In the dissertation mathematical modelling problems in the design of electrical cables and cable fibres in modern vehicles, and of the heating of metals or semiconductors by ultra short (pico- or femtosecond) laser pulses are investigated. The problems are described by systems of differential equations and are solved by applying numerical methods. The methodology of problems being solved includes the following mathematical modelling steps: description of formulated problems using mathematical models, selection of model parameters, development and analysis of numerical algorithms (analysis of approximation errors, solution stability, convergence and accuracy), implementation of algorithms, application of parallel algorithms, comparison of mathematical experiments with results obtained in real experiments. The following main objectives are formulated for this thesis: to create mathematical models of the heat exchange in cable fibres and numerical algorithms, which will enable the virtual simulation of temperature distribution in electrical cables and optimization of geometric parameters of cables; to create mathematical models of laser impact on metals and their numerical algorithms allowing the modelling of material heating and removal processes. The thesis consists of the following main sections: introduction, three chapters, conclusion chapter, bibliography chapter, a list of the author's publications on the dissertation topic. The introductory section of the thesis... [to full text] / Disertacijoje nagrinėjami elektros kabelių ir kabelių pluoštų projektavimo šiuolaikiniuose automobiliuose, metalų arba puslaidininkių kaitinimo ultratrumpais (piko- arba femtosekundiniais) lazerio impulsais matematinio modeliavimo uždaviniai. Nagrinėjami uždaviniai aprašomi diferencialinėmis lygtimis ir sprendžiami skaitiniais metodais. Nagrinėjamų uždavinių metodiką apima šie matematinio modeliavimo etapai: suformuluotų uždavinių aprašymas matematiniais modeliais, modelių parametrų parinkimas, skaitinių algoritmų sudarymas ir tyrimas (aproksimacijos paklaidų, sprendinio stabilumo, konvergavimo ir tikslumo analizė), algoritmų realizavimas, lygiagrečiųjų algoritmų taikymas, skaičiavimo eksperimentų rezultatų palyginimas su realaus eksperimento rezultatais. Disertacijoje suformuluoti šie pagrindiniai darbo tikslai: sukurti šilumos mainų kabelių pluoštuose matematinius modelius ir skaitinės analizės algoritmus, kurie virtualiojo eksperimento būdu leistų modeliuoti temperatūros pasiskirstymą elektros kabeliuose ir optimizuoti geometrinius laidų parametrus; sukurti lazerio poveikio metalui matematinius modelius ir jų skaitinės analizės algoritmus, leidžiančius modeliuoti medžiagos kaitinimo ir pašalinimo procesus. Disertaciją sudaro įvadas, trys skyriai, rezultatų apibendrinimas, naudotos literatūros ir autorės publikacijų disertacijos tema sąrašas. Įvadiniame skyriuje aptariama tiriamoji problema, darbo aktualumas, aprašomas tyrimų objektas, formuluojami darbo tikslai ir... [toliau žr. visą tekstą]

The objective of this work is to develop mathematical models to predict molecular weight distributions (MWDs) of ethylene copolymers produced in an industrial gas-phase reactor using a Ziegler-Natta (Z-N) catalyst. Because of the multi-site nature of Z-N catalysts, models of Z-N catalyzed copolymerization tend to be very large and have many parameters that need to be estimated. It is important that the data that are available for parameter estimation be used effectively, and that a suitable balance is achieved between modeling rigour and simplification. In the thesis, deconvolution analysis is used to gain an understanding of how the polymer produced by various types of active sites on the Z-N catalyst responds to changes in the reactor operating conditions. This analysis reveals which reactions are important in determining the MWD and also shows that some types of active sites share similar behavior and can therefore share some kinetic parameters. With this knowledge, a simplified model is developed to predict MWDs of ethylene/hexene copolymers produced at 90 °C. Estimates of the parameters in this isothermal model provide good initial guesses for parameter estimation in a subsequent more complex model. The isothermal model is extended to account for the effects of butene and temperature. Estimability analysis and cross-validation are used to determine which parameters should be estimated from the available industrial data set. Twenty model parameters are estimated so that the model provides good predictions of MWD and comonomer incorporation. Finally, D-, A-,and V-optimal experimental designs for improving the quality of the model predictions are determined. Difficulties with local minima are addressed and a comparison of the optimality criteria is presented. / Thesis (Ph.D, Chemical Engineering) -- Queen's University, 2009-05-28 20:43:58.37

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<p>The study explored the comparison of grade 8 to 10 urban and peri-urban learners&rsquo / contexts preferences in mathematical literacy. There is currently a strong emphasis on the use of contexts for school mathematics. This has been also the case for South Africa when grade 10 learners have to make a choice between mathematics and mathematical literacy as one of their compulsory subjects for grade 10. This study focused more on the use of mathematics in real life situations. Data was collected by using questionnaires developed as part of the Relevance of School Mathematics Education (ROSME) project. The questionnaire dealt with contexts preferred by grade 10 learners from urban and peri-urban areas. The data were analysed using non-parametric statistical techniques. The findings radicate that there were contexts highly preferred by learners from both urban and peri-urban areas / least preferred by learners from both areas, highly preferred by learners from periurban areas but not by learners from urban areas and least preferred by learners from urban areas but not by those from peri-urban areas and vice versa. It is recommended that contexts highly preferred by learners should be incorporated in the learning experiences of learners.</p>

The embryonic stem cell (ESC) microenvironment contains various localized physical and biochemical cues to direct cell fate. Current approaches for microenvironmental regulation rely on restricting cell behaviour to control endogenous signals such as secreted ligands. This report presents a microfluidic device that can directly manipulate the removal of autoregulatory ligands from culture and control the activation of Signal Transducer and Activator of Transcription-3 (Stat3) in ESCs. Specifically, the response of Stat3 was measured under diffusive and convective mass transfer regimes. A Brownian dynamics algorithm was also developed to simulate ligand transport and predict cellular response under these conditions. Stat3 activation under perfusion culture was found to depend on flow rate and axial distance in the flow direction. Long-term perfusion also allowed for the formation of a sustained gradient of Stat3 activation that led to selective loss of ESC pluripotency. These results demonstrate the utility of microfluidic culture for stem cell bioengineering applications.

For the last two decades, demand for poultry meat has been soared, since it is healthier and less costly than its substitutes. In order to meet this increasing demand, integrated poultry organizations have been established all over the world. Usually, an integrated poultry organization has the divisions of breeder coops, incubation house, broiler coops, feed mill, slaughterhouse and marketing. This complex structure makes production planning activities more difficult for integrated poultry organizations. The aim of this study is to propose a production and financial planning model for &Ouml / nder Integrated Poultry Incorporation using mathematical modelling techniques and statistical methods.

<p>The National Curriculum Statement introduced mathematical literacy officially in 2006. Learners in general perform poorly at mathematics in South Africa but there is strong belief that learners should graduate from schools sufficiently literate to deal with the mathematical issues they will encounter in out-of-school situations. Based on this, this study is an investigation of the contexts, which grades 8 &ndash / 10 learners would prefer to engage with mathematics. The aim of this study was thus to investigate mathematical literacy in relation to learners&rsquo / motivations for the contexts they would prefer to deal with in mathematical literacy. The emphasis of the study is to concentrate on learner&rsquo / s written motivations for mathematical contexts. Data were collected using a questionnaire that deals with contexts for mathematics.</p>

The use of mathematical models in studying disease epidemics can be diverse, from the focused study of the role of a single determinant of the epidemic, or to the overall estimation of morbidity and mortality. In using simple deterministic models, a balance is struck between biological and social complexities, and the high data input demands of mathematical models. This thesis aims to apply the use of deterministic mathematical models to the studies of HIV and hepatitis C epidemiology in the Asia-Pacific region. In Australia, about 85% of reported HIV cases are among homosexual men. Casual homosexual partnerships made up 40% of incident HIV cases in 1995 increasing to 65% in 2004. In the state of New South Wales, it was estimated that over 7,500 people were living with HIV/AIDS in 2005, increasing to over 10,000 by 2016 with existing levels of intervention. Intervention measures were estimated to have prevented some 44,500 cases, the majority being among injecting drug users through the Needle and Syringe Programmes. Models for the HIV epidemics in developing countries were also developed incorporating multiple routes of HIV transmission. For Papua New Guinea, it was estimated 64,000 people were living with HIV/AIDS in 2005, rising to over 500,000 by 2025 with current levels of intervention. High levels of interventions, in particular increased condom use, will be required to achieve a stabilisation or reduction in HIV prevalence. In East Timor, the HIV epidemic is still in the early stages with 138 people estimated to be living with HIV/AIDS, rising to 5,000 by 2025 with minimal intervention. For HCV, models of the epidemic in Australia showed HCV incidence peaking in 1999, followed by a decline reaching 9,700 incident cases in 2005. Of 197,000 estimated chronic HCV cases in 2005, 58% had stage F 0/1 liver disease, 15% F 2/3 liver disease, and 2% HCV-related cirrhosis. Models estimated 210 and 105 people developed HCV-related liver failure and hepatocellular carcinoma, respectively. Comparisons of modelled HCV long-term sequelae projections with linkage data showed relatively good agreement, despite discrepancies in liver-related deaths. To decrease the number of chronic HCV, at least a tripling of treatment coverage would be required. These models provide estimates of the current levels of epidemics as well as projections of future scenarios under different intervention strategies, which have an important role in the planning of strategies, as well as assessment of previous epidemic conditions.

Electric power engineering, as it applies to low-voltage power reticulation in buildings and industrial sites, is ripe for a ‘paradigm shift’ to bring it properly into the Electronic Age. The conventional alternating-current approach, now over a hundred years old, is increasingly unsatisfactory from the point of view of plant and appliance requirements. Alternative approaches can deliver substantial cost savings, higher efficiencies, power quality improvements, and greater safety. Power reticulation systems in the future can be expected to differ from present systems in two key respects. The first is a greatly increased role for direct current; the second is the augmentation of the power system with a wide range of ‘management’ technologies. Combining these two trends, which can already be observed today, leads to consideration of ‘managed DC’ power reticulation systems, operating from AC bulk supply mains via AC-DC converters.

The current study aims to investigate the relative contributions of each of the processes that govern airway smooth muscle mechanical behaviour. Studies have shown that breathing dynamics have a substantial effect on airway constriction in healthy and diseased subjects, yet little is known about the dynamic response of the main instigator of airway constriction, Airway Smooth Muscle (ASM). In this work several models are developed to further the understanding of ASM dynamics, particularly the roles and interactions of the three dominant processes in the muscle: contractile dynamics, length adaptation and passive dynamics. Three individual models have been developed, each describing a distinct process or structure within the muscle. The first is a contractile model which describes the contractile process and the influence of external excitation on contractile behaviour. The second model incorporates the contractile model to describe length adaptation, which includes the reorganisation and polymerisation of contractile elements in response to length changes. The third model describes the passive behaviour of the muscle, which entails the mechanical behaviour of all non-contractile components and processes. As little data on the passive dynamics of the muscle was available in the literature, a number of experiments were conducted to investigate relaxed ASM dynamics. The experimental data and mathematical modelling showed that passive dynamics plays not only a dominant role in relaxed ASM, but contributes considerably to the dynamics of contracted muscle as well. A novel theory of sequential multiplication in passive ASM is proposed and implemented in a mathematical model. Experiments and literature validated the model simulations. Further integration of the models and improved force control modelling of length adaptation is proposed for future study. It is likely that the coupling of the models presented here with models describing other airway wall components will provide a more complete picture of airway dynamics, which will be invaluable for understanding respiratory disease.