocorrelation of the output does not decay faster than the autocorrelation of the input process. Further, there is a possibility that long-term memory in the hysteretic response is more pronounced in the case of uncorrelated driving than in the case of correlated driving. The behavior of the output probability distribution at the saturation values is quite universal. It is not affected by the presence of correlations and allows conclusions whether the input density is much more narrow than the Preisach density or not. Moreover, the existence of effective Preisach densities is shown which define equivalence classes of systems of input and Preisach densities which lead to realizations of the same output variable. The asymptotic behavior of an effective Preisach density determines the asymptotic correlation decay of the system’s response in the case of uncorrelated driving. In the second part, temperature-related effects are considered. It is reviewed how the non-equilibrium Preisach model in its micromagnetic picture can be related to temperature within the framework of extended irreversible thermodynamics. The irreversible response of a ferromagnetic material, namely, Nickel nanoparticles in a fullerene matrix, is simulated. The model includes superparamagnetism where ferromagnetism breaks down at temperatures lower than the Curie temperature and the results are compared to experimental data. Furthermore, we adapt known results for the thermal relaxation of the system’s memory in the form of a front propagation in the Preisach plane derived basically from solving a master equation and by the use of a contradictory assumption. A closer look is taken at short time scales which dissolves the contradiction and shows that the known results apply, taking into account the fact that the dividing line propagation starts with an additional delay time depending on the front coordinates in the Preisach plane. Additionally, it is outlined how thermal relaxation behavior in the Preisach model of hysteresis can be studied using a Fokker-Planck equation. The latter is solved analytically in the non-hysteretic limit using eigenfunction methods. The results indicate a change in the relaxation behavior, especially on short time scales.

The basic idea of this paper is to outline a cross-curricular approach between mathematics and science. The aim is to close the often perceived gap between formal maths and authentic experience and to increase the students’ versatility in the use of mathematical terms. Students are to experience maths as logical, interesting and relevant through extra-mathematical references. Concrete physical or biological correlations may initiate mathematical activities, and mathematical terms are to be understood in logical contexts. Examples: physical experiments can lead to a comprehensive understanding of the concept of functions and of the intersection of medians in triangles. Biological topics can lead to the concepts of similarity and proportion as well as to the construction of pie charts. In the European ScienceMath Project a variety of teaching modules was developed and tested in secondary schools.

Ziel der vorliegenden Arbeit ist es, das Preisach-Modell bezüglich stochastischer äußerer Felder und temperaturbezogener Aspekte zu untersuchen. Das phänomenologische Preisach-Modell wird oft erfolgreich angewendet, um Systeme mit Hysterese zu beschreiben. Im ersten Teil der Arbeit wird die Antwort des Preisach-Modells auf stochastische äußere Felder untersucht. Hier liegt das Augenmerk hauptsächlich auf der Autokorrelation; sie dient dazu den Einfluss des hysteretischen Gedächtnisses zu quantifizieren. Mit analytischen Methoden wird gezeigt, dass sich ein Langzeitgedächtnis, sichtbar in der Autokorrelation der Systemantwort, entwickeln kann, selbst wenn das treibende Feld unkorreliert ist. Im Anschluss werden diese Resultate, m.H. von Simulationen, auf äußere Felder ausgeweitet, die selbst Korrelationen aufweisen können. Der zweite Teil der Arbeit befasst sich mit dem Einfluss einer endlichen Temperatur auf das Preisach-Modell. Es werden unterschiedliche Methoden besprochen, wie das Nichtgleichgewichtsmodell in seiner mikromagnetischen Interpretation mit Temperatur als Gleichgewichtseigenschaft verknüpft werden kann. Eine Formulierung wird genutzt, um die Magnetisierung von Nickelnanopartikeln in einer Fullerenmatrix zu simulieren und mit Experimenten zu vergleichen. Des Weiteren wird die Relaxationsdynamik des Gedächtnisses des Preisach-Modells bei endlichen Temperaturen untersucht. / The aim of this thesis is to investigate the Preisach model in regard to stochastically driving and temperature-related aspects. The Preisach model is a phenomenological model for systems with hysteresis which is often successfully applied. Hysteresis is a widespread phenomenon which is observed in nature and the key feature of certain technological applications. Further, it contributes to phenomena of interest in social science and economics as well. Prominent examples are the magnetization of ferromagnetic materials in an external magnetic field or the adsorption-desorption hysteresis observed in porous media. Hysteresis involves the development of a hysteresis memory, and multistability in the interrelations between external driving fields and system response. In the first part, we mainly investigate the response of Preisach hysteresis models driven by stochastic input processes with regard to autocorrelation functions to quantify the influence of the system’s memory. Using rigorous methods, it is shown that the development of a hysteresis memory is reflected in the possibility of long-time tails in the autocorrelation functions, even for uncorrelated driving fields. In the case of uncorrelated driving, these long-time tails in the autocorrelations of the system’s response are determined only by the tails of the involved densities. They will be observed if there are broad Preisach densities assigning a high weight to elementary loops of large width and narrow input densities such that rare extreme events of the input time series contribute significantly to the output for a long period of time. Afterwards, these results are extended by simulations to driving fields which themselves show correlations. It is shown that the autocorrelation of the output does not decay faster than the autocorrelation of the input process. Further, there is a possibility that long-term memory in the hysteretic response is more pronounced in the case of uncorrelated driving than in the case of correlated driving. The behavior of the output probability distribution at the saturation values is quite universal. It is not affected by the presence of correlations and allows conclusions whether the input density is much more narrow than the Preisach density or not. Moreover, the existence of effective Preisach densities is shown which define equivalence classes of systems of input and Preisach densities which lead to realizations of the same output variable. The asymptotic behavior of an effective Preisach density determines the asymptotic correlation decay of the system’s response in the case of uncorrelated driving. In the second part, temperature-related effects are considered. It is reviewed how the non-equilibrium Preisach model in its micromagnetic picture can be related to temperature within the framework of extended irreversible thermodynamics. The irreversible response of a ferromagnetic material, namely, Nickel nanoparticles in a fullerene matrix, is simulated. The model includes superparamagnetism where ferromagnetism breaks down at temperatures lower than the Curie temperature and the results are compared to experimental data. Furthermore, we adapt known results for the thermal relaxation of the system’s memory in the form of a front propagation in the Preisach plane derived basically from solving a master equation and by the use of a contradictory assumption. A closer look is taken at short time scales which dissolves the contradiction and shows that the known results apply, taking into account the fact that the dividing line propagation starts with an additional delay time depending on the front coordinates in the Preisach plane. Additionally, it is outlined how thermal relaxation behavior in the Preisach model of hysteresis can be studied using a Fokker-Planck equation. The latter is solved analytically in the non-hysteretic limit using eigenfunction methods. The results indicate a change in the relaxation behavior, especially on short time scales.

The basic idea of this paper is to outline a cross-curricular approach between mathematics and science. The aim is to close the often perceived gap between formal maths and authentic experience and to increase the students’ versatility in the use of mathematical terms. Students are to experience maths as logical, interesting and relevant through extra-mathematical references. Concrete physical or biological correlations may initiate mathematical activities, and mathematical terms are to be understood in logical contexts. Examples: physical experiments can lead to a comprehensive understanding of the concept of functions and of the intersection of medians in triangles. Biological topics can lead to the concepts of similarity and proportion as well as to the construction of pie charts. In the European ScienceMath Project a variety of teaching modules was developed and tested in secondary schools.

In dieser Arbeit wird die Abhängigkeit der Photolumineszenz (PL) von CdSe/ZnS-Nanokristallen von der Umgebung und der Einfluss der Filmdicke und -morphologie auf die optische Absorption von Farbstofffilmen untersucht sowie die Oberfläche von Hybridstrukturen durch Funktionalisierung mit Farbstoff analysiert. Untersuchungen von CdSe/ZnS-Nanokristallen in Toluol-Lösung zeigen, dass die PL-Intensität der Nanopartikel durch Zugabe des organischen Halbleiters TPD gequencht wird. Die zusätzliche Auswertung der PL-Lebensdauer verdeutlicht, dass die Abnahme (fast) vollständig durch statisches Quenchen, infolge der Abnahme der Anzahl der mittierenden Nanokristalle verursacht wird, bei einem Anstieg der langlebigsten Lebensdauerkomponente. Die Analyse der PL-Unterbrechung einzelner Nanokristalle auf PVA und Siliziumoxid sowie eingebettet in PS und TPD zeigt eine Ab- bzw. Zunahme der Häufigkeit langer An- bzw. Aus-Zeiten und somit eine deutliche Abhängigkeit der PL-Unterbrechung von den dielektrischen Eigenschaften der Umgebung. Bei Variation der Anregungsleistung zeigt sich für einzelne Nanokristalle auf Siliziumoxid und eingebettet in TPD eine lineare Zunahme der Blinkaktivität und eine Abnahme des An-Zeit-Anteils. Die Änderung der Verteilungen der An- und Aus-Zeiten zeigen eine deutliche Abhängigkeit von der Matrix. Die Untersuchung der optischen Absorption von aufgedampften MePTCDI- und Cl4MePTCDI-Filmen zeigt eine Verschiebung des energieärmsten optischen Überganges mit wachsender mittlere Filmdicke. Es wird ein (geometrisches) Schicht-Modell vorgestellt, das die energetische Verschiebung mit der mittleren Filmdicke korreliert und dabei die kristalline, nadelförmige Morphologie von MePTCDIFilmen und die amorphe Kugelkappen-Struktur von Cl4MePTCDI-Filmen berücksichtigt. Die Oberfläche von Hybridfilmen aus PMMA mit Siliziumoxid-Partikeln wird durch Anbindung von R6G an die Oxid-Partikel gezielt funktionalisiert. Die Ergebnisse von fluoreszenzmikroskopischen Untersuchungen zeigen, dass dadurch der Anteil der freien Oxid-Oberfläche bestimmt werden kann.

Capillary trapping plays a central role in the geological storage of CO2, oil recovery, and water soil infiltration. The key aim of this study is to investigate the impact of surface properties (wettability, roughness, heterogeneous mineral composition) on the dynamics of quasi-static fluid displacement process and capillary trapping efficiency in porous medium. We concluded that for homogeneous wet smooth glass beads surfaces, a transition in fluid displacement pattern occurs from a compact (for θ < 90°; imbibition process) to a fractal front-pattern (for θ > 90°; drainage process) leading to a crossover in capillary trapping efficiency from zero to maximum. The impact of surface roughness on capillary trapping efficiency was also studied, and an opposite trends in terms of wettability dependency was observed. Rough natural sands surfaces depicts a non-monotonous wettability dependency, i.e. a transition from maximal trapping (for θ < 90°) to no-trapping occurs (at θ = 90°), followed by an increase to medium trapping (for θ > 90°). For a fractional-wet media, the percolating cluster of hydrophobic sediments (connected hydrophobic pathways) characterize the fluid displacement pattern and trapping efficiency.

Als Stand der Technik sind einfache, kreisförmige Verrundungen zur Reduktion von Kerbspannungen an Querschnittsübergängen bekannt, für die aus Tabellenwerken / Diagrammen in der Literatur die Formzahl einfach abgelesen werden kann. Die Effizienz der Spannungsreduktion solcher Lösungen ist jedoch sehr begrenzt. Ziel der Arbeit ist es daher, dem Konstrukteur bzw. Berechnungsingenieur ein Verfahren in die Hand zu geben, mit dem er für Standardquerschnittsübergänge und Standardlastfälle "Nicht-Kreiskerben" ohne teure und zeitaufwendige FEM-Analyse einfach durch Nutzung geeigneter Formzahldiagramme auslegen kann. Dabei sind sogar Formzahlen von nahezu eins möglich, d.h., in der "Kerbe" bleibt praktisch nur noch die Nennspannung übrig. Die Präsentation ist zweitgeteilt: Im ersten Teil werden die Arbeitsmethoden bzw. Softwarefunktionen und verwendeten Softwarewerkzeuge vorgestellt: Dies sind die Programme Creo Parametric als vollparametrisches CAD-Werkzeug und Creo Simulate als p-FEM-Programm der Parametric Technology Coprporation (PTC). Der zweite Teil der Präsentation beschreibt den Gültigkeitsbereich sowie die untersuchten Kerbgeometrien: Die einfache kreisförmige Verrundung als Stand der Technik, die Zwei-Radien-Kerbe, die Baud-Kurve, die Methode der Zugdreiecke nach Claus Mattheck, die elliptische Kerbe sowie die konische Rundung als generalisierte elliptische Kerbe. Es wird kurz eine Bibliothek vorgestellt, mit der solche Kerben einfach ausgelegt werden können, d.h. Ihre exakte Geometrie festgelegt sowie die zugehörige Formzahl αk bestimmt werden kann. / Circular (one-radius) fillets are known as state-of-the-art for reducing notch stresses at cross section transitions. The stress concentration factor Kt of such geometries can be read out from diagrams/tables given in the literature. However, the efficiency of stress reduction of circular notches is very limited. The goal of the work therefor is to present a method for the designer/analyst how to design non-circular notches/fillets just by using suitable Kt-diagrams without time-consuming and expensive FEM analyses. Kt-numbers of nearly one are possible, that means in the "notch" just the nominal stress appears and no stress concentration takes place. The presentation has two parts: Part one describes the working methods and software functions as well as software tools: Creo Parametric as fully-parametric CAD program and Creo Simulate as embedded p-FEM-tool from Parametric Technology Corporation (PTC) have been used. The second part describes the range of validity and the examined notch geometries: The one-radius fillet as state-of-the-art, the two-radii filet, the Baud-curve, the method of tensile triangles from Claus Mattheck, the standard elliptical fillet and the conical round as generalized elliptical fillet. A notch layout library is shortly presented that allows to design such fillets, that means exactly determine the notch geometry and the related stress concentration factor Kt.

This thesis deals with regularization parameter selection methods in the context of Tikhonov-type regularization with Poisson distributed data, in particular the reconstruction of images, as well as with the identification of the volatility surface from observed option prices. In Part I we examine the choice of the regularization parameter when reconstructing an image, which is disturbed by Poisson noise, with Tikhonov-type regularization. This type of regularization is a generalization of the classical Tikhonov regularization in the Banach space setting and often called variational regularization. After a general consideration of Tikhonov-type regularization for data corrupted by Poisson noise, we examine the methods for choosing the regularization parameter numerically on the basis of two test images and real PET data. In Part II we consider the estimation of the volatility function from observed call option prices with the explicit formula which has been derived by Dupire using the Black-Scholes partial differential equation. The option prices are only available as discrete noisy observations so that the main difficulty is the ill-posedness of the numerical differentiation. Finite difference schemes, as regularization by discretization of the inverse and ill-posed problem, do not overcome these difficulties when they are used to evaluate the partial derivatives. Therefore we construct an alternative algorithm based on the weak formulation of the dual Black-Scholes partial differential equation and evaluate the performance of the finite difference schemes and the new algorithm for synthetic and real option prices.

No description available.

No description available.