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Embedded systems have become ubiquitous in everyday life, and especially in the automotive industry. New applications challenge their design by introducing a new class of problems that are based on a detailed analysis of the environmental situation. Situation analysis systems rely on models and algorithms of the domain of computational geometry. The basic model is usually an Euclidean plane, which contains polygons to represent the objects of the environment. Usual implementations of computational geometry algorithms cannot be directly used for safety-critical systems. First, a strict analysis of their correctness is indispensable and second, nonfunctional requirements with respect to the limited resources must be considered. This thesis proposes a layered approach to a polygon-processing system. On top of rational numbers, a geometry kernel is formalised at first. Subsequently, geometric primitives form a second layer of abstraction that is used for plane sweep and polygon algorithms. These layers do not only divide the whole system into manageable parts but make it possible to model problems and reason about them at the appropriate level of abstraction. This structure is used for the verification as well as the implementation of the developed polygon-processing library.

The present work deals with the (global and local) modeling of the windfield on the real topography of Rheinland-Pfalz. Thereby the focus is on the construction of a vectorial windfield from low, irregularly distributed data given on a topographical surface. The developed spline procedure works by means of vectorial (homogeneous, harmonic) polynomials (outer harmonics) which control the oscillation behaviour of the spline interpoland. In the process the characteristic of the spline curvature which defines the energy norm is assumed to be on a sphere inside the Earth interior and not on the Earth’s surface. The numerical advantage of this method arises from the maximum-minimum principle for harmonic functions.

The present thesis deals with multi-user mobile radio systems, and more specifically, the downlinks (DL) of such systems. As a key demand on future mobile radio systems, they should enable highest possible spectrum and energy efficiency. It is well known that, in principle, the utilization of multi-antennas in the form of MIMO systems, offers considerable potential to meet this demand. Concerning the energy issue, the DL is more critical than the uplink. This is due to the growing importance of wireless Internet applications, in which the DL data rates and, consequently, the radiated DL energies tend to be substantially higher than the corresponding uplink quantities. In this thesis, precoding schemes for MIMO multi-user mobile radio DLs are considered, where, in order to keep the complexity of the mobile terminals as low as possible, the rationale receiver orientation (RO) is adopted, with the main focus to further reduce the required transmit energy in such systems. Unfortunately, besides the mentioned low receiver complexity, conventional RO schemes, such as Transmit Zero Forcing (TxZF), do not offer any transmit energy reductions as compared to conventional transmitter oriented schemes. Therefore, the main goal of this thesis is the design and analysis of precoding schemes in which such transmit energy reductions become feasible - under virtually maintaining the low receiver complexity - by means of replacing the conventional unique mappings by the selectable representations of the data. Concerning the channel access scheme, Orthogonal Frequency Division Multiplex (OFDM) is presently being favored as the most promising candidate in the standardization process of the enhanced 3G and forthcoming 4G systems, because it allows a very flexible resource allocation and low receiver complexity. Receiver oriented MIMO OFDM multi-user downlink transmission, in which channel equalization is already performed in the transmitter of the access point, further contributes to low receiver complexity in the mobile terminals. For these reasons, OFDM is adopted in the target system of the considered receiver oriented precoding schemes. In the precoding schemes considered the knowledge of channel state information (CSI) in the access point in the form of the channel matrix is essential. Independently of the applied duplexing schemes FDD or TDD, the provision of this information to the access point is always erroneous. However, it is shown that the impact of such deviations not only scales with the variance of the channel estimation errors, but also with the required transmit energies. Accordingly, the reduced transmit energies of the precoding schemes with selectable data representation also have the advantage of a reduced sensitivity to imperfect knowledge of CSI. In fact, these two advantages are coupled with each other.

Elastomeric and other rubber-like materials are often simultaneously exposed to short- and long-time loads within engineering applications. When aiming at establishing a general simulation tool for viscoelastic media over these different time scales, a suitable material model and its corresponding material parameters can only be determined if an appropriate number of experimental data is taken into account. In this work an algorithm for the identification of material parameters for large strain viscoelasticity is presented. Thereby, data of multiple experiments are considered. Based on this method the experimental loading intervals for long-time experiments can be shortened in time and the parameter identification procedure is now referred to experimental data of tests under short- and long-time loads without separating the parameters due to these different time scales. The employed viscoelastic material law is based on a nonlinear evolution law and valid far from thermodynamic equilibrium. The identification is carried out by minimizing a least squares functional comparing inhomogeneous displacement fields from experiments and FEM simulations at given (measured) force loads. Within this optimization procedure all material parameters are identified simultaneously by means of a gradient based method for which a semi-analytical sensitivity analysis is calculated. Representative numerical examples are referred to measured data for different polyurethanes. In order to show the general applicability of the identification method for multiple tests, in the last part of this work the parameter identification for small strain plasticity is presented. Thereby three similar test programs on three specimen of the aluminum alloy AlSi9Cu3 are analyzed, and the parameter sets for the respective individual identifications, and for the combination of all tests in one identification, is compared.

Modelling languages are important in the process of software development. The suitability of a modelling language for a project depends on its applicability to the target domain. Here, domain-specific languages have an advantage over more general modelling languages. On the other hand, modelling languages like the Unified Modeling Language can be used in a wide range of domains, which supports the reuse of development knowledge between projects. This thesis treats the syntactical and semantical harmonisation of modelling languages and their combined use, and the handling of complexity of modelling languages by providing language subsets - called language profiles - with tailor-made formal semantics definitions, generated by a profile tool. We focus on the widely-used modelling languages SDL and UML, and formal semantics definitions specified using Abstract State Machines.

In the theoretical part of this thesis, the difference of the solutions of the elastic and the elastoplastic boundary value problem is analysed, both for linear kinematic and combined linear kinematic and isotropic hardening material. We consider both models in their quasistatic, rate-independent formulation with linearised geometry. The main result of the thesis is, that the differences of the physical obervables (the stresses, strains and displacements) can be expressed as composition of some linear operators and play operators with respect to the exterior forces. Explicit homotopies between both solutions are presented. The main analytical devices are Lipschitz estimates for the stop and the play operator. We present some generalisations of the standard estimates. They allow different input functions, different initial memories and different scalar products. Thereby, the underlying time involving function spaces are the Sobolov spaces of first order with arbitrary integrability exponent between one and infinity. The main results can easily be generalised for the class of continuous functions with bounded total variation. In the practical part of this work, a method to correct the elastic stress tensor over a long time interval at some chosen points of the body is presented and analysed. In contrast to widespread uniaxial corrections (Neuber or ESED), our method takes multiaxiality phenomena like cyclic hardening/softening, ratchetting and non-masing behaviour into account using Jiang's model of elastoplasticity. It can be easily adapted to other constitutive elastoplastic material laws. The theory for our correction model is developped for linear kinematic hardening material, for which error estimated are derived. Our numerical algorithm is very fast and designed for the case that the elastic stress is piecewise linear. The results for the stresses can be significantly improved with Seeger's empirical strain constraint. For the improved model, a simple predictor-correcor algorithm for smooth input loading is established.

In the present work the modelling and numerical treatment of discontinuities in thermo-mechanical solids is investigated and applied to diverse physical problems. From this topic a structure for this work results, which considers the formulation of thermo-mechanical processes in continua in the first part and which forms the mechanical and thermodynamical framework for the description of discontinuities and interfaces, that is performed in the second part. The representation of the modelling of solid materials bases on the detailed derivation of geometrically nonlinear kinematics, that yields different strain and stress measures for the material and spatial configuration. Accordingly, this results in different formulations of the mechanical and thermodynamical balance equations. On these foundations we firstly derive by means of the concepts of the plasticity theory an elasto-plastic prototype-model, that is extended subsequently. In the centre of interest is the formulation of damage models in consideration of rate-dependent material behaviour. In the next step follows the extension of the isothermal material models to thermo-mechanically coupled problems, whereby also the special case of adiabatic processes is discussed. Within the representation of the different constitutive laws, the importance is attached to their modular structure. Moreover, a detailed discussion of the isothermal and the thermo-mechanically coupled problem with respect to their numerical treatment is performed. For this purpose the weak forms with respect to the different configurations and the corresponding linearizations are derived and discretized. The derived material models are highlighted by numerical examples and also proved with respect to plausibility. In order to take discontinuities into account appropriate kinematics are introduced and the mechanical and thermodynamical balance equations have to be modified correspondingly. The numerical description is accomplished by so-called interface-elements, which are based on an adequate discretization. In this context two application fields are distinguished. On the one side the interface elements provide a tool for the description of postcritical processes in the framework of localization problems, which include material separation and therefore they are appropriate for the description of cutting processes. Here in turn one has to make the difference between the domain-dependent and the domain-independent formulation, which mainly differ in the definition of the interfacial strain measure. On the other side material properties are attached to the interfaces whereas the spatial extension is neglectable. A typical application of this type of discontinuities can be found in the scope of the modelling of composites, for instance. In both applications the corresponding thermo-mechanical formulations are derived. Finally, the different interface formulations are highlighted by some numerical examples and they are also proved with respect to plausibility.

The main aim of this work was to obtain an approximate solution of the seismic traveltime tomography problems with the help of splines based on reproducing kernel Sobolev spaces. In order to be able to apply the spline approximation concept to surface wave as well as to body wave tomography problems, the spherical spline approximation concept was extended for the case where the domain of the function to be approximated is an arbitrary compact set in R^n and a finite number of discontinuity points is allowed. We present applications of such spline method to seismic surface wave as well as body wave tomography, and discuss the theoretical and numerical aspects of such applications. Moreover, we run numerous numerical tests that justify the theoretical considerations.

In this dissertation we present analysis of macroscopic models for slow dense granular flow. Models are derived from plasticity theory with yield condition and flow rule. Corner stone equations are conservation of mass and conservation of momentum with special constitutive law. Such models are considered in the class of generalised Newtonian fluids, where viscosity depends on the pressure and modulo of the strain-rate tensor. We showed the hyperbolic nature for the evolutionary model in 1D and ill-posed behaviour for 2D and 3D. The steady state equations are always hyperbolic. In the 2D problem we derived a prototype nonlinear backward parabolic equation for the velocity and the similar equation for the shear-rate. Analysis of derived PDE showed the finite blow up time. Blow up time depends on the initial condition. Full 2D and antiplane 3D model were investigated numerically with finite element method. For 2D model we showed the presence of boundary layers. Antiplane 3D model was investigated with the Runge Kutta Discontinuous Galerkin method with mesh addoption. Numerical results confirmed that such a numerical method can be a good choice for the simulations of the slow dense granular flow.

In the thesis the author presents a mathematical model which describes the behaviour of the acoustical pressure (sound), produced by a bass loudspeaker. The underlying physical propagation of sound is described by the non--linear isentropic Euler system in a Lagrangian description. This system is expanded via asymptotical analysis up to third order in the displacement of the membrane of the loudspeaker. The differential equations which describe the behaviour of the key note and the first order harmonic are compared to classical results. The boundary conditions, which are derived up to third order, are based on the principle that the small control volume sticks to the boundary and is allowed to move only along it. Using classical results of the theory of elliptic partial differential equations, the author shows that under appropriate conditions on the input data the appropriate mathematical problems admit, by the Fredholm alternative, unique solutions. Moreover, certain regularity results are shown. Further, a novel Wave Based Method is applied to solve appropriate mathematical problems. However, the known theory of the Wave Based Method, which can be found in the literature, so far, allowed to apply WBM only in the cases of convex domains. The author finds the criterion which allows to apply the WBM in the cases of non--convex domains. In the case of 2D problems we represent this criterion as a small proposition. With the aid of this proposition one is able to subdivide arbitrary 2D domains such that the number of subdomains is minimal, WBM may be applied in each subdomain and the geometry is not altered, e.g. via polygonal approximation. Further, the same principles are used in the case of 3D problem. However, the formulation of a similar proposition in cases of 3D problems has still to be done. Next, we show a simple procedure to solve an inhomogeneous Helmholtz equation using WBM. This procedure, however, is rather computationally expensive and can probably be improved. Several examples are also presented. We present the possibility to apply the Wave Based Technique to solve steady--state acoustic problems in the case of an unbounded 3D domain. The main principle of the classical WBM is extended to the case of an external domain. Two numerical examples are also presented. In order to apply the WBM to our problems we subdivide the computational domain into three subdomains. Therefore, on the interfaces certain coupling conditions are defined. The description of the optimization procedure, based on the principles of the shape gradient method and level set method, and the results of the optimization finalize the thesis.

Haustoria of the rust fungus pathogen Uromyces fabae deliver RTP1 (Rust Transferred Protein1) into host plant cells. In this work, different heterologous expression systems were used to study RTP1 biological function as well as RTP1 transfer mechanism. The first part of this thesis focused on the identification of the subcellular target compartment of RTP1 in plant cells. In this respect we could identify a functional bipartite nuclear localization signal within RTP1. However, stable and transient expression studies of RTP1 in different plant species, including the host plant Vicia faba, interfered with plant cell vitality but did not result in detection of RTP1 protein. These findings led us to propose that RTP1 interferes with plant gene expression. However, the molecular basis of this interference remains unclear. By deletion studies, we could localize the active region of RTP1 within a 45 amino acid central domain. In the second part of this study, two different lines of approaches were taken to study RTP1 transfer mechanism. First, transient expression of secreted RTP1 (sRTP1) also interfered with plant cell vitality. Addition of an endoplasmic reticulum retention signal abolished sRTP1 interference with plant cell vitality, suggesting that RTP1 can reenter the plant cell from the apoplast after secretion in the absence of the pathogen. We have identified a PEST-like region within RTP1, however, contribution of this region to the stability of RTP1 is not clear. Site directed mutagenesis analysis showed that the PEST-like region is likely to play a role during the transfer of RTP1 through plant plasma membrane. In the second line of approach, we established a recombinant delivery model, using Ustilago maydis/Zea mays pathosystem, to pursue RTP1 translocation into the plant cell. Our results indicate that U. maydis is capable of secreting high amounts of recombinant RTP1, showing similar glycosylation pattern as RTP1 secreted from rust haustoria. Our data propose the use of this model system to study RTP1 domains mediating its entry into the plant cell. Haustoria of the rust fungus pathogen Uromyces fabae deliver RTP1 (Rust Transferred Protein1) into host plant cells. In this work, different heterologous expression systems were used to study RTP1 biological function as well as RTP1 transfer mechanism. The first part of this thesis focused on the identification of the subcellular target compartment of RTP1 in plant cells. In this respect we could identify a functional bipartite nuclear localization signal within RTP1. However, stable and transient expression studies of RTP1 in different plant species, including the host plant Vicia faba, interfered with plant cell vitality but did not result in detection of RTP1 protein. These findings led us to propose that RTP1 interferes with plant gene expression. However, the molecular basis of this interference remains unclear. By deletion studies, we could localize the active region of RTP1 within a 45 amino acid central domain. In the second part of this study, two different lines of approaches were taken to study RTP1 transfer mechanism. First, transient expression of secreted RTP1 (sRTP1) also interfered with plant cell vitality. Addition of an endoplasmic reticulum retention signal abolished sRTP1 interference with plant cell vitality, suggesting that RTP1 can reenter the plant cell from the apoplast after secretion in the absence of the pathogen. We have identified a PEST-like region within RTP1, however, contribution of this region to the stability of RTP1 is not clear. Site directed mutagenesis analysis showed that the PEST-like region is likely to play a role during the transfer of RTP1 through plant plasma membrane. In the second line of approach, we established a recombinant delivery model, using Ustilago maydis/Zea mays pathosystem, to pursue RTP1 translocation into the plant cell. Our results indicate that U. maydis is capable of secreting high amounts of recombinant RTP1, showing similar glycosylation pattern as RTP1 secreted from rust haustoria. Our data propose the use of this model system to study RTP1 domains mediating its entry into the plant cell.

Analog sensor electronics requires special care during design in order to increase the quality and precision of the signal, and the life time of the product. Nevertheless, it can experience static deviations due to the manufacturing tolerances, and dynamic deviations due to operating in non-ideal environment. Therefore, the advanced applications such as MEMS technology employs calibration loop to deal with the deviations, but unfortunately, it is considered only in the digital domain, which cannot cope with all the analog deviations such as saturation of the analog signal, etc. On the other hand, rapid-prototyping is essential to decrease the development time, and the cost of the products for small quantities. Recently, evolvable hardware has been developed with the motivation to cope with the mentioned sensor electronic problems. However the industrial specifications and requirements are not considered in the hardware learning loop. Indeed, it minimizes the error between the required output and the real output generated due to given test signal. The aim of this thesis is to synthesize the generic organic-computing sensor electronics and return hardware with predictable behavior for embedded system applications that gains the industrial acceptance; therefore, the hardware topology is constrained to the standard hardware topologies, the hardware standard specifications are included in the optimization, and hierarchical optimization are abstracted from the synthesis tools to evolve first the building blocks, then evolve the abstract level that employs these optimized blocks. On the other hand, measuring some of the industrial specifications needs expensive equipments and some others are time consuming which is not fortunate for embedded system applications. Therefore, the novel approach "mixtrinsic multi-objective optimization" is proposed that simulates/estimates the set of the specifications that is hard to be measured due to the cost or time requirements, while it measures intrinsically the set of the specifications that has high sensitivity to deviations. These approaches succeed to optimize the hardware to meet the industrial specifications with low cost measurement setup which is essential for embedded system applications.

This dissertation is intended to transport the theory of Serre functors into the context of A-infinity-categories. We begin with an introduction to multicategories and closed multicategories, which form a framework in which the theory of A-infinity-categories is developed. We prove that (unital) A-infinity-categories constitute a closed symmetric multicategory. We define the notion of A-infinity-bimodule similarly to Tradler and show that it is equivalent to an A-infinity-functor of two arguments which takes values in the differential graded category of complexes of k-modules, where k is a commutative ground ring. Serre A-infinity-functors are defined via A-infinity-bimodules following ideas of Kontsevich and Soibelman. We prove that a unital closed under shifts A-infinity-category over a field admits a Serre A-infinity-functor if and only if its homotopy category admits an ordinary Serre functor. The proof uses categories and Serre functors enriched in the homotopy category of complexes of k-modules. Another important ingredient is an A-infinity-version of the Yoneda Lemma.

Nowadays, accounting, charging and billing users' network resource consumption are commonly used for the purpose of facilitating reasonable network usage, controlling congestion, allocating cost, gaining revenue, etc. In traditional IP traffic accounting systems, IP addresses are used to identify the corresponding consumers of the network resources. However, there are some situations in which IP addresses cannot be used to identify users uniquely, for example, in multi-user systems. In these cases, network resource consumption can only be ascribed to the owners of these hosts instead of corresponding real users who have consumed the network resources. Therefore, accurate accountability in these systems is practically impossible. This is a flaw of the traditional IP address based IP traffic accounting technique. This dissertation proposes a user based IP traffic accounting model which can facilitate collecting network resource usage information on the basis of users. With user based IP traffic accounting, IP traffic can be distinguished not only by IP addresses but also by users. In this dissertation, three different schemes, which can achieve the user based IP traffic accounting mechanism, are discussed in detail. The inband scheme utilizes the IP header to convey the user information of the corresponding IP packet. The Accounting Agent residing in the measured host intercepts IP packets passing through it. Then it identifies the users of these IP packets and inserts user information into the IP packets. With this mechanism, a meter located in a key position of the network can intercept the IP packets tagged with user information, extract not only statistic information, but also IP addresses and user information from the IP packets to generate accounting records with user information. The out-of-band scheme is a contrast scheme to the in-band scheme. It also uses an Accounting Agent to intercept IP packets and identify the users of IP traffic. However, the user information is transferred through a separated channel, which is different from the corresponding IP packets' transmission. The Multi-IP scheme provides a different solution for identifying users of IP traffic. It assigns each user in a measured host a unique IP address. Through that, an IP address can be used to identify a user uniquely without ambiguity. This way, traditional IP address based accounting techniques can be applied to achieve the goal of user based IP traffic accounting. In this dissertation, a user based IP traffic accounting prototype system developed according to the out-of-band scheme is also introduced. The application of user based IP traffic accounting model in the distributed computing environment is also discussed.

Esterases and lipases are widely used as industrial enzymes and for the synthesis of chiral drugs. Because of their rich secondary metabolism, Streptomyces species offer a relatively untapped source of interesting esterases and lipases. S. coelicolor and S. avermitilis contain 51 genes annotated as esterases and/or lipases. In this study I have cloned 14 different genes encoding for lipolytic enzymes from S. coelicolor (11 genes) and S. avermitilis (four genes). Some of these genes were over-expressed in E. coli. Three of the produced enzymes, which were produced by the genes SCO 7131, SCO6966 and SCO3644, were characterized biochemically and one of them was subjected for directed evolution. The gene estA (locus SCO 7131) was annotated as a putative lipase/esterase in the genome sequence of S. coelicolor A3(2), but does not have a homologue in the genome sequence of S. avermitilis or in other known Streptomyces sequences. estA was cloned and expressed in E. coli as a His-tagged protein. The protein was purified and could be recovered in its non-tagged form after digestion with factor Xa. The relative molecular weight was estimated to be 35.5kDa. The enzyme was only active towards acetate esters and not on larger substrates. It had a stereospecificity towards α-naphathylacetate. It was thermostable, with a half-life at 50C of 4.5 hours. Est A showed stability over pH range 5.5-10, and had optimum pH of 7.5. Its activity was drastically decreased when it was pre-incubated in 10mM PMSF, Cu+2 and Hg+2. It was not very stable in most organic solvents and had only slight enantioselectivity. Est A belongs to the HSL family whose founder member is the human hormone-sensitive lipase. I have developed a protein profile for the HSL family modifying the conserved motifs found by Arpigny and Jaeger (1999). Due to the presence of several HSL members with known 3D structure and good homology to Est A, I was able to make a homology model of Est A. Five different mutants of Est A were produced through site directed mutagenesis: W87F, V158A, W87F/V158A, M162L and S163A. The mutants M162L and S163A did not produce a significant change either in substrate specificity or enzyme kinetics. The mutants V158A and W87F/V158A could act on the larger substrates p-nitrophenylbutyrate and caproate and tributyrin. The mutant V158A had improved thermostability and its t1/2 at 50ºC increased to 24h. The affinity of V158A towards p-nitrophenyacetate increased 6-fold when compared with the wild type, whereas the affinity of W87F decreased 4-fold. Directed evolution of Est A was done through random mutagenesis and ER-PCR. A library of 6336 mutants was constructed and screened for mutants with a broader spectrum of substrate specificity. The mutant XXVF7 did show alteration in the substrate specificity of Est A. The mutant XXVF7 had 5 amino acids changes L76R, L146P, S196G, W213R and L267R. The gene locus SCO 6966 (estB gene) was cloned and expressed in E. coli as a His-tagged protein. It was not possible to remove the His-tag using factor Xa. The tagged protein had a molecular weight 31.9kDa. Est B was active against short chain fatty acid esters (C2-C6). Its optimum temperature was 30ºC and was stable for 1h at temperatures up to 37ºC. The enzyme had maximum activity at pH 8-8.5 and was stable over pH range 7.5-11 for 24h. It was highly sensitive for PMSF, Cu+2 and Hg+2. The enzymatic activity deceased in presence of organic solvents, however it was fairly stable for 1h in 20% organic solvents solutions. A third esterase was produced from the gene locus SCO 3644. This esterase was a thermosensitive one with optimum temperature of 35ºC. The three characterized enzymes included a thermophilic, mesophilic and psychrophilic ones. This indicates the high variation in the characters of Streptomyces lipolytic enzymes and highlighting Streptomyces as a source for esterases and lipases of interesting catalytic activity. This study was an initial trial to provide a strategy for a comprehensive use of genome data.

The lattice Boltzmann method (LBM) is a numerical solver for the Navier-Stokes equations, based on an underlying molecular dynamic model. Recently, it has been extended towardsthe simulation of complex fluids. We use the asymptotic expansion technique to investigate the standard scheme, the initialization problem and possible developments towards moving boundary and fluid-structure interaction problems. At the same time, it will be shown how the mathematical analysis can be used to understand and improve the algorithm. First of all, we elaborate the tool "asymptotic analysis", proposing a general formulation of the technique and explaining the methods and the strategy we use for the investigation. A first standard application to the LBM is described, which leads to the approximation of the Navier-Stokes solution starting from the lattice Boltzmann equation. As next, we extend the analysis to investigate origin and dynamics of initial layers. A class of initialization algorithms to generate accurate initial values within the LB framework is described in detail. Starting from existing routines, we will be able to improve the schemes in term of efficiency and accuracy. Then we study the features of a simple moving boundary LBM. In particular, we concentrate on the initialization of new fluid nodes created by the variations of the computational fluid domain. An overview of existing possible choices is presented. Performing a careful analysis of the problem we propose a modified algorithm, which produces satisfactory results. Finally, to set up an LBM for fluid structure interaction, efficient routines to evaluate forces are required. We describe the Momentum Exchange algorithm (MEA). Precise accuracy estimates are derived, and the analysis leads to the construction of an improved method to evaluate the interface stresses. In conclusion, we test the defined code and validate the results of the analysis on several simple benchmarks. From the theoretical point of view, in the thesis we have developed a general formulation of the asymptotic expansion, which is expected to offer a more flexible tool in the investigation of numerical methods. The main practical contribution offered by this work is the detailed analysis of the numerical method. It allows to understand and improve the algorithms, and construct new routines, which can be considered as starting points for future researches.

In this thesis we classify simple coherent sheaves on Kodaira fibers of types II, III and IV (cuspidal and tacnode cubic curves and a plane configuration of three concurrent lines). Indecomposable vector bundles on smooth elliptic curves were classified in 1957 by Atiyah. In works of Burban, Drozd and Greuel it was shown that the categories of vector bundles and coherent sheaves on cycles of projective lines are tame. It turns out, that all other degenerations of elliptic curves are vector-bundle-wild. Nevertheless, we prove that the category of coherent sheaves of an arbitrary reduced plane cubic curve, (including the mentioned Kodaira fibers) is brick-tame. The main technical tool of our approach is the representation theory of bocses. Although, this technique was mainly used for purely theoretical purposes, we illustrate its computational potential for investigating tame behavior in wild categories. In particular, it allows to prove that a simple vector bundle on a reduced cubic curve is determined by its rank, multidegree and determinant, generalizing Atiyah's classification. Our approach leads to an interesting class of bocses, which can be wild but are brick-tame.

The nowadays increasing number of fields where large quantities of data are collected generates an emergent demand for methods for extracting relevant information from huge databases. Amongst the various existing data mining models, decision trees are widely used since they represent a good trade-off between accuracy and interpretability. However, one of their main problems is that they are very instable, which complicates the process of the knowledge discovery because the users are disturbed by the different decision trees generated from almost the same input learning samples. In the current work, binary tree classifiers are analyzed and partially improved. The analysis of tree classifiers goes from their topology from the graph theory point of view to the creation of a new tree classification model by means of combining decision trees and soft comparison operators (Mlynski, 2003) with the purpose to not only overcome the well known instability problem of decision trees, but also in order to confer the ability of dealing with uncertainty. In order to study and compare the structural stability of tree classifiers, we propose an instability coefficient which is based on the notion of Lipschitz continuity and offer a metric to measure the proximity between decision trees. This thesis converges towards its main part with the presentation of our model ``Soft Operators Decision Tree\'\' (SODT). Mainly, we describe its construction, application and the consistency of the mathematical formulation behind this. Finally we show the results of the implementation of SODT and compare numerically the stability and accuracy of a SODT and a crisp DT. The numerical simulations support the stability hypothesis and a smaller tendency to overfitting the training data with SODT than with crisp DT is observed. A further aspect of this inclusion of soft operators is that we choose them in a way so that the resulting goodness function (used by this method) is differentiable and thus allows to calculate the best split points by means of gradient descent methods. The main drawback of SODT is the incorporation of the unpreciseness factor, which increases the complexity of the algorithm.

In urban planning, sophisticated simulation models are key tools to estimate future population growth for measuring the impact of planning decisions on urban developments and the environment. Simulated population projections usually result in large, macro-scale, multivariate geospatial data sets. Millions of records have to be processed, stored, and visualized to help planners explore and analyze complex population patterns. We introduce a database driven framework for visualizing geospatial multidimensional simulation data based on the output from UrbanSim, a software for the analysis and planning of urban developments. The designed framework is extendable and aims at integrating empirical-stochastic methods and urban simulation models with techniques developed for information visualization and cartography. First, we develop an empirical model for the estimation of residential building types based on demographic household characteristics. The predicted dwelling type information is important for the analysis of future material use, carbon footprint calculations, and for visualizing simultaneously the results of land usage, density, and other significant parameters in 3D space. Our model uses multinomial logistic regression to derive building types at different scales. The estimated regression coefficients are applied to UrbanSim output in order to predict residential building types. The simulation results and the estimated building types are managed in an object-relational geodatabase. From the database, density, building types, and significant demographic variables are visually encoded as scalable, georeferenced 3D geometries and displayed on top of aerial photographs in a Google Earth visual synthesis. The geodatabase can be accessed and the visualization parameters can be chosen through a web-based user interface. The geometries are encoded in KML, Google's markup language, as ready-to-visualize data sets. The goal is to enhance human cognition by displaying abstract representations of multidimensional data sets in a realistic context and thus to support decision making in planning processes.

The visualization of numerical fluid flow datasets is essential to the engineering processes that motivate their computational simulation. To address the need for visual representations that convey meaningful relations and enable a deep understanding of flow structures, the discipline of Flow Visualization has produced many methods and schemes that are tailored to a variety of visualization tasks. The ever increasing complexity of modern flow simulations, however, puts an enormous demand on these methods. The study of vortex breakdown, for example, which is a highly transient and inherently three-dimensional flow pattern with substantial impact wherever it appears, has driven current techniques to their limits. In this thesis, we propose several novel visualization methods that significantly advance the state of the art in the visualization of complex flow structures. First, we propose a novel scheme for the construction of stream surfaces from the trajectories of particles embedded in a flow. These surfaces are extremely useful since they naturally exploit coherence between neighboring trajectories and are highly illustrative in nature. We overcome the limitations of existing stream surface algorithms that yield poor results in complex flows, and show how the resulting surfaces can be used a building blocks for advanced flow visualization techniques. Moreover, we present a visualization method that is based on moving section planes that travel through a dataset and sample the flow. By considering the changes to the flow topology on the plane as it moves, we obtain a method of visualizing topological structures in three-dimensional flows that are not accessible by conventional topological methods. On the same algorithmic basis, we construct an algorithm for the tracking of critical points in such flows, thereby enabling the treatment of time-dependent datasets. Last, we address some problems with the recently introduced Lagrangian techniques. While conceptually elegant and generally applicable, they suffer from an enormous computational cost that we significantly use by developing an adaptive approximation algorithm. This allows the application of such methods on very large and complex numerical simulations. Throughout this thesis, we will be concerned with flow visualization aspect of general practical significance but we will particularly emphasize the remarkably challenging visualization of the vortex breakdown phenomenon.

The main concern of this contribution is the computational modeling of biomechanically relevant phenomena. To minimize resource requirements, living biomaterials commonly adapt to changing demands. One way to do so is the optimization of mass. For the modeling of biomaterials with changing mass, we distinguish between two different approaches: the coupling of mass changes and deformations at the constitutive level and at the kinematic level. Mass change at the constitutive level is typically realized by weighting the free energy function with respect to the density field, as experimentally motivated by Carter and Hayes [1977] and computationally realized by Harrigan and Hamilton [1992]. Such an ansatz enables the simulation of changes in density while the overall volume remains unaffected. In this contribution we call this effect remodeling. Although in principle applicable for small and large strains, this approach is typically adopted for hard tissues, e.g. bone, which usually undergo small strain deformations. Remodeling in anisotropic materials is realized by choosing an appropriate anisotropic free energy function. <br> Within the kinematic coupling, a changing mass is characterized through a multiplicative decomposition of the deformation gradient into a growth part and an elastic part, as first introduced in the context of plasticity by Lee [1969]. In this formulation, which we will refer to as growth in the following, mass changes are attributed to changes in volume while the material density remains constant. This approach has classically been applied to model soft tissues undergoing large strains, e.g. the arterial wall. The first contribution including this ansatz is the work by Rodriguez, Hoger and McCulloch [1994]. To model anisotropic growth, an appropriate anisotropic growth deformation tensor has to be formulated. In this contribution we restrict ourselves to transversely isotropic growth, i.e., growth characterized by one preferred direction. On that account, we define a transversely isotropic growth deformation tensor determined by two variables, namely the stretch ratios parallel and perpendicular to the characteristic direction. <br> Another method of material optimization is the adaption of the inner structure f a material to its loading conditions. In anisotropic materials this can be realized by a suitable orientation of the material directions. For example, the trabeculae in the human femur head are oriented such that they can carry the daily loads with an optimum mass. Such a behavior can also be observed in soft tissues. For instance, the fibers of muscles and the collagen fibers in the arterial wall are oriented along the loading directions to carry a maximum of mechanical load. If the overall loading conditions change, for instance during a balloon angioplasty or a stent implantation, the material orientation readapts, which we call reorientation. The anisotropy type in biomaterials is often characterized by fiber reinforcement. A particular subclass of tissues, which includes muscles, tendons and ligaments, is featured by one family of fibers. More complex microstructures, such as arterial walls, show two fiber families, which do not necessarily have to be perpendicular. Within this contribution we confine ourselves to the first case, i.e., transversely isotropic materials indicated by one characteristic direction. The reorientation of the fiber direction in biomaterials is commonly smooth and continuous. For transverse isotropy it can be described by a rotation of the characteristic direction. Analogous to the theory of shells, we additionally exclude drilling rotations, see also Menzel [2006]. However, the driving force for these reorientation processes is still under discussion. Mathematical considerations promote strain driven reorientations. As discussed, for instance, in Vianello [1996], the free energy reaches a critical state for coaxial stresses and strains. For transverse isotropy, it can be shown that this can be achieved if the characteristic direction is aligned with a principal strain direction. From a biological point of view, depending on the kind of material (i.e. bone, muscle tissue, cartilage tissue, etc.), both strains and stresses can be suggested as stimuli for reorientation. Thus, whithin this contribution both approaches are investigated. <br> In contrast to previous works, in which remodeling, growth and reorientation are discussed separately, the present work provides a framework comprising all of the three mentioned effects at once. This admits a direct comparison how and on which level the individual phenomenon is introduced into the material model, and which influence it has on the material behavior. For a uniform description of the phenomenological quantities an internal variable approach is chosen. Moreover, we particularly focus on the algorithmic implementation of the three effects, each on its own, into a finite element framework. The nonlinear equations on the local and the global level are solved by means of the Newton-Raphson scheme. Accordingly, the local update of the internal variables and the global update of the deformation field are consistently linearized yielding the corresponding tangent moduli. For an efficient implementation into a finite element code, unitized update algorithms are given. The fundamental characteristics of the effects are illustrated by means of some representative numerical simulations. Due to the unified framework, combinations of the individual effects are straightforward.

Thermoelasticity represents the fusion of the fields of heat conduction and elasticity in solids and is usually characterized by a twofold coupling. Thermally induced stresses can be determined as well as temperature changes caused by deformations. Studying the mutual influence is subject of thermoelasticity. Usually, heat conduction in solids is based on Fourier’s law which describes a diffusive process. It predicts unnatural infinite transmission speed for parts of local heat pulses. At room temperature, for example, these parts are strongly damped. Thus, in these cases most engineering applications are described satisfactorily by the classical theory. However, in some situations the predictions according to Fourier’s law fail miserable. One of these situations occurs at temperatures near absolute zero, where the phenomenon of second sound1 was discovered in the 20th century. Consequently, non-classical theories experienced great research interest during the recent decades. Throughout this thesis, the expression “non-classical” refers to the fact that the constitutive equation of the heat flux is not based on Fourier’s law. Fourier’s classical theory hypothesizes that the heat flux is proportional to the temperature gradient. A new thermoelastic theory, on the one hand, needs to be consistent with classical thermoelastodynamics and, on the other hand, needs to describe second sound accurately. Hence, during the second half of the last century the traditional parabolic heat equation was replaced by a hyperbolic one. Its coupling with elasticity leads to non-classical thermomechanics which allows the modeling of second sound, provides a passage to the classical theory and additionally overcomes the paradox of infinite wave speed. Although much effort is put into non-classical theories, the thermoelastodynamic community has not yet agreed on one approach and a systematic research is going on worldwide.Computational methods play an important role for solving thermoelastic problems in engineering sciences. Usually this is due to the complex structure of the equations at hand. This thesis aims at establishing a basic theory and numerical treatment of non-classical thermoelasticity (rather than dealing with special cases). The finite element method is already widely accepted in the field of structural solid mechanics and enjoys a growing significance in thermal analyses. This approach resorts to a finite element method in space as well as in time.

Nonlinear diffusion filtering of images using the topological gradient approach to edges detection
(2007)

In this thesis, the problem of nonlinear diffusion filtering of gray-scale images is theoretically and numerically investigated. In the first part of the thesis, we derive the topological asymptotic expansion of the Mumford-Shah like functional. We show that the dominant term of this expansion can be regarded as a criterion to edges detection in an image. In the numerical part, we propose the finite volume discretization for the Catté et al. and the Weickert diffusion filter models. The proposed discretization is based on the integro-interpolation method introduced by Samarskii. The numerical schemes are derived for the case of uniform and nonuniform cell-centered grids of the computational domain \(\Omega \subset \mathbb{R}^2\). In order to generate a nonuniform grid, the adaptive coarsening technique is proposed.

The thesis is concerned with multiscale approximation by means of radial basis functions on hierarchically structured spherical grids. A new approach is proposed to construct a biorthogonal system of locally supported zonal functions. By use of this biorthogonal system of locally supported zonal functions, a spherical fast wavelet transform (SFWT) is established. Finally, based on the wavelet analysis, geophysically and geodetically relevant problems involving rotation-invariant pseudodifferential operators are shown to be efficiently and economically solvable.

Feature Based Visualization
(2007)

In this thesis we apply powerful mathematical tools such as interval arithmetic for applications in computational geometry, visualization and computer graphics, leading to robust, general and efficient algorithms. We present a completely novel approach for computing the arrangement of arbitrary implicit planar curves and perform ray casting of arbitrary implicit functions by jointly achieving, for the first time, robustness, efficiency and flexibility. Indeed we are able to render even the most difficult implicits in real-time with guaranteed topology and at high resolution. We use subdivision and interval arithmetic as key-ingredients to guarantee robustness. The presented framework is also well-suited for applications to large and unstructured data sets due to the inherent adaptivity of the techniques that are used. We also approach the topic of tensors by collaborating with mechanical engineers on comparative tensor visualization and provide them with helpful visualization paradigms to interpret the data.

Im Zuge der steigenden Anzahl von Einsatzmöglichkeiten der
Faserverbundwerkstoffe in den verschiedensten Industriebereichen spielt die
Entwicklung bzw. Weiterentwicklung neuer und effektiverer Verarbeitungstechniken
eine bedeutende Rolle.
Dabei findet derzeit das Harzinjektionsverfahren (LCM) ausschließlich für kleinere bis
mittlere Stückzahlen seinen Einsatz. Aufgrund der sehr großen Stückzahlen im
Automobilbereich, ist dieses Verfahren hier zurzeit weniger interessant. Daher
werden große Anstrengungen unternommen, das Harzinjektionsverfahren besonders
für solche Bauteile attraktiver zu machen, die gegenwärtig mit Hilfe des Prepreg-
Verfahrens hergestellt werden. Dabei spielt die Reduktion der hier vergleichsweise
hohen Zykluszeit eine tragende Rolle. Die Dauer eines Zyklus wird hierbei
hauptsächlich durch die Vorbereitung und Herstellung der Verstärkungsstruktur
(Preform) sowie durch die Bestückung des Werkzeuges bestimmt. Diese so
genannte Preform-Technik weist daher ein sehr großes Entwicklungspotential auf,
mit dem Ziel, solche Verstärkungsstrukturen herzustellen, die nach der Injektion
keine Nacharbeit erfordern. Solche Strukturen werden auch als „net shape, ready-toimpregnate“-
Preform bezeichnet. Die hierfür notwendigen Techniken stammen
vornehmend aus der Textilindustrie, wie z.B. die direkte Preformtechnik, das Nähen
oder Kleben (Binder-Technik).
Ziel der vorliegenden Dissertation ist es, die Möglichkeiten der Nähtechnik bezogen
auf die Herstellung der Preforms zu untersuchen. Hierfür werden die verschiedenen
Naht- und Verbindungsarten hinsichtlich ihres Einsatzes in der Preformtechnik, wie
die Fixier- und Positionier-, die Füge- oder Verbindungsnaht und die Montagenaht,
untersucht.
Im Rahmen dieser Arbeit wurde zunächst innerhalb einer Studie zur „net shape“-
Preformtechnik eine Versteifungsstruktur entwickelt und hergestellt. Diese Struktur
soll dabei der Veranschaulichung der Möglichkeiten und Einsatzbereiche der
Nähtechnik bei der Preformtechnologie dienen. Zudem kann so ein mehrstufiger
Preformherstellungsprozess demonstriert werden. Ferner zeigt diese Studie, dass
ein hochgradiger, automatisierter Prozess, welcher zudem eine durchgängige
Qualitätskontrolle ermöglicht, realisiert werden konnte. Als ein weiterer Schritt wurde ein Prozess zur Herstellung eine dreidimensionalen
Preform, der die Anwendung verschiedener thermoplastischer,
niedrigtemperaturschmelzender Nähgarne zulässt, ausgearbeitet. Hierbei wurden die
Vorteile der Näh- und der Binder-Technologie miteinander verbunden. Außerdem
konnte durch die bereits formstabile und imprägnierungsfertige Preformstruktur, die
Bestückung des Werkzeuges wesentlich vereinfacht werden. Um die mechanischen
Eigenschaften der Preforms bestimmen zu können, wurden quantitative
Messmethoden erarbeitet. Hierdurch konnten anschließend die Einflüsse der
Orientierung sowie der Stichdichte ermittelt werden. Zudem wurden die folgenden
drei grundlegenden Eigenschaften untersucht: die spezifische Biegesteifigkeit, der so
genannte Rückspringwinkel sowie die Rückstellkraft nach dem Thermoformen
hinsichtlich der verschiedenen Nähtypen.
Um dies zu ergänzen, wurden weiterführende Untersuchungen zu den
Materialeigenschaften der Nähfäden, die bei der dreidimensionalen Preformtechnik
eingesetzt werden können, durchgeführt. Dabei ist neben der niedrigen
Schmelztemperatur die vollständige Auflösbarkeit der Nähgarne in den ungesättigten
Polyester- und Epoxidharzen besonders wichtig. Auf Grund dieser vollständigen
Auflösung der Fäden in der Matrix können die Stichlöcher wieder vollkommen
verschlossen werden. Dadurch kann eine Reduktion des Einflusses solcher
Stichlöcher auf die mechanischen Eigenschaften des Faserverbundwerkstoffes
erreicht werden. Mit Hilfe dieser Untersuchungen wurden schließlich zwei polymere
Nähgarne als vielversprechend beurteilt. Diese weisen eine Schmelztemperatur von
weniger als 100 °C sowie eine gute Lösbarkeit, besonders im Harzsystem RTM 6,
auf.
In der Preformtechnik werden die Nähte nicht nur als Positionier- oder Montagenaht
eingesetzt, sondern können in einer Struktur als auch als Verstärkungselement, eine
so genannte Verstärkungsnaht, verwendet werden. Der Zweck einer solchen Naht ist
die interlaminare Verstärkung von monolitischen oder Sandwichstrukturen. Zudem
besteht die Möglichkeit, diese zur Fixierung von metallischen Funktionselementen
(Inserts) in den Faserverbundwerkstoff zu benutzen. Hinsichtlich diese Möglichkeiten
wurden im Rahmen dieser Arbeit erfolgreich Untersuchung durchgeführt. Dabei
wiesen die eingenähten Krafteinleitungselemente in durchgeführten statischen
Zugversuchen eine annähernd 200 % höhere maximale Zugkraft verglichen mit
entsprechenden Elementen (BigHead®), die nicht durch eine Naht fixiert wurden. Weitere Untersuchungen zeigten auch, dass eine doppelte Naht nicht eine
proportionale Verdoppelung der maximal erreichbaren Zugkraft bewirkt. Der Grund
hierfür liegt an einer partiellen Zerstörung des vorhandenen Nähgarns der ersten
Naht begründet durch den doppelten Einstich in die bereits bestehenden Löcher
beim mehrmaligen Durchlaufen der Nadel. Der größte Verstärkungseffekt konnte
schließlich bei der interlaminaren Einbettung und der Vernähung des Insert erreicht
werden. In diesem Fall kann eine Delamination, wie sie bei lediglich interlaminar
eingebetteten Inserts auftritt, verhindert werden.
Zusätzlich wurden statische Scherversuche durchgeführt, um auch in diesem
Belastungsfall die Versagensart zu untersuchen. Dabei stellte sich heraus, dass nicht
die Nähte sondern der Insert versagte. Auf Grund des Materialbruchs des Inserts,
sowohl in Zug- als auch in Scherversuchen, wurde in einem weiteren Schritt ein
optimiertes Insert entwickelt. Bei diesem wurde der Sockel in soweit modifiziert, dass
die maximale Versagenslast des Nähgarns ermittelt werden konnte. Dabei stellte
sich heraus, dass Glas-, Kohlenstoff- und Aramidfasern sich nur bedingt als
Verstärkungsgarn zur Fixierung von Inserts eignen. Im Gegensatz dazu sind die
Polyestergarne als ausreichende Verstärkung gut geeignet. Weitere Vorteile des
Polyestergarns sind die niedrigeren Kosten sowie die gute Vernähbarkeit.
Anschließend wurde eine solche Verbindung des Inserts mit einem
Faserverbundwerkstoff mit Hilfe der Finite-Elemente-Methode (FEM) simuliert. Dabei
zeigte sich eine gute Übereinstimmung der simulierten Ergebnisse mit denen aus
dem statischen Zugversuch mit dem weiterentwickelten Insert.
Auf Grund der elektrischen Leitfähigkeit von Kohlenstofffasern, können Fäden aus
diesem Material auch als Sensoren zur Überwachung einer Struktur oder Verbindung
eingesetzt werden. Hierfür wurden ebenfalls Untersuchungen durchgeführt. Dabei
konnte mit Hilfe der Änderung des elektrischen Widerstandes auf Schädigungen der
Fasern geschlossen werden. Somit können nicht nur das Bestehen einer
Schädigung, sondern auch der annähernde Ort ermittelt werden. Die
Untersuchungen zeigten somit, dass die Kohlenstofffasern nicht lediglich als
Verstärkung sondern auch als Überwachungssensor bei einem eingebetteten Insert
dienen können.
Im Rahmen aller Untersuchungen konnte das große und vielversprechende Potential
der Nähtechnik bei der Herstellung von Preform-Bauteilen aufgezeigt sowie ein
Einblick in einige von vielen Anwendungsmöglichkeiten gegeben werden.

Sewn net-shape preform based composite manufacturing technology is widely
accepted in combination with liquid composite molding technologies for the
manufacturing of fiber reinforced polymer composites. The development of threedimensional
dry fibrous reinforcement structures containing desired fiber orientation
and volume fraction before the resin infusion is based on the predefined preforming
processes. Various preform manufacturing aspects influence the overall composite
manufacturing processes. Sewing technology used for the preform manufacturing
has number of challenges to overcome which includes consistency in preform quality,
composite quality, and composite mechanical properties.
Experimental studies are undertaken to investigate the influence of various sewing
parameters on the preform manufacturing processes, preform quality, and the fiber
reinforced polymer composite quality and properties. Sewing thread, sewing machine
parameters, shortcomings of sewing process, and remedies are explained according
to their importance during preforming and liquid composite molding. The stitches and
fiber free zone in the form of ellipse that are generated in the thickness direction were
investigated by evaluating the laminate micrographs. Correlation between ellipse
formation phenomenon, sewing thread, and sewing machine parameters is
established. A statistical tool, analysis of variance, was used to emphasize the major
preform processing factors influencing the preform imperfections.
For assessing the preform quality, the observations of sewing thread requirements
for preform and structural sewing were well documented during the experimental
studies and explained according to their significance in the composite processing.
Furthermore, selection criteria for sewing thread according to end application are
discussed in detail. Investigations on polyester sewing thread as a high speed
preform manufacturing element are also performed. Applicability of polyester sewing
thread for the preform sewing and challenges to be overcome for its extensive
utilization in the composite components are explained. Apart from this, influence of
physical structure of sewing thread on the laminate quality and properties are
explained and relationship between them is discussed in brief. Furthermore,
challenges caused due to applied spin-finishes and sizing and remedies for the same
are discussed. Sewing threads made of high performance fibers that are available in the market,
e.g., carbon, glass, and Zylon are studied for effect of thread material on through-thethickness
laminate properties. Threads made up of carbon or glass fibers are very
rigid and produces number of defects, which is a major cause of concern. Optimized
sewing procedure has been implemented to minimize the in-plane and through-thethickness
imperfections and to improve mechanical properties and surface
characteristics of composite laminate.
Preform sewing process and final ready to impregnate preforms were analyzed for
quality appearance. The sewing defects and their influence on composite structure
are monitored. Preform compressibility before and after the sewing operations are
intensively studied and correlation with sewing parameters is developed. Influence of
sewing process parameters on the warpage and change in preform area weight are
also explained in detail. Results of analytical experiments can help to improve further
exploitation of sewn preforms for composite manufacturing and overall preform and
laminate quality.

In recent years, nanofiller-reinforced polymer composites have attracted considerable
interest from numerous researchers, since they can offer unique mechanical,
electrical, optical and thermal properties compared to the conventional polymer
composites filled with micron-sized particles or short fibers. With this background, the
main objective of the present work was to investigate the various mechanical
properties of polymer matrices filled with different inorganic rigid nanofillers, including
SiOB2B, TiOB2B, AlB2BOB3B and multi-walled carbon nanotubes (MWNT). Further, special
attention was paid to the fracture behaviours of the polymer nanocomposites. The
polymer matrices used in this work contained two types of epoxy resin (cycloaliphatic
and bisphenol-F) and two types of thermoplastic polymer (polyamide 66 and isotactic
polypropylene).
The epoxy-based nanocomposites (filled with nano-SiOB2B) were formed in situ by a
special sol-gel technique supplied by nanoresins AG. Excellent nanoparticle
dispersion was achieved even at rather high particle loading. The almost
homogeneously distributed nanoparticles can improve the elastic modulus and
fracture toughness (characterized by KBICB and GBICB) simultaneously. According to
dynamic mechanical and thermal analysis (DMTA), the nanosilica particles in epoxy
resins possessed considerable "effective volume fraction" in comparison with their
actual volume fraction, due to the presence of the interphase. Moreover, AFM and
high-resolution SEM observations also suggested that the nanosilica particles were
coated with a polymer layer and therefore a core-shell structure of particle-matrix was
expected. Furthermore, based on SEM fractography, several toughening
mechanisms were considered to be responsible for the improvement in toughness,
which included crack deflection, crack pinning/bowing and plastic deformation of
matrix induced by nanoparticles.
The PA66 or iPP-based nanocomposites were fabricated by a conventional meltextrusion
technique. Here, the nanofiller content was set constant as 1 vol.%. Relatively good particle dispersion was found, though some small aggregates still
existed. The elastic modulus of both PA66 and iPP was moderately improved after
incorporation of the nanofillers. The fracture behaviours of these materials were
characterized by an essential work fracture (EWF) approach. In the case of PA66
system, the EWF experiments were carried out over a broad temperature range
(23~120 °C). It was found that the EWF parameters exhibited high temperature
dependence. At most testing temperatures, a small amount of nanoparticles could
produce obvious toughening effects at the cost of reduction in plastic deformation of
the matrix. In light of SEM fractographs and crack opening tip (COD) analysis, the
crack blunting induced by nanoparticles might be the major source of this toughening.
The fracture behaviours of PP filled with MWNTs were investigated over a broad
temperature range (-196~80 °C) in terms of notched impact resistance. It was found
that MWNTs could enhance the notched impact resistance of PP matrix significantly
once the testing temperature was higher than the glass transition temperature (TBgB) of
neat PP. At the relevant temperature range, the longer the MWNTs, the better was
the impact resistance. SEM observation revealed three failure modes of nanotubes:
nanotube bridging, debonding/pullout and fracture. All of them would contribute to
impact toughness to a degree. Moreover, the nanotube fracture was considered as
the major failure mode. In addition, the smaller spherulites induced by the nanotubes
would also benefit toughness.

The broad engineering applications of polymers and composites have become the
state of the art due to their numerous advantages over metals and alloys, such as
lightweight, easy processing and manufacturing, as well as acceptable mechanical
properties. However, a general deficiency of thermoplastics is their relatively poor
creep resistance, impairing service durability and safety, which is a significant barrier
to further their potential applications. In recent years, polymer nanocomposites have
been increasingly focused as a novel field in materials science. There are still many
scientific questions concerning these materials leading to the optimal property
combinations. The major task of the current work is to study the improved creep
resistance of thermoplastics filled with various nanoparticles and multi-walled carbon
nanotubes.
A systematic study of three different nanocomposite systems by means of
experimental observation and modeling and prediction was carried out. In the first
part, a nanoparticle/PA system was prepared to undergo creep tests under different
stress levels (20, 30, 40 MPa) at various temperatures (23, 50, 80 °C). The aim was
to understand the effect of different nanoparticles on creep performance. 1 vol. % of
300 nm and 21 nm TiO2 nanoparticles and nanoclay was considered. Surface
modified 21 nm TiO2 particles were also investigated. Static tensile tests were
conducted at those temperatures accordingly. It was found that creep resistance was
significantly enhanced to different degrees by the nanoparticles, without sacrificing
static tensile properties. Creep was characterized by isochronous stress-strain curves,
creep rate, and creep compliance under different temperatures and stress levels.
Orientational hardening, as well as thermally and stress activated processes were
briefly introduced to further understanding of the creep mechanisms of these
nanocomposites. The second material system was PP filled with 1 vol. % 300 nm and 21 nm TiO2
nanoparticles, which was used to obtain more information about the effect of particle
size on creep behavior based on another matrix material with much lower Tg. It was
found especially that small nanoparticles could significantly improve creep resistance.
Additionally, creep lifetime under high stress levels was noticeably extended by
smaller nanoparticles. The improvement in creep resistance was attributed to a very
dense network formed by the small particles that effectively restricted the mobility of
polymer chains. Changes in the spherulite morphology and crystallinity in specimens
before and after creep tests confirmed this explanation.
In the third material system, the objective was to explore the creep behavior of PP
reinforced with multi-walled carbon nanotubes. Short and long aspect ratio nanotubes
with 1 vol. % were used. It was found that nanotubes markedly improved the creep
resistance of the matrix, with reduced creep deformation and rate. In addition, the
creep lifetime of the composites was dramatically extended by 1,000 % at elevated
temperatures. This enhancement contributed to efficient load transfer between
carbon nanotubes and surrounding polymer chains.
Finally, a modeling analysis and prediction of long-term creep behaviors presented a
comprehensive understanding of creep in the materials studied here. Both the
Burgers model and Findley power law were applied to satisfactorily simulate the
experimental data. The parameter analysis based on Burgers model provided an
explanation of structure-to-property relationships. Due to their intrinsic difference, the
power law was more capable of predicting long-term behaviors than Burgers model.
The time-temperature-stress superposition principle was adopted to predict long-term
creep performance based on the short-term experimental data, to make it possible to
forecast the future performance of materials.

Induktionsschweißen kann sowohl für das Schweißen von thermoplastischen Faser-
Kunststoff-Verbunden als auch für das Verbinden von Metall/Faser-Kunststoff-
Verbunden eingesetzt werden. Nach Betrachtung der Möglichkeiten einer solchen
Verbindung wurde festgestellt, dass die Verbindungsqualität durch die
Oberflächenvorbehandlung des metallischen und des polymeren Fügepartners und
durch die Prozessbedingungen bestimmt wird.
Verschiedene neue Werkzeuge (z.B. spezielle Probenhalterungen, temperierbarer
Anpressstempel, Erwärmungs- und Konsolidierungsrolle) wurden entwickelt und in
die Induktionsschweißanlage zur Herstellung von Metall/Faser-Kunststoff-Verbunden
integriert. Topografische Analysen mittels Rasterelektronenmikroskopie und
Laserprofilometrie zeigen einen großen Einfluss der Vorbehandlungsmethoden auf
die Oberflächenrauhigkeit. Zusätzlich ändert die Vorbehandlung die physikalischen
(Oberflächenenergie) und die chemischen Eigenschaften (Atomkonzentration). Die
Eigenschaften der Verbindungen wurden zuerst anhand von Zugscherprüfungen und
parallel durch Oberflächenanalysen untersucht. Die Ergebnisse dieser
Untersuchungen zeigen:
• Die Vorbehandlungsmethoden Korundstrahlen und Sauerbeizen führen bei
dem metallischen Fügepartner zu den höchsten Verbundfestigkeiten. Die
Atmosphären-Plasmareinigung des polymeren Fügepartners ergibt eine
Zunahme der Zugscherfestigkeit von ca. 10 % sowie auch eine Verkleinerung
des Vertrauensbereiches.
• Die Zugscherfestigkeit hängt vom Prozessdruck und damit vom Fließverhalten
des Polymers in der Fügezone ab.
• Die Orientierung der Prüfkraft relativ zur Faserorientierung hat keinen Einfluss
auf die Zugscherfestigkeit der eingesetzten faserverstärkten Materialien.
• Die Leinwand-Bindung, mit mehr polymerreichen Zonen, führt zu einem
geringen Anstieg der Zugscherfestigkeit im Vergleich zu einer Atlas 1/4-
Bindung. Die Gelege-Struktur ergibt durch Faserverschiebungen ähnliche
Festigkeiten wie die Leinwand-Bindung. Es zeigt sich, dass die
Verbundfestigkeit durch das Polymer bestimmt wird. • Die Zugscherfestigkeit gewinnt einen großen Anstieg durch eine zusätzliche
Polymerfolie in der Fügezone. Die Schliffbilder zeigen eine polymere
Zwischenschichtdicke von 5 bis 20 μm für AlMg3-CF/PA66.
• Durch den gezielten Einsatz verschiedener Vorbehandlungsmethoden
(Korundstrahlen mit zusätzlichem Polymer) kann die Zugscherfestigkeit auf bis
zu 14 MPa für AlMg3-CF/PA66-Verbunde und 18 MPa für DC01-CF/PEEKVerbunde
gegenüber dem unbehandelten Zustand verdoppelt werden. Weitere Untersuchungen an den Prozessparametern ergaben für DC01-CF/PEEKVerbunde,
dass folgende Einstellungen zu einer weiteren Steigerung der
Zugscherfestigkeit auf 19 MPa führen:
• Eine Starttemperatur des Anpresstempels von 370 °C.
• Eine Haltezeit von 7 Minuten.
• Eine Abkühlrate von 6 °C/min.
Für AlMg3-CF/PA66 zeigte sich, dass eine Anpresstemperatur von 10 °C zu einer
Zugscherfestigkeit von 14,5 MPa führt. Diese beiden Zugscherfestigkeiten sind
lediglich 10 – 15 % geringer als die unter optimalen Bedingungen hergestellten
Klebeverbindungen.
Erste Untersuchungen zeigen, dass bei galvanischer Korrosion von Metall/FKVVerbunden
eine schnelle Abnahme der Zugscherfestigkeit erfolgt. Hierfür wurden die
Proben drei Wochen in Wasser gelagert. Beim direkten Kontakt zwischen
Kohlenstofffaser und Aluminium erklärt sich dies durch Korrosion in der Fügezone.
Dabei sinken die Zugscherfestigkeiten der Proben bis auf 5 MPa. Bei Proben mit
einer Glasfaserlage als Isolationsschicht zeigen sich keine Korrosionsprodukte und
die Zugscherfestigkeit nimmt um 30 % bis auf 8 – 9 MPa ab.
Bei in Salzwasser gelagerten Proben ist die galvanische Korrosion deutlich stärker
ausgeprägt. Bereits nach einer Woche besitzen die acetongereinigten Proben mit
zusätzlichem Polymer lediglich eine Restzugscherfestigkeit von 3 bis 4 MPa. Die
korundgestrahlten Proben zeigen Korrosionsprodukte am Rande der Fügezone und
in der Fügezone, weisen aber dennoch eine Zugscherfestigkeit von ca. 10 MPa auf.
Die glasfaserverstärkten Proben zeigen weder Korrosionsprodukte noch eine
Abnahme der Zugscherfestigkeit. Dynamisch thermografische Analysen wurden in verschiedenen Umgebungsgasen
durchgeführt, um die Zersetzungstemperatur des faserverstärkten Polymers zu
bestimmen. Im Falle von CF/PA66 führte dies nicht zu einer Vergrößerung des
Prozessfensters, da die Zersetzung hauptsächlich thermisch und nicht thermooxidativ
ist. Die festgestellte Zersetzungstemperatur von CF/PEEK in Luft betrug
550 °C. Die Vergrößerung des Prozessfensters ist für CF/PA66 gering und zeigte
auch keinen Anstieg in der Zugscherfestigkeit nach dem Schweißen in Stickstoff.
Trotzdem hat das Induktionsschweißen unter Schutzgas ein großes Potential für
gesättigte Kohlenwasserstoffe wie z.B. glasfaserverstärktes Polypropylen. Hier wurde
die Zersetzungstemperatur von 230 °C in Luft auf 390 °C in Stickstoff erhöht.
Es wurde ein Demonstrator bestehend aus einem Aluminium-Profil und einer
CF/PA66-Platte hergestellt, womit gezeigt werden konnte, dass die erworbenen
Kenntnisse auch für die industrielle Anwendung umsetzbar sind. Mittels analytischer
Modelle und FE-Berechnungen wurde die induktive Erwärmung erfolgreich
nachgebildet.

In this thesis, the quasi-static Biot poroelasticity system in bounded multilayered domains in one and three dimensions is studied. In more detail, in the one-dimensional case, a finite volume discretization for the Biot system with discontinuous coefficients is derived. The discretization results in a difference scheme with harmonic averaging of the coefficients. Detailed theoretical analysis of the obtained discrete model is performed. Error estimates, which establish convergence rates for both primary as well as flux unknowns are derived. Besides, modified and more accurate discretizations, which can be applied when the interface position coincides with a grid node, are obtained. These discretizations yield second order convergence of the fluxes of the problem. Finally, the solver for the solution of the produced system of linear equations is developed and extensively tested. A number of numerical experiments, which confirm the theoretical considerations are performed. In the three-dimensional case, the finite volume discretization of the system involves construction of special interpolating polynomials in the dual volumes. These polynomials are derived so that they satisfy the same continuity conditions across the interface, as the original system of PDEs. This technique allows to obtain such a difference scheme, which provides accurate computation of the primary as well as of the flux unknowns, including the points adjacent to the interface. Numerical experiments, based on the obtained discretization, show second order convergence for auxiliary problems with known analytical solutions. A multigrid solver, which incorporates the features of the discrete model, is developed in order to solve efficiently the linear system, produced by the finite volume discretization of the three-dimensional problem. The crucial point is to derive problem-dependent restriction and prolongation operators. Such operators are a well-known remedy for the scalar PDEs with discontinuous coefficients. Here, these operators are derived for the system of PDEs, taking into account interdependence of different unknowns within the system. In the derivation, the interpolating polynomials from the finite volume discretization are employed again, linking thus the discretization and the solution processes. The developed multigrid solver is tested on several model problems. Numerical experiments show that, due to the proper problem-dependent intergrid transfer, the multigrid solver is robust with respect to the discontinuities of the coefficients of the system. In the end, the poroelasticity system with discontinuous coefficients is used to model a real problem. The Biot model, describing this problem, is treated numerically, i.e., discretized by the developed finite volume techniques and then solved by the constructed multigrid solver. Physical characteristics of the process, such as displacement of the skeleton, pressure of the fluid, components of the stress tensor, are calculated and then presented at certain cross-sections.