Gegenstand der Dissertation ist die Untersuchung von wiederkehrenden Ausbrüchen (wie z.B. Epidemien) in der Natur. Dies gelang anhand von Modellen, die die Dynamik von Phytoplankton und die Ausbreitung von Krankheiten zwischen Städten beschreiben. Diese beide Systeme bilden hervorragende Beispiele für solche Phänomene. Die Frage, ob die in der Zeit wiederkehrenden Ausbrüche ein Ausdruck chaotischer Dynamik sein können, ist aktuell in der Ökologie und fasziniert Wissenschaftler dieser Disziplin. Wir konnten zeigen, dass sich das Plankton-Modell im Falle von periodischem Antreiben über die Nährstoffe in einem chaotischen Regime befindet. Diese Dynamik wurde als die komplexe Wechselwirkung zweier Oszillatoren verstanden. Ebenfalls wurde die Ausbreitung von Epidemien in Netzwerken wechselwirkender Städte mit unterschiedlichen Grössen untersucht. Dafür wurde zunächst die Kopplung zwischen zwei Städten als Verhältnis der Stadtgrössen eingeführt. Es konnte gezeigt werden, dass das System sich in einem globalen zweijährigen Zyklus, der auch in den realen Daten beobachtet wird, befinden kann. Der Effekt von Heterogenität in der Grösseverteilung ist durch gewichtete Kopplung von generischen Modellen (Zelt- und Logistische Abbildung) in Netzwerken im Detail untersucht worden. Eine neue Art von Kopplungsfunktion mit nichtlinearer Sättigung wurde eingeführt, um die Stabilität des Systems zu gewährleisten. Diese Kopplung beinhaltet einen Parameter, der es erlaubt, die Netzwerktopologie von globaler Kopplung in gerichtete Netzwerke gleichmässig umzuwandeln. Die Dynamik des Systems wurde anhand von Bifurkationsdiagrammen untersucht. Zum Verständnis dieser Dynamik wurde eine effektive Theorie, die die beobachteten Bifurkationen sehr gut nachahmt, entwickelt. / One of the most striking features of ecological systems is their ability to undergo sudden outbreaks in the population numbers of one or a small number of species. The similarity of outbreak characteristics, which is exhibited in totally different and unrelated (ecological) systems naturally leads to the question whether there are universal mechanisms underlying outbreak dynamics in Ecology. It will be shown into two case studies (dynamics of phytoplankton blooms under variable nutrients supply and spread of epidemics in networks of cities) that one explanation for the regular recurrence of outbreaks stems from the interaction of the natural systems with periodical variations of their environment. Natural aquatic systems like lakes offer very good examples for the annual recurrence of outbreaks in Ecology. The idea whether chaos is responsible for the irregular heights of outbreaks is central in the domain of ecological modeling. This question is investigated in the context of phytoplankton blooms. The dynamics of epidemics in networks of cities is a problem which offers many ecological and theoretical aspects. The coupling between the cities is introduced through their sizes and gives rise to a weighted network which topology is generated from the distribution of the city sizes. We examine the dynamics in this network and classified the different possible regimes. It could be shown that a single epidemiological model can be reduced to a one-dimensional map. We analyze in this context the dynamics in networks of weighted maps. The coupling is a saturation function which possess a parameter which can be interpreted as an effective temperature for the network. This parameter allows to vary continously the network topology from global coupling to hierarchical network. We perform bifurcation analysis of the global dynamics and succeed to construct an effective theory explaining very well the behavior of the system.

Introduction Combined thermal and fluid modeling is useful for design and optimization of cyclotron water targets. Previous heat transfer models assumed either a distribution of void under saturation conditions [1] or a static volumetric heat distribution [2]. This work explores the coupling of Monte Carlo radiation transport and Computation Fluid Dynamics (CFD) software in a computational model of the BTI Targetry visualization target [3]. In a batch water target, as the target medium is heated by energy deposition from the proton beam, a non-uniform density distribution develops. Production target operation is ultimately limited by the range thickness of the target un-der conditions of reduced water density. Since proton range is a function of target density, the system model must include the corresponding change in the volumetric heat distribution. As an initial attempt to couple the radiation transport and fluid dynamics calculations, the scope of this work was limited to subcooled target conditions. With the increasing availability of multi-phase CFD capabilities, this work provides the basis for extending these calculations to boiling targets where the coupling of the radiation transport and fluid dynamics is expected to be much stronger. Material and Methods The Monte Carlo radiation transport code MCNPX was used to create energy deposition data tallies from proton interaction with the target water and beam window. The beam was modeled as a Gaussian distribution with 50% transmission through a 10 mm diameter collimator. The energy deposition tally was translated into a 3-dimensional, point-wise heat generation table and supplied as an input to the CFD code ANSYS CFX. An iterative method was developed to couple the volumetric heat distribution from MCNPX to the fluid density distribution computed within ANSYS CFX. A 3-dimensional table of water density was exported from ANSYS CFX and imported into MCNPX. MCNPX was then used to calculate the heat generation rate (due to proton interactions) based on the assumed density profile. Applying the new heat generation profile to the ANSYS CFX model resulted in changes to the beam shape and penetration depth. The iterative scheme continued until converged values for density and heat generation rate were achieved. Monte Carlo methods are computationally ex-pensive due to the large number of particle histories needed to generate accurate results. CFD simulations are also computationally expensive due to the large number of mesh elements needed. Optimization methods were used for both MCNPX and ANSYS CFX to result in achievable solution times and memory requirements. Local mesh refinement in the beam strike area was necessary for convergence. This was achieved by extending the boundary layer of the mesh within the target water domain deeper into the fluid. This allowed for better resolution within the beam strike area without significantly increasing the expense in the remainder of the fluid domain. Additionally, direct simulation of the cooling water domain was decoupled from the computational model during the iterative process. Heat transfer coefficients from the first iteration were applied as a boundary condition for subsequent iterations. Once the beam and density distributions reached convergence, the beam data was applied to a high fidelity “full” model, which included the cooling water domain as well as increased particle histories in MCNPX. Results and Conclusions The target was initially modeled assuming a 10 μA beam of 18 MeV protons into uniform density target water with operating pressure of 400 psi. These conditions resulted in predicted maximum temperatures below the saturation temperature. The final converged beam data was compared to the original (uniform density) beam data. As expected, the density-dependent beam penetrates farther into the target water than when a uniform density is assumed. The density-dependent beam has a broader Bragg peak region with a lower maximum heat generation rate than the original beam. A line plot of the volumetric heat generation rate through the center of the beam is shown in FIG. 2. Even though the maximum volumetric heat generation rate was lower, the density-dependent beam resulted in a higher maximum fluid temperature. Experiments were performed with the visualization target on an IBA 18/9 cyclotron, and video was recorded for a range of target operating conditions. Analysis of the video recordings from the experiment gives a peak fluid velocity in the target chamber of roughly 5–10 centimeters per second with a 10 A beam current. The velocities predicted by the CFD model are within the same range. There is also good agreement be-tween proton beam range between the experiment and model. The effective proton range can be seen in FIGURES 3 and 4. Future work will include applying the coupling technique for two-phase boiling conditions and to gas targets. If successful, this method should be a powerful tool for design and optimization of liquid and gas targets.

Introduction Combined thermal and fluid modeling is useful for design and optimization of cyclotron water targets. Previous heat transfer models assumed either a distribution of void under saturation conditions [1] or a static volumetric heat distribution [2]. This work explores the coupling of Monte Carlo radiation transport and Computation Fluid Dynamics (CFD) software in a computational model of the BTI Targetry visualization target [3]. In a batch water target, as the target medium is heated by energy deposition from the proton beam, a non-uniform density distribution develops. Production target operation is ultimately limited by the range thickness of the target un-der conditions of reduced water density. Since proton range is a function of target density, the system model must include the corresponding change in the volumetric heat distribution. As an initial attempt to couple the radiation transport and fluid dynamics calculations, the scope of this work was limited to subcooled target conditions. With the increasing availability of multi-phase CFD capabilities, this work provides the basis for extending these calculations to boiling targets where the coupling of the radiation transport and fluid dynamics is expected to be much stronger. Material and Methods The Monte Carlo radiation transport code MCNPX was used to create energy deposition data tallies from proton interaction with the target water and beam window. The beam was modeled as a Gaussian distribution with 50% transmission through a 10 mm diameter collimator. The energy deposition tally was translated into a 3-dimensional, point-wise heat generation table and supplied as an input to the CFD code ANSYS CFX. An iterative method was developed to couple the volumetric heat distribution from MCNPX to the fluid density distribution computed within ANSYS CFX. A 3-dimensional table of water density was exported from ANSYS CFX and imported into MCNPX. MCNPX was then used to calculate the heat generation rate (due to proton interactions) based on the assumed density profile. Applying the new heat generation profile to the ANSYS CFX model resulted in changes to the beam shape and penetration depth. The iterative scheme continued until converged values for density and heat generation rate were achieved. Monte Carlo methods are computationally ex-pensive due to the large number of particle histories needed to generate accurate results. CFD simulations are also computationally expensive due to the large number of mesh elements needed. Optimization methods were used for both MCNPX and ANSYS CFX to result in achievable solution times and memory requirements. Local mesh refinement in the beam strike area was necessary for convergence. This was achieved by extending the boundary layer of the mesh within the target water domain deeper into the fluid. This allowed for better resolution within the beam strike area without significantly increasing the expense in the remainder of the fluid domain. Additionally, direct simulation of the cooling water domain was decoupled from the computational model during the iterative process. Heat transfer coefficients from the first iteration were applied as a boundary condition for subsequent iterations. Once the beam and density distributions reached convergence, the beam data was applied to a high fidelity “full” model, which included the cooling water domain as well as increased particle histories in MCNPX. Results and Conclusions The target was initially modeled assuming a 10 μA beam of 18 MeV protons into uniform density target water with operating pressure of 400 psi. These conditions resulted in predicted maximum temperatures below the saturation temperature. The final converged beam data was compared to the original (uniform density) beam data. As expected, the density-dependent beam penetrates farther into the target water than when a uniform density is assumed. The density-dependent beam has a broader Bragg peak region with a lower maximum heat generation rate than the original beam. A line plot of the volumetric heat generation rate through the center of the beam is shown in FIG. 2. Even though the maximum volumetric heat generation rate was lower, the density-dependent beam resulted in a higher maximum fluid temperature. Experiments were performed with the visualization target on an IBA 18/9 cyclotron, and video was recorded for a range of target operating conditions. Analysis of the video recordings from the experiment gives a peak fluid velocity in the target chamber of roughly 5–10 centimeters per second with a 10 A beam current. The velocities predicted by the CFD model are within the same range. There is also good agreement be-tween proton beam range between the experiment and model. The effective proton range can be seen in FIGURES 3 and 4. Future work will include applying the coupling technique for two-phase boiling conditions and to gas targets. If successful, this method should be a powerful tool for design and optimization of liquid and gas targets.

Das menschliche Skelett besteht aus einem dynamischen Material welches in der Lage ist zu heilen, sowie sich durch strukturellen Umbau an mechanische Beanspruchung anzupassen. In dieser Arbeit ist die mechanische Regulierung dieser Prozesse untersucht worden. Hierfür ist ein Computermodell, sowie die dreidimensionale Abbildung des Knochens und die Auswertung dieser Bilder benutzt worden. An dem Heilungsprozesses von Knochen sind verschiedene Gewebetypen beteiligt. Dabei hängt die räumliche und zeitliche Anordnung dieser Gewebe von der mechanischen Belastung ab. Ein Computermodell, welches den vollständigen Verlauf der Heilung beschreibt, wurde mit der dokumentierten Gewebeentwicklung eines Tierexperimentes verglichen. Verschiedene Hypothesen, wie die mechanische Stimulation die Bildung verschiedene Gewebe beeinflusst, wurden getestet. Zwar ließen sich durch den Vergleich mit dem Experiment keine der Hypothesen verwerfen, jedoch konnten wir Vorschläge machen, worauf bei zukünftigen Experimenten verstärkt geachtet werden soll. Es wird angenommen dass der Umbauprozesses des Knochens vom dichten Netzwerk der Osteozyten mechanisch reguliert wird. Diese Zellen sind in den Knochen eingebettet und über ein dichtes Netzwerk aus engen Kanälen, den sogenannten Canaliculi, miteinander verbunden. Dieses Netzwerk mittels konfokaler Mikrokopie dreidimensional abgebildet. Spezielle Routinen zur Auswertung der Netzwerkorientierung sowie dessen Dichte wurden entwickelt. Die Hauptorientierung des Netzwerkes entspricht der Richtung in der Knochengewebe aufgebaut wird. Die Orientierung des zu dieser Richtung senkrechten Anteils des Netzwerkes rotiert abhängig von der Position entlang der Aufbaurichtung. Dies verdeutlicht den Zusammenhang zwischen der Netzwerkorientierung und der Vorzugsrichtung des Kollagens, dem faserigen Bestandteils des Knochens. Darüber hinaus zeigt die Auswertung der Daten weitere strukturelle Unterschiede im Netzwerk. / Our skeleton is composed of a dynamic material that is capable of healing and of adapting to changing mechanical loads through structural remodeling. In this thesis the mechano-regulation of these dynamic processes are addressed using computer modeling and 3-dimensional imaging and image analysis. During bone healing an intricate pattern of different newly formed tissues around the fracture site evolves in time and is influenced by the mechanical loading. Using a computer model which is describing this temporal-spatial evolution of tissue types for the full time-course of healing, this evolution is compared to the documented evolution of an animal experiment. Different hypotheses were tested how the mechanical stimulation results in the formation of different tissues. While the comparison with the outcome of the animal experiments does not allow to falsify any of the hypotheses, it suggests a different design of future animal experiments. Bone remodeling is thought to be mechano-regulated by the dense network of osteocytes. These osteocytes are embedded in bone and are connected to each other via a network of narrow canaliculi. The 3-dimensional structure of the network was imaged using rhodamine staining and laser scanning confocal microscopy. Image analysis tools were developed to determine the network topology and to analyze its density and orientation. The analysis focused on osteons, the building blocks of cortical bone. Within an osteon we found a large variability of the network density with extensive regions without network. Most of the network is oriented radially towards the center of the osteon, i.e.\ parallel to the direction in which the bone material is deposited. The network perpendicular to this direction twists when moving along the direction of bone deposition. A correlation with the main orientation the fibrous constituent of bone, collagen, was detected. Furthermore indicates our data additional structural changes in the network alignment.

Kognitive Diagnosemodelle (DCMs) sind konfirmatorische probabilistische Modelle mit kategorialen latenten Variablen, die Mehrfachladungsstrukturen erlauben. Sie ermöglichen die Abbildung der Kompetenzen in mehrdimensionalen Profilen, die zur Erstellung informativer Rückmeldungen dienen können. Diese Dissertation untersucht in zwei Anwendungsstudien und einer Simulationsstudie wichtige methodische Aspekte bei der Schätzung der DCMs. In der Arbeit wurde ein neuer Mathematiktest entwickelt basierend auf theoriegeleiteten vorab definierten Q-Matrizen. In den Anwendungsstudien (a) illustrierten wir die Anwendung der DCMs für empirische Daten für den neu entwickelten Mathematiktest, (b) verglichen die DCMs mit konfirmatorischen Faktorenanalysemodellen (CFAs), (c) untersuchten die inkrementelle Validität der mehrdimensionalen Profile und (d) schlugen eine Methode zum Vergleich konkurrierender DCMs vor. Ergebnisse der Anwendungsstudien zeigten, dass die geschätzten DCMs meist einen nicht akzeptablen Modellfit aufwiesen. Zudem fanden wir nur eine vernachlässigbare inkrementelle Validität der mehrdimensionalen Profile nach der Kontrolle der Personenparameter bei der Vorhersage der Mathematiknote. Zusammengenommen sprechen diese Ergebnisse dafür, dass DCMs per se keine zusätzliche Information über die mehrdimensionalen CFA-Modelle hinaus bereitstellen. DCMs erlauben jedoch eine andere Aufbereitung der Information. In der Simulationsstudie wurde die Präzision der Parameterschätzungen in log-linearen DCMs sowie die Sensitivität ausgewählter Indizes der Modellpassung auf verschiedene Formen der Fehlspezifikation der Interaktionsterme oder der Q-Matrix untersucht. Die Ergebnisse der Simulationsstudie zeigen, dass die Parameterwerte für große Stichproben korrekt geschätzt werden, während die Akkuratheit der Parameterschätzungen bei kleineren Stichproben z. T. beeinträchtigt ist. Ein großer Teil der Personen wird in Modellen mit fehlspezifizierten Q-Matrizen falsch klassifiziert. / Cognitive diagnostic classification models (DCMs) have been developed to assess the cognitive processes underlying assessment responses. Current dissertation aims to provide theoretical and practical considerations for estimation of DCMs for educational applications by investigating several important underexplored issues. To avoid problems related to retrofitting of DCMs to an already existing data, test construction of the newly mathematics assessment for primary school DMA was based on a-priori defined Q-matrices. In this dissertation we compared DCMs with established psychometric models and investigated the incremental validity of DCMs profiles over traditional IRT scores. Furthermore, we addressed the issue of the verification of the Q-matrix definition. Moreover, we examined the impact of invalid Q-matrix specification on item, respondent parameter recovery, and sensitivity of selected fit measures. In order to address these issues one simulation study and two empirical studies illustrating applications of several DCMs were conducted. In the first study we have applied DCMs in general diagnostic modelling framework and compared those models to factor analysis models. In the second study we implemented a complex simulation study and investigated the implications of Q-matrix misspecification on parameter recovery and classification accuracy for DCMs in log-linear framework. In the third study we applied results of the simulation study to a practical application based on the data for 2032 students for the DMA. Presenting arguments for additional gain of DCMs over traditional psychometric models remains challenging. Furthermore, we found only a negligible incremental validity of multivariate proficiency profiles compared to the one-dimensional IRT ability estimate. Findings from the simulation study revealed that invalid Q-matrix specifications led to decreased classification accuracy. Information-based fit indices were sensitive to strong model misspecifications.

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