## Dissertation

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- Dissertation (545) (entfernen)

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- Englisch (545) (entfernen)

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- Visualisierung (13)
- Finite-Elemente-Methode (7)
- finite element method (7)
- Algebraische Geometrie (6)
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- Finanzmathematik (5)
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- Numerische Strömungssimulation (5)
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- Visualization (5)

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- Fachbereich Mathematik (204)
- Fachbereich Informatik (110)
- Fachbereich Maschinenbau und Verfahrenstechnik (80)
- Fachbereich Chemie (53)
- Fachbereich Elektrotechnik und Informationstechnik (43)
- Fachbereich Biologie (24)
- Fachbereich Sozialwissenschaften (13)
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- Fraunhofer (ITWM) (4)

The dissertation is concerned with the numerical solution of Fokker-Planck equations in high dimensions arising in the study of dynamics of polymeric liquids. Traditional methods based on tensor product structure are not applicable in high dimensions for the number of nodes required to yield a fixed accuracy increases exponentially with the dimension; a phenomenon often referred to as the curse of dimension. Particle methods or finite point set methods are known to break the curse of dimension. The Monte Carlo method (MCM) applied to such problems are 1/sqrt(N) accurate, where N is the cardinality of the point set considered, independent of the dimension. Deterministic version of the Monte Carlo method called the quasi Monte Carlo method (QMC) are quite effective in integration problems and accuracy of the order of 1/N can be achieved, up to a logarithmic factor. However, such a replacement cannot be carried over to particle simulations due to the correlation among the quasi-random points. The method proposed by Lecot (C.Lecot and F.E.Khettabi, Quasi-Monte Carlo simulation of diffusion, Journal of Complexity, 15 (1999), pp.342-359) is the only known QMC approach, but it not only leads to large particle numbers but also the proven order of convergence is 1/N^(2s) in dimension s. We modify the method presented there, in such a way that the new method works with reasonable particle numbers even in high dimensions and has better order of convergence. Though the provable order of convergence is 1/sqrt(N), the results show less variance and thus the proposed method still slightly outperforms standard MCM.

The goal of this thesis is a physically motivated and thermodynamically consistent formulation of higher gradient inelastic material behavior. Thereby, the influence of the material microstructure is incorporated. Next to theoretical aspects, the thesis is complemented with the algorithmic treatment and numerical implementation of the derived model. Hereby, two major inelastic effects will be addressed: on the one hand elasto-plastic processes and on the other hand damage mechanisms, which will both be modeled within a continuum mechanics framework.

Matrix Compression Methods for the Numerical Solution of Radiative Transfer in Scattering Media
(2002)

Radiative transfer in scattering media is usually described by the radiative transfer equation, an integro-differential equation which describes the propagation of the radiative intensity along a ray. The high dimensionality of the equation leads to a very large number of unknowns when discretizing the equation. This is the major difficulty in its numerical solution. In case of isotropic scattering and diffuse boundaries, the radiative transfer equation can be reformulated into a system of integral equations of the second kind, where the position is the only independent variable. By employing the so-called momentum equation, we derive an integral equation, which is also valid in case of linear anisotropic scattering. This equation is very similar to the equation for the isotropic case: no additional unknowns are introduced and the integral operators involved have very similar mapping properties. The discretization of an integral operator leads to a full matrix. Therefore, due to the large dimension of the matrix in practical applcation, it is not feasible to assemble and store the entire matrix. The so-called matrix compression methods circumvent the assembly of the matrix. Instead, the matrix-vector multiplications needed by iterative solvers are performed only approximately, thus, reducing, the computational complexity tremendously. The kernels of the integral equation describing the radiative transfer are very similar to the kernels of the integral equations occuring in the boundary element method. Therefore, with only slight modifications, the matrix compression methods, developed for the latter are readily applicable to the former. As apposed to the boundary element method, the integral kernels for radiative transfer in absorbing and scattering media involve an exponential decay term. We examine how this decay influences the efficiency of the matrix compression methods. Further, a comparison with the discrete ordinate method shows that discretizing the integral equation may lead to reductions in CPU time and to an improved accuracy especially in case of small absorption and scattering coefficients or if local sources are present.

Semiparametric estimation of conditional quantiles for time series, with applications in finance
(2003)

The estimation of conditional quantiles has become an increasingly important issue in insurance and financial risk management. The stylized facts of financial time series data has rendered direct applications of extreme value theory methodologies, in the estimation of extreme conditional quantiles, inappropriate. On the other hand, quantile regression based procedures work well in nonextreme parts of a given data but breaks down in extreme probability levels. In order to solve this problem, we combine nonparametric regressions for time series and extreme value theory approaches in the estimation of extreme conditional quantiles for financial time series. To do so, a class of time series models that is similar to nonparametric AR-(G)ARCH models but which does not depend on distributional and moments assumptions, is introduced. We discuss estimation procedures for the nonextreme levels using the models and consider the estimates obtained by inverting conditional distribution estimators and by direct estimation using Koenker-Basset (1978) version for kernels. Under some regularity conditions, the asymptotic normality and uniform convergence, with rates, of the conditional quantile estimator for strong mixing time series, are established. We study the estimation of scale function in the introduced models using similar procedures and show that under some regularity conditions, the scale estimate is weakly consistent and asymptotically normal. The application of introduced models in the estimation of extreme conditional quantiles is achieved by augmenting them with methods in extreme value theory. It is shown that the overal extreme conditional quantiles estimator is consistent. A Monte Carlo study is carried out to illustrate the good performance of the estimates and real data are used to demonstrate the estimation of Value-at-Risk and conditional expected shortfall in financial risk management and their multiperiod predictions discussed.

Different aspects of geomagnetic field modelling from satellite data are examined in the framework of modern multiscale approximation. The thesis is mostly concerned with wavelet techniques, i.e. multiscale methods based on certain classes of kernel functions which are able to realize a multiscale analysis of the funtion (data) space under consideration. It is thus possible to break up complicated functions like the geomagnetic field, electric current densities or geopotentials into different pieces and study these pieces separately. Based on a general approach to scalar and vectorial multiscale methods, topics include multiscale denoising, crustal field approximation and downward continuation, wavelet-parametrizations of the magnetic field in Mie-representation as well as multiscale-methods for the analysis of time-dependent spherical vector fields. For each subject the necessary theoretical framework is established and numerical applications examine and illustrate the practical aspects.

The immiscible lattice BGK method for solving the two-phase incompressible Navier-Stokes equations is analysed in great detail. Equivalent moment analysis and local differential geometry are applied to examine how interface motion is determined and how surface tension effects can be included such that consistency to the two-phase incompressible Navier-Stokes equations can be expected. The results obtained from theoretical analysis are verified by numerical experiments. Since the intrinsic interface tracking scheme of immiscible lattice BGK is found to produce unsatisfactory results in two-dimensional simulations several approaches to improving it are discussed but all of them turn out to yield no substantial improvement. Furthermore, the intrinsic interface tracking scheme of immiscible lattice BGK is found to be closely connected to the well-known conservative volume tracking method. This result suggests to couple the conservative volume tracking method for determining interface motion with the Navier-Stokes solver of immiscible lattice BGK. Applied to simple flow fields, this coupled method yields much better results than plain immiscible lattice BGK.

One crucial assumption of continuous financial mathematics is that the portfolio can be rebalanced continuously and that there are no transaction costs. In reality, this of course does not work. On the one hand, continuous rebalancing is impossible, on the other hand, each transaction causes costs which have to be subtracted from the wealth. Therefore, we focus on trading strategies which are based on discrete rebalancing - in random or equidistant times - and where transaction costs are considered. These strategies are considered for various utility functions and are compared with the optimal ones of continuous trading.

In this work the investigation of a (Ti, Al, Si) N system was done. The main point of investigation was to study the possibility of getting the nanocomposite coatings structures by deposition of multilayer films from TiN, AlSiN, . This tries to understand the relation between the mechanical properties (hardness, Young s modulus), and the microstructure (nanocrystalline with individual phases). Particularly special attention was given to the temperature effects on microstructural changes in annealing at 600 °C for the coatings. The surface hardness, elastic modulus, and the multilayers diffusion and compositions were the test tools for the comparison between the different coated samples with and without annealing at 600 °C. To achieve this object a rectangular aluminum vacuum chamber with three unbalanced sputtering magnetrons for the deposition of thin film coatings from different materials was constructed The chamber consists mainly of two chambers, the pre-vacuum chamber to load the workpiece, and the main vacuum chamber where the sputtering deposition of the thin film coatings take place. The workpiece is moving on a car travel on a railway between the two chambers to the position of the magnetrons by step motors. The chambers are divided by a self constructed rectangular gate controlled manually from outside the chamber. The chamber was sealed for vacuum use using glue and screws. Therefore, different types of glue were tested not only for its ability to develop an uniform thin layer in the gap between the aluminum plates to seal the chamber for vacuum use, but also low outgassing rates which made it suitable for vacuum use. A epoxy was able to fulfill this tasks. The evacuation characteristics of the constructed chamber was improved by minimizing the inner surface outgassing rate. Therefore, the throughput outgassing rate test method was used in the comparisons between the selected two aluminum materials (A2017 and A5353) samples short time period (one hour) outgassing rates. Different machining methods and treatments for the inner surface of the vacuum chamber were tested. The machining of the surface of material A (A2017) with ethanol as coolant fluid was able to reduce its outgassing rate a factor of 6 compared with a non-machined sample surface of the same material. The reduction of the surface porous oxide layer on the top of the aluminum surface by the pickling process with HNO3 acid, and the protection of it by producing another passive non-porous oxides layer using anodizing process will protect the surface for longer time and will minimize the outgassing rates even under humid atmosphere The residual gas analyzer (RGA) 6. Summary test shows that more than 85% of the gases inside the test chamber were water vapour (H2O) and the rests are (N2, H2, CO), so liquid nitrogen water vapor trap can enhance the chamber pumping down process. As a result it was possible to construct a chamber that can be pumped down using a turbo molecular pump (450 L/s) to the range of 1x10-6 mbar within one hour of evacuations where the chamber volume is 160 Litters and the inner surface area is 1.6 m2. This is a good base pressure for the process of sputtering deposition of hard thin film coatings. Multilayer thin film coating was deposited to demonstrate that nanostructured thin film within the (Ti, Al, Si) N system could be prepared by reactive magnetron sputtering of multi thin film layers of TiN, AlSiN. The (SNMS) spectrometry of the test samples show that a complete diffusion between the different deposited thin film coating layers in each sample takes place, even at low substrate deposition temperature. The high magnetic flux of the unbalanced magnetrons and the high sputtering power were able to produce a high ion-toatom flux, which give high mobility to the coated atoms. The interactions between the high mobility of the coated atoms and the ion-to-atom flux were sufficient to enhance the diffusion between the different deposited thin layers. It was shown from the XRD patterns for this system that the structure of the formed mixture consists of two phases. One phase is noted as TiN bulk and another detected unknown amorphous phase, which can be SiNx or AlN or a combination of Ti-Al-Si-N. As a result we where able to deposit a nanocomposite coatings by the deposition of multilayers from TiN, AlSiN thin film coatings using the constructed vacuum chamber

Lung cancer, mainly caused by tobacco smoke, is the leading cause of cancer mortality. Large efforts in prevention and cessation have reduced smoking rates in the U.S. and other countries. Nevertheless, since 1990, rates have remained constant and it is believed that most of those currently smoking (~25%) are addicted to nicotine, and therefore are unable to stop smoking. An alternative strategy to reduce lung cancer mortality is the development of chemopreventive mixtures used to reduce cancer risk. Before entering clinical trails, it is crucial to know the efficacy, toxicity and the molecular mechanism by which the active compounds prevent carcinogenesis. 4-(methylnitrosamino)-1-(3-pyridyl)-1-butanone (NNK), N-nitrosonornicotine (NNN) and benzo[a]pyrene (B[a]P) are among the most carcinogenic compounds in tobacco smoke. All have been widely used as model carcinogens and their tumorigenic activities are well established. It is believed that formation of DNA adducts is a crucial step in carcinogenesis. NNK and NNN form 4-hydroxy-1-(3-pyridyl)-1-butanone releasing and methylating adducts, while B[a]P forms B[a]P-tetraol-releasing adducts. Different isothiocyanates (ITCs) are able to prevent NNK-, NNN- or B[a]P-induced tumor formation, but relative little is know about the mechanism of these preventive effects. In this thesis, the influence of different ITCs on adduct formation from NNK plus B[a]P and NNN were evaluated. Using an A/J mouse lung tumor model, it was first shown that the formation of HPB-releasing, O6-mG and B[a]P-tetraol-releasing adducts were not affected when NNK and B[a]P were given individually or in combination, of by gavage. Using the same model, the effects of different mixtures of PEITC and BITC, given by gavage or in the diet, on DNA adduct formation were evaluated. Dietary treatment with phenethyl isothiocyanate (PEITC) or PEITC plus benzyl isothiocyanate (BITC) reduced levels of HPB-releasing adducts by 40*50%. This is consistent with a previously shown 40% inhibition of tumor multiplicity for the same treatment. In the gavage treatments with ITCs it seemed that PEITC reduced HPB-releasing DNA adducts, while levels of BITC counteracted these effects. Levels of O6-mG were minimally affected by any of the treatments. Levels of B[a]P-tetraol releasing adducts were reduced by gavaged PEITC Summary Page XII and BITC, 120 h after the last carcinogen treatment, while dietary treatment had no effects. We then extended our investigation to F-344 rats by using a similar ITC treatment protocol as in the mouse model. NNK was given in the drinking water and B[a]P in diet. Dietary PEITC reduced the formation of HPB-releasing globin and DNA adducts in lung but not in liver, while levels of B[a]P-tetraol-releasing adducts were unaffected. Additionally, the effects of PEITC, 3-phenlypropyl isothiocyanate, and their N-acetylcystein conjugates in diet on adducts from NNN in drinking water were evaluated in rat esophageal DNA and globin. Using a protocol known to inhibit NNNinduced esophageal tumorigenesis, the levels of HPB-releasing adduct levels were unaffected by the ITCs treatment. The observations that dietary PEITC inhibited the formation of HPB-releasing DNA adducts only in mice where the control levels were above 1 fmol/µg DNA and adduct levels in rat lung were reduced to levels seen in liver, lead to the conclusion that in mice and rats, there are at least two activation pathway of NNK. One is PEITC-sensitive and responsible for the high adduct levels in lung and presumably also for higher carcinogenicity of NNK in lung. The other is PEITC-insensitive and responsible for the remaining adduct levels and tumorigenicity. In conclusion, our results demonstrated that the preventive mechanism by which ITCs inhibit carcinogenesis is only in part due to inhibition of DNA adduct formation and that other mechanisms are involved. There is a large body of evidence indicating that induction of apoptosis may be a mechanism by which ITCs prevent tumor formation, but further studies are required.

In this work we present and estimate an explanatory model with a predefined system of explanatory equations, a so called lag dependent model. We present a locally optimal, on blocked neural network based lag estimator and theorems about consistensy. We define the change points in context of lag dependent model, and present a powerfull algorithm for change point detection in high dimensional high dynamical systems. We present a special kind of bootstrap for approximating the distribution of statistics of interest in dependent processes.