Understanding the bearing response of the footings on layered soils has always been a challenge for researchers. Due to the limitations of analytical and empirical solutions it had been difficult to understand the true bearing behavior. Some researchers have tried solving this problem by numerical analysis and have found some success. In this study the numerical analysis approach has been applied using a commercial tool FLAC (Fast Lagrangian Analysis of Continua) to study the bearing response of surface footings on layered clays. First, small deformation analyses were taken up to study the undrained bearing response of strip and circular footings resting on a horizontally layered strong over a soft clay foundation, and then over soft over strong clay foundation. In the end application of large strain mode of FLAC was explored to investigate the large deformation behavior of the strip footing resting on the surface of a strong over soft clay foundation. All models were run by applying velocity loading and a elastic-perfectly plastic Tresca yield criterion has been used. The results are compared with published Finite Element Method (FEM) results, and with analytical, empirical and semi-empirical solutions. It was found that bearing capacity results from the present small-strain FLAC analyses agree well with the FEM results. However, these results in most of the cases tend to differ (as much as 49% for certain layered clay foundations) from those predicted with analytical, empirical and semi-empirical solutions, mainly due to the assumptions made in these solutions. Since no such assumptions are made in the present FLAC analyses, the results and the methodology of this thesis can be applied to predict the bearing capacity of the practical problems. Application of the large-strain mode of FLAC to study the large deformation of shallow foundations has pointed out a limitation of FLAC in completing such analyses. However, it is observed from the early trends of these analyses that whereas the small deformation analysis may under estimate the ultimate bearing capacity for certain cases of layered foundations where the upper clay is moderately stiffer than the lower clay layer, it might also over predict the ultimate bearing capacity for other cases when the upper clay is very stiff in comparison to the lower clay layer. / February 2007

Thin metal films have found their use in many magnetic devices. They form pseudo two-dimensional systems, where the mechanisms for the magnetic interactions between the layers are not completely understood. Layered crystal structures have an advantage over such artificial systems, since the layers can be strictly mono-atomic without any unwanted admixture. In this study, some model systems of layered magnetic crystal structures and their solid solutions have been investigated by x-ray and neutron diffraction, Mössbauer and electron spectroscopy, heat-capacity and magnetic measurements, and first-principle electronic structure calculations, with the goal of deepening our understanding through controlled chemical synthesis. The compounds TlCo2S2, TlCo2Se2 and their solid solution TlCo2Se2-xSx, all containing well separated cobalt atom sheets, order with the moments ferromagnetically aligned within the sheets. In TlCo2S2, the net result is ferromagnetism, while TlCo2Se2 exhibits antiferromagnetism. The inter-layer distance is crucial for the long-range coupling, and it was varied systematically through Se-S substitution. The incommensurate helical magnetic structure found for TlCo2Se2 (x = 0) prevails in the composition range 0 ≤ x ≤ 1.5 but the pitch of the helix changes. The accompanying reduction in inter-layer distance on sulphur substitution varies almost linearly with the coupling angle of the helix. An additional competing commensurate helix (90°) appears in the medium composition range (found for x = 0.5 and 1.0). The systems TlCo2-xMexSe2 show helical magnetic ordering for Me = Fe or Cu, while a collinear antiferromagnetic structure occurs for Me = Ni. Magnetic order is created by iron substitution for copper in the Pauli paramagnetic TlCu2Se2, but now with the moments perpendicular to the metal sheets. TlCrTe2 forms a quite different crystal structure, with intra-layer ferromagnetic alignment and net collinear antiferromagnetism. In contrast to the other phases, the values of the moments conform well to a localised model for Cr3+.

Infinitely divisible distributions and processes have been the object of extensive research not only from the theoretical point of view but also for practical use, for example, in queueing theory or mathematical finance. In this thesis, we will study some of their subclasses with a view towards financial modeling. As generalizations of stable distributions, we study the tempered stable distributions and introduce the new classes of layered stable distributions as well as the mixed stable distributions, along with the corresponding Levy processes. As a further generalization of infinitely divisible processes, fractional tempered stable motions are defined. These theoretical studies will be complemented by some more practical ones, such as the simulation of sample paths, parameter estimations, financial portfolio hedging, and solving stochastic differential equations.

The subject of this dissertation is to develop a rigorous transverse-mode integral equation formulation for analyzing TE/TM electromagnetic mode field solutions for dielectric waveguides. The main topics are composed of two related parts. The first part deals with scalar problems. In which we propose a transverse-mode integral-equation formulation for problems such as mode solutions of the ridged microwave waveguides. This same technique also applies to EM waves scattering off the facet of dielectric slab waveguides terminating in free space. For both problems we constructed a specifically chosen basis for the unknown tangential field functions, and we were able to reduce the kernel matrix size by more than one half without noticeable degradation of the field solutions. In the second part of the thesis, we apply a full-vector integral-equation formulation to analyze modal characteristics of the complex, two-dimensional, rectangular-like dielectric waveguide that is divisible into vertical slices of one-dimensional layered structures. The entire electromagnetic vector mode field solution is completely determined by the y-component electric and magnetic field functions on the interfaces between slices. These interfacial functions are governed by a system of vector-coupled transverse-mode integral equations (VCTMIE) whose kernels are made of orthonormal sets of both TE-to-y and TM-to-y modes from each slice. Finally, we show the numerical results to present the stable and quick convergence of this method as well as to improve the Gibb¡¦s phenomenon in the recreation of the transverse fields.

Trapping centres in as-grown TlInS2 layered single crystals have been studied by using a thermally stimulated current (TSC) technique. TSC measurements have been performed in the temperature range of 10-300 K with various heating rates. Experimental evidence has been found for the presence of five trapping centres with activation energies 12, 14, 400, 570 and 650 meV. Their capture cross-sections and concentrations were also determined. It is concluded that in these centres retrapping is negligible as confirmed by the good agreement between the experimental results and the theoretical predictions of the model that assumes slow retrapping. An exponential distribution of traps was revealed from the analysis of the TSC data obtained at different light excitation temperatures. The transmission and reflection spectra of TlInS2 crystals were measured over the spectral region of 400-1100 nm to determine the absorption coefficient and refractive index. The analysis of the room temperature absorption data revealed the coexistence of the indirect and direct transitions. The absorption edge was observed to shift toward the lower energy values as temperature increases from 10 to 300 K. The oscillator and the dispersion energies, and the zero-frequency refractive index were also reported. Furthermore, the chemical composition of TlInS2 crystals was determined from energy dispersive spectroscopic analysis. The parameters of monoclinic unit cell were found by studying the x-ray powder diffraction.

The prediction of moisture and contaminant transport through unsaturated soil to ground water is becoming increasingly important in the fields of hydrology, agriculture and environmental engineering. Computer aided simulation techniques enables one to conduct a series of systematic numerical experiments to analyze flow phenomenon in subsurface hydrology under various physical and chemical processes. The flow movement depends upon medium characteristics, initial and boundary conditions, which reflect, physical processes occurring below the ground. To understand the effects of physical process an efficient and accurate model is needed. Thus the model developed must be able to handle varied initial and boundary conditions. In this regard, infiltration into a very dry soil becomes a very important problem of study. Most of the earlier numerical models developed are concentrated on the development of an efficient algorithm or the modelling of a particular process which govern the flow in unsaturated or saturated-unsaturated homogeneous medium. Not much work has been done on the analysis of variably saturated flow in layered soil medium. Models to simulate unsaturated flow through dry soils, especially through layered soils with varied boundary conditions are very limited. Further, not much studies have been reported in the literature on the prediction of seepage face development and the phreatic surface movement in variably saturated media with layering. These aspects are very important in determining the flow field and the discharge from the domain. A detailed literature review covering above aspects has been made and is reported in this thesis. In the present work, two dimensional numerical models to predict the movement of wetting front in unsaturated domain and the movement of the phreatic surface in homogeneous and layered porous media under various initial and boundary conditions are developed based on finite difference and finite volume techniques. These models can handle flow in both rectangular flow domains and radial flow domains. The initial condition settings include the handling of very dry soil medium without any transformation of the governing equation, handling of infiltration and constant head conditions at the boundaries under steady state as well as transient scenarios. The models are also able to handle various soil moisture characteristics which depict the nonlinear behaviour between hydraulic conductivity, moisture content and pressure head in a soil media. A mixed form of the governing partial differential equation is used in the present study as it leads to better mass conservation. The finite difference model uses a central difference approximation for the space derivatives and an Eulerian backward difference approximation for the time derivative. The fully implicit formulation is solved iteratively using Strongly Implicit Procedure after making Picard approximation for the highly nonlinear coefficients. The process of infiltration into an initially dry soil leads to the development of a steep wetting front. As the finite volume technique is naturally an upwind method, it is expected to play a positive role in modelling such processes accurately. Hence, a finite volume model is also developed by approximating the convective part using a MUSCL approach and a fully implicit central difference method for the diffusive part of the governing equation. The models developed are validated using both experimental data and numerical solutions for problems reported in the literature. The validation problems cover a wide range of physical scenarios such as: infiltration into a very dry soil, infiltration into a dry soil column with gravity drainage, development of water table mound, steady state drainage in a sand filled wedge shaped tank with seepage face development and transient seepage face development in a rectangular domain. Five test problems are used for the validation of the models. The developed models perform very well for the test problems considered, indicating the models' capability in handling such situations. The results obtained by using the present models for simulating flow through highly unsaturated (very dry) soils show that the models perform very well when compared with models which use transformation techniques to handle such problems. The performance of the present models in comparison with the experimental data and numerical models available in the literature show the suitability of the present models in handling such situations. The present models are also used to analyse various types of unsaturated flow problems with varying initial and boundary conditions. The boundary conditions considered are no flow and /or free flow conditions along the left, right and bottom boundaries with infiltration condition along a part of the top boundary. For the various cases considered in the present study, infiltration rate varies from 5 cm/day to 50cm/day through an initially very dry soil of -15000 cm pressure head in homogeneous and layered soils. Different types of soil media considered vary from sandy loam, loam and clay with horizontal and vertical layering of these soils. A total number of 14 cases are analysed. The results are discussed in terms of pressure head variation in the flow domain along with moisture redistribution for all the cases under consideration. It is observed from these studies that the infiltration rate play an important role on the wetting front movement through layered soils depending on the type of layering and the boundary conditions considered. The soil properties of various layers affect the movement of wetting front by changing the direction of movement. Even though the wetting front movement is predominantly vertical, there is a tendency for the wetting front to move in the horizontal direction as it moves from a coarse soil to fine soil. It is also observed that the vertical layering of soils with different hydraulic conductivity helps in redirecting the flow towards the bottom boundary through the neighboring coarser layers. As finite volume method is more suitable for simulating sharp fronts, it is expected to perform better than finite difference method for simulating infiltration into very dry soils. So, a comparison is made between the performance of these two models by using the above test problems. It is observed from these studies that the performance of both the models are same except that the finite volume method takes much more CPU time than the finite difference model. Considering the type of problems tested, it is observed that for modelling unsaturated and saturated-unsaturated flows, finite difference method is better in comparison to finite volume method. It may be due to the predominant diffusive characteristics of the governing equation even while modelling flow through very dry soils. Proper estimation of the seepage height is an important aspect in finding the discharge through the porous medium. It is observed from the literature that the use of a saturated flow model in such situations can lead to an underestimation of the discharge through the porous medium. This effect is more important when dealing with small dimension problems. It is also observed that various parameters which govern the moisture movement through saturated-unsaturated regions affect proper estimation of the seepage face height and there by discharge. Various factors like effect of boundary conditions, type of soil layering, problem dimension and aspect ratio on seepage face development and the associated phreatic surface formation is studied in the present work. It is seen from the present study that the seepage face development is more in rectangular flow domain than in radial flow domain for both homogeneous and layered soils. It is also seen that the seepage face development in rectangular problems are more sensitive than radial flow problems for various factors considered. The seepage height is also influenced by the tail water level. It is seen from the present study that as the tail water level increases the seepage face reduces with no seepage face development for some of the cases studied. This influence is relatively less for radial flow problems. As the length of the domain increases the seepage height decreases. It is seen that for different cases with same horizontal dimension, as the height of the domain increases the seepage face height also increases. This phenomenon is observed for both homogeneous and layered soil medium. The influence of the aspect ratio, which is the ratio of the length to height of the domain indicate that as the aspect ratio increases the seepage height decreases. The type of the soil layering is observed to have a very strong influence on the seepage face development. The study for understanding the effect of soil layering on the development of seepage face and phreatic surface suggest that as the coarseness of the material increases, the phreatic surface become flatter and its steepness increases with the fineness of the soil. The present model is also used for studying the transient phreatic surface movement and the seepage face development. This is studied for homogeneous and layered rectangular soil medium. The present study is used to understand the effect of specific storage on the phreatic surface movement and the seepage face development. The studies indicate that the influence of specific storage on the seepage face development is insignificant in homogeneous soils with only very little effect in the early time for longer domains. It is also observed that the influence of the specific storage is significant in the case of layered soils. This effect depends on the type of layering and the problem dimension and is observed to have influence for relatively longer period. This observation suggests the importance of specific storage on transient seepage face development. When the specific storage effect is considered the drainage of the soil become faster resulting in a faster decline of the phreatic surface with time. The influence of specific storage is also studied considering the problem dimension effect. It is seen that as the aspect ratio increases, the effect of specific storage on the phreatic surface development decreases. The studies with change in the upstream boundary condition from a constant head to a no flow condition indicate that the effect of specific storage has no significant influence on the phreatic surface development for both homogeneous and layered soils.

Im Rahmen der vorliegenden Arbeit ist es gelungen, ein Siliciumsubnitrid der Summenformel Si2N chemisch und strukturell zu charakterisieren. Die braune, metastabile Verbindung ist über eine topotaktische Reaktion aus der Zintl-Phase Calciumdisilicid und Ammoniumbromid im molaren Verhältnis 1:2 zugänglich. Charakteristisch für das Siliciumsubnitrid sind eine schichtartige Morphologie und perfekte Spaltbarkeit parallel zu den Schichten. Thermoanalytische und röntgenografische Untersuchungen belegen, dass die Reaktion im Temperaturbereich 165°- 350°C abläuft. Beim Einsatz pulverförmiger Eduktmischungen wird das Siliciumsubnitrid als röntgenamorphes Pulver im mikroskopischen Gemisch mit kristallinem CaBr2 erhalten. Die Abtrennung des Calciumbromids gelingt bisher nur unvollständig. Mit spektroskopischen Methoden (NMR, IR und Raman) konnten die Baueinheiten im Siliciumsubnitrid identifiziert werden. Stickstoff liegt im Siliciumsubnitrid in Form einer trigonalen [N(Si)3]-Koordination vor. Über REDOR-NMR-Experimente wurde belegt, dass das Subnitrid zwei unterschiedliche Siliciumspezies, eine [Si(Si4)]- und eine [Si(Si,N3)]-Umgebung, enthält. Ergebnisse elektronenmikroskopischer Untersuchungen (REM, TEM) sind mit der Bildung des Siliciumsubnitrids über eine topotaktische Reaktion im Sinne des Erhalts schichtartiger Strukturverbände aus dem Calciumdisilicid vereinbar. Im Transmissionselektronenmikroskop werden extrem dünne Schichten beobachtet. Beugungsexperimente (SAD) an partiell geordneten Bereichen zeigen den Erhalt eines hexagonalen Reflexmusters. Die topotaktische Reaktion wurde auch mit CaSi2-Einkristallen durchgeführt, deren Oberflächen durch Aufsublimation mit Ammoniumbromid belegt waren. Die Untersuchung von Edukt und Produkt mit Röntgen-Einkristallbeugungsmethoden deutet auf weitgehende Erhaltung einer periodischen Struktur während der topotaktischen Reaktion hin. Die neue Verbindung kann durch elektrisch neutrale Schichtpakete von etwa 650 pm beschrieben werden.

In der Dissertation wurden Nanokomposite mit unterschiedlichen Kautschuken (HNBR, EPDM, MAH-g-EPDM) als Basismaterial sowie diversen modifizierten Schichtsilikaten als Füllstoff hergestellt und charakterisiert. Untersucht wurden die sich ausbildenden Strukturen bzw. die Morphologie (Aggregation, mögliche Orientierungen), die mechanischen Eigenschafte (Verstärkungswirkung) sowie die Füllstoff-Füllstoff-Wechselwirkungen und die Polymer-Füllstoff-Wechselwirkungen.

In this bachelor thesis we report on our numerical investigations into the optimal design of protective multi-layer coatings subject to an external force of Hertzian form. In view of mechanical reliablity and durability of the substrate and the coating we aim to find the best composition of given materials with the least computational effort. Numerical studies are carried out using the simulation software ELASTICA being the first non-FEM approach for the computation of stress fields within multi-layer coated, elastic materials. We thereby made use of the massive parallel computer CLiC (Chemnitzer Linux Cluster) where we ran our Windows based application in a Wine Environment. The outcome of the optimization is in general very sensitive towards the input parameters(i.e., material properties) which are not always available in the desired accuracy. However, the scheme outlined in this work is shown to produce very good results and could contribute a great deal to find optimal solutions for real applications. / Diese Bachelorarbeit befasst sich mit numerischen Untersuchungen zum optimalen Design von schützenden Mehrschichtbeschichtungen, die einer externen, Hertzschen Last ausgesetzt sind. Hinsichtlich der mechanischen Zuverlässigkeit und Haltbarkeit von Substrat und Beschichtung, versuchen wir die beste Zusammensetzung von gegebenen Materialien mit möglichst geringem Rechenaufwand zu finden. Die numerischen Berechungen wurden mit der Simulationssoftware ELASTICA durchgeführt, welches das erste kommerzielle, nicht-FEM-basierte Programm zur Berechnung von Stressfeldern innerhalb mehrfach beschichteter, elastischer Materialien darstellt. Dafür benutzten wir auf dem massiven Parrallelrechner CLiC (Chemnitzer Linux Cluster) unsere Windows basierte Anwendung unter der Emulationssoftware Wine. Das Ergebnis der Optimierung hängt im allgemeinen sehr stark von der Qualität der Eingangsparameter (z.B. Materialeigenschaften) ab, welche nicht immer in der erwünschten Genauigkeit vorliegen. Es wird gezeigt, dass die in dieser Arbeit vorgestellte Vorgehensweise sehr gute Resultate liefert und für reale Anwendungen einen äusserst ressourcenschonenden Lösungsweg darstellt.

Solid oxide fuel cells (SOFCs) offer the advantages of (i) employing less expensive catalysts compared to the expensive Pt catalyst used in proton exchange membrane fuel cells and (ii) directly using hydrocarbon fuels without requiring external fuel reforming due to the high operating temperature. However, the conventional high operating temperatures of 800 - 1000 °C lead to interfacial reactions and thermal expansion mismatch among the components and limitations in the choice of electrode and interconnect materials. These problems have prompted a lowering of the operating temperature to an intermediate range of 500 - 800 °C, but the poor oxygen reduction reaction kinetics of the conventional La[subscript 1-x]Sr[subscript x]MnO₃ perovskite cathode remains a major obstacle for the intermediate temperature SOFC. In this regard, cobalt-containing oxides with perovskite or perovskite-related structures have been widely investigated, but they suffer from large thermal expansion coefficient (TEC) mismatch with the electrolytes. With an aim to lower the TEC and maximize the electrochemical performance, this dissertation focuses on perovskite-related and trigonal RBaCo₄O₇-based oxide cathode materials. First, the effect of M = Fe and Cu in the perovskite-related layered LnBaCo₂₋xMxO₊[delta] (Ln = Nd and Gd) oxides has been investigated. The Fe and Cu substitutions lower the polarization resistance and offer fuel cell performance comparable to that of La[subscript 1-x]Sr[subscript x]CoO₃₋[delta] perovskite due to improved chemical stability with the electrolyte and a better matching of the TEC with those of standard electrolytes. Second, the perovskite-related intergrowth oxides Ln(Sr,Ca)₃Fe₁.₅Co₁.₅O₀ and La₁.₈₅Sr₁.₁₅Cu[subscript 2-x]Co[subscript x]O[subscript 6 +delta] and their composites with gadolinia-doped ceria (GDC) have been investigated. The electrical conductivity, TEC, and catalytic activity increase with increasing Co content. The composite cathodes exhibit enhanced electrochemical performance due to lower TEC and increased triple-phase boundary. Third, RBa(Co,Zn)₄O₇ (R = Y, Ca, and In) oxides with a trigonal structure and tetrahedral-site Con+ ions have been investigated. The chemical instability normally encountered with this class of oxides has been overcome by appropriate cationic substitutions as in (Y₀.₅Ca₀.₅)Ba(Co₂.₅Zn₁.₅)O₇ and (Y₀.₅In₀.₅)BaCo₃ZnO₇. With an ideal matching of TEC with those of standard electrolytes, the RBa(Co,Zn)₄O₇ (R = Y, Ca, and In) + GDC composite cathodes exhibit low polarization resistance and electrochemical performance comparable to that of perovskite oxides. / text