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In the last few years a lot of work has been done in the investigation of Brownian motion with point interaction(s) in one and higher dimensions. Roughly speaking a Brownian motion with point interaction is nothing else than a Brownian motion whose generator is disturbed by a measure supported in just one point.
The purpose of the present work is the introducing of curve interactions of the two dimensional Brownian motion for a closed curve \(\mathcal{C}\). We will understand a curve interaction as a self-adjoint extension of the restriction of the Laplacian to the set of infinitely often continuously differentiable functions with compact support in \(\mathbb{R}^{2}\) which are constantly 0 at the closed curve. We will give a full description of all these self-adjoint extensions.
In the second chapter we will prove a generalization of Tanaka's formula to \(\mathbb{R}^{2}\). We define \(g\) to be a so-called harmonic single layer with continuous layer function \(\eta\) in \(\mathbb{R}^{2}\). For such a function \(g\) we prove
\begin{align}
g\left(B_{t}\right)=g\left(B_{0}\right)+\int\limits_{0}^{t}{\nabla g\left(B_{s}\right)\mathrm{d}B_{s}}+\int\limits_{0}^{t}\eta\left(B_{s}\right)\mathrm{d}L\left(s,\mathcal{C}\right)
\end{align}
where \(B_{t}\) is just the usual Brownian motion in \(\mathbb{R}^{2}\) and \(L\left(t,\mathcal{C}\right)\) is the connected unique local time process of \(B_{t}\) on the closed curve \(\mathcal{C}\).
We will use the generalized Tanaka formula in the following chapter to construct classes of processes related to curve interactions. In a first step we get the generalization of point interactions in a second step we get processes which behaves like a Brownian motion in the complement of \(\mathcal{C}\) and has an additional movement along the curve in the time- scale of \(L\left(t,\mathcal{C}\right)\). Such processes do not exist in the one point case since there we cannot move when the Brownian motion is in the point.
By establishing an approximation of a curve interaction by operators of the form Laplacian \(+V_{n}\) with "nice" potentials \(V_{n}\) we are able to deduce the existence of superprocesses related to curve interactions.
The last step is to give an approximation of these superprocesses by a sytem of branching particles. This approximation gives a better understanding of the related mass creation.

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.

Aim of this work was the extension and development of a coupled Computational Fluid Dynamics (CFD) and population balance model (PBM) solver to enable a simulation aided design of stirred liquid-liquid extraction columns. The principle idea is to develop a new design methodology based on a CFD-PBM approach and verify it with existing data and correlations. On this basis, the separation performance in any apparatus geometry should be possible to predict without any experimental input. Reliable “experiments in silico” (computer calculations) should give the engineer a valuable and user-friendly tool for early design studies at minimal costs.
The layout of extraction columns is currently based on experimental investigations from miniplant to pilot plant and a scale-up to the industrial scale. The hydrodynamic properties can be varied by geometrical adjustments of the stirrer diameter, the stirrer height, the free cross sectional area of the stator, the compartment height as well as the positioning and the size of additional baffles. The key parameter for the liquid–liquid extraction is the yield which is mainly determined at the in- and outlets of the column. Local phenomena as the swirl structure are influenced by geometry changes. However, these local phenomena are generally neglected in state-of-the are design methodologies due to the complex required measurement techniques. A geometrical optimization of the column therefore still results in costs for validation experiments as assembly and operation of the column, which can be reduced by numerical investigations. The still mainly in academics used simulation based layout of counter-current extraction columns is based at the beginning of this work on one dimensional simulations of extraction columns and first three dimensional simulations. The one dimensional simulations are based on experimental derived, geometrical dependent correlations for the axial backmixing (axial dispersion), the hold-up, the phase fraction, the droplet sedimentation and the energy dissipation. A combination of these models with droplet population balance modeling resulted in a description of the complex droplet-droplet interactions (droplet size) along the column height. The three dimensional CFD simulations give local information about the flow field (velocity, swirl structure) based on the used numerical mesh corresponding to the real geometry. A coupling of CFD with population balance modeling further provides information about the local droplet size. A backcoupling of the droplet size with the CFD (drag model) results in an enhancement of the local hydrodynamics (e.g. hold-up, dispersed phase velocity). CFD provided local information about the axial dispersion coefficient of simple geometrical design (e.g. Rotating Disc Contactor (RDC) column). First simulations of the RDC column using a two dimensional rotational geometry combined with population balance modeling were performed and gave local information about the droplet size for different boundary conditions (rotational speed, different column sizes).
In this work, two different column types were simulated using an extended OpenSource CFD code. The first was the RDC column, which were mainly used for code development due to its simple geometry. The Kühni DN32 column is equipped with a six-baffled stirring device and flat baffles for disturbing the flow and requires a full three dimensional description. This column type was mainly used for experimental validation of the simulations due to the low required volumetric flow rate. The Kühni DN60 column is similar to the Kühni DN32 column with slight changes to the stirring device (4-baffles) and was used for scale up investigations. For the experimental validation of the hydrodynamics, laser based measurement techniques as Particle Image Velocimetry (PIV) and Laser Induced Fluorescence (LIF) were used. A good agreement between the experimental derived values for velocity, hold-up and energy dissipation, experimentally derived correlations from literature and the simulations with a modified Euler-Euler based OpenSource CFD code could be found. The experimental derived axial dispersion coefficient was further compared to Euler-Lagrange simulations. The experimental derived correlations for the Kühni DN32 in literature fit to the simulated values. Also the axial dispersion coefficient for the dispersed phase satisfied a correlation from literature. However, due to the complexity of the dispersed phase axial dispersion coefficient measurement, the available correlations gave no distinct agreement to each other.
A coupling of the modified Euler-Euler OpenSource CFD code was done with a one group population balance model. The implementation was validated to the analytical solution of the population balance equation for constant breakage and coalescence kernels. A further validation of the population balance transport equation was done by comparing the results of a five compartment section to the results of the commercial CFD code FLUENT using the Quadrature Method of Moments (QMOM).
For the simulation of the droplet-droplet interactions in liquid-liquid extraction columns, several breakage and coalescence models are available in the literature. The models were compared to each other using the one-group population balance model in Matlab which allows the determination of the minimum stable droplet diameter at a certain energy dissipation. Based on this representation, it was possible to determine the parameters for a specific breakage and coalescence model combination which allowed the simulation of a Kühni miniplant column at different rotational speeds. The resulting simulated droplet size was in very good agreement to the experimental derived droplet size from literature. Several column designs of the DN32 were investigated by changing the compartment height and the axial stirrer position. It could be shown that a decrease of the stirrer position increases the phase fraction inside the compartment. At the same time, the droplet size decreases inside the compartment, which allows a higher mass transfer due to a higher available interfacial area. However, the shifting results in an expected earlier flooding of the column due to a compressed flow structure underneath the stirring device. In a next step, the code was further extended by mass transfer equations based on the two-film theory. Mass transfer coefficient models for the dispersed and continuous phase were investigated for the RDC column design.
A first mass transfer simulation of a full miniplant column was done. The change in concentration was accounted by the mixture density, viscosity and interfacial tension in dependence of the concentration, which affects the calculation of the droplet size. The results of the column simulation were compared to own experimental data of the column. It could be shown that the concentration profile along the column height can be predicted by the presented CFD/population balance/mass transfer code. The droplet size decreases corresponding to the interfacial tension along the column height. Compared to the experimental derived droplet size at the outlet, the simulation is in good agreement.
Besides the occurrence of a mono dispersed droplet size, high breakage may lead to the generation of small satellite droplets and coalescence underneath the stator leads to larger droplets inside the column and hence to a change of the hold-up and of the flooding point. A multi-phase code was extended by the Sectional Quadrature Method of Moment (SQMOM) allowing a modeling of the droplet interactions of bimodal droplet interactions or multimodal distributions. The implementations were in good agreement to the analytical solution. In addition, the simulation of an RDC column section showed the different distribution of the smaller droplets and larger droplets. The smaller droplets tend to follow the continuous phase flow structure and show a higher distribution of inside the column. The larger droplets tend to rise directly through the column and show only a low influence to the continuous phase flow.
The current results strengthen the use of CFD for the layout of liquid-liquid extraction columns in future. The coupling of CFD/PBM and mass transfer using an OpenSource CFD code allows the investigation of computational intensive column designs (e.g. pilot plant columns). Furthermore the coupled code enhances the accuracy of the hydrodynamics simulations and leads to a better understanding of counter-current liquid-liquid extraction columns. The gained correlation were finally used as an input for one dimensional mass transfer simulations, where a perfect fit of the concentration profiles at varied boundary conditions could be obtained. By using the multi-scale approach, the computational time for mass transfer simulations could be reduced to minutes. In future, with increasing computational power, a further extend of the multiphase CFD/SQMOM model including mass transfer equation will provide an efficient tool to model multimodal and multivariate systems as bubble column reactors.

An huge amount of computational models and programming languages have been proposed
for the description of embedded systems. In contrast to traditional sequential programming
languages, they cope directly with the requirements for embedded systems: direct support for
concurrent computations and periodic interaction with the environment are only some of the
features they offer. Synchronous languages are one class of languages for the development of
embedded systems and they follow the fundamental principle that the execution is divided into
a sequence of logical steps. Thereby, each step follows the simplification that the computation
of the outputs is finished directly when the inputs are available. This rigorous abstraction leads
to well-defined deterministic parallel composition in general, and to deterministic abortion
and suspension in imperative synchronous languages in particular. These key features also
allow to translate programs to hardware and software, and also formal verification techniques
like model checking can be easily applied.
Besides the advantages of imperative synchronous languages, also some drawbacks can
be listed. Over-synchronization is an effect being caused by parallel threads which have to
synchronize for each execution step, even if they do not communicate, since the synchronization
is implicitly forced by the control-flow. This thesis considers the idea of clock refinement to
introduce several abstraction layers for communication and synchronization in addition to the
existing single-clock abstraction. Thereby, clocks can be refined by several independent clocks
so that a controlled amount of asynchrony between subsequent synchronization points can be
exploited by compilers. The declarations of clocks form a tree, and clocks can be defined within
the threads of the parallel statement, which allows one to do independent computations based
on these clocks without synchronizing the threads. However, the synchronous abstraction is
kept at each level of the abstraction.
Clock refinement is introduced in this thesis as an extension to the imperative synchronous
language Quartz. Therefore, new program statements are introduced which allow to define
a new clock as a refinement of an existing one and to finish a step based on a certain clock.
Examples are considered to show the impact of the behavior of the new statements to
the already existing statements, before the semantics of this extension is formally defined.
Furthermore, the thesis presents a compile algorithm to translate programs to an intermediate
format, and to translate the intermediate format to a hardware description. The advantages
obtained by the new modeling feature are finally evaluated based on examples.

Recent progresses and advances in the field of consumer electronics, driven by display
technologies and also the sector of mobile, hand-held devices, enable new ways in
presenting information to users, as well as new ways of user interaction, therefore
providing a basis for user-centered applications and work environments.
My thesis focuses on how arbitrary display environments can be utilized to improve
both the user experience, regarding perception of information, and also to provide
intuitive interaction possibilities. On the one hand advances in display technologies
provide the basis for new ways of visualizing content and collaborative work, on the
other hand forward-pressing developments in the consumer market, especially the
market of smart phones, offer potential to enhance usability in terms of interaction
and therefore can provide additional benefit for users.
Tiled display setups, combining both large screen real estate and high resolution,
provide new possibilities and chances to visualize large datasets and to facilitate col-
laboration in front of a large screen area. Furthermore these display setups present
several advantages over the traditional single-user-workspace environments: con-
trary to single-user-workspaces, multiple users are able to explore a dataset displayed
on a tiled display system, at the same time, thus allowing new forms of collabora-
tive work. Based on that, face-to-face discussions are enabled, an additional value
is added. Large displays also allow the utilization of the user’s spatial memory, al-
lowing physical navigation without the need of switching between different windows
to explore information.
With Tiled++ I contributed a versatile approach to address the bezel problem. The
bezel problem is one of the Top Ten research challenges in the research field of LCD-
based tiled wall setups. By applying the Tiled++ approach a large high resolution
Focus & Context screen is created, combining high resolution focus areas with low
resolution context information, projected onto the bezel area.
Additionally the field of user interaction poses an important challenge, especially
regarding the utilization of large tiled displays, since traditional keyboard & mouse
interaction devices reached their limits. My focus in this thesis is on Mobile HCI.Devices like mobile phones are utilized to interact with large displays, since they
feature various interaction modalities and preserve user mobility.
Large public displays, as a modernized form of traditional bulletin boards, also en-
able new ways of handling information, displaying content, and user interaction.
Utilized in hot spots, Digital Interactive Public Pinboards can provide an adequate
answer to questions like how to approach pressing issues like disaster and crisis man-
agement for both responders as well as citizens and also new ways of how to handle
information flow (contribution & distribution & accession). My contribution to the
research field of public display environments was the conception and implementa-
tion of an easy-to-use and easy-to-set-up architecture to overcome shortcomings of
current approaches and to cover the needs of aid personnel.
Although being a niche, Virtual Reality (VR) environments can provide additional
value for visualizing specific content. Disciplines like earth sciences & geology, me-
chanical engineering, design, and architecture can benefit from VR environments. In
order to consider the variety of users, I introduce a more intuitive and user friendly
interaction metaphor, the ARC metaphor.
Visualization challenges base on being able to cope with more and more complex
datasets and to bridge the gap between comprehensibility and loss of information.
Furthermore the visualization approach has to be reasonable, which is a crucial
factor when working in interdisciplinary teams, where the standard of knowledge
is diverse. Users have to be able to conceive the visualized content in a fast and
reliable way. My contribution are visualization approaches in the field of supportive
visualization.
Finally, my work illuminates how the synthesis of visualization, interaction and dis-
play technologies enhance the user experience. I promote a holistic view. The user
is brought back into the focus of attention, provided with a tool-set to support him,
without overextending the abilities of, for example, non-expert users, a crucial factor
in the more and more interdisciplinary field of computer science.

Tire-soil interaction is important for the performance of off-road vehicles and the soil compaction in the agricultural field. With an analytical model, which is integrated in multibody-simulation software, and a Finite Element model, the forces and moments generated on the tire-soil contact patch were studied to analyze the tire performance. Simulations with these two models for different tire operating conditions were performed to evaluate the mechanical behaviors of an excavator tire. For the FE model validation a single wheel tester connected to an excavator arm was designed. Field tests were carried out to examine the tire vertical stiffness, the contact pressure on the tire – hard ground interface, the longitudinal/vertical force and the compaction of the sandy clay from the test field under specified operating conditions. The simulation and experimental results were compared to evaluate the model quality. The Magic Formula was used to fit the curves of longitudinal and lateral forces. A simplified tire-soil interaction model based on the fitted Magic Formula could be established and further applied to the simulation of vehicle-soil interaction.