This thesis examined the biological treatment of gas streams containing benzene, toluene, ethylbenzene and o-xylene (BTEX) using solid-liquid two-phase partitioning bioscrubbers (SL-TPPBs). SL-TPPBs consist of a cell containing aqueous phase and a polymeric solid phase that sequesters poorly water soluble and/or toxic substrates, mitigating substrate toxicity in the aqueous phase and improving the gas mass transfer during treatment of VOC contaminated gases. An initial investigation of oxygen transport determined that the polymers in a stirred-tank SL-TPPB enhance gas-liquid mass transfer. In addition, a study on biodegradation kinetics of BTEX by a bacterial consortium identified and quantified substrate interactions such as inhibition, enhancement and cometabolism. The stirred-tank SL-TPPB was then experimentally investigated for treatment of BTEX gas streams during steady-state and dynamic step-change operation to determine performance of the system relative to other biotreatment methods. A mathematical model was developed to predict system performance, which included the microbial kinetic model structure and parameters estimated during kinetic and oxygen mass transfer studies. As a less energy intensive alternative, an airlift SL-TPPB was operated and characterized. The airlift SL-TPPB was compared to an airlift liquid-liquid TPPB (silicone oil as sequestering phase) and a single phase airlift over dynamic step-change loadings, which showed that the airlift SL-TPPB outperformed the single phase airlift by >30% and had similar performance to the liquid-liquid airlift. However, the airlift SL-TPPB performance was lower relative to the stirred-tank SL-TPPB by >15%. Steady-state operation of the airlift SL-TPPB identified a range of operating conditions that provided maximum performance and conditions that were not oxygen limited. This prompted a study of oxygen mass transfer and hydrodynamics in the airlift system, which identified that the addition of polymers to an airlift does not cause physical enhancement of the gas-liquid mass transfer coefficient, but improves aqueous phase mixing and enhances overall oxygen transfer rate. A tanks-in-series mathematical model was formulated to predict performance of the airlift SL-TPPB, wherein the number of tanks-in-series to describe mixing in the airlift was obtained from a residence time distribution analysis of the airlift system completed during the hydrodynamic investigation. This thesis contributes a low-energy solution for the effective treatment of gases contaminated with BTEX. / Thesis (Ph.D, Chemical Engineering) -- Queen's University, 2009-08-18 16:16:22.598

This dissertation has two overall aims; to explore and develop the use of SNA in sociology, and to demonstrate that sociology has much to give to other sciences. Interdisciplinary collaboration is necessary because we do not live in a world in which subject areas are strictly isolated. Human beings are social animals, and a sociological understanding is crucial in all human-related science. The examination in this thesis of different kinds of social networks and how they affect the lives of individuals (and vice versa) will provide knowledge both in the development of methods for analyzing social networks, and in their areas specific scientific areas. Paper I-III investigates sexual networks and how the number of sexual encounters involving intercourse in combination with the number of sexual partners affects the dynamics of sexually transmitted infections (STIs). The results show that this relationship is non-linear, indicating that it may not be the individuals with the largest number of partners who have the most impact on the spread of STIs. One might also have to focus interventions on individuals who have a large number of sexual encounters involving intercourse per partner, and who have several (but not necessarily a very large number of) partners. In the fourth paper, we apply the theoretical concept of so-called small worlds to a sexual network. The spread of epidemics can be difficult to stop in such networks, and we show that the sexual network of individuals infected with chlamydia can be characterized as such. The fifth and last paper differs from the four first. In this paper, we focus on how individuals who committed suicide in Stockholm during the 1990s where connected to each other. The social-interaction exposure effect is larger for the individual within the family than at the workplace; yet work-domain exposure is more important for the overall suicide rate because individuals are more often exposed to suicides of co-workers than family members.

HIV/AIDS is one of the largest health problems the world is currently facing. Even with anti-retroviral therapies (ART), many resource-constrained countries are unable to meet the treatment needs of their infected populations. ART-distribution methods need to be created that prevent the largest number of future HIV infections. We have developed a compartment model that tracks the spread of HIV in multiple two-sex populations over time in the presence of limited treatment. The model has been fit to represent the HIV epidemic in rural and urban areas in Uganda. With the model we examine the spread of HIV among urban and rural regions and observe the effects of preferential treatment to rural areas on the spread of HIV in the country as a whole. We also investigate the effects of preferentially treating women on the spread of HIV. We find that preferentially treating urban women produces the most dramatic effect in reducing the number of infected male and females in rural and urban areas.

Increasing environmental concerns as well as diminishing fossil fuel reserves call for a new generation of energy conversion technologies. Fuel cells, which convert the chemical energy of a fuel directly to electrical energy, have been identified as one of the leading alternative energy conversion technologies. Fuel cells are more efficient than conventional heat engines with minimal pollutant emissions and superior scalability. Proton Exchange Membrane Fuel Cells (PEMFCs) which produce electricity from hydrogen have been widely investigated for transportation and stationary applications. The focus of this study is on the Direct Propane Fuel Cell (DPFC), which belongs to the PEMFC family, but consumes propane instead of hydrogen as feedstock. A drawback associated with DPFCs is that the propane reaction rate is much slower than that of hydrogen. Two ideas were suggested to overcome this issue: (i) operating at high temperatures (150-230oC), and (ii) keeping the propane partial pressure at the maximum possible value. An electrolyte material composed of zirconium phosphate (ZrP) and polytetrafluoroethylene (PTFE) was suggested because it is an acceptable proton conductor at high temperatures. In order to keep the propane partial pressure at the maximum value, interdigitated flow-fields were chosen to distribute propane through the anode catalyst layer. In order to evaluate the performance of a DPFC which operates at high temperature and uses interdigitated flow-fields, a computational approach was chosen. Computational Fluid Dynamics (CFD) was used to create two 2-D mathematical models for DPFCs based on differential conservation equations. Two different approaches were investigated to model species transport in the electrolyte phase of the anode and cathode catalyst layers and the membrane layer. In the first approach, the migration phenomenon was assumed to be the only mechanism of proton transport. However, both migration and diffusion phenomena were considered as mechanisms of species transport in the second approach. Therefore, Ohm's law was used in the first approach and concentrated solution theory (Generalized Stefan-Maxwell equations) was used for the second one. Both models are isothermal. The models were solved numerically by implementing the partial differential equations and the boundary conditions in FreeFEM++ software which is based on Finite Element Methods. Programming in the C++ language was performed and the existing library of C++ classes and tools in FreeFEM++ were used. The final model contained 60 pages of original code, written specifically for this thesis. The models were used to predict the performance of a DPFC with different operating conditions and equipment design parameters. The results showed that using a specific combination of interdigitated flow-fields, ZrP-PTFE electrolyte having a proton conductivity of 0.05 S/cm, and operating at 230oC and 1 atm produced a performance (polarization curve) that was (a) far superior to anything in the DPFC published literature, and (b) competitive with the performance of direct methanol fuel cells. In addition, it was equivalent to that of hydrogen fuel cells at low current densities (30 mA/cm2).

Modeling and prediction of gene-expression patterns has an important place in computational biology and bioinformatics. The measure of gene expression is determined from the genomic analysis at the mRNA level by means of microarray technologies. Thus, mRNA analysis informs us not only about genetic viewpoints of an organism but also about the dynamic changes in environment of that organism. Different mathematical methods have been developed for analyzing experimental data. In this study, we discuss the modeling approaches and the reasons why we concentrate on models derived from differential equations and improve the pioneering works in this field by including affine terms on the right-hand side of the nonlinear differential equations and by using Runge- Kutta instead of Euler discretization, especially, with Heun&rsquo / s method. Herewith, for stability analysis we apply modified Brayton and Tong algorithm to time-discrete dynamics in an extended space.

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.

Certainly one of the most powerful and important modeling languages of our time is the Calculus. But research consistently shows that students do not understand how the variables in calculus-based mathematical models relate to aspects of the systems that those models are supposed to represent. Because of this, students never access the true power of calculus: its suitability to model a wide variety of real-world systems across domains. In this paper, we describe the motivation and theoretical foundations for the DeltaTick and HotLink Replay applications, an effort to address these difficulties by a) enabling students to model a wide variety of systems in the world that change over time by defining the behaviors of that system, and b) making explicit how a system\'s behavior relates to the mathematical trends that behavior creates. These applications employ the visualization and codification of behavior rules within the NetLogo agent-based modeling environment (Wilensky, 1999), rather than mathematical symbols, as their primary building blocks. As such, they provide an alternative to traditional mathematical techniques for exploring and solving advanced modeling problems, as well as exploring the major underlying concepts of calculus.

Η τεχνική FUE είναι μια ελάχιστα επεμβατική μέθοδος μεταμόσχευσης μαλλιών η οποία χρησιμοποιείται από πολλούς ιατρούς τα τελευταία 10 χρόνια. Ο σκοπός της εργασίας αυτής είναι η εφαρμογή μεθόδων μαθηματικής μοντελοποίησης με ώστε να περιγράψει τα κυριότερα τμήματα της μεταμόσχευσης μαλλιών, ποσοτικοποιώντας πολύ σημαντικά θέματα όπως το τραύμα της δότριας ζώνης,το πρόβλημα της ασφαλούς και με ακρίβεια εξαγωγής των τριχοθυλακιων,την άριστη κατανομή και την λεπτομερή εκτίμηση και επίτευξη της πυκνότητας της λήπτριας περιοχής. Για τους προαναφερθέντες λόγους, ψηφιακές μικροφωτογραφίες από την δότρια και λήπτρια περιοχή αναλύθηκαν με επεξεργασία εικόνας, η οποία βασίστηκε σε ειδικούς μαθηματικούς αλγορίθμους που αναπτύχθηκαν κατά τη διάρκεια αυτής της μελέτης. Τέλος ένα ολοκληρωμένο πλάνο θεραπείας προτείνεται από τον συγγραφέα για περιπτώσεις μεταμόσχευσης μαλλιών που αντιμετωπίζονται με την τεχνική FUE. / The FUE technique is a minimally invasive hair transplantation method, which has been used by many Doctors over the last 10 years. The aim of this study is mathematical principles to be applied in order to describe the major steps of the hair transplantation, quantitating very important issues like the trauma in the donor area, the problem of safe and accurate extraction of the follicular units, the optimal distribution and the precise estimation and achievement of the recipient area density. For the fore mentioned reasons digital micropictures from donor and recipient area were analyzed by using image processing which was based on special mathematical algorithms which were developed during this study. Finally an integrated treatment planning program is proposed by the Author for hair transplantation cases which are treated by using FUE technique.

Thesis (MScFor)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: One of the major objectives in plantation forestry is to achieve a high level of homogeneity of distribution and dimension of trees within the stand. Precise planting geometries, intensive silviculture and genetic selection are used to achieve this homogeneity. However, a natural variability is still introduced by micro-­‐site conditions and disturbances. A substantial source of variation is caused by edge effects of neighbouring stands or other land use forms. The edge effect causes trees at the stand edge to develop differently from trees in the interior of the stand. The overarching objective of this study is to simulate the edge effect based on average stand interior variables as typically received from an enumeration and spatial information on the current and historic stand neighbourhood. With re-­‐introducing this natural variance as well as its spatial pattern, we expect to derive improved planning information. A major aim is thus separating the effect of the edge interaction from the other factors contributing to stand variance and quantifying the result in terms of stand output. A methodology is introduced for quantifying interaction at stand edges between a given stand and its neighbouring stands over its lifetime. Transferring the edge interaction value from the edges to all the trees within the stand is then done by applying inverse distance weighting interpolation from the edges to the tree position within the stand. Once an edge interaction value has been calculated for each point, the extent of the edge effect is quantified. The spatial extent of the edge effect is derived empirically from an existing fully spatially mapped stand by means of breakpoint regression. The expected variance as a result of edge influence is then quantified by producing a set of models, which can reproduce the effect of the edge interaction on tree height, diameter and volume. The edge effect is treated as a dynamic interaction for which the temporal aspect needs to be considered, because the current spatial structure of a stand is influenced by its current neighbourhood, but also by the historic development of the neighbourhood in relation to the stand in question. Each stand therefore undergoes an edge effect which is completely unique to that stand, within a given time period. For this reason the presented methodology is a spatial-­‐temporal one, aimed at providing a way in which growth and yield forest modelling can be augmented by the inclusion of the edge effect in a practical way. To explicitly quantify edge effects, the natural variance had to be separated into a component explained by edge effect and a second component introduced by other factors such as micro site conditions and disturbance. The second component is treated as an unexplained residual variance. In order to provide a realistic simulation of a stand output at a finer, tree level, this second stand variance needs nonetheless to be quantified. The variance attributable to factors other than the edge effect is mimicked by generating a random number by means of a parameterised stochastic process based on the variance of the inner stand region, which is beyond the reach of the edge effect. In this way, a realistic spatial pattern of a plantation forest stand, taking into account the edge effect and combining it with the natural stand variance is achieved. This study, within the field of plantation forest management, aspires to land use optimization both in terms of productive capacity estimation and for the provision of information for effective land use management planning. It makes use of open source software resources namely the R framework and QGIS and explores aerial stereophotogrammetry as an option for data collection. / AFRIKAANSE OPSOMMING: Een van die hoofdoelwitte in plantasie bosbou praktyk is hoё vlakke van homogeniteit met betrekking tot die verspreiding en die dimensies van die bome in die plantasie opstand. Simetriese aanplantings, intensiewe bosboupraktyk en genetiese seleksie word gebruik om hierdie homogeniteit te verkry. Natuurlike verskille word egter nog steeds gevind as gevolg van groeiplek mikro toestande en ander versteurings in die opstand. Een van die hoofbronne van hierdie variasie is die randeffekte van buurplantasies en ander gebruike van grond. Hierdie randeffekte veroorsaak dat bome aan die rand van die opstand anders ontwikkel as die bome binne in die opstand. Die oorhoofse doelwit met hierdie navorsing is om die randeffekte te simuleer. Hierdie randeffekte is gegrond op die gemiddelde binneopstand boom veranderlikes soos afgelei uit die opmeting en uit ruimtelike inligting oor die huidige en geskiedkundige toestande in die omgewing. As hierdie natuurlike variasies asook die ruimtelike patrone weer in berekening gebring word, verwag ons om beter beplanningsinligting te bekom. ’n Belangrike doelwit tydens hierdie navorsing is dus om die effek van die rand-­‐interaksie te skei van die effek van ander faktore wat bydra tot variasies binne-­‐in die opstand en om die resultaat in terme van plantasie produksie te kwantifiseer. ’n Metodiek word voorgestel vir die kwantifisering van die interaksie op die rande tussen die opstand en die buuropstande tydens die leeftyd van die opstand. Die oorplasing van die rand interaksie waarde van die rand af na al die bome in die plantasie word dan gedoen deur om geweegde inverse afstand interpolasie vanaf die rand tot by die ligging van die boom, toe te pas. As die rand interaksie waarde vir elke punt bereken is, kan die omvang van die randeffek gekwantifiseer word. Die ruimtelike omvang van die rand effek is, met die gebruik van breekpunt regressie, empiries afgelei van ’n bestaande ten volle karteerde plantasie. Die verwagte variasie as gevolg van die randeffek word dan met die gebruik van ’n stel modelle gekwantifiseer, wat dan die effek van die rand interaksie op boomhoogte, deursnit en volume kan weergee. Die randeffek word as ’n dinamiese interaksie beskou waarvan die tydsaspek in ag geneem moet word, want die huidige ruimtelike struktuur van die plantasie word beïnvloed deur die huidige omgewing asook deur die historiese ontwikkeling van die omgewing met betrekking tot die opstand onder bespreking. Elke opstand ondergaan ’n randeffek wat uniek is aan daardie plantasie op die gegewe tydstip. Die doelwit is om ’n wyse te vind waarvolgens groei-­‐en-­‐opbrengs plantasie modellering deur die insluiting van randeffek op ’n praktiese wyse, aangevul kan word. Om hierdie rede is die aanbevole metodiek ruimtelik-­‐tydelik en gerig daarop om ’n wyse te vind waarvolgens groei-­‐en-­‐opbrengs modellering deur die insluiting van die randeffek, op ’n praktiese wyse aangevul kan word. Om randeffek eksplisiet te kwantifiseer, moes die natuurlike afwyking gedeel word in die komponent wat die gevolg is van die randeffek, en ’n tweede komponent wat die gevolg is van ander faktore soos mikroligging toestande en versteurings. Die tweede komponent word behandel as ’n onverklaarde oorblywende afwyking. Hierdie tweede plantasie afwyking moet nogtans kwantifiseer word om sodoende ’n realistiese simulasie van plantasie opbrengs op ’n fyner boom vlak te verkry. Die afwyking wat toegeskryf kan word aan faktore buiten die randeffek, word nageboots deur om ’n lukrake nommer (wat gebaseer word op die afwyking van die binne-­‐plantasie gebied wat buite die strekwydte van die randeffek is) deur middel van ‘n geparameteriseerde stogastiese proses te genereer. Sodoende word ’n realistiese ruimtelike patroon van ’n plantasie opstand verkry, wat die randeffek in ag neem en dit kombineer met die natuurlike plantasie afwyking.

Mathematical modeling is seen in this paper as a strategy to combine the teaching and learning of mathematics with real problems of a technical course in furniture. Our goal was to enable students in 1st year study the theme Furniture School's Manufacturing for children's through modeling. We developed a teaching sequence that seeks to math topics present in the school's furniture manufacturing, since the furniture design until the manufacturing cost calculation, part of teaching sequence was applied with volunteer students. Analyzing the manufacturing of school's table considering mathematical view, the student is easily led to the field of geometry and algebra. During the process, retook concepts present in the technical course practices such as the scale rule use, and present in high school math discipline, as surfaces and perimeters, increasing the understanding of the meaning of these. In addition, the experiment showed the need of mathematical content for the involved, in a situation of future professional practice from them. / A modelagem matemática é vista neste trabalho como uma estratégia para aliar o ensinoaprendizagem de matemática com problemas concretos de um curso Técnico em Móveis. Nosso objetivo foi oportunizar a alunos do 1o ano a exploração do tema Fabricação de Mobiliário Escolar Infantil por meio da modelagem. Elaborou-se uma sequência didática que busca trabalhar tópicos de matemática presentes na fabricação de mobiliário escolar, desde o desenho do projeto de um móvel até o cálculo do custo para fabricá-lo, parte da qual foi aplicada com alunos voluntários. Ao analisar a fabricação da mesa escolar a nível matemático, o aluno é levado facilmente ao campo da geometria e da álgebra. Durante o processo, resgatou-se conceitos presentes nas práticas do curso técnico, como o uso do escalímetro, e presentes na disciplina de matemática do Ensino Médio, como superfícies e perímetros, ampliando a compreensão do significado desses. Além disso, a experiência evidenciou para os envolvidos a necessidade de conteúdos matemáticos em uma situação da futura prática profissional deles.