The presented study was motivated by the dynamic phenomena observed in basic catalytic surface reactions, especially by bi- and tristability, and the interactions between these stable states. In this regard, three reaction-diffusion models were developed and examined using bifurcation theory and numerical simulations. A first model was designed to extend the bistable CO oxidation on Ir(111) to include hydrogen and its oxidation. The differential equation system was analyzed within the framework of bifurcation theory, revealing three branches of stable solutions. One state is characterized by high formation rates (upper rate state, UR), while the other two branches display low formation rates (lower rate (LR) \& very low rate (VLR) states). The overlapping branches form the shape of a `swallowtail', the curve of saddle-node bifurcations forming two cusps. Increasing the temperature leads to a subsequent unfolding and hence decreases the system complexity. A series of numerical simulations representing possible experiments was conducted to illustrate the experimental accessibility (or the lack) of said states. Relaxation experiments show partially long decay times. Quasistatic scanning illustrates the existence of all three states within the tristable regime and their respective conversion once crossing a fold. A first attempt regarding the state dominance in reaction-diffusion fronts was done. While UR seems to dominate in 1D, a 2D time-evolution shows that LR invades the interphase between UR and VLR. Subsequently, a generic monospecies mock model was used for the comprehensive study of reaction-diffusion fronts. A quintic polynomial as reaction term was chosen, derived by the sixth-order potential associated with the `butterfly bifurcation'. This ensures up to three stable solutions($u_{0}$,$u_{1}$,$u_{2}$), depending on the four-dimensional parameter space. The model was explored extensively, identifying regions with similar behaviors. A term for the front velocity connecting two stable states was derived, depending only on the relative difference of the states' potential wells. Equipotential curves were found, where the front velocity vanishes of a given front. Numerical simulations on a two-dimensional, finite disk using a triangulated mesh supported these findings. Additionally, the front-splitting instability was observed for certain parameters. The front solution $u_{02}$ becomes unstable and divides into $u_{01}$ and $u_{12}$, exhibiting different front velocities. A good estimate for the limit of the front splitting region was given and tested using time evolutions. Finally, the established mock model was modified from continuous to discrete space, utilizing a simple domain in 1D and three different lattices in 2D (square, hexagonal, triangular). For low diffusivities or large distances between coupling nodes, fronts can become pinned, if the parameters are within range of the equipotential lines. This phenomenon is known as propagation failure and its extent in parameter space was explored in 1D. In 2D, an estimate was given for remarkable front orientations respective to the lattice using a pseudo-2D approximation. Near the pinning region, front velocities differ significantly from the continuous expectation as the shape of the curve potential becomes significant. Factors that decide the size and shape of the pinning regions are the coupling strength, the lattice, the front orientation relative to the lattice, and the front itself. The bifurcation diagram shows a snaking curve in the pinning region, each alternating branch representing a stable or unstable frozen front solution. Numerical simulations supported the observations concerning propagation failure and lattice dependence. Furthermore, the influence of front orientation on the front velocity was explored in greater detail, showing that fronts with certain lattice-dependent orientations are more or less prone to propagation failure. This leads to the possibility of pattern formation, reflecting the lattice geometry. An attempt to quantify the front movement depending on angular front orientation has shown reasonable results and good agreement with the pseudo-2D approach.

Over the past few decades, Single-Particle Analysis (SPA), in combination with cryo-transmission electron microscopy, has evolved into one of the leading technologies for structural analysis of biological macromolecules. It allows the investigation of biological structures in a close to native state at the molecular level. Within the last five years the achievable resolution of SPA surpassed 2°A and is now approaching atomic resolution, which so far has only been possible with Xray crystallography in a far from native environment. One remaining problem of Cryo-Electron Microscopy (cryo-EM) is the weak image contrast. Since the introduction of cryo-EM in the 1980s phase plates have been investigated as a potential tool to overcome these contrast limitations. Until now, technical problems and instrumental deficiencies have made the use of phase plates difficult; an automated workflow, crucial for the acquisition of 1000s of micrographs needed for SPA, was not possible. In this thesis, a new Zernike-type Phase Plate (PP) was developed and investigated. Freestanding metal films were used as a PP material to overcome the ageing and contamination problems of standard carbon-based PPs. Several experiments, evaluating and testing various metals, ended with iridium as the best-suited material. A thorough investigation of the properties of iridium PP followed in the second part of this thesis. One key outcome is a new operation mode, the rocking PP. By using this rocking-mode, fringing artifacts, another obstacle of Zernike PPs, could be solved. In the last part of this work, acquisition and reconstruction of SPA data of apoferritin was performed using the iridium PP in rocking-mode. A special semi-automated workflow for the acquisition of PP data was developed and tested. The recorded PP data was compared to an additional reference dataset without a PP, acquired following a conventional workflow.

The three biodegradable polymers polylactic acid (PLA), polyhydroxybutyrate (PHB) and polybutylene adipate terephthalate (PBAT) were coated with hydrogenated amorphous carbon layers (a-C:H) in the context of this thesis. A direct alignment of the sample surface to the source was chosen, resulting in the deposition of a robust, r-type a-C:H. At the same time, a partly covered silicon wafer was placed together with the polymers in the coating chamber and was coated. Silicon is a hard material and serves as a reference for the applied layers. Due to the hardness of the material, no mixed phase occurs between the substrate and the applied layer (no interlayer formation). In addition, the thickness of the applied layer can be estimated with the help of the silicon sample. The deposition of the layer was realized by radio frequency plasma enhanced chemical vapor deposition (RF-PECVD). For the coating the samples were pre-treated with an oxygen plasma. Acetylene was used as precursor gas for the plasma coating. Coatings with increasing thickness in 50 nm steps from 0-500 nm were realised. The surface analysis was performed using several techniques: The morphology and layer stability were analyzed with scanning electron microscopy (SEM) measurements. The wettability was determined by contact angle technique. In addition, the contact angles provide macroscopic information about the bond types of the carbon atoms present on the surface. For microscopic analysis of the chemical composition of the sample and layer surfaces, diffuse reflectance Fourier transform infrared spectroscopy (DRIFT) as well as synchrotron based X-ray photon spectroscopy (XPS) and near edge X-ray absorption fine structure spectroscopy (NEXAFS) were used. All coated polymers showed several cases of layer failure due to internal stress in the layers. However, these were at different layer thicknesses, so there was a substrate effect. In addition, it is visible in the SEM images that the coatings of PLA and PHB can cause the applied layer to wave, the so-called cord buckling. This does not occur with polymer PBAT, which indicates a possible better bonding of the layer to the polymer. The chemical analyses of the layer surfaces show for each material a layer thickness dependent ratio of sp² to sp³ bonds of carbon, which alternately dominate the layer. In all polymers, the sp³ bond initially dominates, but the sp² to sp³ ratio changes at different intervals. Although the polymers were coated in the same plasma, i.e. the respective layer thicknesses (50 nm, 100 nm, ...) were applied in the same plasma process, the respective systems differed considerably from each other. A substrate effect is therefore demonstrably present. In addition, it was found that a change in the dominant bond from sp³ to sp² is an indication ofan upcoming layer failure of the a-C:H layer deposited on the polymer. In the case of PLA, this occurs immediately with change to sp² as the dominant bond; in the case of PHB and PBAT, this occurs with different delay to increased layer thicknesses (at PHB 100 nm, at PBAT approx. 200 nm. Overall, this thesis shows that there is a substrate effect in the coating of the biodegradable polymers PLA, PHB and PBAT, since despite the same coating there is a different chemical composition of the surface at the respective layer thicknesses. In addition, a layer failure can be predicted by analyzing the existing bond.

The analysis of three-dimensional and complex motion sequences of human gait and therefore the most important question of kenesiology ”why are we falling?” is the essence of this paper. The gerontology and its science of movement is currently limited to simple and one-dimensional methods and models. An extensive literature research shows the latest state of research of the three common methods to determine the stability of human gait. To assess the margin of stability, local stability and orbital stability it is shown, how those methods are applicable to evaluate the subject’s ability to recover from any disturbences of the subject’s gait. Based on this assessment and the method’s advantages and disadvantages a new method will be derived that allows spatial analysis of dynamic instability of linear and non-linear human gait. A motion capture system and the timed up and go test serve as a basis for this new method and will be explained. A numerical approximation to optimise the number of markers within a marker-set of a motion capture analysis and its maximum correlation with the full-body-marker-set will be given. This simplification is very helpful for further clinical or scientific research. To validate the new method a trial with subjects will be shown and discussed. New appreciable variables and snapshots of specific situations during the gait offer new and different interpretations of the human gait. The new method is the most applicable and appropriate assessment of human gait and the individual development of the human gait while aging, as well as to detect and prevent falling and associated injuries. Especially directional change of a non-linear gait become assessable with the new method.

Different techniques (weight loss, electrochemical, and spray corrosion measurements) have been used to evaluate four sarcosine derivatives to inhibit corrosion and one commercial compound as synergist. The basic metal was low carbon steel CR4 tested at different conditions. As working media mainly neutral water and 0.1 M NaCl was applied. The protective film was formed on the steel surface via direct absorption of the tested substances during the immersion process. A highly improved corrosion protection with direct correlation to the molecular weight and carbon chain length of the tested compounds was detected. The protection of steel CR4 against corrosion in 0.1 M NaCl enhanced with increasing concentration of selected sarcosine compounds. The best inhibitor throughout all tested concentrations and all evaluation systems was Oleoylsarcosine (O) with efficiencies up to 97 % in potentiodynamic polarization (PP), 83 % electrochemical impedance spectroscopy (EIS), and 85 % weight loss (WL) at 100 mmol/L as highest concentration tested here. The second best inhibitor was Myristoylsarcosine (M) with efficiencies up to 82 % in PP, 69 % in EIS, and 75 % in WL at highest concentration. The inhibitor with the shortest hydrocarbon chain in this series is Lauroylsarcosine (L). It showed lowest effects to inhibit corrosion compared to O and M. The efficiencies of L were a bit more than 50 % at 75 and 100 mmol/L and less than 50 % at 25 and 50 mmol/L in all used evaluation systems. Furthermore, the overall efficiency is promoted with longer dip coating times during the steel CR4 immersion as shown for 50 mmol/L for all present derivatives. This survey indicated 10 min as best time in respect of cost and protection efficiency. The commercial inhibitor Oley-Imidazole (OI) improved significantly the effectiveness of compound Cocoylsarcosine (C), which contains the naturally mixture of carbon chain lengths from coconut oil (C8 - C18), and enhanced protection when used in combination (C+OI, 1:1 molar ration). In this system the efficiency increased from 47 % to 91 % in PP, from 40 % to 84 % in EIS, and from 45 % to 82 % in WL at highest concentration. Spray corrosion tests were used to evaluate all present sarcosine substances on steel CR4 in a more realistic system. The best inhibitor after a 24 h test was O followed by the combination C+OI and M with efficiencies up to 99 %, 80 %, and 79 %, respectively. The obtained results indicate a good stability of the protective film formed by the present inhibitors even after 24 h. All evaluation systems used in the current investigation were in good agreement and resulted in the same inhibitor sequence. Furthermore, the adsorption process of the tested compounds is assumed to follow the Langmuir type isotherm. Response surface methodology (RSM) is an optimization method depending on Box- Behnken Design (BBD). It was used in the current system to find the optimum efficiency for inhibitor O to protect steel CR4 against corrosion in salt water. Four independent variables were used here: inhibitor concentration (A), dip coating time (B), temperature (C), and NaCl concentration (D); each with three respective levels: lower (-1), mid (0), and upper (+1). According to the present result, temperature has the greatest effect on the protection process as individual parameter followed by the inhibitor concentration itself. In this investigation an optimum efficiency of 99 % is calculated by the following parameter and level combination: upper level (+1) for inhibitor concentration, dip coating time, and NaCl concentration while lower level (-1) for temperature.

Die laserinduzierte Plasmaspektroskopie (”Laser Induced Breakdown Spectroscopy”, im Folgenden auch ”LIBS” genannt) stellt eine schnelle und berührungslose Messmethode zur Elementanalyse von festen, flüssigen oder gasförmigen Stoffen unter normalen Umgebungsbedingungen ohne besondere Probenvorbereitung dar. Dazu wird ein gepulster Laser, dessen Intensität einen bestimmten Grenzwert überschreiten muss, auf eine Probe fokussiert. Das dort bestrahlte Material verdampft schlagartig und es bildet sich bei einer Temperatur von rund 10000 K ein Plasma aus. Die angeregten Atome und Ionen im Plasma strahlen bei der Rückkehr in energetisch niedrigere Zustände ein charakteristisches optisches Emissionsspektrum ab, welches über eine schnelle spektroskopische Analyse die Elementzusammensetzung des untersuchten Materials liefert. LIBS bietet in diesem Fall auch die Möglichkeit, ein unkompliziertes und bildgebendes Messverfahren aufzubauen, indem Elementverteilungen auf einer topographischen Oberfläche analysiert werden, um beispielsweise Materialübergänge, Einschlüsse oder Verschmutzungen sicher zu detektieren. Bei unebenen Oberflächen wird eine ständige Anpassung des Laserfokus an die Probenkontur benötigt, da die notwendige Intensität zur Erzeugung des Plasmas nur im Fokus aufgebracht werden kann. Als Grundlage dafür dient ein neu entwickelter Fokussieralgorithmus, der ohne jegliche Zusatzgeräte auskommt, und die Reproduzierbarkeit von LIBS-Messungen deutlich steigern kann, da die Messungen kontrolliert im Fokus stattfinden. Durch ihn ergeben sich neue Möglichkeiten des sogenannten „Element-Mappings", dem Erzeugen von Elementlandkarten, welche die Elementverteilungen in Falschfarben grafisch darstellen. Dabei ist das System nun nicht mehr auf eine ebene Oberfläche angewiesen, sondern kann beliebige Strukturen, auch mit scharfen Kanten und Löchern, sicher vermessen. Als Ergebnis erhält man ein flächiges Höhenprofil, welches zusätzlich die Elementinformationen für jeden Messpunkt beinhaltet. Dies erleichtert es dem Benutzer, gezielt Punkte von Interesse schnell wiederzufinden und zu analysieren. Die vorliegende Arbeit beschreibt die Entwicklung eines bildgebenden Low-Power-LIBSSystems mit niedriger Pulsenergie und hoher Pulsrate, welches sich mit dem dazugehörigen Fokussieralgorithmus automatisiert an unebene Probenoberflächen anpassen kann. Als Ergebnisse werden die Analysen von ausgewählten metallhaltigen, geologischen, organischen und archäologischen Proben bzw. Fundstücken gezeigt.