Denna studie syftar till att undersöka vilka möjligheter som gymnasium elever får attträna modelleringsförmågan genom läroboksuppgifter. Studien går inte in på ommodellering är möjlig att använda i uppgifterna utan undersöker i stället hur ofta studenten bliruppmanad att använda det. För att göra detta så har ett analytiskt schema tagits fram ochett urval av tre läroboksserier gjorts. Resultaten indikerar att det finns en stor skillnad ihur ofta olika modelleringsdelprocesser ges möjlighet att tränas. Det visar sig att detskiljer sig i hur många övningstillfällen som ges mellan olika svårighetsnivåer: närkomplexiteten i uppgiften ökar så minskar möjligheten. Det visar sig även att det skiljersig mellan olika matematiska områden från att inte alls ge möjlighet till att ha stor del avmöjligheterna. Till sist så visar det sig att modellering sällan uttrycks explicit iuppgifterna. / This study aims to investigate what opportunities textbook exercises in upper secondaryschool offer students to practice their modeling competency. This study does not addressif the student is able to use modeling in a specific task but rather how often the student isprompted to do so. To answer this, an analytical framework is developed and used on asample of three textbook series. The results indicate that there is a large difference in howoften different parts of the modeling process get prompted to train. Further, thefrequency of the opportunities that are given differs between difficulties of the tasks.When the complexity is increasing the number of opportunities decreases. The result alsoshow that the opportunity given differs between the mathematical areas: from noopportunity at all to a large part of the opportunities. Finally, the results show thatmodeling is seldom explicitly mentioned in the tasks.

This diploma thesis deals with the calculation of pressure losses in the flue gas ducts. First part of this work describes properties of flue gas and flow dynamics. Part of the theoretical analysis was detailed study of pipeline elements with emphasis on the reasons for the existence of pressure loss in the flow, calculations of the resistance coefficients and possible methods of reducing the losses. In the practical part, a model of the pressure loss calculation of the existing flue gas line installed in the incineration plant was created. At the end of the thesis a proposal for optimization of this route was made with emphasis on the reduction of the overall pressure loss. By optimization the pressure drop of the specified route was reduced from 3581 Pa to 2647 Pa, i.e by 26% and the required power input of the fan was reduced from 225 kW to 166,5 kW.

The subject topic of this thesis is to establish a suitable technique of tunnel construction using New Austrian Tunnelling Method with the help of mathematical modeling. Based on the mathematical modelling output the dimensioning primary moulding model was executed.

This thesis deals with analysis of operation data for purposes of optimization. The thesis is divided into four chapters. First chapter focuses on present and future development in waste management legislation. It mainly deals with prevention, recycling and disposal of waste. Second chapter more closely describes waste-to-energy process. This chapter also describes the technology of municipal waste incinerator in Liberec, Termizo, a.s. Third chapter starts with description of tools used in design of the models based on operation data. Then the models for individual technological nodes are described. The last part is focused on building a complex model of Termizo using previous results.

Mathematical modeling is an important tool in improving the understanding of complex biological processes. However, mathematical models are often faced with challenges that arise due to the limited knowledge of the underlying biological processes and the high number of parameters for which exact values are unknown. The method of generalized modeling is an alternative modeling approach that aims to address these challenges by extracting information about stability and bifurcations of classes of models while making only minimal assumptions on the specific functional forms of the model. This is achieved by a direct parameterization of the Jacobian in the steady state, introducing a set of generalized parameters which have a biological interpretation. In this thesis, the method of generalized modeling is extended and applied to different problems from cell biology. In the first part, we extend the method to include also the higher derivatives at the steady state. This allows an analysis of the normal form of bifurcations and thereby a more specific description of the nearby dynamics. In models of gene-regulatory networks, it is shown that the extended method can be applied to better characterize oscillatory systems and to detect bistable dynamics. In the second part, we investigate mathematical models of bone remodeling, a process that renews the human skeleton constantly. We investigate the connection between structural properties of mathematical models and the stability of steady states in different models. We find that the dynamical system operates from a stable steady state that is situated in the vicinity of bifurcations where stability can be lost, potentially leading to diseases of bone. In the third part of this thesis, models of the MAPK signal transduction pathway are analyzed. Since mathematical models for this system include a high number of parameters, statistical methods are employed to analyze stability and bifurcations. Thereby, the parameters with a strong influence on the stability of steady states are identified. By an analysis of the bifurcation structure of the MAPK cascade, it is found that a combination of multiple layers in a cascade-like way allows for additional types of dynamic behavior such as oscillations and chaos. In summary, this thesis shows that generalized modeling is a fruitful alternative modeling approach for various types of systems in cell biology. / Mathematische Modelle stellen ein wichtiges Hilfmittel zur Verbesserung des Verständnisses komplexer biologischer Prozesse dar. Sie stehen jedoch vor Schwierigkeiten, wenn wenig über die zugrundeliegende biologischen Vorgänge bekannt ist und es eine große Anzahl von Parametern gibt, deren exakten Werte unbekannt sind. Die Methode des Verallgemeinerten Modellierens ist ein alternativer Modellierungsansatz mit dem Ziel, diese Schwierigkeiten dadurch anzugehen, dass dynamische Informationen über Stabilität und Bifurkationen aus Klassen von Modellen extrahiert werden, wobei nur minimale Annahmen über die spezifischen funktionalen Formen getätigt werden. Dies wird erreicht durch eine direkte Parametrisierung der Jacobimatrix im Gleichgewichtszustand, bei der neue, verallgemeinerte Parameter eingeführt werden, die eine biologische Interpretation besitzen. In dieser Arbeit wird die Methode des Verallgemeinerten Modellierens erweitert und auf verschiedene zellbiologische Probleme angewandt. Im ersten Teil wird eine Erweiterung der Methode vorgestellt, bei der die Analyse höherer Ableitungen im Gleichgewichtszustand integriert wird. Dies erlaubt die Bestimmung der Normalform von Bifurkationen und hierdurch eine spezifischere Beschreibung der Dynamik in deren Umgebung. In Modellen für genregulatorische Netzwerke wird gezeigt, dass die so erweiterte Methode zu einer besseren Charakterisierung oszillierender Systeme sowie zur Erkennung von Bistabilität verwendet werden kann. Im zweiten Teil werden mathematische Modelle zur Knochenremodellierung untersucht, einem Prozess der das menschliche Skelett kontinuierlich erneuert. Wir untersuchen den Zusammenhang zwischen strukturellen Eigenschaften verschiedener Modelle und der Stabilität von Gleichgewichtszuständen. Wir finden, dass das dynamische System von einem stabilen Zustand operiert, in dessen Nähe Bifurkationen existieren, welche das System destabilisieren und so potentiell Knochenkranheiten verursachen können. Im dritten Teil werden Modelle für den MAPK Signaltransduktionsweg analysiert. Da mathematische Modelle für dieses System eine hohe Anzahl von Parametern beinhalten, werden statistische Methoden angewandt zur Analyse von Stabilität und Bifurkationen. Zunächst werden Parameter mit einem starken Einfluss auf die Stabilität von Gleichgewichtszuständen identifizert. Durch eine Analyse der Bifurkationsstruktur wird gezeigt, dass eine kaskadenartige Kombination mehrerer Ebenen zu zusätzliche Typen von Dynamik wie Oszillationen und Chaos führt. Zusammengefasst zeigt diese Arbeit, dass Verallgemeinertes Modellieren ein fruchtbarer alternativer Modellierungsansatz für verschiedene zellbiologische Probleme ist.

Electroactive microorganisms possess the unique capability to transfer catabolically generated electrons via extracellular electron transfer (EET) to solid electron acceptors beyond their cell membranes. Presumably, electroactive microorganisms have a considerable impact on natural redox processes and show potential for being harnessed in microbial electrochemical technologies (METs) providing novel solutions for environmental issues. Although many aspects of electroactive microorganisms and EET have been elucidated, the respective thermodynamics and the energy fluxes during growth are almost untapped. However, understanding thermodynamics is the key for realisticall assessing the influence of electroactive microorganisms on natural ecosystems and the feasibility of METs. Thus, the intention of the present thesis was to establish methods for analyzing the thermodynamics of electroactive microorganisms. This was achieved by developing the method bioelectrocalorimetry and a model framework for biofilm anodes. A bioelectrocalorimeter was used to measure the heat production of a Geobacter species dominated biofilm performing EET. By creating a heat flux balance, the microbial electrochemical Peltier heat was identified representing an entropic hurdle for EET reactions. The mathematical model for biofilm anodes comprises calculations of microbial growth thermodynamics and kinetics as well as physical, chemical, and electrochemical processes at different spatial and temporal scales. It demonstrates that more detailed experimental assessments of thermodynamic parameters of electroactive microorganisms are urgently required. Furthermore, the thesis at hand provides a comprehensive data set on the energy content of wastewater that can be used to evaluate the feasibility as well as the thermodynamic efficiencies of METs. In conclusion, the thesis provides tools and useful thermodynamic information for the establishment of a complete energy balance of electroactive microorganisms and the elucidation of the driving forces for EET.

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<p>Mathematical and computational modeling allow for the rationalization of complex phenomenon observed in our reality. Through the careful selection of assumptions, the intractable task of simulating reality can be reduced to the simulation of a practical system whose behavior can be replicated. The development of computational models allow for the full comprehension of the defined system, and the model itself can be used to evaluate the results of thousands of simulate experiments to aid in the rational design process.</p> <p>Biomedical engineering is the application of engineering principles to the field of medicine and biology. This discipline is composed of numerous diverse subdisciplines that span from genetic engineering to biomechanics. Each of these subdisciplines is concerned with its own complex and seemingly chaotic systems, whose behavior is difficult to characterize. The development and application of computational modeling to rationalize these systems is often necessary in this field and will be the focus of this thesis.</p> <p>This thesis is centered on the development and application of mathematical and computational modeling in three diverse systems in biomedical engineering. First, computational modeling is employed to investigate the behavior of key proteins in the post-synapse centered around learning and memory. Second, computational modeling is utilized to characterize the drug release rate from implantable drug delivery depots, and produce a tool to aid in the tailoring of the release rate. Finally, computational modeling is utilized to understand the motion of particles through an inertial focusing microfluidics chip and optimize the size selective capture efficiency.</p> <p> </p>

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