### Refine

#### Year of publication

- 2013 (36) (remove)

#### Document Type

- Doctoral Thesis (36) (remove)

#### Language

- English (36) (remove)

#### Keywords

- IR-MPD (2)
- cobalt (2)
- dipeptide (2)
- metal (2)
- Ahr Knockout Model (1)
- Analytical method (1)
- Aryl hydrocarbon Receptor (1)
- Baeocyte (1)
- Biogeographie (1)
- Biogeography (1)

#### Faculty / Organisational entity

This thesis reports on investigations on the structure and reactivity of dipeptide-alkali metal complexes, a series of ruthenium bearing catalysts, dysprosium based single molecule magnets and organometallic di-cobalt complexes. A variety of experimental and theoretical methods was used dependent on the problem: collision induced dissociation, hydrogen/deuterium exchange reactions, gas phase reactions with \(D_2\), infrared multiple-photon dissociation and the determination of minimum energy structures, IR absorption spectra, transition states and electronic transitions based on density functional theory.
A case study was carried out to explore the influence of alkali metal ions on the gas phase structure of the dipeptide Carnosine. CID experiments on protonated Carnosine and its alkali metal complexes in an ion trap resulted in different fragment pathways dependent on the size of the alkali metal. The complexation of small ions (\(Li^+\) and \(Na^+\)) promoted the cleavage of bonds in the molecules backbone under CID, while \(Rb^+\)- and \(Cs^+\)-Carnosine complexes underwent the exclusive loss of the alkali metal. CID breakdown curves reflected the different binding behavior of the alkali ions to Carnosine. Gas phase H/D exchange reactions with \(D_2O\) resulted in the exchange of several protons of the protonated dipeptide, while its alkali metal complexes underwent no exchange reactions. DFT derived energetical minimum isomers exhibited only charge solvated tridentate structures, whereas salt bridge as well as charge solvated binding motives are reported in literature on complexes of alkali metal ions and oligopeptides. This study was published in a similar version as a paper in Zeitschrift für Physikalische Chemie.
A combination of the four dipeptides Carnosine, Anserine, GlyHis and HisGly with alkali metal ions was investigated with the help of CID, IR-MPD spectroscopy and H/D exchange reactions with \(ND_3\). The aim of the survey was to elucidate the influence of the methyl-group at the histidine ring, of the peptide sequence and chain length on the binding motives of the alkali ions. The experimental results were compared to DFT derived minimum energetical isomers. A moderate accordance was found for DFT predicted IR absorptions to IR-MPD spectra. A systematic nomenclature was developed reflecting all binding motives of the four dipeptides to alkali ions. Carnosine complexes all alkali metal ions in an uniform motive. DFT derived energetical minimum isomers of the three other dipeptides showed strong conformational changes with increasing size of the alkali ion. The most favored binding motive of all peptides was the tridentate complexation of the alkali ion by a carboxylic and an amidic oxygen atom, while the electron donating nitrogen atom either belongs to the Histidine ring or the amine group. The ability to form hydrogen bonds in a certain binding motive is essential for the preference of the Histidine or amine nitrogen atom as an electron donor. The charge solvated binding motive is the most common within all found isomers. Several structures exhibited hydrogen bonded protons. Those can be interpretated as intermediates between the charge solvated and the salt bridge binding motive. CID breakdown curves of the cationic complexes of the dipeptides with \(K^+\), \(Rb^+\) and \(Cs^+\) resulted in a fair agreement of \(E^{50\%}_{com}\) values with DFT derived Gibbs free binding energies. CID led to multiple fragments of the \(Li^+\) and \(Na^+\) dipeptide complexes and to an insufficient correlation between the \(E^{50\%}_{com}\) values and metal-dipeptide free binding enthalpies. Gas phase H/D exchange reactions of the protonated dipeptides with \(ND_3\) resulted in the exchange of all labile protons with comparable relative partial rate constants. The assumption of coexisting single and double exchange reactions per single collision led to an enhancement in quality of the pseudo first order kinetic fits of the experimental derived data. The \(Li^+\), \(Na^+\) and \(K^+\) complexes of the dipeptides exhibited a reduction in the number of exchanged protons, significantly lower rate constants for H/D exchange and only single exchange reactions.
The complexation of the doubly charged cationic transition metal \(Zn^{2+}\) by deprotonated Carnosine led to crucial conformational changes with respect to the alkali metal complexes. Former DFT calculations on the gas phase structure of \([Carn-H,Zn^{II}]^+\) were now compared to IR-MPD spectra. IR-MPD spectra exhibited several of the DFT predicted IR absorptions while the overall agreement in the position of bands is only partially satisfactory. The complex \([Carn-H,Zn^{II}]^+\) was furthermore used in order to study the band dependent enhancement of fragmentation efficiency by application of a resonant 2-color IR-MPD pump/probe scheme. In literature, it is assumed that the slopes of linear fits to the log-log scale of experimental data (fragmentation efficiency vs. laser pulse energy) correlate to the number of photons needed for fragmentation. No reasonable number of photons for the fragmentation of the molecule was derived with this approach. However, it could be shown that the number of photons of the pump laser needed for fragmentation is reduced by the use of a second IR color. The change of the delay between the pump and probe laser pulse had an influence on the shape of the absorption bands. Irradiation with the probe laser pulse before the pump laser caused a heating of the molecule which resulted in a broadening of bands. No broadening was observed when the probe laser was applied simultaneously or after the pump laser. CID and IR-MPD fragmentation channels differed in their relative abundance. Furthermore, relative abundancies of fragments were specific to the excited vibrational motions. This study provides essential approaches for the further study of the mechanism of resonant 2-color IR-MPD spectroscopy.
Several ruthenium catalysts for transfer hydrogenation reactions were synthesized by L. Ghoochany (research group W. Thiel, TU Kaiserlautern). CID measurements on isotopic labeled species led to the following conclusion about the activation process of the catalyst: a nitrogen-ruthenium bond is broken, the pyrimidine ring of the substituted 2-R-4-(2-pyridinyl)pyrimidine ligand rotates about 160° and a carbon-ruthenium bond is formed under subsequent loss of a HCl (or DCl) molecule. The mass spectrometers CID amplitude was calibrated with a set of “thermometer ions”. CID breakdown curves were used for determination of \(E^{50\%}_{com}\) values of three differently substituted catalysts. Finally, activation energies were estimated by means of the calibration. The resulting activation energies showed a qualitative correlation to DFT derived activation energies. These results are part of a manuscript which was submitted to Chemistry – A European Journal and is currently in the review process. Further studies on this series of transition metal complexes included CID on ligand exchanged species, 1- and 2-color IR-MPD spectroscopy, gas phase reactions with \(D_2\) and DFT based modeling of the reaction coordinate of the \(D_2\) insertion. The exchange of the anionic chlorido ligand in solution led to three complexes with different fragmentation thresholds. CID derived activation amplitudes correspond well to the order predicted by the hard/soft acids/bases (HSAB) concept. 1-color IR-MPD experiments on two complexes showed only a few bands. Resonant 2-color IR-MPD increased the overall fragmentation efficiency and uncovered several dark bands. DFT derived IR absorption spectra correlate well to IR-MPD spectra while some bands are still not observable. Gas phase reactions with \(D_2\) showed an increase of the mass of the activated complex of +4 m/z. This was interpreted in terms of an incorporation of a \(D_2\) molecule under heterolytical cleavage of the \(D_2\) molecule and can be compared to a back reaction of the activation. The reaction coordinate of the \(D_2\) incorporation was modeled with DFT at the B3LYP/cc-pVTZ level of theory and different activation energies were derived dependent on the substituent. Reactions of three differently substituted complexes with \(D_2\) resulted in different relative partial rate constants. The comparison to rate constants derived from transition state theory showed a qualitative but not quantitative correlation to the experimental results. This study contributes to our ongoing work on the assignment and isolation of reaction intermediates in the gas phase.
A series of dysprosium based complexes was synthesized by A. Bhunia (research group P. W. Roesky, KIT) and studied within the collaborative research center SFB/TRR 88 “3MET”. We contributed to this work with ESI-MS, CID and experiments on H/D exchange reactions with \(ND_3\) in the gas phase. Those complexes consist of a central triple-charged dysprosium cation and two identical salen-type ligands which allow for a complexation of up to two transition metals. The monometallic dysprosium complex shows single molecule magnet (SMM) behavior in SQUID measurements, while the incorporation of two double-charged manganese cations leads to ferromagnetic behavior. The interaction of terminal amine groups with the manganese ions caused a hinderance of the exchange H/D exchange reaction with \(ND_3\) in the gas phase. Alternatively, the terminal amine groups of the monometallic dysprosium complex allow for the bond of two \(Ni^{2+}(tren)\) complexes. ESI-MS studies showed anionic as well as cationic complexes due to deprotonation or protonation in solution. CID studies led to fragmentation schemes which correlate quite well to the predicted structures of the complexes. These results are part of two publications in Inorganic Chemistry and Dalton Transactions. Further studies on this series of mono-, di- and trimetallic complexes are reported in this thesis. H/D exchange reactions with \(D_2O\) in solution yielded in an exchange of all labile protons for the cationic complexes. Anionic complexes underwent a partial or a complete exchange of labile protons. A comparison of 1- and 2-color IR-MPD spectra of anionic and cationic complexes as well as H/D exchanged species allowed for the assignment of vibrational bands. Furthermore, preferred protonation sites were derived by comparing the results of IR-MPD experiments and H/D exchange reactions in solution and in the gas phase. This study contributes to our ongoing work on the determination of magnetic properties of isolated ions in the gas phase at the Helmholtz-Zentrum Berlin.
The complex \([(^4CpCo)_2(\mu-C_2Ph_2)]\) (\(^4Cp\) = tetraisopropyl-cyclopentadiene) was synthesized by J. Becker (research group H. Sitzmann, TU Kaiserslautern). The cationic complex and several reaction products were characterized by ESI-MS. Some of the experimental data contributed to the diploma thesis of J. Becker. The cationic reaction products and the complex itself were subject of IR spectroscopic characterization. IR-MPD efficiency changed crucially with modification of the complex, yielding \([(^4CpCo)_2(\mu-C_2Ph_2)X]^+ (X=H, (H+CH_3CN), Cl, O)\). The contribution of various fragmentation channels to the overall fragmentation efficiency was studied in detail. An increase of photon flux resulted in a saturation of preferred \(C_2Ph_2\) loss, additional alkyl fragments out of the \(^4Cp\) rings arising. Several absorption bands were found in the mid- and near-IR region. A model system from literature was used to identify seemingly levels of DFT theory by reference to X-ray crystal structure data. The B3LYP and the B97D functional with cc-pVDZ and Stuttgart 1997 ECP basis sets were identified for calculations of the complex \([(^4CpCo)_2(\mu-C_2Ph_2)]^+\) and of its reaction products. An elongation of the Co-Co bond distance was observed for the cationic reaction products with \(Cl^-\) and \(O^{2-}\). Calculations with B3LYP and B97D resulted in different electronic ground states. We did not obtain a good agreement of calculated vibrational modes and recorded IR-MPD spectra. DFT predicted more absorption bands than observed, especially those corresponding to aliphatic symmetric \(CH_n (n=2, 3)\) and aromatic CH stretch motions. Future 2-color IR-MPD experiments might resolve currently prevailing discrepancies. TD-DFT calculations yielded several electronic transitions that do not correspond to the IR-MPD spectra. The chosen levels of theory for DFT and TD-DFT calculations does not seem to be appropriate. IR-MPD spectra have to be remeasured in order to normalize the spectra to photon flux. Furthermore, a different strategy has to be developed for ab initio calculations on the complexes under study.
A combination of various methods applied to isolated ions in the gas phase and in solution allowed for the study of their structure, binding energies and reactivity. 1- and 2-color IR-MPD spectroscopy combined with DFT predicted absorption spectra of different isomers enabled an assignment of vibrational bands and binding motives of the molecules. The derived results are important for further studies on the binding behavior of peptides and the reaction behavior of metal complexes.

Factorization of multivariate polynomials is a cornerstone of many applications in computer algebra. To compute it, one uses an algorithm by Zassenhaus who used it in 1969 to factorize univariate polynomials over \(\mathbb{Z}\). Later Musser generalized it to the multivariate case. Subsequently, the algorithm was refined and improved.
In this work every step of the algorithm is described as well as the problems that arise in these steps.
In doing so, we restrict to the coefficient domains \(\mathbb{F}_{q}\), \(\mathbb{Z}\), and \(\mathbb{Q}(\alpha)\) while focussing on a fast implementation. The author has implemented almost all algorithms mentioned in this work in the C++ library factory which is part of the computer algebra system Singular.
Besides, a new bound on the coefficients of a factor of a multivariate polynomial over \(\mathbb{Q}(\alpha)\) is proven which does not require \(\alpha\) to be an algebraic integer. This bound is used to compute Hensel lifting and recombination of factors in a modular fashion. Furthermore, several sub-steps are improved.
Finally, an overview on the capability of the implementation is given which includes benchmark examples as well as random generated input which is supposed to give an impression of the average performance.

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 thesis deals with generalized inverses, multivariate polynomial interpolation and approximation of scattered data. Moreover, it covers the lifting scheme, which basically links the aforementioned topics. For instance, determining filters for the lifting scheme is connected to multivariate polynomial interpolation. More precisely, sets of interpolation sites are required that can be interpolated by a unique polynomial of a certain degree. In this thesis a new class of such sets is introduced and elements from this class are used to construct new and computationally more efficient filters for the lifting scheme.
Furthermore, a method to approximate multidimensional scattered data is introduced which is based on the lifting scheme. A major task in this method is to solve an ordinary linear least squares problem which possesses a special structure. Exploiting this structure yields better approximations and therefore this particular least squares problem is analyzed in detail. This leads to a characterization of special generalized inverses with partially prescribed image spaces.

Many real life problems have multiple spatial scales. In addition to the multiscale nature one has to take uncertainty into account. In this work we consider multiscale problems with stochastic coefficients.
We combine multiscale methods, e.g., mixed multiscale finite elements or homogenization, which are used for deterministic problems with stochastic methods, such as multi-level Monte Carlo or polynomial chaos methods.
The work is divided into three parts.
In the first two parts we study homogenization with different stochastic methods. Therefore we consider elliptic stationary diffusion equations with stochastic coefficients.
The last part is devoted to the study of mixed multiscale finite elements in combination with multi-level Monte Carlo methods. In the third part we consider multi-phase flow and transport equations.

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.

This thesis is concerned with a phase field model for brittle fracture.
The high potential of phase field modeling in computational fracture mechanics lies in the generality of the approach and the straightforward numerical implementation, combined with a good accuracy of the results in the sense of continuum fracture mechanics.
However, despite the convenient numerical application of phase field fracture models, a detailed understanding of the physical properties is crucial for a correct interpretation of the numerical results. Therefore, the driving mechanisms of crack propagation and nucleation in the proposed phase field fracture model are explored by a thorough numerical and analytical investigation in this work.

This thesis is concerned with tropical moduli spaces, which are an important tool in tropical enumerative geometry. The main result is a construction of tropical moduli spaces of rational tropical covers of smooth tropical curves and of tropical lines in smooth tropical surfaces. The construction of a moduli space of tropical curves in a smooth tropical variety is reduced to the case of smooth fans. Furthermore, we point out relations to intersection theory on suitable moduli spaces on algebraic curves.

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 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.

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.

Fluid extraction is a typical chemical process where two types of fluids are mixed together. The high complexity of this process which involves droplet coalescence, breakup, mass transfer, and counter-current flow often makes design difficult. The industrial design of these processes is still based on expensive mini-plant and pilot plant experiments. Therefore, there is a strong need for research into the stimulation of fluid-fluid interaction processes using computational fluid dynamics (CFD).
Previous multi-phase fluid simulations have focused on the development of models that couple mass and momentum using the Navier-Stokes equation. Recent population balance models (PBM) have proved to be important methods for analyzing droplet breakage and collisions. A combination of CFD and PBM facilitates the simulation of flow property by solving coupling equations, and the calculation of the droplet size and numbers. In our study, we successfully coupled an Euler-Euler CFD model with the breakup and coalescence models proposed by Luo and Svendsen (59).
The simulation output of extraction columns provides a mathematical understand- ing of how fluids are mixed inside a mixing device. This mixing process shows that the dispersed phase of a flow generates large blobs and bubbles. Current mathemati- cal simulation results often fail to provide an intuitive representation of how well two different types of fluid interact, so intuitive and physically plausible visualization tech- niques are in high demand to help chemical engineers to explore and analyze bubble column simulation data. In chapter 3, we present the visualization tools we developed for extraction column data.
Fluid interfaces and free surfaces are topics of growing interest in the field of multi- phase computational fluid dynamics. However, the analysis of the flow field relative to the material interface shape and topology is a challenging task. In chapter 5, we present a technique that facilitates the visualization and analysis of complex material interface behaviors over time. To achieve this, we track the surface parameterization of time-varying material interfaces and identify locations where there are interactions between the material interfaces and fluid particles. Splatting and surface visualization techniques produce an intuitive representation of the derived interface stability. Our results demonstrate that the interaction of a flow field with a material interface can be understood using appropriate extraction and visualization techniques, and that our techniques can help the analysis of mixing and material interface consistency.
In addition to texture-based methods for surface analysis, the interface of two- phase fluid can be considered as an implicit function of the density or volume fraction values. High-level visualization techniques such as topology-based methods can re- veal the hidden structure underlying simple simulation data, which will enhance and advance our understanding of multi-fluid simulation data. Recent feature-based vi- sualization approaches have explored the possibility of using Reeb graphs to analyze scalar field topologies(19, 107). In chapter 6, we present a novel interpolation scheme for interpolating point-based volume fraction data and we further explore the implicit fluid interface using a topology-based method.

There is growing international concern about the necessity to re-think the university so that it might remain relevant in a modern society. In the traditional task division at universities, knowledge is the main resource. Universities make use of both the cognitive and the informational approach. It was expected that universities use each approach to improve overall university performance. To effectively use the informational approach, universities should apply the tools from knowledge management. To effectively use the cognitive approach, universities must update their teaching-learning strategies to incorporate some of the recent advances in neuroscience and biology of knowledge, specifically from neurobiology and autopoiesis. With this frame, the main contribution of this work is the result of merging pedagogy and biology, towards an ideal future university. This goal was achieved through an exploratory study conducted to identify opportunities and difficulties in improving the teaching-learning process for the future of higher education in Honduras. The Delphi Study was used as a predictive method. Nineteen Honduran experts participated in this study, and two rounds were necessary to achieve consensus.
The multi-disciplinary approach of this research addresses three different fields whose core element is knowledge. First, input from the present field of higher education is used to speak about the future. Second, input is taken from the biology of knowledge, and its contributions from neurobiology and autopoiesis that allow modifying and completing the already existing learning theories with a biological basis. Third, input is taken from the knowledge process, which is traditionally used as an organizational tool and know is translated to the individual level. The exploration shows that experts are concerned about all the missions and responsibilities of universities, but they agree that changes should primarily take place in the teaching dimension. Even though they are not aware of the possible contributions of biology, they suggest new forms of teaching that more favor skills development, promotes values, pertinent knowledge, and personal development over short-term contents. The resulting BRAIN Model encompasses the ideal future of higher education regarding teaching and learning, according to experts’ answers. It provides a useful guide that any reform in teaching should take into account for a holistic, integral, and therefore more efficient learning task.

Palladium-Catalyzed C–C Bond Formations via Activation of Carboxylic Acids and Their Derivatives
(2013)

Applications of carboxylic acids and their derivatives in transition metal-catalyzed cross-coupling reactions regio-selectively forming Csp3-Csp2, and Csp2-Csp2 bonds were explored in this thesis. Several important organic building blocks such as aryl acetates, diaryl acetates, imines, ketones, biaryls, styrenes and polysubstituted alkenes were successfully accessed from carboxylic acids and their derivatives by the means of C–H activation and decarboxylative cross-couplings.
An efficient and practical protocol for the synthesis of biologically important ethyl 2-arylacates through the dealkoxycarbonlative cross-coupling reaction between aryl halides and malonates was developed. Activation of the alpha-proton of alkyl esters by a copper catalyst allowed the deprotonation of esters even in the presence of mild bases, leading to a straightforward and efficient approach to alkyl alpha-diarylacetate from simple alkyl acetates and aryl halides.
The addition of a primary amine into the coupling reaction of alpha-oxocarboxylic acids and aryl halides led to an unprecedented low-temperature redox-neutral decarboxylative coupling process, providing a green and efficient method for the preparation of azomethines, in which all the three substituents can be independently varied. A minor modification of this protocol allowed us to easily access the corresponding ketones.
The decarboxylative coupling of robust aryl mesylates as well as polysubstituted alkenyl mesylates using our customized imidazolyl phosphine ligands was realized, further expanding the scope of carbon electrophiles in decarboxylative coupling reactions. Variation of the ligands led to two complementary protocols, providing the corresponding biaryls and polysubstituted olefins in high yields.
The use of a new class of pyrimidinyl phosphine ligands dramatically reduced the reaction temperatures of decarboxylative cross-coupling reactions between aromatic carboxylic acids and aryl or alkenyl triflates. The new catalyst system for the first time allowed the efficient decarboxylative biaryls synthesis at only 100 °C, representing a significant achievement in redox-neutral decarboxylative coupling reactions.

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.

Data integration aims at providing uniform access to heterogeneous data, managed by distributed source systems. Data sources can range from legacy systems, databases, and enterprise applications to web-scale data management systems. The materialized approach to data integration, extracts data from the sources, transforms and consolidates the data, and loads it into an integration system, where it is persistently stored and can be queried and analyzed.
To support materialized data integration, so called Extract-Transform-Load (ETL) systems have been built and are widely used to populate data warehouses today. While ETL is considered state-of-the-art in enterprise data warehousing, a new paradigm known as MapReduce has recently gained popularity for web-scale data transformations, such as web indexing or page rank computation.
The input data of both, ETL and MapReduce programs keeps changing over time, while business transactions are processed or the web is crawled, for instance. Hence, the results of ETL and MapReduce programs get stale and need to be recomputed from time to time. Recurrent computations over changing input data can be performed in two ways. The result may either be recomputed from scratch or recomputed in an incremental fashion. The idea behind the latter approach is to update the existing result in response to incremental changes in the input data. This is typically more efficient than the full recomputation approach, because reprocessing unchanged portions of the input data can often be avoided.
Incremental recomputation techniques have been studied by the database research community mainly in the context of the maintenance of materialized views and have been adopted by all major commercial database systems today. However, neither today's ETL tools nor MapReduce support incremental recomputation techniques. The situation of ETL and MapReduce programmers nowadays is thus much comparable to the situation of database programmers in the early 1990s. This thesis makes an effort to transfer incremental recomputation techniques into the ETL and MapReduce environments. This poses interesting research challenges, because these environments differ fundamentally from the relational world with regard to query and programming models, change data capture, transactional guarantees and consistency models. However, as this thesis will show, incremental recomputations are feasible in ETL and MapReduce and may lead to considerable efficiency improvements.

In recent years, recommender systems have been widely used for a variety of different kinds of items such as books, movies, and music. However, current recommendation approaches have often been criticized to suffer from overspecialization thus not enough considering a user’s diverse topics of interest. In this thesis we present a novel approach to extracting contextualized user profiles which enable recommendations taking into account a user’s full range of interests. The method applies algorithms from the domain of topic detection and tracking to automatically identify diverse user interests and to represent them with descriptive labels. That way manual annotations of interest topics by the users, e. g., from a predefined domain taxonomy, are no longer required. The approach has been tested in two scenarios: First, we implemented a content-based recommender system for an Enterprise 2.0 resource sharing platform where the contextualized user interest profiles have been used to generate recommendations with a high degree of inter-topic diversity. In an effort to harness the collective intelligence of the users, the resources in the system were described by making use of user-generated metadata. The evaluation experiments show that our approach is likely to capture a multitude of diverse interest topics per user. The labels extracted are specific for these topics and can be used to retrieve relevant on-topic resources. Second, a slightly adapted variation of the algorithm has been used to target music recommendations based on the user’s current mood. In this scenario music artists are described by using freely available Semantic Web data from the Linked Open Data cloud thus not requiring expensive metadata annotations by experts. The evaluation experiments conducted show that many users have a multitude of different preferred music styles. However a correlation between these music styles and music mood categories could not be observed. An integration of our proposed user profiles with existing user model ontologies seems promising for enabling context-sensitive recommendations.

The main purpose of the study was to improve the physical properties of the modelling of compressed materials, especially fibrous materials. Fibrous materials are finding increasing application in the industries. And most of the materials are compressed for different applications. For such situation, we are interested in how the fibre arranged, e.g. with which distribution. For given materials it is possible to obtain a three-dimensional image via micro computed tomography. Since some physical parameters, e.g. the fibre lengths or the directions for points in the fibre, can be checked under some other methods from image, it is beneficial to improve the physical properties by changing the parameters in the image.
In this thesis, we present a new maximum-likelihood approach for the estimation of parameters of a parametric distribution on the unit sphere, which is various as some well known distributions, e.g. the von-Mises Fisher distribution or the Watson distribution, and for some models better fit. The consistency and asymptotic normality of the maximum-likelihood estimator are proven. As the second main part of this thesis, a general model of mixtures of these distributions on a hypersphere is discussed. We derive numerical approximations of the parameters in an Expectation Maximization setting. Furthermore we introduce a non-parametric estimation of the EM algorithm for the mixture model. Finally, we present some applications to the statistical analysis of fibre composites.

Cyanobacteria are the only prokaryotes with the ability to conduct oxygenic photosynthesis,
therefore having major influence on the evolution of life on earth. Their diverse morphology
was traditionally the basis for taxonomy and classification. For example, the genus
Chroococcidiopsis has been classified within the order Pleurocapsales, based on a unique
reproduction modus by baeocytes. Recent phylogenetic results suggested a closer
relationship of this genus to the order Nostocales. However, these studies were based
mostly on the highly conserved 16S rRNA and a small selection of Chroococcidiopsis
strains. One aim of this present thesis was to investigate the evolutionary relationships of
the genus Chroococcidiopsis, the Pleurocapsales and remaining cyanobacteria using
16S rRNA, rpoC1 and gyrB gene. Including the single gene, as the multigene analyses of
97 strains clearly showed a separation of the genus Chroococcidiopsis from the
Pleurocapsales. Furthermore, a sister relationship between the genus Chroococcidiopsis
and the order Nostocales was confirmed. Consequently, the monogeneric family
Chroococcidiopsidaceae Geitler ex. Büdel, Donner & Kauff familia nova is justified. The
phylogenetic analyses also revealed the polyphyly of the remaining Pleurocapsales, due to
the fact that the strain Pleurocapsa PCC 7327 was always separated from other strains.
This is supported by differences in their metabolism, ecology and physiology.
A second aim of this study was to investigate the thylakoid arrangement of
Chroococcidiopsis and a selection of cyanobacterial strains. The investigation of 13 strains
with Low Temperature Scanning Electron Microscopy revealed two unknown thylakoidal
arrangements within Chroococcidiopsis (parietal and stacked). This result revised the
knowledge of the thylakoid arrangement in this genus. Previously, only a coiled
arrangement was known for three strains. Based on the data of 66 strains, the feature
thylakoid arrangement was tested as a potential feature for morphological identification of
cyanobacteria. The results showed a strong relationship between the group assignment of
cyanobacteria and their thylakoid arrangements. Hence, it is in general possible to
conclude from this certain phenotypic character the affiliation to a particular family, order
or genus.
The third aim of this study was to investigate biogeographical patterns of the worldwide
distributed genus Chroococcidiopsis. The phylogenetic analysis suggested that the genus do not have biogeographical patterns, which is in contrast with a recent study on hypolithic
living Chroococcidiopsis strains and the majority of phylogeographic analysis of
microorganisms. Further analysis showed no separation of different life-strategies within
the genus. These results could be related to the genetic markers utilized, which may not
contain biogeographical information. Hence the present study can neither exclude nor
prove the possibility of biogeographic and life-strategy patterns in the genus
Chroococcidiopsis.
Future research should be focused on finding appropriate genetic markers investigate of
evolutionary relationships and biogeographical patterns within Chroococcidiopsis.

The use of trading stops is a common practice in financial markets for a variety of reasons: it provides a simple way to control losses on a given trade, while also ensuring that profit-taking is not deferred indefinitely; and it allows opportunities to consider reallocating resources to other investments. In this thesis, it is explained why the use of stops may be desirable in certain cases.
This is done by proposing a simple objective to be optimized. Some simple and commonly-used rules for the placing and use of stops are investigated; consisting of fixed or moving barriers, with fixed transaction costs. It is shown how to identify optimal levels at which to set stops, and the performances of different rules and strategies are compared. Thereby, uncertainty and altering of the drift parameter of the investment are incorporated.