### Refine

#### Year of publication

- 2010 (56) (remove)

#### Document Type

- Report (26)
- Doctoral Thesis (22)
- Preprint (4)
- Bachelor Thesis (1)
- Diploma Thesis (1)
- Master's Thesis (1)
- Periodical Part (1)

#### Language

- English (56) (remove)

#### Keywords

- Erwarteter Nutzen (2)
- Lagrangian mechanics (2)
- Numerische Strömungssimulation (2)
- Portfolio Selection (2)
- Stochastische dynamische Optimierung (2)
- numerical upscaling (2)
- optimal control (2)
- portfolio choice (2)
- work effort (2)
- Abstraction (1)

#### Faculty / Organisational entity

We consider a highly-qualified individual with respect to her choice between two distinct career paths. She can choose between a mid-level management position in a large company and an executive position within a smaller listed company with the possibility to directly affect the company’s share price. She invests in the financial market includ- ing the share of the smaller listed company. The utility maximizing strategy from consumption, investment, and work effort is derived in closed form for logarithmic utility. The power utility case is discussed as well. Conditions for the individual to pursue her career with the smaller listed company are obtained. The participation constraint is formulated in terms of the salary differential between the two posi- tions. The smaller listed company can offer less salary. The salary shortfall is offset by the possibility to benefit from her work effort by acquiring own-company shares. This gives insight into aspects of optimal contract design. Our framework is applicable to the pharma- ceutical and financial industry, and the IT sector.

Laser-induced thermotherapy (LITT) is an established minimally invasive percutaneous technique of tumor ablation. Nevertheless, there is a need to predict the effect of laser applications and optimizing irradiation planning in LITT. Optical attributes (absorption, scattering) change due to thermal denaturation. The work presents the possibility to identify these temperature dependent parameters from given temperature measurements via an optimal control problem. The solvability of the optimal control problem is analyzed and results of successful implementations are shown.

The main focus of this dissertation is the synthesis and characterization of more recent zeolites with different pore architectures. The unique shape-selective properties of the zeolites are important in various chemical processes and the new zeolites containing novel internal pore architectures are of high interest, since they could lead to further improvement of existing processes or open the way to new applications. This dissertation is organized in the following way: The first part is focused on the synthesis of selected recent zeolites with different pore architectures and their modification to the acidic and bifunctional forms. The second part comprises the characterization of the physicochemical properties of the prepared zeolites by selected physicochemical methods, viz. powder X-ray diffractometry (XRD), N2 adsorption, thermogravimetric analysis (TGA/DTA/MS), ultraviolet-visible (UV-Vis) spectroscopy, atomic absorption spectroscopy (AAS), infrared (IR) spectroscopy, scanning electron microscopy (SEM), 27Al and 29Si magic angle spinning nuclear magnetic resonance (MAS NMR) spectroscopy, temperature-programmed reduction (TPR), temperature-programmed desorption of pyridine (pyridine TPD) and adsorption experiments with hydrocarbon adsorptives. The third part of this work is devoted to the application of test reactions, i.e., the acid catalyzed disproportionation of ethylbenzene and the bifunctional hydroconversion of n-decane, to characterize the pore size and architecture of the prepared zeolites. They are known to be valuable tools for exploring the pore structure of zeolites. Finally, an additional test, viz. the competitive hydrogenation of 1-hexene and 2,4,4-trimethyl-1-pentene, has been applied to probe the location of noble metals in medium pore zeolite. The synthesis of the following zeolite molecular sieves was successfully performed in the frame of this thesis (they are ranked according to the largest window size in the respective structure): • 14-MR pores: UTD-1, CIT-5, SSZ-53 and IM-12 • 12-MR pores: ITQ-21 and MCM-68 • 10-MR pores: SSZ-35 and MCM-71 All of them were obtained as pure phase (except zeolite MCM-71 with a minor impurity phase that is hardly to avoid and also present in samples shown in the patent literature). The synthesis conditions are very critical with respect to the formation of the zeolite with a given structure. In this work, the recommended synthesis recipes are included. Among the 14-MR zeolites, the aluminosilicates UTD-1 (nSi/nAl = 28), CIT-5 (nSi/nAl = 116) and SSZ-53 (nSi/nAl = 55) with unidimensional extra-large pore opening formed from 14-MR rings exhibit promising catalytic properties with high thermal stability and they possess strong Brønsted-acid sites. By contrast, the germanosilicate IM-12 with a structure containing 14-MR channels intersecting with 12-MR channels is unstable toward moisture. It was found that UTD-1 and SSZ-53 zeolites are highly active catalysts for the acid catalyzed disproportionation of ethylbenzene and n-decane hydroconversion due to their high Brønsted acidity. To explore their pore structures, the applied two test reactions suggest that UTD-1, CIT-5 and SSZ-53 zeolites contain a very open pore system (12-MR or larger pore systems) because the product distributions are not hampered by too small pores. ITQ-21, a germanoaluminosilicate zeolite with a three-dimensional pore system and large spherical cages accessible through six 12-MR windows, can be synthesized with nSi/nAl ratios between 27 and >200. It possesses a large amount of Brønsted-acid sites. The aluminosilicate zeolite MCM-68 (nSi/nAl = 9) is an extremely active catalyst in the disproportionation of ethylbenzene and in the n-decane hydroconversion. This is due to the presence of a high density of strong Brønsted-acid sites in its structure. The disproportionation of ethylbenzene suggests that MCM-68 is a large pore (i.e., at least 12-MR) zeolite, in agreement with its crystallographic structure. In the hydroconversion of n-decane, the presence of tribranched and ethylbranched isomers and a high isopentane yield of 58 % in the hydrocracked products suggest the presence of large (12-MR) pores in its structure. By contrast, a relatively high value for CI* (modified constraint index) of 2.9 suggests the presence of medium (10-MR) pores in its structure. As a whole, the results are in-line with the crystallographic structure of MCM-68. SSZ-35, a 10-MR zeolite, can be synthesized in a broad range of nSi/nAl ratios between 11 and >500. This zeolite is interesting in terms of shape selectivity resulting from its unusual pore system having unidimensional channels alternating between 10-MR windows and large 18-MR cages. This thermally very stable zeolite contains both, strong Brønsted- and strong Lewis-acid sites. The disproportionation of ethylbenzene classifies SSZ-35 as a large pore zeolite. In the hydroconversion of n-decane, the suppression of bulky ethyloctanes and propylheptane clearly suggests the presence of 10-MR sections in the pore system. By contrast, the low CI* values of 1.2-2.3 and the high isopentane yields of 56-60 % in the hydrocracked products suggest that SSZ-35 also possesses larger intracystalline voids, i.e., the 18-MR cages. The results from the catalytic characterization are in good agreement with the crystallographic structure of zeolite SSZ-35. It was also found that the nSi/nAl ratio influences the crystallite size and therefore the external surface area. As a consequence, product selectivities are also influenced: The lowest nSi/nAl ratio or the smallest crystallite size sample produces larger amounts of the relatively bulky products. The formation of these products probably results from the higher conversion or they are preferentially formed on the external surface area of the catalyst. Zeolite MCM-71 (nSi/nAl = 8) possesses an extremely thermally stable structure and contains a high concentration of Brønsted-acid sites. Its structure allows for the separation of n-alkanes from branched alkanes by selective adsorption. MCM-71 exhibits unique shape-selective properties towards the product distribution in ethylbenzene disproportionation, which is different to those obtained in the medium pore SSZ-35 zeolite. All reaction parameters are fulfilled to classify MCM-71 as medium pore zeolite and this is in good agreement with its reported structure consisting of two-dimensional network of elliptical 10-MR channels and an orthogonal sinusoidal 8-MR channels. The competitive hydrogenation of 1-hexene and 2,4,4-trimethyl-1-pentene was exploited to probe that the major part of the noble metal is located inside the intracrystalline void volume of the medium pore zeolite SSZ-35.

This paper discusses a numerical subgrid resolution approach for solving the Stokes-Brinkman system of equations, which is describing coupled ow in plain and in highly porous media. Various scientic and industrial problems are described by this system, and often the geometry and/or the permeability vary on several scales. A particular target is the process of oil ltration. In many complicated lters, the lter medium or the lter element geometry are too ne to be resolved by a feasible computational grid. The subgrid approach presented in the paper is aimed at describing how these ne details are accounted for by solving auxiliary problems in appropriately chosen grid cells on a relatively coarse computational grid. This is done via a systematic and a careful procedure of modifying and updating the coecients of the Stokes-Brinkman system in chosen cells. This numerical subgrid approach is motivated from one side from homogenization theory, from which we borrow the formulations for the so called cell problem, and from the other side from the numerical upscaling approaches, such as Multiscale Finite Volume, Multiscale Finite Element, etc. Results on the algorithm's eciency, both in terms of computational time and memory usage, are presented. Comparison with solutions on full ne grid (when possible) are presented in order to evaluate the accuracy. Advantages and limitations of the considered subgrid approach are discussed.

Modeling of species and charge transport in Li-Ion Batteries based on non-equilibrium thermodynamics
(2010)

In order to improve the design of Li ion batteries the complex interplay of various physical phenomena in the active particles of the electrodes and in the electrolyte has to be balanced. The separate transport phenomena in the electrolyte and in the active particle as well as their coupling due to the electrochemical reactions at the interfaces between the electrode particles and the electrolyte will inuence the performance and the lifetime of a battery. Any modeling of the complex phenomena during the usage of a battery has therefore to be based on sound physical and chemical principles in order to allow for reliable predictions for the response of the battery to changing load conditions. We will present a modeling approach for the transport processes in the electrolyte and the electrodesbased on non-equilibrium thermodynamics and transport theory. The assumption of local charge neutrality, which is known to be valid in concentrated electrolytes, is explicitly used to identify the independent thermodynamic variables and uxes. The theory guarantees strictly positive entropy production. Dierences to other theories will be discussed.

In this article we present a method to generate random objects from a large variety of combinatorial classes according to a given distribution. Given a description of the combinatorial class and a set of sample data our method will provide an algorithm that generates objects of size n in worst-case runtime O(n^2) (O(n log(n)) can be achieved at the cost of a higher average-case runtime), with the generated objects following a distribution that closely matches the distribution of the sample data.

In this work a 3-dimensional contact elasticity problem for a thin fiber and a rigid foundation is studied. We describe the contact condition by a linear Robin-condition (by meaning of the penalized and linearized non-penetration and friction conditions).
The dimension of the problem is reduced by an asymptotic approach. Scaling the Robin parameters appropriately we obtain a recurrent chain of Neumann type boundary value problems which are considered only in the microscopic scale. The problem for the leading term is a homogeneous Neumann problem, hence the leading term depends only on the slow variable. This motivates the choice of a multiplicative ansatz in the asymptotic expansion.
The theoretical results are illustrated with numerical examples performed with a commercial finite-element software-tool.

Wireless sensor networks are the driving force behind many popular and interdisciplinary research areas, such as environmental monitoring, building automation, healthcare and assisted living applications. Requirements like compactness, high integration of sensors, flexibility, and power efficiency are often very different and cannot be fulfilled by state-of-the-art node platforms at once. In this paper, we present and analyze AmICA: a flexible, compact, easy-to-program, and low-power node platform. Developed from scratch and including a node, a basic communication protocol, and a debugging toolkit, it assists in an user-friendly rapid application development. The general purpose nature of AmICA was evaluated in two practical applications with diametric requirements. Our analysis shows that AmICA nodes are 67% smaller than BTnodes, have five times more sensors than Mica2Dot and consume 72% less energy than the state-of-the-art TelosB mote in sleep mode.

Wireless Sensor Networks (WSN) are dynamically-arranged networks typically composed of a large number of arbitrarily-distributed sensor nodes with computing capabilities contributing to –at least– one common application. The main characteristic of these networks is that of being functionally constrained due to a scarce availability of resources and strong dependence on uncontrollable environmental factors. These conditions introduce severe restrictions on the applicability of classic real-time methods aiming at guaranteeing time-bounded communications. Existing real-time solutions tend to apply concepts that were originally not conceived for sensor networks, idealizing realistic application scenarios and overlooking at important design limitations. This results in a number of misleading practices contributing to approaches of restricted validity in real-world scenarios. Amending the confrontation between WSNs and real-time objectives starts with a review of the basic fundamentals of existing approaches. In doing so, this thesis presents an alternative approach based on a generalized timeliness notion suitable to the particularities of WSNs. The new conceptual notion allows the definition of feasible real-time objectives opening a new scope of possibilities not constrained to idealized systems. The core of this thesis is based on the definition and application of Quality of Service (QoS) trade-offs between timeliness and other significant QoS metrics. The analysis of local and global trade-offs provides a step-by-step methodology identifying the correlations between these quality metrics. This association enables the definition of alternative trade-off configurations (set points) influencing the quality performance of the network at selected instants of time. With the basic grounds established, the above concepts are embedded in a simple routing protocol constituting a proof of concept for the validity of the presented analysis. Extensive evaluations under realistic scenarios are driven on simulation environments as well as real testbeds, validating the consistency of this approach.

In this work, we develop a framework for analyzing an executive’s own- company stockholding and work effort preferences. The executive, character- ized by risk aversion and work effectiveness parameters, invests his personal wealth without constraint in the financial market, including the stock of his own company whose value he can directly influence with work effort. The executive’s utility-maximizing personal investment and work effort strategy is derived in closed form for logarithmic and power utility and for exponential utility for the case of zero interest rates. Additionally, a utility indifference rationale is applied to determine his fair compensation. Being unconstrained by performance contracting, the executive’s work effort strategy establishes a base case for theoretical or empirical assessment of the benefits or otherwise of constraining executives with performance contracting. Further, we consider a highly-qualified individual with respect to her choice between two distinct career paths. She can choose between a mid-level management position in a large company and an executive position within a smaller listed company with the possibility to directly affect the company’s share price. She invests in the financial market including the share of the smaller listed company. The utility maximizing strategy from consumption, investment, and work effort is derived in closed form for logarithmic utility and power utility. Conditions for the individual to pursue her career with the smaller listed company are obtained. The participation constraint is formulated in terms of the salary differential between the two positions. The smaller listed company can offer less salary. The salary shortfall is offset by the possibilityto benefit from her work effort by acquiring own-company shares. This givesinsight into aspects of optimal contract design. Our framework is applicable to the pharmaceutical and financial industry, as well as the IT sector.

In a dynamic network, the quickest path problem asks for a path such that a given amount of flow can be sent from source to sink via this path in minimal time. In practical settings, for example in evacuation or transportation planning, the problem parameters might not be known exactly a-priori. It is therefore of interest to consider robust versions of these problems in which travel times and/or capacities of arcs depend on a certain scenario. In this article, min-max versions of robust quickest path problems are investigated and, depending on their complexity status, exact algorithms or fully polynomial-time approximation schemes are proposed.

Simulation of multibody systems (mbs) is an inherent part in developing and design of complex mechanical systems. Moreover, simulation during operation gained in importance in the recent years, e.g. for HIL-, MIL- or monitoring applications. In this paper we discuss the numerical simulation of multibody systems on different platforms. The main section of this paper deals with the simulation of an established truck model [9] on different platforms, one microcontroller and two real-time processor boards. Additional to numerical C-code the latter platforms provide the possibility to build the model with a commercial mbs tool, which is also investigated. A survey of different ways of generating code and equations of mbs models is given and discussed concerning handling, possible limitations as well as performance. The presented benchmarks are processed under terms of on-board real time applications. A further important restriction, caused by the real-time requirement, is a fixed integration step size. Whence, carefully chosen numerical integration algorithms are necessary, especially in the case of closed loops in the model. We investigate linearly-implicit time integration methods with fixed step size, so-called Rosenbrock methods, and compare them with respect to their accuracy and performance on the tested processors.

We will present a rigorous derivation of the equations and interface conditions for ion, charge and heat transport in Li-ion insertion batteries. The derivation is based exclusively on universally accepted principles of nonequilibrium thermodynamics and the assumption of a one step intercalation reaction at the interface of electrolyte and active particles. Without loss of generality the transport in the active particle is assumed to be isotropic. The electrolyte is described as a fully dissociated salt in a neutral solvent. The presented theory is valid for transport on a spatial scale for which local charge neutrality holds i.e. beyond the scale of the diffuse double layer. Charge neutrality is explicitely used to determine the correct set of thermodynamically independent variables. The theory guarantees strictly positive entropy production. The various contributions to the Peltier coeficients for the interface between the active particles and the electrolyte as well as the contributions to the heat of mixing are obtained as a result of the theory.

The scope of this paper is to enhance the model for the own-company stockholder (given in Desmettre, Gould and Szimayer (2010)), who can voluntarily performance-link his personal wealth to his management success by acquiring stocks in the own-company whose value he can directly influence via spending work effort. The executive is thereby characterized by a parameter of risk aversion and the two work effectiveness parameters inverse work productivity and disutility stress. We extend the model to a constant absolute risk aversion framework using an exponential utility/disutility set-up. A closed-form solution is given for the optimal work effort an executive will apply and we derive the optimal investment strategies of the executive. Furthermore, we determine an up-front fair cash compensation applying an indifference utility rationale. Our study shows to a large extent that the results previously obtained are robust under the choice of the utility/disutility set-up.

The optimal design of rotational production processes for glass wool manufacturing poses severe computational challenges to mathematicians, natural scientists and engineers. In this paper we focus exclusively on the spinning regime where thousands of viscous thermal glass jets are formed by fast air streams. Homogeneity and slenderness of the spun fibers are the quality features of the final fabric. Their prediction requires the computation of the fuidber-interactions which involves the solving of a complex three-dimensional multiphase problem with appropriate interface conditions. But this is practically impossible due to the needed high resolution and adaptive grid refinement. Therefore, we propose an asymptotic coupling concept. Treating the glass jets as viscous thermal Cosserat rods, we tackle the multiscale problem by help of momentum (drag) and heat exchange models that are derived on basis of slender-body theory and homogenization. A weak iterative coupling algorithm that is based on the combination of commercial software and self-implemented code for ow and rod solvers, respectively, makes then the simulation of the industrial process possible. For the boundary value problem of the rod we particularly suggest an adapted collocation-continuation method. Consequently, this work establishes a promising basis for future optimization strategies.

In this paper a three dimensional stochastic model for the lay-down of fibers on a moving conveyor belt in the production process of nonwoven materials is derived. The model is based on stochastic diferential equations describing the resulting position of the fiber on the belt under the influence of turbulent air ows. The model presented here is an extension of an existing surrogate model, see [6, 3].

The modelling of hedge funds poses a difficult problem since the available reported data sets are often small and incomplete. We propose a switching regression model for hedge funds, in which the coefficients are able to switch between different regimes. The coefficients are governed by a Markov chain in discrete time. The different states of the Markov chain represent different states of the economy, which influence the performance of the independent variables. Hedge fund indices are chosen as regressors. The parameter estimation for the switching parameter as well as for the switching error term is done through a filtering technique for hidden Markov models developed by Elliott (1994). Recursive parameter estimates are calculated through a filter-based EM-algorithm, which uses the hidden information of the underlying Markov chain. Our switching regression model is applied on hedge fund series and hedge fund indices from the HFR database.

We consider multiple objective combinatiorial optimization problems in which the first objective is of arbitrary type and the remaining objectives are either bottleneck or k-max objective functions. While the objective value of a bottleneck objective is determined by the largest cost value of any element in a feasible solution, the kth-largest element defines the objective value of the k-max objective. An efficient solution approach for the generation of the complete nondominated set is developed which is independent of the specific combinatiorial problem at hand. This implies a polynomial time algorithm for several important problem classes like shortest paths, spanning tree, and assignment problems with bottleneck objectives which are known to be NP-hard in the general multiple objective case.

Point defects in piezoelectric materials – continuum mechanical modelling and numerical simulation
(2010)

The topic of this work is the continuum mechanic modelling of point defects in piezoelectric materials. Devices containing piezoelectric material and especially ferroelectrics require a high precision and are exposed to a high number of electrical and mechanical load cycles. As a result, the relevant material properties may decrease with increasing load cycles. This phenomenon is called electric fatigue. The transported ionic and electric charge carriers can interact with each other, as well as with structural elements (grain boundaries, inhomogeneities) or with material interfaces (domain walls). A reduced domain wall mobility also reduces the electromechanical coupling effect, which leads to the electric fatigue effect. The materials considered here are barium titanate and lead zirconate titanate (PZT), in which oxygen vacancies is the most mobile and most frequently appearing defect species. Intentionally introduced foreign atoms (dopants) can adjust the material properties according to their field of application by generating electric dipoles with the vacancies. Agglomerations of point defects can strongly influence the domain wall motion. The domain wall can be slowed down or even be stopped by the locally varying fields in the vicinity of the clusters. Accumulations of point defects can be detected at electrodes, pores or in the bulk of fatigued samples. The present thesis concentrates focuses on the self interaction behaviour of point defects in the bulk. A micro mechanical continuum model is used to show the qualitative and the quantitative interaction behaviour of defects in a static setup and during drift processes. The modelling neglects the ferroelectric switching mechanisms, but is applicable to every piezoelectric material. The underlying differential equations are solved by means of analytical (Green's functions) and numerical (Finite Differences with discrete Fourier Transform) methods, depending on the boundary conditions. The defects are introduced as localised Eigenstrains, as electric charges and as electric dipoles. The required defect parameters are obtained by comparisons with atomistic methods (lattice statics). There are no standardised procedures available for the parameter identification. In this thesis, the mechanical parameter is obtained by a comparison of relaxation volumes of the atomic lattice and the continuum solution. Parameters for isotropic and anisotropic defect descriptions are identified. The strength of the electric defect is obtained by a comparison of the electric internal energies of atomistics and continuum. The appearing singularities are eliminated by taking only the energy difference of a infinite crystal and a periodic cell into account. Both identification processes are carried out for the cubic structure of barium titanate, which decouples the mechanical and the electrical problem. The defect interaction is analysed by means of configurational forces. The mechanical defect parameter generates a directional short-range attraction between defects. An electrical defect parameter produces the long-range Coulomb interaction, which predicts a repulsion of two similar charges. Additionally, an interaction with defect dipoles is taken into account. It is shown that a defect agglomeration is possible for any static defect configuration. Finally, defect drift is simulated using a thermodynamically motivated migration law based on configurational forces. In this context, the migration of point defects due to self interaction, and the influence of external fields is investigated.

It has been observed that for understanding the biological function of certain RNA molecules, one has to study joint secondary structures of interacting pairs of RNA. In this thesis, a new approach for predicting the joint structure is proposed and implemented. For this, we introduce the class of m-dimensional context-free grammars --- an extension of stochastic context-free grammars to multiple dimensions --- and present an Earley-style semiring parser for this class. Additionally, we develop and thoroughly discuss an implementation variant of Earley parsers tailored to efficiently handle dense grammars, which embraces the grammars used for structure prediction. A currently proposed partitioning scheme for joint secondary structures is transferred into a two-dimensional context-free grammar, which in turn is used as a stochastic model for RNA-RNA interaction. This model is trained on actual data and then used for predicting most likely joint structures for given RNA molecules. While this technique has been widely used for secondary structure prediction of single molecules, RNA-RNA interaction was hardly approached this way in the past. Although our parser has O(n^3 m^3) time complexity and O(n^2 m^2) space complexity for two RNA molecules of sizes n and m, it remains practically applicable for typical sizes if enough memory is available. Experiments show that our parser is much more efficient for this application than classical Earley parsers. Moreover the predictions of joint structures are comparable in quality to current energy minimization approaches.