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A Consistent Large Eddy Approach for Lattice Boltzmann Methods and its Application to Complex Flows
(2015)

Lattice Boltzmann Methods have shown to be promising tools for solving fluid flow problems. This is related to the advantages of these methods, which are among others, the simplicity in handling complex geometries and the high efficiency in calculating transient flows. Lattice Boltzmann Methods are mesoscopic methods, based on discrete particle dynamics. This is in contrast to conventional Computational Fluid Dynamics methods, which are based on the solution of the continuum equations. Calculations of turbulent flows in engineering depend in general on modeling, since resolving of all turbulent scales is and will be in near future far beyond the computational possibilities. One of the most auspicious modeling approaches is the large eddy simulation, in which the large, inhomogeneous turbulence structures are directly computed and the smaller, more homogeneous structures are modeled.
In this thesis, a consistent large eddy approach for the Lattice Boltzmann Method is introduced. This large eddy model includes, besides a subgrid scale model, appropriate boundary conditions for wall resolved and wall modeled calculations. It also provides conditions for turbulent domain inlets. For the case of wall modeled simulations, a two layer wall model is derived in the Lattice Boltzmann context. Turbulent inlet conditions are achieved by means of a synthetic turbulence technique within the Lattice Boltzmann Method.
The proposed approach is implemented in the Lattice Boltzmann based CFD package SAM-Lattice, which has been created in the course of this work. SAM-Lattice is feasible of the calculation of incompressible or weakly compressible, isothermal flows of engineering interest in complex three dimensional domains. Special design targets of SAM-Lattice are high automatization and high performance.
Validation of the suggested large eddy Lattice Boltzmann scheme is performed for pump intake flows, which have not yet been treated by LBM. Even though, this numerical method is very suitable for this kind of vortical flows in complicated domains. In general, applications of LBM to hydrodynamic engineering problems are rare. The results of the pump intake validation cases reveal that the proposed numerical approach is able to represent qualitatively and quantitatively the very complex flows in the intakes. The findings provided in this thesis can serve as the basis for a broader application of LBM in hydrodynamic engineering problems.

We consider the multiscale model for glioma growth introduced in a previous work and extend it to account
for therapy effects. Thereby, three treatment strategies involving surgical resection, radio-, and
chemotherapy are compared for their efficiency. The chemotherapy relies on inhibiting the binding
of cell surface receptors to the surrounding tissue, which impairs both migration and proliferation.

A new solution approach for solving the 2-facility location problem in the plane with block norms
(2015)

Motivated by the time-dependent location problem over T time-periods introduced in
Maier and Hamacher (2015) we consider the special case of two time-steps, which was shown
to be equivalent to the static 2-facility location problem in the plane. Geometric optimality
conditions are stated for the median objective. When using block norms, these conditions
are used to derive a polygon grid inducing a subdivision of the plane based on normal cones,
yielding a new approach to solve the 2-facility location problem in polynomial time. Combinatorial algorithms for the 2-facility location problem based on geometric properties are
deduced and their complexities are analyzed. These methods differ from others as they are
completely working on geometric objects to derive the optimal solution set.

A nonlocal stochastic model for intra- and extracellular proton dynamics in a tumor is proposed.
The intracellular dynamics is governed by an SDE coupled to a reaction-diffusion
equation for the extracellular proton concentration on the macroscale. In a more general context
the existence and uniqueness of solutions for local and nonlocal
SDE-PDE systems are established allowing, in particular, to analyze the proton dynamics model both,
in its local version and the case with nonlocal path dependence.
Numerical simulations are performed
to illustrate the behavior of solutions, providing some insights into the effects of randomness on tumor acidity.

In this paper we propose a phenomenological model for the formation of an interstitial gap between the tumor and the stroma. The gap
is mainly filled with acid produced by the progressing edge of the tumor front. Our setting extends existing models for acid-induced tumor invasion models to incorporate
several features of local invasion like formation of gaps, spikes, buds, islands, and cavities. These behaviors are obtained mainly due to the random dynamics at the intracellular
level, the go-or-grow-or-recede dynamics on the population scale, together with the nonlinear coupling between the microscopic (intracellular) and macroscopic (population)
levels. The wellposedness of the model is proved using the semigroup technique and 1D and 2D numerical simulations are performed to illustrate model predictions and draw
conclusions based on the observed behavior.

The present thesis describes the development and validation of a viscosity adaption method for the numerical simulation of non-Newtonian fluids on the basis of the Lattice Boltzmann Method (LBM), as well as the development and verification of the related software bundle SAM-Lattice.
By now, Lattice Boltzmann Methods are established as an alternative approach to classical computational fluid dynamics
methods. The LBM has been shown to be an accurate and efficient tool for the numerical simulation of weakly compressible or incompressible fluids. Fields of application reach from turbulent simulations through thermal problems to acoustic calculations among others. The transient nature of the method and the need for a regular grid based, non body conformal discretization makes the LBM ideally suitable for simulations involving complex solids. Such geometries are common, for instance, in the food processing industry, where fluids are mixed by static mixers or agitators. Those fluid flows are often laminar and non-Newtonian.
This work is motivated by the immense practical use of the Lattice Boltzmann Method, which is limited due to stability issues. The stability of the method is mainly influenced by the discretization and the viscosity of the fluid. Thus, simulations of non-Newtonian fluids, whose kinematic viscosity depend on the shear rate, are problematic. Several authors have shown that the LBM is capable of simulating those fluids. However, the vast majority of the simulations in the literature are carried out for simple geometries and/or moderate shear rates, where the LBM is still stable. Special care has to be taken for practical non-Newtonian Lattice Boltzmann simulations in order to keep them stable. A straightforward way is to truncate the modeled viscosity range by numerical stability criteria. This is an effective approach, but from the physical point of view the viscosity bounds are chosen arbitrarily. Moreover, these bounds depend on and vary with the grid and time step size and, therefore, with the simulation Mach number, which is freely chosen at the start of the simulation. Consequently, the modeled viscosity range may not fit to the actual range of the physical problem, because the correct simulation Mach number is unknown a priori. A way around is, to perform precursor simulations on a fixed grid to determine a possible time step size and simulation Mach number, respectively. These precursor simulations can be time consuming and expensive, especially for complex cases and a number of operating points. This makes the LBM unattractive for use in practical simulations of non-Newtonian fluids.
The essential novelty of the method, developed in the course of this thesis, is that the numerically modeled viscosity range is consistently adapted to the actual physically exhibited viscosity range through change of the simulation time step and the simulation Mach number, respectively, while the simulation is running. The algorithm is robust, independent of the Mach number the simulation was started with, and applicable for stationary flows as well as transient flows. The method for the viscosity adaption will be referred to as the "viscosity adaption method (VAM)" and the combination with LBM leads to the "viscosity adaptive LBM (VALBM)".
Besides the introduction of the VALBM, a goal of this thesis is to offer assistance in the spirit of a theory guide to students and assistant researchers concerning the theory of the Lattice Boltzmann Method and its implementation in SAM-Lattice. In Chapter 2, the mathematical foundation of the LBM is given and the route from the BGK approximation of the Boltzmann equation to the Lattice Boltzmann (BGK) equation is delineated in detail.
The derivation is restricted to isothermal flows only. Restrictions of the method, such as low Mach number flows are highlighted and the accuracy of the method is discussed.
SAM-Lattice is a C++ software bundle developed by the author and his colleague Dipl.-Ing. Andreas Schneider. It is a highly automated package for the simulation of isothermal flows of incompressible or weakly compressible fluids in 3D on the basis of the Lattice Boltzmann Method. By the time of writing of this thesis, SAM-Lattice comprises 5 components. The main components are the highly automated lattice generator SamGenerator and the Lattice Boltzmann solver SamSolver. Postprocessing is done with ParaSam, which is our extension of the
open source visualization software ParaView. Additionally, domain decomposition for MPI
parallelism is done by SamDecomposer, which makes use of the graph partitioning library MeTiS. Finally, all mentioned components can be controlled through a user friendly GUI (SamLattice) implemented by the author using QT, including features to visually track output data.
In Chapter 3, some fundamental aspects on the implementation of the main components, including the corresponding flow charts will be discussed. Actual details on the implementation are given in the comprehensive programmers guides to SamGenerator and SamSolver.
In order to ensure the functionality of the implementation of SamSolver, the solver is verified in Chapter 4 for Stokes's First Problem, the suddenly accelerated plate, and for Stokes's Second Problem, the oscillating plate, both for Newtonian fluids. Non-Newtonian fluids are modeled in SamSolver with the power-law model according to Ostwald de Waele. The implementation for non-Newtonian fluids is verified for the Hagen-Poiseuille channel flow in conjunction with a convergence analysis of the method. At the same time, the local grid refinement as it is implemented in SamSolver, is verified. Finally, the verification of higher order boundary conditions is done for the 3D Hagen-Poiseuille pipe flow for both Newtonian and non-Newtonian fluids.
In Chapter 5, the theory of the viscosity adaption method is introduced. For the adaption process, a target collision frequency or target simulation Mach number must be chosen and the distributions must be rescaled according to the modified time step size. A convenient choice is one of the stability bounds. The time step size for the adaption step is deduced from the target collision frequency \(\Omega_t\) and the currently minimal or maximal shear rate in the system, while obeying auxiliary conditions for the simulation Mach number. The adaption is done in the collision step of the Lattice Boltzmann algorithm. We use the transformation matrices of the MRT model to map from distribution space to moment space and vice versa. The actual scaling of the distributions is conducted on the back mapping, because we use the transformation matrix on the basis of the new adaption time step size. It follows an additional rescaling of the non-equilibrium part of the distributions, because of the form of the definition for the discrete stress tensor in the LBM context. For that reason it is clear, that the VAM is applicable for the SRT model as well as the MRT model, where there is virtually no extra cost in the latter case. Also, in Chapter 5, the multi level treatment will be discussed.
Depending on the target collision frequency and the target Mach number, the VAM can be used to optimally use the viscosity range that can be modeled within the stability bounds or it can be used to drastically accelerate the simulation. This is shown in Chapter 6. The viscosity adaptive LBM is verified in the stationary case for the Hagen-Poiseuille channel flow and in the transient case for the Wormersley flow, i.e., the pulsatile 3D Hagen-Poiseuille pipe flow. Although, the VAM is used here for fluids that can be modeled with the power-law approach, the implementation of the VALBM is straightforward for other non-Newtonian models, e.g., the Carreau-Yasuda or Cross model. In the same chapter, the VALBM is validated for the case of a propeller viscosimeter developed at the chair SAM. To this end, the experimental data of the torque on the impeller of three shear thinning non-Newtonian liquids serve for the validation. The VALBM shows excellent agreement with experimental data for all of the investigated fluids and in every operating point. For reasons of comparison, a series of standard LBM simulations is carried out with different simulation Mach numbers, which partly show errors of several hundred percent. Moreover, in Chapter 7, a sensitivity analysis on the parameters used within the VAM is conducted for the simulation of the propeller viscosimeter.
Finally, the accuracy of non-Newtonian Lattice Boltzmann simulations with the SRT and the MRT model is analyzed in detail. Previous work for Newtonian fluids indicate that depending on the numerical value of the collision frequency \(\Omega\), additional artificial viscosity is introduced due to the finite difference scheme, which negatively influences the accuracy. For the non-Newtonian case, an error estimate in the form of a functional is derived on the basis of a series expansion of the Lattice Boltzmann equation. This functional can be solved analytically for the case of the Hagen-Poiseuille channel flow of non-Newtonian fluids. The estimation of the error minimum is excellent in regions where the \(\Omega\) error is the dominant source of error as opposed to the compressibility error.
Result of this dissertation is a verified and validated software bundle on the basis of the viscosity adaptive Lattice Boltzmann Method. The work restricts itself on the simulation of isothermal, laminar flows with small Mach numbers. As further research goals, the testing of the VALBM with minimal error estimate and the investigation of the VALBM in the case of turbulent flows is suggested.

Real-time systems are systems that have to react correctly to stimuli from the environment within given timing constraints.
Today, real-time systems are employed everywhere in industry, not only in safety-critical systems but also in, e.g., communication, entertainment, and multimedia systems.
With the advent of multicore platforms, new challenges on the efficient exploitation of real-time systems have arisen:
First, there is the need for effective scheduling algorithms that feature low overheads to improve the use of the computational resources of real-time systems.
The goal of these algorithms is to ensure timely execution of tasks, i.e., to provide runtime guarantees.
Additionally, many systems require their scheduling algorithm to flexibly react to unforeseen events.
Second, the inherent parallelism of multicore systems leads to contention for shared hardware resources and complicates system analysis.
At any time, multiple applications run with varying resource requirements and compete for the scarce resources of the system.
As a result, there is a need for an adaptive resource management.
Achieving and implementing an effective and efficient resource management is a challenging task.
The main goal of resource management is to guarantee a minimum resource availability to real-time applications.
A further goal is to fulfill global optimization objectives, e.g., maximization of the global system performance, or the user perceived quality of service.
In this thesis, we derive methods based on the slot shifting algorithm.
Slot shifting provides flexible scheduling of time-constrained applications and can react to unforeseen events in time-triggered systems.
For this reason, we aim at designing slot shifting based algorithms targeted for multicore systems to tackle the aforementioned challenges.
The main contribution of this thesis is to present two global slot shifting algorithms targeted for multicore systems.
Additionally, we extend slot shifting algorithms to improve their runtime behavior, or to handle non-preemptive firm aperiodic tasks.
In a variety of experiments, the effectiveness and efficiency of the algorithms are evaluated and confirmed.
Finally, the thesis presents an implementation of a slot-shifting-based logic into a resource management framework for multicore systems.
Thus, the thesis closes the circle and successfully bridges the gap between real-time scheduling theory and real-world implementations.
We prove applicability of the slot shifting algorithm to effectively and efficiently perform adaptive resource management on multicore systems.

In this dissertation, we discuss how to price American-style options. Our aim is to study and improve the regression-based Monte Carlo methods. In order to have good benchmarks to compare with them, we also study the tree methods.
In the second chapter, we investigate the tree methods specifically. We do research firstly within the Black-Scholes model and then within the Heston model. In the Black-Scholes model, based on Müller's work, we illustrate how to price one dimensional and multidimensional American options, American Asian options, American lookback options, American barrier options and so on. In the Heston model, based on Sayer's research, we implement his algorithm to price one dimensional American options. In this way, we have good benchmarks of various American-style options and put them all in the appendix.
In the third chapter, we focus on the regression-based Monte Carlo methods theoretically and numerically. Firstly, we introduce two variations, the so called "Tsitsiklis-Roy method" and the "Longstaff-Schwartz method". Secondly, we illustrate the approximation of American option by its Bermudan counterpart. Thirdly we explain the source of low bias and high bias. Fourthly we compare these two methods using in-the-money paths and all paths. Fifthly, we examine the effect using different number and form of basis functions. Finally, we study the Andersen-Broadie method and present the lower and upper bounds.
In the fourth chapter, we study two machine learning techniques to improve the regression part of the Monte Carlo methods: Gaussian kernel method and kernel-based support vector machine. In order to choose a proper smooth parameter, we compare fixed bandwidth, global optimum and suboptimum from a finite set. We also point out that scaling the training data to [0,1] can avoid numerical difficulty. When out-of-sample paths of stock prices are simulated, the kernel method is robust and even performs better in several cases than the Tsitsiklis-Roy method and the Longstaff-Schwartz method. The support vector machine can keep on improving the kernel method and needs less representations of old stock prices during prediction of option continuation value for a new stock price.
In the fifth chapter, we switch to the hardware (FGPA) implementation of the Longstaff-Schwartz method and propose novel reversion formulas for the stock price and volatility within the Black-Scholes and Heston models. The test for this formula within the Black-Scholes model shows that the storage of data is reduced and also the corresponding energy consumption.

Open distributed systems are a class of distributed systems where (i) only partial information about the environment, in which they are running, is present, (ii) new resources may become available at runtime, and (iii) a subsystem may become aware of other subsystems after some interaction. Modeling and implementing such systems correctly is a complex task due to the openness and the dynamicity aspects. One way to ensure that the resulting systems behave correctly is to utilize formal verification.
Formal verification requires an adequate semantic model of the implementation, a specification of the desired behavior, and a reasoning technique. The actor model is a semantic model that captures the challenging aspects of open distributed systems by utilizing actors as universal primitives to represent system entities and allowing them to create new actors and to communicate by sending directed messages as reply to received messages. To enable compositional reasoning, where the reasoning task is reduced to independent verification of the system parts, semantic entities at a higher level of abstraction than actors are needed.
This thesis proposes an automaton model and combines sound reasoning techniques to compositionally verify implementations of open actor systems. Based on I/O automata, the model allows automata to be created dynamically and captures dynamic changes in communication patterns. Each automaton represents either an actor or a group of actors. The specification of the desired behavior is given constructively as an automaton. As the basis for compositionality, we formalize a component notion based on the static structure of the implementation instead of the dynamic entities (the actors) occurring in the system execution. The reasoning proceeds in two stages. The first stage establishes the connection between the automata representing single actors and their implementation description by means of weakest liberal preconditions. The second stage employs this result as the basis for verifying whether a component specification is satisfied. The verification is done by building a simulation relation from the automaton representing the implementation to the component's automaton. Finally, we validate the compositional verification approach through a number of examples by proving correctness of their actor implementations with respect to system specifications.

An efficient multiscale approach is established in order to compute the macroscopic response of nonlinear composites. The micro problem is rewritten in an integral form of the Lippmann-Schwinger type and solved efficiently by Fast Fourier Transforms. Using realistic microstructure models complex nonlinear effects are reproduced and validated with measured data of fiber reinforced plastics. The micro problem is integrated in a Finite Element framework which is used to solve the macroscale. The scale coupling technique and a consistent numerical algorithm is established. The method provides an efficient way to determine the macroscopic response considering arbitrary microstructures, constitutive behaviors and loading conditions.

Annual Report 2014
(2015)

Annual Report, Jahrbuch AG Magnetismus

The overall goal of the work is to simulate rarefied flows inside geometries with moving boundaries. The behavior of a rarefied flow is characterized through the Knudsen number \(Kn\), which can be very small (\(Kn < 0.01\) continuum flow) or larger (\(Kn > 1\) molecular flow). The transition region (\(0.01 < Kn < 1\)) is referred to as the transition flow regime.
Continuum flows are mainly simulated by using commercial CFD methods, which are used to solve the Euler equations. In the case of molecular flows one uses statistical methods, such as the Direct Simulation Monte Carlo (DSMC) method. In the transition region Euler equations are not adequate to model gas flows. Because of the rapid increase of particle collisions the DSMC method tends to fail, as well
Therefore, we develop a deterministic method, which is suitable to simulate problems of rarefied gases for any Knudsen number and is appropriate to simulate flows inside geometries with moving boundaries. Thus, the method we use is the Finite Pointset Method (FPM), which is a mesh-free numerical method developed at the ITWM Kaiserslautern and is mainly used to solve fluid dynamical problems.
More precisely, we develop a method in the FPM framework to solve the BGK model equation, which is a simplification of the Boltzmann equation. This equation is mainly used to describe rarefied flows.
The FPM based method is implemented for one and two dimensional physical and velocity space and different ranges of the Knudsen number. Numerical examples are shown for problems with moving boundaries. It is seen, that our method is superior to regular grid methods with respect to the implementation of boundary conditions. Furthermore, our results are comparable to reference solutions gained through CFD- and DSMC methods, respectevly.

The Wilkie model is a stochastic asset model, developed by A.D. Wilkie in 1984 with a purpose to explore the behaviour of investment factors of insurers within the United Kingdom. Even so, there is still no analysis that studies the Wilkie model in a portfolio optimization framework thus far. Originally, the Wilkie model is considering a discrete-time horizon and we apply the concept of Wilkie model to develop a suitable ARIMA model for Malaysian data by using Box-Jenkins methodology. We obtained the estimated parameters for each sub model within the Wilkie model that suits the case of Malaysia, and permits us to analyse the result based on statistics and economics view. We then tend to review the continuous time case which was initially introduced by Terence Chan in 1998. The continuous-time Wilkie model inspired is then being employed to develop the wealth equation of a portfolio that consists of a bond and a stock. We are interested in building portfolios based on three well-known trading strategies, a self-financing strategy, a constant growth optimal strategy as well as a buy-and-hold strategy. In dealing with the portfolio optimization problems, we use the stochastic control technique consisting of the maximization problem itself, the Hamilton-Jacobi-equation, the solution to the Hamilton-Jacobi-equation and finally the verification theorem. In finding the optimal portfolio, we obtained the specific solution of the Hamilton-Jacobi-equation and proved the solution via the verification theorem. For a simple buy-and-hold strategy, we use the mean-variance analysis to solve the portfolio optimization problem.

The main goal of this thesis is twofold. First, the thesis aims at bridging the gap between existing Pattern Recognition (PR) methods of automatic signature verification and the requirements for their application in forensic science. This gap, attributed by various factors ranging from system definition to evaluation, prevents automatic methods from being used by Forensic Handwriting Examiners (FHEs). Second, the thesis presents novel signature verification methods developed particularly considering the implications of forensic casework, and outperforming the state-of-the-art PR methods.
The first goal of the thesis is attributed by four important factors, i.e., data, terminology, output reporting, and how evaluation of automatic systems is carried out today. It is argued that traditionally the signature data used in PR are not actual/close representative of the real world data (especially that available in forensic cases). The systems trained on such data are, therefore, not suitable for forensic environments. This situation can be tackled by providing more realistic data to PR researchers. To this end, various signature and handwriting datasets are gathered in collaboration with FHEs and are made publicly available through the course of this thesis. A special attention is given to disguised signatures--where authentic authors purposefully make their signatures look like a forgery. This genre was at large neglected in PR research previously.
The terminology used, in the two communities - PR and FHEs, differ greatly. In fact, even in PR, there is no standard terminology and people often differ in the usage of various terms particularly related to various types of forged signatures/handwriting. The thesis presents a new terminology that is equally useful for both forensic scientists and PR researchers. The proposed terminology is hoped to increase the general acceptability of automatic signature analysis systems in forensic science.
The outputs reported by general signature verification systems are not acceptable for FHEs and courts as they are either binary (yes/no) or score (raw evidence) based on similarity/difference. The thesis describes that automatic systems should rather report the probability of observing the evidence (e.g., a certain similarity/difference score) given the signature belongs to the acclaimed identity, and the probability of observing the same evidence given the signature does not belong to the acclaimed identity. This will take automatic systems from hard decisions to soft decisions, thereby enabling them to report likelihood ratios that actually represent the evidential value of the score rather than the raw score (evidence).
When automatic systems report soft decisions (as in the form of likelihood ratios), the thesis argues that there must be some methods to evaluate such systems. This thesis presents one such adaptation. The thesis argues that the state-of-the-art evaluation methods, like equal error rate and area under curve, do not address the needs of forensic science. These needs require an assessment of the evidential value of signature verification, rather than a hard/pure classification (accept/reject binary decision). The thesis demonstrates and validates a relatively simple adaptation of the current verification methods based on the Bayesian inference dependent calibration of continuous scores rather than hard classifications (binary and/or score based classification).
The second goal of this thesis is to introduce various local features based techniques which are capable of performing signature verification in forensic cases and reporting results as anticipated by FHEs and courts. This is an important contribution of the thesis because of the following two reasons. First, to the best of author's knowledge, local feature descriptors are for the first time used for development of signature verification systems for forensic environments (particularly considering disguised signatures). Previously, such methods have been heavily used for recognition tasks, rather than verification of writing behaviors, such as character and digit recognition. Second, the proposed methods not only report the more traditional decisions (like scores-usually reported in PR) but also the Bayesian inference based likelihood ratios (suitable for courts and forensic cases).
Furthermore, the thesis also provides a detailed man vs. machine comparison for signature verification tasks. The men, in this comparison, are forensic scientists serving as forensic handwriting examiners and having experience of varying number of years. The machines are the local features based methods proposed in this thesis, along with various other state-of-the-art signature verification systems. The proposed methods clearly outperform the state-of-the-art systems, and sometimes the human experts.
Finally, the thesis details various tasks that have been performed in the areas closely related to signature verification and its application in forensic casework. These include, developing novel local feature based methods for extraction of signatures/handwritten text from document images, hyper-spectral image analysis for extraction of signatures from forensic documents, and analysis of on-line signatures acquired through specialized pens equipped with Accelerometer and Gyroscope. These tasks are important as they enable the thesis to take PR systems one step further close to direct application in forensic cases.

Accurate path tracking control of tractors became a key technology for automation in agriculture. Increasingly sophisticated solutions, however, revealed that accurate path tracking control of implements is at least equally important. Therefore, this work focuses on accurate path tracking control of both tractors and implements. The latter, as a prerequisite for improved control, are equipped with steering actuators like steerable wheels or a steerable drawbar, i.e. the implements are actively steered. This work contributes both new plant models and new control approaches for those kinds of tractor-implement combinations. Plant models comprise dynamic vehicle models accounting for forces and moments causing the vehicle motion as well as simplified kinematic descriptions. All models have been derived in a systematic and automated manner to allow for variants of implements and actuator combinations. Path tracking controller design begins with a comprehensive overview and discussion of existing approaches in related domains. Two new approaches have been proposed combining the systematic setup and tuning of a Linear-Quadratic-Regulator with the simplicity of a static output feedback approximation. The first approach ensures accurate path tracking on slopes and curves by including integral control for a selection of controlled variables. The second approach, instead, ensures this by adding disturbance feedforward control based on side-slip estimation using a non-linear kinematic plant model and an Extended Kalman Filter. For both approaches a feedforward control approach for curved path tracking has been newly derived. In addition, a straightforward extension of control accounting for the implement orientation has been developed. All control approaches have been validated in simulations and experiments carried out with a mid-size tractor and a custom built demonstrator implement.

In embedded systems, there is a trend of integrating several different functionalities on a common platform. This has been enabled by increasing processing power and the arise of integrated system-on-chips.
The composition of safety-critical and non-safety-critical applications results in mixed-criticality systems. Certification Authorities (CAs) demand the certification of safety-critical applications with strong confidence in the execution time bounds. As a consequence, CAs use conservative assumptions in the worst-case execution time (WCET) analysis which result in more pessimistic WCETs than the ones used by designers. The existence of certified safety-critical and non-safety-critical applications can be represented by dual-criticality systems, i.e., systems with two criticality levels.
In this thesis, we focus on the scheduling of mixed-criticality systems which are subject to certification. Scheduling policies cognizant of the mixed-criticality nature of the systems and the certification requirements are needed for efficient and effective scheduling. Furthermore, we aim at reducing the certification costs to allow faster modification and upgrading, and less error-prone certification. Besides certification aspects, requirements of different operational modes result in challenging problems for the scheduling process. Despite the mentioned problems, schedulers require a low runtime overhead for an efficient execution at runtime.
The presented solutions are centered around time-triggered systems which feature a low runtime overhead. We present a transformation to include event-triggered activities, represented by sporadic tasks, already into the offline scheduling process. Further, this transformation can also be applied on periodic tasks to shorten the length of schedule tables which reduces certification costs. These results can be used in our method to construct schedule tables which creates two schedule tables to fulfill the requirements of dual-criticality systems using mode changes at runtime. Finally, we present a scheduler based on the slot-shifting algorithm for mixed-criticality systems. In a first version, the method schedules dual-criticality jobs without the need for mode changes. An already certified schedule table can be used and at runtime, the scheduler reacts to the actual behavior of the jobs and thus, makes effective use of the available resources. Next, we extend this method to schedule mixed-criticality job sets with different operational modes. As a result, we can schedule jobs with varying parameters in different modes.

In this thesis, collision-induced dissociation (CID) studies serve to elucidate relative stabilities and to determine bond strengths within a given structure type of transition metal complexes. The infrared multi photon dissociation (IRMPD) spectroscopy combined with density functional theory (DFT) allow for structural analysis and provide insights into the coordination sphere of transition metal centers. The used combination of CID and IRMPD experiments is a powerful tool to obtain a detailed and comprehensive characterization and understanding of interactions between transition metals and organic ligands. The compounds’ spectrum comprises mono- or oligonuclear transition metal complexes containing iron, palladium, and ruthenium as well as lanthanide containing single molecule magnets (SMM). The presented investigations on the different transition metal complexes reveal manifold effects for each species leading to valuable results. A fundamental understanding of metal to ligand interactions is mandatory for the development of new and better organometallic complexes with catalytic, optical or magnetic properties.

Many tasks in image processing can be tackled by modeling an appropriate data fidelity term \(\Phi: \mathbb{R}^n \rightarrow \mathbb{R} \cup \{+\infty\}\) and then solve one of the regularized minimization problems \begin{align*}
&{}(P_{1,\tau}) \qquad \mathop{\rm argmin}_{x \in \mathbb R^n} \big\{ \Phi(x) \;{\rm s.t.}\; \Psi(x) \leq \tau \big\} \\ &{}(P_{2,\lambda}) \qquad \mathop{\rm argmin}_{x \in \mathbb R^n} \{ \Phi(x) + \lambda \Psi(x) \}, \; \lambda > 0 \end{align*} with some function \(\Psi: \mathbb{R}^n \rightarrow \mathbb{R} \cup \{+\infty\}\) and a good choice of the parameter(s). Two tasks arise naturally here: \begin{align*} {}& \text{1. Study the solver sets \({\rm SOL}(P_{1,\tau})\) and
\({\rm SOL}(P_{2,\lambda})\) of the minimization problems.} \\ {}& \text{2. Ensure that the minimization problems have solutions.} \end{align*} This thesis provides contributions to both tasks: Regarding the first task for a more special setting we prove that there are intervals \((0,c)\) and \((0,d)\) such that the setvalued curves \begin{align*}
\tau \mapsto {}& {\rm SOL}(P_{1,\tau}), \; \tau \in (0,c) \\ {} \lambda \mapsto {}& {\rm SOL}(P_{2,\lambda}), \; \lambda \in (0,d) \end{align*} are the same, besides an order reversing parameter change \(g: (0,c) \rightarrow (0,d)\). Moreover we show that the solver sets are changing all the time while \(\tau\) runs from \(0\) to \(c\) and \(\lambda\) runs from \(d\) to \(0\).
In the presence of lower semicontinuity the second task is done if we have additionally coercivity. We regard lower semicontinuity and coercivity from a topological point of view and develop a new technique for proving lower semicontinuity plus coercivity.
Dropping any lower semicontinuity assumption we also prove a theorem on the coercivity of a sum of functions.

We study an online flow shop scheduling problem where each job consists of several tasks that have to be completed in t different stages and the goal is to maximize the total weight of accepted jobs.
The set of tasks of a job contains one task for each stage and each stage has a dedicated set of identical parallel machines corresponding to it that can only process tasks of this stage. In order to gain the weight (profit) associated with a job j, each of its tasks has to be executed between a task-specific release date and deadline subject to the constraint that all tasks of job j from stages 1, …, i-1 have to be completed before the task of the ith stage can be started. In the online version, jobs arrive over time and all information about the tasks of a job becomes available at the release date of its first task. This model can be used to describe production processes in supply chains when customer orders arrive online.
We show that even the basic version of the offline problem with a single machine in each stage, unit weights, unit processing times, and fixed execution times for all tasks (i.e., deadline minus release date equals processing time) is APX-hard. Moreover, we show that the approximation ratio of any polynomial-time approximation algorithm for this basic version of the problem must depend on the number t of stages.
For the online version of the basic problem, we provide a (2t-1)-competitive deterministic online algorithm and a matching lower bound. Moreover, we provide several (sometimes tight) upper and lower bounds on the competitive ratio of online algorithms for several generalizations of the basic problem involving different weights, arbitrary release dates and deadlines, different processing times of tasks, and several identical machines per stage.