Territory design may be viewed as the problem of grouping small geographic areas into larger geographic clusters called territories in such a way that the latter are acceptable according to relevant planning criteria. In this paper we review the existing literature for applications of territory design problems and solution approaches for solving these types of problems. After identifying features common to all applications we introduce a basic territory design model and present in detail two approaches for solving this model: a classical location–allocation approach combined with optimal split resolution techniques and a newly developed computational geometry based method. We present computational results indicating the efficiency and suitability of the latter method for solving large–scale practical problems in an interactive environment. Furthermore, we discuss extensions to the basic model and its integration into Geographic Information Systems.

Annual Report, Jahrbuch AG Magnetismus

Consider a cooling process described by a nonlinear heat equation. We are interested to recover the initial temperature from temperature measurements which are available on a part of the boundary for some time. Up to now even for the linear heat equation such a problem has been usually studied as a nonlinear ill-posed operator equation, and regularization methods involving Frechet derivatives have been applied. We propose a fast derivative-free iterative method. Numerical results are presented for the glass cooling process, where nonlinearity appears due to radiation.

In modern geoscience, understanding the climate depends on the information about the oceans. Covering two thirds of the Earth, oceans play an important role. Oceanic phenomena are, for example, oceanic circulation, water exchanges between atmosphere, land and ocean or temporal changes of the total water volume. All these features require new methods in constructive approximation, since they are regionally bounded and not globally observable. This article deals with methods of handling data with locally supported basis functions, modeling them in a multiscale scheme involving a wavelet approximation and presenting the main results for the dynamic topography and the geostrophic flow, e.g., in the Northern Atlantic. Further, it is demonstrated that compressional rates of the occurring wavelet transforms can be achieved by use of locally supported wavelets.

Music Information Retrieval (MIR) is an interdisciplinary research area that has the goal to improve the way music is accessible through information systems. One important part of MIR is the research for algorithms to extract meaningful information (called feature data) from music audio signals. Feature data can for example be used for content based genre classification of music pieces. This masters thesis contributes in three ways to the current state of the art: • First, an overview of many of the features that are being used in MIR applications is given. These methods – called “descriptors” or “features” in this thesis – are discussed in depth, giving a literature review and for most of them illustrations. • Second, a large part of the described features are implemented in a uniform framework, called T-Toolbox which is programmed in the Matlab environment. It also allows to do classification experiments and descriptor visualisation. For classification, an interface to the machine-learning environment WEKA is provided. • Third, preliminary evaluations are done investigating how well these methods are suited for automatically classifying music according to categorizations such as genre, mood, and perceived complexity. This evaluation is done using the descriptors implemented in the T-Toolbox, and several state-of-the-art machine learning algorithms. It turns out that – in the experimental setup of this thesis – the treated descriptors are not capable to reliably discriminate between the classes of most examined categorizations; but there is an indication that these results could be improved by developing more elaborate techniques.

We work in the setting of time series of financial returns. Our starting point are the GARCH models, which are very common in practice. We introduce the possibility of having crashes in such GARCH models. A crash will be modeled by drawing innovations from a distribution with much mass on extremely negative events, while in ''normal'' times the innovations will be drawn from a normal distribution. The probability of a crash is modeled to be time dependent, depending on the past of the observed time series and/or exogenous variables. The aim is a splitting of risk into ''normal'' risk coming mainly from the GARCH dynamic and extreme event risk coming from the modeled crashes. We will present several incarnations of this modeling idea and give some basic properties like the conditional first and second moments. For the special case that we just have an ARCH dynamic we can establish geometric ergodicity and, thus, stationarity and mixing conditions. Also in the ARCH case we formulate (quasi) maximum likelihood estimators and can derive conditions for consistency and asymptotic normality of the parameter estimates. In a special case of genuine GARCH dynamic we are able to establish L_1-approximability and hence laws of large numbers for the processes itself. We can formulate a conditional maximum likelihood estimator in this case, but cannot completely establish consistency for them. On the practical side we look for the outcome of estimating models with genuine GARCH dynamic and compare the result to classical GARCH models. We apply the models to Value at Risk estimation and see that in comparison to the classical models many of ours seem to work better although we chose the crash distributions quite heuristically.

Metallocenes containing diarylethene type photochromic switches are synthesized, characterized and tested in polyolefin catalysts. Propylene polymerizations using unbridged bis(2,3-dibenzo[b]thiophen-3-yl)cyclopenta[b]thien-3-yl)zirconium dichloride/MAO (80) treated with 254nm UV irradiation produced bimodal polymer distributions by GPC. This was due to an increase in the low molecular weight fractions when the closed form of the catalyst/photoswitch was made. Comparison with similarly structured catalyst without photoisomerization properties did not produce bimodal polymer under identical conditions. Propylene polymerizations made with dimethylsilyl[(1,5-dimethyl-3-phenylcyclopenta[b]thien-6-yl)][(2,3-dibenzothien-3-yl)cyclopenta[b]thien-6-yl)]zirconium dichloride/MAO (86) with 254nm UV irradiation caused a 3 fold increase in the polymer molecular weight. Polymers made with ethylene and ethylene/hexene using (80) after UV irradiation did not show differences in measured polymer properties. Polymerizations with ethylene/ hexene mixtures using (86) had increased activity and co-monomer (hexene) incorporation with UV irradiation.

Within the last decades, a remarkable development in materials science took place -- nowadays, materials are not only constructed for the use of inert structures but rather designed for certain predefined functions. This innovation was accompanied with the appearance of smart materials with reliable recognition, discrimination and capability of action as well as reaction. Even though ferroelectric materials serve smartly in real applications, they also possess several restrictions at high performance usage. The behavior of these materials is almost linear under the action of low electric fields or low mechanical stresses, but exhibits strong non-linear response under high electric fields or mechanical stresses. High electromechanical loading conditions result in a change of the spontaneous polarization direction with respect to individual domains, which is commonly referred to as domain switching. The aim of the present work is to develop a three-dimensional coupled finite element model, to study the rate-independent and rate-dependent behavior of piezoelectric materials including domain switching based on a micromechanical approach. The proposed model is first elaborated within a two-dimensional finite element setting for piezoelectric materials. Subsequently, the developed two-dimensional model is extended to the three-dimensional case. This work starts with developing a micromechanical model for ferroelectric materials. Ferroelectric materials exhibit ferroelectric domain switching, which refers to the reorientation of domains and occurs under purely electrical loading. For the simulation, a bulk piezoceramic material is considered and each grain is represented by one finite element. In reality, the grains in the bulk ceramics material are randomly oriented. This property is taken into account by applying random orientation as well as uniform distribution for individual elements. Poly-crystalline ferroelectric materials at un-poled virgin state can consequently be characterized by randomly oriented polarization vectors. Energy reduction of individual domains is adopted as a criterion for the initiation of domain switching processes. The macroscopic response of the bulk material is predicted by classical volume-averaging techniques. In general, domain switching does not only depend on external loads but also on neighboring grains, which is commonly denoted as the grain boundary effect. These effects are incorporated into the developed framework via a phenomenologically motivated probabilistic approach by relating the actual energy level to a critical energy level. Subsequently, the order of the chosen polynomial function is optimized so that simulations nicely match measured data. A rate-dependent polarization framework is proposed, which is applied to cyclic electrical loading at various frequencies. The reduction in free energy of a grain is used as a criterion for the onset of the domain switching processes. Nucleation in new grains and propagation of the domain walls during domain switching is modeled by a linear kinetics theory. The simulated results show that for increasing loading frequency the macroscopic coercive field is also increasing and the remanent polarization increases at lower loading amplitudes. The second part of this work is focused on ferroelastic domain switching, which refers to the reorientation of domains under purely mechanical loading. Under sufficiently high mechanical loading, however, the strain directions within single domains reorient with respect to the applied loading direction. The reduction in free energy of a grain is used as a criterion for the domain switching process. The macroscopic response of the bulk material is computed for the hysteresis curve (stress vs strain) whereby uni-axial and quasi-static loading conditions are applied on the bulk material specimen. Grain boundary effects are addressed by incorporating the developed probabilistic approach into this framework and the order of the polynomial function is optimized so that simulations match measured data. Rate dependent domain switching effects are captured for various frequencies and mechanical loading amplitudes by means of the developed volume fraction concept which relates the particular time interval to the switching portion. The final part of this work deals with ferroelectric and ferroelastic domain switching and refers to the reorientation of domains under coupled electromechanical loading. If this free energy for combined electromechanical loading exceeds the critical energy barrier elements are allowed to switch. Firstly, hysteresis and butterfly curves under purely electrical loading are discussed. Secondly, additional mechanical loads in axial and lateral directions are applied to the specimen. The simulated results show that an increasing compressive stress results in enlarged domain switching ranges and that the hysteresis and butterfly curves flatten at higher mechanical loading levels.

This thesis aims at an overall improvement of the diffusion coefficient predictions. For this reason the theoretical determination of diffusion, viscosity, and thermodynamics in liquid systems is discussed. Furthermore, the experimental determination of diffusion coefficients is also part of this work. All investigations presented are carried out for organic binary liquid mixtures. Diffusion coefficient data of 9 highly nonideal binary mixtures are reported over the whole concentration range at various temperatures, (25, 30, and 35) °C. All mixtures investigated in a Taylor dispersion apparatus consist of an alcohol (ethanol, 1-propanol, or 1-butanol) dissolved in hexane, cyclohexane, carbon tetrachloride, or toluene. The uncertainty of the reported data is estimated to be within 310-11 m2s-1. To compute the thermodynamic correction factor an excess Gibbs energy model is required. Therefore, the applicability of COSMOSPACE to binary VLE predictions is thoroughly investigated. For this purpose a new method is developed to determine the required molecular parameters such as segment types, areas, volumes, and interaction parameters. So-called sigma profiles form the basis of this approach which describe the screening charge densities appearing on a molecule’s surface. To improve the prediction results a constrained two-parameter fitting strategy is also developed. These approaches are crucial to guarantee the physical significance of the segment parameters. Finally, the prediction quality of this approach is compared to the findings of the Wilson model, UNIQUAC, and the a priori predictive method COSMO-RS for a broad range of thermodynamic situations. The results show that COSMOSPACE yields results of similar quality compared to the Wilson model, while both perform much better than UNIQUAC and COSMO-RS. Since viscosity influences also the diffusion process, a new mixture viscosity model has been developed on the basis of Eyring’s absolute reaction rate theory. The nonidealities of the mixture are accounted for with the thermodynamically consistent COSMOSPACE approach. The required model and component parameters are derived from sigma-profiles, which form the basis of the a priori predictive method COSMO-RS. To improve the model performance two segment parameters are determined from a least-squares analysis to experimental viscosity data, whereas a constraint optimisation procedure is applied. In this way the parameters retain their physical meaning. Finally, the viscosity calculations of this approach are compared to the findings of the Eyring-UNIQUAC model for a broad range of chemical mixtures. These results show that the new Eyring-COSMOSPACE approach is superior to the frequently employed Eyring-UNIQUAC method. Finally, on the basis of Eyring’s absolute reaction rate theory a new model for the Maxwell-Stefan diffusivity has been developed. This model, an extension of the Vignes equation, describes the concentration dependence of the diffusion coefficient in terms of the diffusivities at infinite dilution and an additional excess Gibbs energy contribution. This energy part allows the explicit consideration of thermodynamic nonidealities within the modelling of this transport property. If the same set of interaction parameters, which has been derived from VLE data, is applied for this part and for the thermodynamic correction, a theoretically sound modelling of VLE and diffusion can be achieved. The influence of viscosity and thermodynamics on the model accuracy is thoroughly investigated. For this purpose diffusivities of 85 binary mixtures consisting of alkanes, cycloalkanes, halogenated alkanes, aromatics, ketones, and alcohols are computed. The average relative deviation between experimental data and computed values is approximately 8 % depending on the choice of the gE-model. These results indicate that this model is superior to some widely used methods. In summary, it can be said that the new approach facilitates the prediction of diffusion coefficients. The final equation is mathematically simple, universally applicable, and the prediction quality is as good as other models recently developed without having to worry about additional parameters, like pure component physical property data, self diffusion coefficients, or mixture viscosities. In contrast to many other models, the influence of the mixture viscosity can be omitted. Though a viscosity model is not required in the prediction of diffusion coefficients with the new equation, the models presented in this work allow a consistent modelling approach of diffusion, viscosity, and thermodynamics in liquid systems.

The aim of the thesis is the numerical investigation of saturated, stationary, incompressible Newtonian flow in porous media when inertia is not negligible. We focus our attention to the Navier-Stokes system with two pressures derived by two-scale homogenization. The thesis is subdivided into five Chapters. After the introductory remarks on porous media, filtration laws and upscaling methods, the first chapter is closed by stating the basic terminology and mathematical fundamentals. In Chapter 2, we start by formulating the Navier-Stokes equations on a periodic porous medium. By two-scale expansions of the velocity and pressure, we formally derive the Navier-Stokes system with two pressures. For the sake of completeness, known existence and uniqueness results are repeated and a convergence proof is given. Finally, we consider Stokes and Navier-Stokes systems with two pressures with respect to their relation to Darcy's law. Chapter 3 and Chapter 4 are devoted to the numerical solution of the nonlinear two pressure system. Therefore, we follow two approaches. The first approach which is developed in Chapter 3 is based on a splitting of the Navier-Stokes system with two pressures into micro and macro problems. The splitting is achieved by Taylor expanding the permeability function or by discretely computing the permeability function. The problems to be solved are a series of Stokes and Navier-Stokes problems on the periodicity cell. The Stokes problems are solved by an Uzawa conjugate gradient method. The Navier-Stokes equations are linearized by a least-squares conjugate gradient method, which leads to the solution of a sequence of Stokes problems. The macro problem consists of solving a nonlinear uniformly elliptic equation of second order. The least-squares linearization is applied to the macro problem leading to a sequence of Poisson problems. All equations will be discretized by finite elements. Numerical results are presented at the end of Chapter 3. The second approach presented in Chapter 4 relies on the variational formulation in a certain Hilbert space setting of the Navier-Stokes system with two pressures. The nonlinear problem is again linearized by the least-squares conjugate gradient method. We obtain a sequence of Stokes systems with two pressures. For the latter systems, we propose a fast solution method which relies on pre-computing Stokes systems on the periodicity cell for finite element basis functions acting as right hand sides. Finally, numerical results are discussed. In Chapter 5 we are concerned with modeling and simulation of the pressing section of a paper machine. We state a two-dimensional model of a press nip which takes into account elasticity and flow phenomena. Nonlinear filtration laws are incorporated into the flow model. We present a numerical solution algorithm and the chapter is closed by a numerical investigation of the model with special focus on inertia effects.