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Hydrogels are known to be covalently or ionic cross-linked, hydrophilic three-dimensional
polymer networks, which exist in our bodies in a biological gel form such as the vitreous
humour that fills the interior of the eyes. Poly(N-isopropylacrylamide) (poly(NIPAAm))
hydrogels are attracting more interest in biomedical applications because, besides others, they
exhibit a well-defined lower critical solution temperature (LCST) in water, around 31–34°C,
which is close to the body temperature. This is considered to be of great interest in drug
delivery, cell encapsulation, and tissue engineering applications. In this work, the
poly(NIPAAm) hydrogel is synthesized by free radical polymerization. Hydrogel properties
and the dimensional changes accompanied with the volume phase transition of the
thermosensitive poly(NIPAAm) hydrogel were investigated in terms of Raman spectra,
swelling ratio, and hydration. The thermal swelling/deswelling changes that occur at different
equilibrium temperatures and different solutions (phenol, ethanol, propanol, and sodium
chloride) based on Raman spectrum were investigated. In addition, Raman spectroscopy has
been employed to evaluate the diffusion aspects of bovine serum albumin (BSA) and phenol
through the poly(NIPAAm) network. The determination of the mutual diffusion coefficient,
\(D_{mut}\) for hydrogels/solvent system was achieved successfully using Raman spectroscopy at
different solute concentrations. Moreover, the mechanical properties of the hydrogel, which
were investigated by uniaxial compression tests, were used to characterize the hydrogel and to
determine the collective diffusion coefficient through the hydrogel. The solute release coupled
with shrinking of the hydrogel particles was modelled with a bi-dimensional diffusion model
with moving boundary conditions. The influence of the variable diffusion coefficient is
observed and leads to a better description of the kinetic curve in the case of important
deformation around the LCST. A good accordance between experimental and calculated data
was obtained.

This thesis combined gas phase mass spectrometric investigations of ionic transition metal clusters that are either homogeneous \((Nb_n^{+/-}, Co_n^{+/-})\) or heterogeneous \(([Co_nPt_m]^{+/-})\), of their organo metallic reaction products, and of organic molecules (aspartame and Asp-Phe) and their alkali metal ion adducts.At the Paris FEL facility CLIO a newly installed FT-ICR mass spectrometer has been modified by inclusion of an ion bender that allows for the usage of additional ion sources beyond the installed ESI source. The installation of an LVAP metal cluster source served to produce metal cluster adsorbate complex ions of the type \([Nb_n(C_6H_6)]^{+/-}\). IR-MPD of the complexes \([Nb_n(C_6H_6)]^{+/-} (n = 18, 19)\) resulted in \([Nb_n(C_6)]^{+/-} (n = 18, 19)\) fragments. Spectra are broad, possibly because of vibronic / electronic transitions. In Kaiserslautern the capabilities of the LVAP source were extended by adding a gas pick up unit. Complex gases containing C-H bonds otherwise break within the cluster forming plasma. More stable gases like CO seem to attach at least partially intact. Metal cluster production with argon tagged onto the cluster failed when introducing argon through the pick up source, but succeeded when using argon as expansion gas. A new mass spectrometer concept of an additional multipole collision cell for metal cluster adsorbate formation is currently under construction. Subsequent cooling shall achieve high resolution IR-MPD spectra of transition metal cluster adsorbate complexes.Prior work on reaction of transition metal clusters with benzene was extended by investigating the reaction with benzene and benzene-d6 of size selected cationic cobalt clusters \(Co_n^+\) and of anionic cobalt clusters \(Co_n^-\) in the size range \(n = 3 - 28\) and of bimetallic cobalt platinum clusters \([Co_nPt_m]^{+/-}\) in the size range \(n + m \le 8\). Dehydrogenation by cationic cobalt clusters \(Co_n^+\) is sparse, it is effective in small bimetallic clusters \([Co_nPt_m]^+ (n + m \le 3)\). Thus single platinum atoms promote benzene dehydrogenation while further cobalt atoms quench it. Dehydrogenation is ubiquitous in reactions of anionic cobalt clusters. Mixed triatomic clusters \([Co_2Pt_1]^-\) and \([Co_1Pt_2]^-\) are special in causing effective reactions and single dehydrogenation through some kind of cooperativity while \([Co_nPt_{1,2}]^- (n \ge 3)\) do not react at all. Kinetic isotope effects KIE(n) in total reaction rates are inverse and - in part - large, dehydrogenation isotope effects DIE(n) are normal. A multistep model of adsorption and stepwise dehydrogenation from the precursor adsorbate proves suitable to rationalize the found KIEs and DIEs in principle. Particular insights into the effects of charge and of cluster size are largely beyond this model. Some DFT calculations - though preliminary - lend strong support to the otherwise assumed structures and enthalpies. More insights into the cause of the found effects of charge, size and composition of both pure and mixed clusters shall arise from ongoing high level ab initio modeling (of especially the \(n + m = 3\) case for mixed clusters).The influence of the methylester group in the molecules aspartame (Asp-PheOMe) and Asp-Phe has been explored. Therefore, their protonated and deprotonated species and their complexes with alkali metal ions attached were investigated with different techniques utilizing mass spectrometry.Gas phase H-/D-exchange with \(ND_3\) has proven that in both molecules all acidic NH and OH binding motifs do exchange their hydrogen atom and that simultaneous multi exchange is present. Kinetic studies revealed that with alkali metal ions attached the speed of the first exchange step decreases with increasing ion size. The additional OH of the carboxylic COOHPhe group in Asp-Phe increases the exchange speed by a constant value. CID experiments yielded water and the protonated Asp-Phe anhydride as main fragments out of the protonated molecules, neutral Asp anhydride and \([Phe M]^+ / [PheOMe M]^+\) for \(Li^+\) and \(Na^+\) attached, and neutral aspartame / Asp-Phe and ionic \(M^+\) for \(K^+\), \(Rb^+\) and \(Cs^+\) attached. The threshold energy \(E_{CID}\), indicating ion stability, decreases with increasing ion size. For aspartame fragmentation occurs at lower \(E_{CID}\) values for complexes with \(H^+\), \(Li^+\) and \(Na^+\) than for the Asp-Phe analoga. Complexes with \(K^+\), \(Rb^+\) and \(Cs^+\) give the same \(E_{CID}\) value for aspartame and Asp-Phe. IR-MPD investigations lead to the same fragments as the CID experiments. In combination with quantum mechanical calculations a change in the preferred structure from charge-solvated, tridentate type for complexes with small alkali metal ions (\(Li^+\)) to salt-bridge type structure for large alkali metal ions (\(Cs^+\)) could be confirmed. Calculations thereby reveal nearly no structural differences between aspartame and Asp-Phe for cationized species. The deprotonation of the additional COOHPhe group in Asp-Phe is preferred against other acidic positions. A better experimental distinction between possible (calculated) structure types would arise from additional FEL IR-MPD measurements in the energy range of 600 to 1800 \(cm^{-1}\). The comparison of the \(E_{CID}\) values with calculated fragmentation energy values proves that not only for alkali metal complexes with \(K^+\), \(Rb^+\) and \(Cs^+\), but also for \(Li^+\) and \(Na^+\) the bond breaking of all metal atom bonds is part of the transition state. The lower \(E_{CID}\) values for aspartame with small cations may be explained in terms of internal energy. Aspartame is a larger molecule, possesses more internal energy and can be recognized as the larger heat bath. Less energy is needed for fragmentation, if the Phe part with the additional methylester group is involved in the fragmentation process.

This thesis provides a fully automatic translation from synchronous programs to parallel software for different architectures, in particular, shared memory processing (SMP) and distributed memory systems. Thereby, we exploit characteristics of the synchronous model of computation (MoC) to reduce communication and to improve available parallelism and load-balancing by out-of-order (OOO) execution and data speculation.
Manual programming of parallel software requires the developers to partition a system into tasks and to add synchronization and communication. The model-based approach of development abstracts from details of the target architecture and allows to make decisions about the target architecture as late as possible. The synchronous MoC supports this approach by abstracting from time and providing implicit parallelism and synchronization. Existing compilation techniques translate synchronous programs into synchronous guarded actions (SGAs) which are an intermediate format abstracting from semantic problems in synchronous languages. Compilers for SGAs analyze causality problems, ensure logical correctness and the absence of schizophrenia problems. Hence, SGAs are a simplified and general starting point and keep the synchronous MoC at the same time. The instantaneous feedback in the synchronous MoC makes the mapping of these systems to parallel software a non-trivial task. In contrast, other MoCs such as data-flow processing networks (DPNs) directly match with parallel architectures. We translate the SGAs into DPNs,which represent a commonly used model to create parallel software. DPNs have been proposed as a programming model for distributed parallel systems that have communication paths with unpredictable latencies. The purely data-driven execution of DPNs does not require a global coordination and therefore DPNs can be easily mapped to parallel software for architectures with distributed memory. The generation of efficient parallel code from DPNs challenges compiler design with two issues: To perfectly utilize a parallel system, the communication and synchronization has to be kept low, and the utilization of the computational units has to be balanced. The variety of hardware architectures and dynamic execution techniques in processing units of these systems make a statically balanced distributed execution impossible.
The synchronous MoC is still reflected in our generated DPNs, which exhibits characteristics that allow optimizations concerning the previously mentioned issues. In particular, we apply a general communication reduction and OOO execution to achieve a dynamically balanced execution which is inspired from hardware design.

Efficient time integration and nonlinear model reduction for incompressible hyperelastic materials
(2013)

This thesis deals with the time integration and nonlinear model reduction of nearly incompressible materials that have been discretized in space by mixed finite elements. We analyze the structure of the equations of motion and show that a differential-algebraic system of index 1 with a singular perturbation term needs to be solved. In the limit case the index may jump to index 3 and thus renders the time integration into a difficult problem. For the time integration we apply Rosenbrock methods and study their convergence behavior for a test problem, which highlights the importance of the well-known Scholz conditions for this problem class. Numerical tests demonstrate that such linear-implicit methods are an attractive alternative to established time integration methods in structural dynamics. In the second part we combine the simulation of nonlinear materials with a model reduction step. We use the method of proper orthogonal decomposition and apply it to the discretized system of second order. For a nonlinear model reduction to be efficient we approximate the nonlinearity by following the lookup approach. In a practical example we show that large CPU time savings can achieved. This work is in order to prepare the ground for including such finite element structures as components in complex vehicle dynamics applications.

This thesis is separated into three main parts: Development of Gaussian and White Noise Analysis, Hamiltonian Path Integrals as White Noise Distributions, Numerical methods for polymers driven by fractional Brownian motion.
Throughout this thesis the Donsker's delta function plays a key role. We investigate this generalized function also in Chapter 2. Moreover we show by giving a counterexample, that the general definition for complex kernels is not true.
In Chapter 3 we take a closer look to generalized Gauss kernels and generalize these concepts to the case of vector-valued White Noise. These results are the basis for Hamiltonian path integrals of quadratic type. The core result of this chapter gives conditions under which pointwise products of generalized Gauss kernels and certain Hida distributions have a mathematical rigorous meaning as distributions in the Hida space.
In Chapter 4 we discuss operators which are related to applications for Feynman Integrals as differential operators, scaling, translation and projection. We show the relation of these operators to differential operators, which leads to the well-known notion of so called convolution operators. We generalize the central homomorphy theorem to regular generalized functions.
We generalize the concept of complex scaling to scaling with bounded operators and discuss the relation to generalized Radon-Nikodym derivatives. With the help of this we consider products of generalized functions in chapter 5. We show that the projection operator from the Wick formula for products with Donsker's deltais not closable on the square-integrable functions..
In Chapter 5 we discuss products of generalized functions. Moreover the Wick formula is revisited. We investigate under which conditions and on which spaces the Wick formula can be generalized to. At the end of the chapter we consider the products of Donsker's delta function with a generalized function with help of a measure transformation. Here also problems as measurability are concerned.
In Chapter 6 we characterize Hamiltonian path integrands for the free particle, the harmonic oscillator and the charged particle in a constant magnetic field as Hida distributions. This is done in terms of the T-transform and with the help of the results from chapter 3. For the free particle and the harmonic oscillator we also investigate the momentum space propagators. At the same time, the $T$-transform of the constructed Feynman integrands provides us with their generating functional. In Chapter 7, we can show that the generalized expectation (generating functional at zero) gives the Greens function to the corresponding Schrödinger equation.
Moreover, with help of the generating functional we can show that the canonical commutation relations for the free particle and the harmonic oscillator in phase space are fulfilled. This confirms on a mathematical rigorous level the heuristics developed by Feynman and Hibbs.
In Chapter 8 we give an outlook, how the scaling approach which is successfully applied in the Feynman integral setting can be transferred to the phase space setting. We give a mathematical rigorous meaning to an analogue construction to the scaled Feynman-Kac kernel. It is open if the expression solves the Schrödinger equation. At least for quadratic potentials we can get the right physics.
In the last chapter, we focus on the numerical analysis of polymer chains driven by fractional Brownian motion. Instead of complicated lattice algorithms, our discretization is based on the correlation matrix. Using fBm one can achieve a long-range dependence of the interaction of the monomers inside a polymer chain. Here a Metropolis algorithm is used to create the paths of a polymer driven by fBm taking the excluded volume effect in account.

In this article we present a method to extend high order finite volume schemes
to networks of hyperbolic conservation laws with algebraic coupling conditions. This method is based on an ADER approach in time to solve the
generalized Riemann problem at the junction. Additionally to the high order accuracy, this approach maintains an exact conservation of quantities if
stated by the coupling conditions. Several numerical examples confirm the
benefits of a high order coupling procedure for high order accuracy and stable
shock capturing.

In the present paper scalar macroscopic models for traffic and pedestrian flows are coupled and the resulting system is investigated numerically. For the traffic flow the classical
Lighthill-Whitham model on a network of roads and for the pedestrian flow the Hughes
model are used. These models are coupled via terms in the fundamental diagrams mod-
eling an influence of the traffic and pedestrian flow on the maximal velocities of the
corresponding models. Several physical situations, where pedestrians and cars interact,
are investigated.

Compared to traditional software design, the design of embedded software is even more challenging: In addition to the correct implementation of the systems, one has to consider non-functional constraints such as real-time behavior, reliability, and energy consumption. Moreover, many embedded systems are used in safety-critical applications where errors can lead to enormous damages and even to the loss of human live. For this reason, formal verification is applied in many design flows using different kinds of formal verification methods.
The synchronous model of computation has shown to be well-suited in this context. Its core is the paradigm of perfect synchrony which assumes that the overall system behavior is divided into a sequence of reactions, and all computations within a reaction are completed in zero time. This temporal abstraction simplifies reactive programming in that developers do not have to bother about many low-level details related to timing, synchronization and scheduling. This thesis is dedicated to this design flow, and it presents the author's contributions to it.

The application behind the subject of this thesis are multiscale simulations on highly heterogeneous particle-reinforced composites with large jumps in their material coefficients. Such simulations are used, e.g., for the prediction of elastic properties. As the underlying microstructures have very complex geometries, a discretization by means of finite elements typically involves very fine resolved meshes. The latter results in discretized linear systems of more than \(10^8\) unknowns which need to be solved efficiently. However, the variation of the material coefficients even on very small scales reveals the failure of most available methods when solving the arising linear systems. While for scalar elliptic problems of multiscale character, robust domain decomposition methods are developed, their extension and application to 3D elasticity problems needs to be further established.
The focus of the thesis lies in the development and analysis of robust overlapping domain decomposition methods for multiscale problems in linear elasticity. The method combines corrections on local subdomains with a global correction on a coarser grid. As the robustness of the overall method is mainly determined by how well small scale features of the solution can be captured on the coarser grid levels, robust multiscale coarsening strategies need to be developed which properly transfer information between fine and coarse grids.
We carry out a detailed and novel analysis of two-level overlapping domain decomposition methods for the elasticity problems. The study also provides a concept for the construction of multiscale coarsening strategies to robustly solve the discretized linear systems, i.e. with iteration numbers independent of variations in the Young's modulus and the Poisson ratio of the underlying composite. The theory also captures anisotropic elasticity problems and allows applications to multi-phase elastic materials with non-isotropic constituents in two and three spatial dimensions.
Moreover, we develop and construct new multiscale coarsening strategies and show why they should be preferred over standard ones on several model problems. In a parallel implementation (MPI) of the developed methods, we present applications to real composites and robustly solve discretized systems of more than \(200\) million unknowns.

This work shall provide a foundation for the cross-design of wireless networked control systems with limited resources. A cross-design methodology is devised, which includes principles for the modeling, analysis, design, and realization of low cost but high performance and intelligent wireless networked control systems. To this end, a framework is developed in which control algorithms and communication protocols are jointly designed, implemented, and optimized taking into consideration the limited communication, computing, memory, and energy resources of the low performance, low power, and low cost wireless nodes used. A special focus of the proposed methodology is on the prediction and minimization of the total energy consumption of the wireless network (i.e. maximization of the lifetime of wireless nodes) under control performance constraints (e.g. stability and robustness) in dynamic environments with uncertainty in resource availability, through the joint (offline/online) adaptation of communication protocol parameters and control algorithm parameters according to the traffic and channel conditions. Appropriate optimization approaches that exploit the structure of the optimization problems to be solved (e.g. linearity, affinity, convexity) and which are based on Linear Matrix Inequalities (LMIs), Dynamic Programming (DP), and Genetic Algorithms (GAs) are investigated. The proposed cross-design approach is evaluated on a testbed consisting of a real lab plant equipped with wireless nodes. Obtained results show the advantages of the proposed cross-design approach compared to standard approaches which are less flexible.