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Portable electronic devices like smartphones, tablet PC’s or wearables have become an essential part of everyday life. Continuous integration of more features like GPS or Bluetooth has led to significant technical improvements and convenience, but also to increased energy requirements. However, the development of new battery technologies with higher energy density is lacking behind which results in lower usage duration between single recharge cycles. Hence, the identification of alternative technologies is crucial for future success of portable, connected devices, especially in the field of the internet of things. The development of innovative micro fuel cells may be an interesting approach to reach the goal of high energy capacity with minimal volumetric requirements. For this, it is mandatory to find solutions for miniaturization of the fuel cell. In this thesis, essential concepts for fabrication of silicon-based micro electrode membrane assemblies are developed with a focus on applicability of mass fabrication. On the one hand, this includes the design of a concept to manufacture ultra-thin, microstructured membranes which serve as mechanical basis for the membrane electrode assemblies as well as development of a process to integrate a proton conducting ionomer into the microstructure of the membrane. On the other hand, different electrode configurations were realized and characterized in detail. This includes the use of established methods like measurement of polarization curves and the use of electrochemical impedance spectroscopy, but also the application of specialized characterization methods, namely electrochemical atomic force microscopy which makes it possible to validate the proton conductivity of single micro channels of the proton conducting membrane. The last part of the thesis investigates the potential of silicon-based micro membrane electrode assemblies to be used in high throughput material research. An experimental setup was designed, manufactured and assembled which allows initiating a fuel cell reaction under defined ambient conditions on a number of different electrode configurations. The electrodes are characterized regarding their heat of reaction with the help of emissivity corrected infrared spectroscopy. Because of the utilization of semiconductor processes, it is possible to manufacture a large quantity of varying electrode configurations. At the same time, the ultra-thin design of the micro membrane electrode assemblies makes it possible to allocate the origin of the heat of reaction precisely. This allows to evaluate different electrodes in parallel and to draw conclusion regarding the effectivity of the fuel cell reaction. Dissertation, Universität Duisburg-Essen, 2019

Die Nadel im Heuhaufen zu suchen erscheint bisweilen einfacher als neue Materialien für verbesserte Brennstoffzellen zu finden. Methoden der kombinatorischen Materialentwicklung versuchen Abhilfe zu schaffen., Fuel cells have succeeded in finding their way onto the market. Automotive, portable and combined heat and power applications are commercially available. Still, one major drawback of fuel cells can be found in the use of expensive materials, especially precious metal catalysts. However, the development of new catalyst materials has turned out to be a challenging task because the electrochemical reactions at the electrodes depend on numerous, interdependent parameters. That is why statistical approaches, so-called high-throughput or combinatorial methods, in material processing as well as material characterization have been established. They allow the manufacturing and validation of material libraries which exhibit a wide variety of material parameters, e. g. in the range of morphology or content of certain metal alloys. In this way, development times can be reduced significantly. In addition, micro fuel cells can also be interesting for material development. The small size is advantageous when it comes to material usage, temperature distribution and characterization times. Thus, the combination of combinatorial methods and micro fuel cells can boost material development in fuel cells to a new level. That is why the Fuel Cell Research Center (ZBT) in Duisburg and the Chair for MEMS materials at the Ruhr University of Bochum have merged their competences and developed a new method for the manufacturing and characterization of innovative micro fuel cell libraries. State-of-the-art technologies such as sputter deposition and infrared-thermography are used to generate silicon-based micro fuel cells with changing material properties and to validate them insitu while the fuel cell reaction takes place. Besides a successful proof of concept in a MERCUR-funded research project a first application of the method will be developed in the field of alkaline fuel cells where catalyst and electrolyte materials are lagging behind acid-based fuel cell systems., UNIKATE: Berichte aus Forschung und Lehre, no. 48Materials Chain: Forschung aus dem UA Ruhr-Profilschwerpunkt, p. 44

Diese Arbeit handelt von der nichtparametrischen Schätzung von Koeffizienten in verschiedenen Diffusions-Modellen. Im ersten Teil konstruieren wir einen nichtparametrischen punktweisen Nadaraya-Watson Schätzer für die unbekannte Driftfunktion $b$ eines Sprungdiffusionsprozesses, der auf einer Approximation des infinitesimalen Erzeugers der zu Grunde liegenden Diffusion basiert. Wir leiten asymptotische Eigenschaften wie Konsistenz und asymptotische Normalität her. Dabei arbeiten wir mit Hochfrequenz-Daten, welche über einen anwachsenden Zeithorizont beobachtet werden. Weiterhin geben wir einen konsistenten Schätzer für die asymptotische Varianz der Grenzverteilung des eingeführten Dichteschätzers an, welcher für die Konstruktion praktikabler punktweiser Konfidenzintervalle benötigt wird. Anschließen betrachten wir den Fall von verrauschten Daten und nutzen den “Pre-Averaging“ Ansatz an, welcher ursprünglich von Podolskij und Vetter (2006) für die nichtparametrische Schätzung der integrierten Volatilität von Itô-Semimartingalen eingeführt wurde. Unter entsprechenden Voraussetzungen zeigen wir, dass der neue Schätzer ebenfalls asymptotisch normalverteilt ist. Das erste Kapitel schließt mit einer Betrachtung von integrierten Diffusionen ab. Hier wird, analog zu vorher, ein “Pre-Averaging“ Ansatz verfolgt, um die Driftfunktion der integrierten Diffusion zu schätzen. Im zweiten Teil der Arbeit werden verschiedene Bias-Reduzierungsmöglichkeiten untersucht. Hierfür wird zunächst eine adaptive Version des Nadaraya-Watson Schätzers für bedingte Erwartungswerte betrachtet, bei der die Bandbreite zustandsabhängig ist. Hierbei führt eine adäquate Wahl der Bandbreitenfunktion zu einer Bias-Verringerung. Danach beschäftigen wir uns hauptsächlich mit Methoden, die dem sehr bekannten “Boundary Bias“-Effekt von nichtparametrischen Schätzern, welche auf symmetrischen Kernfunktionen basieren, entgegenwirken. Konkret führen wir zwei multivariate Dichteschätzer für die gemeinsame Dichte mehrdimensionaler Zufallsvektoren ein, deren Randverteilungen einen beschränkten Träger besitzen. Diese Schätzer basieren auf nicht-negativen multiplikativen Bias-Reduzierung Techniken. Diese Schätzer werden anschließend für die komponentenweise nichtparametrische Schätzung des Driftvektors in einem von einer Brownschen Bewegung angetriebenen multivariaten Diffusionsmodell vorgeschlagen. Das letzte Kapitel beschäftigt sich mit dem “Boundary Bias“ Effekt nicht parametrischer Schätzer für Dichten, welche einen kompakten Träger besitzen. Hierfür bilden Copula Dichten ein kanonisches Beispiel. Basierend auf dem Satz von Sklar wird eine alternative Darstellung des bedingten Erwartungswertes hergeleitet, der im Laufe der Arbeit stets als Approximation für die Driftfunktion diente. Hierfür wird dann abschließend eine alternative Möglichkeit vorgestellt, bedingte Erwartungswerte mit Hilfe von Bernstein-Polynomen zu schätzen., This thesis deals with the nonparametric estimation of the coefficients in different diffusion models. In the first part, based on an approximation of the infinitesimal generator of the underlying diffusion process, we investigate a Nadaraya-Watson like estimator for the pointwise estimation of the unknown drift function $b$. We derive its asymptotic properties as consistency and asymptotic normality under a double asymptotics scheme. In fact, we work with high-frequency data on an enlarging time horizon. Moreover, a consistent estimator of the asymptotic variance is proposed, which is useful for the construction of feasible pointwise confidence intervals. Subsequently, we consider the case of noisy data. We suggest the use of the pre-averaging approach proposed by Podolskij and Vetter (2006) for the nonparametric estimation of integrated volatility of Itô-semimartingales. We show how to use this approach in our setting and, moreover, derive the asymptotic distribution of the new estimator. Finally, the case of integrated diffusions is treated, where we make use of an analogous approach to estimate the drift of the underlying and hidden diffusion, too. The second part deals with bias correction methods for symmetrical kernel based nonparametric estimators. At first, we investigate an adaptive version of the Nadaraya-Watson estimator possessing a state-dependent bandwidth function. We show that an appropriate choice of the function yields to a bias reduction. Afterwards, boundary bias correction methods are investigate. In particular, we will focus on an approach by Chen (1999, 2000), who suggested the use of asymmetric kernels for estimating a probability density possessing bounded or compact support. Based on asymmetric kernels, we propose two multiplicative bias correction (``MBC") methods for the nonparametric estimation of the joint density of a random vector possessing bounded marginals. Subsequently, we investigate multivariate diffusions for which analogous approximations of the drift vector and the diffusion matrix exist. For the nonparametric estimation of the drift vector, we propose a componentwise estimator based on the introduced MBC techniques. Finally, in the third part of this thesis we focus on boundary bias effects of nonparametric estimators of compact supported densities. In particular, copula densities are toy-examples of this class of densities. Via Bernstein polynomials and based on Sklar´s theorem, we propose an alternative approach for estimating conditional expectations, which act, in turn, as approximations of the drift function in the previous chapters of this thesis.

In this article, a pointwise nonparametric kernel based estimator for the drift function in a Levy driven jump diffusion model is proposed. Under ergodicity and stationarity of the underlying process X, we derive asymptotic properties as consistency and asymptotic normality of the estimator. In addition, we propose a consistent estimator of the asymptotic variance. Moreover, we show that this approach is robust under microstructure noise by using the preaveraging approach proposed in Podolskij and Vetter (2006)., Discussion Paper / SFB 823;3,/2015

In this article we propose two new Multiplicative Bias Correction (MBC) techniques for nonparametric multivariate density estimation. We deal with positively supported data but our results can easily be ex- tended to the case of mixtures of bounded and unbounded supports. Both methods improve the optimal rate of convergence of the mean squared error up to O(n-8=(8+d)), where d is the dimension of the under- lying data set. Moreover, they overcome the boundary effect near the origin and their values are always non-negative. We investigate asymptotic properties like bias and variance as well as the performance of our estimators in Monte Carlo Simulations and in a real data example., Discussion Paper / SFB 823;39/2014