This dissertation presents analytical solutions to address several unresolved issues on the modeling of CO₂ flow in permeable media. Analytical solutions are important as numerical simulations do not yield explicit expressions in terms of the model parameters. In addition, simulations that provide the most comprehensive solutions to multiphase flow problems are computationally intensive. Accordingly, we address the following topics in this dissertation. The method of characteristics (MOC) solution of the overall mass conservation equation of CO₂ in two-phase flow through permeable media is derived in the presence of compressibility. The formally developed MOC solutions rely on the incompressible fluid and rock assumptions that are rarely met in practice; hence, the incompressible assumption is relaxed and the first semi-analytic MOC solution for compressible flow is derived. The analytical solution is verified by simulation results. Fractional flow theory is applied to evaluate the CO2 storage capacity of one-dimensional (1D) saline aquifers. Lack of an accurate estimation of the CO₂ storage capacity stands in the way of the fully implementation of CO₂ storage in aquifers. The notion of optimal solvent-water-slug size is incorporated into the graphical solution of combined geochemical front propagation and fractional flow theory to determine the CO₂ storage capacity of aquifers. The analytical solution is verified by simulation results. The limits of the Walsh and Lake (WL) method to predict the performance of CO₂ injection is examined when miscibility is not achieved. The idea of an analogous first-contact miscible flood is implemented into the WL method to study miscibly-degraded simultaneous water and gas (SWAG) displacements. The simulation verifies the WL solutions. For the two-dimensional (2D) displacements, the predicted optimal SWAG ratio is accurate when the permeable medium is fairly homogeneous with a small cross-flow or heterogeneous with a large lateral correlation length (the same size or greater than the interwell spacing). We conclude that the WL solution is accurate when the mixing zone grows linearly with time. We examine decoupling of large and small-scale heterogeneity in multilayered reservoirs. In addition, using an analytical solution derived in this research, the fraction of layers in which the channeling occurs is determined as a function of the Koval factor and input dispersivity. We successfully present a simulation configuration to verify the off-diagonal elements of the numerical dispersion tensor. Numerical dispersion is inevitably introduced into the finite difference approximations of the 2D convection-dispersion equation. We show that the off-diagonal elements of the numerical dispersion tensor double when the flow velocity changes with distance. In addition, the simulation results reveal that the flow becomes more dispersive with distance travelled if there is convective cross-flow. In addition, local mixing increases with the convective cross-flow between layers. A numerical indicator is presented to describe the nature of CO₂ miscible displacements in heterogeneous permeable media. Hence, the quantitative distinction between flow patterns becomes possible despite the traditionally qualitative approach. The correlation coefficient function is adopted to assign numerical values to flow patterns. The simulation results confirm the accuracy of the descriptive flow pattern values. The order-of-one scaling analysis procedure is implemented to provide a unique set of dimensionless scaling groups of 2D SWAG displacements. The order-of-one scaling analysis is a strong mathematical approach to determine approximations that are allowed for a particular transport phenomenon. For the first time, we implement the scaling analysis of miscible displacements while considering effects of water salinity, dissolution of CO₂ in the aqueous phase, and complex configurations of injection and production wells. / text

Significant research has been initiated recently to devise control strategies that could predict and compensate manufacturing errors using so called explicit Stream-of-Variation(SoV) models that relate process parameters in a Multistage Manufacturing Process (MMP) with product quality. This doctoral dissertation addresses several important scientific and engineering problems that will significantly advance the model-based, active control of quality in MMPs. First, we will formally introduce and study the new concept of compensability in MMPs, analogous to the concept of controllability in the traditional control theory. The compensability in an MMP is introduced as the property denoting one’s ability to compensate the errors in quality characteristics of the workpiece, given the allocation and character of measurements and controllable tooling. The notions of “within-station” and “between-station” compensability are also introduced to describe the ability to compensate upstream product errors within a given operation or between arbitrarily selected operations, respectively. The previous research also failed to concurrently utilize the historical and on-line measurements of product key characteristics for active model-based quality control. This dissertation will explore the possibilities of merging the well-known Run-to-Run (RtR) quality control methods with the model-based feed-forward process control methods. The novel method is applied to the problem of control of multi-layer overlay errors in lithography processes in semiconductor manufacturing. In this work, we first devised a multi-layer overlay model to describe the introduction and flow of overlay errors from one layer to the next, which was then used to pursue a unified approach to RtR and feedforward compensation of overlay errors in the wafer. At last, we extended the existing methodologies by considering inaccurately indentified noise characteristics in the underlying error flow model. This is also a very common situation, since noise characteristics are rarely known with absolute accuracy. We formulated the uncertainty in process noise characteristics using Linear Fractional Transformation (LFT) representation and solved the problem by deriving a robust control law that guaranties the product quality even under the worst case scenario of parametric uncertainties. Theoretical results have been evaluated and demonstrated using a linear state-space model of an actual industrial process for automotive cylinder head machining. / text

Understanding, monitoring and managing savanna ecosystems require characterizing both functional and structural properties of vegetation. Due to functional diversity and structural heterogeneity in savannas, characterizing these properties using remote sensing is methodologically challenging. Focusing on the semi-arid savanna in the central Kalahari, the objective of this dissertation was to combine in situ data with multi-scale satellite imagery and two image analysis approaches (i.e. Multiple Endmember Spectral Mixture Analysis (MESMA) and Object Based Image Analysis (OBIA)) to : (i) determine the superior method for estimating fractional photosynthetic vegetation (fPV), non-photosynthetic vegetation (fNPV) and bare soil (fBS) when high spatial resolution multispectral imagery is used, (ii) examine the suitability of OBIA for mapping vegetation morphology types using a Landsat TM imagery, (iii) examine the impact of changing spatial resolution on magnitude and accuracy of fractional cover and (iv) examine how the fractional cover magnitude and accuracy are spatially associated with vegetation morphology. Using the GeoEye-1 imagery, MESMA provided more accurate fractional cover estimates than OBIA. The increasing segmentation scale in OBIA resulted in a consistent increase in error. While areas under woody cover produced lower errors even at coarse segmentation scales, those with herbaceous cover provided low errors only at the fine segmentation scale. Vegetation morphology type mapping results suggest that classes with dominant woody life forms attained higher accuracy at fine segmentation scales, while those with dominant herbaceous vegetation reached higher classification accuracy at coarse segmentation scales. Contrarily, for bare areas accuracy was relatively unaffected by changing segmentation scale. Multi-scale fractional cover mapping results indicate that increasing pixel size caused consistent increases in variance of and error in fractional cover estimates. Even at a coarse spatial resolution, fPV was estimated with higher accuracy compared to fNPV and fBS. At a larger pixel size, in areas with dominant woody vegetation, fPV was overestimated at the cost of mainly underestimating fBS; in contrast, in areas with dominant herbaceous vegetation, fNPV was overestimated with a corresponding underestimation of both fPV and fBS. These results underscore that structural and functional heterogeneity in savannas impact retrieval of fractional cover, suggesting that comprehensive remote sensing of savannas needs to take both structure and cover into account. / text

We considered a non-centered parameterization of the standard random-effects model, which is based on the Cholesky decomposition of the variance-covariance matrix. The regression type structure of the non-centered parameterization allows to choose a simple, conditionally conjugate normal prior on the Cholesky factor. Based on the non-centered parameterization, we search for a parsimonious variance-covariance matrix by identifying the non-zero elements of the Cholesky factors using Bayesian variable selection methods. With this method we are able to learn from the data for each effect, whether it is random or not, and whether covariances among random effects are zero or not. An application in marketing shows a substantial reduction of the number of free elements of the variance-covariance matrix. (author's abstract) / Series: Research Report Series / Department of Statistics and Mathematics

The integer and fractional quantum Hall effects arise in two-dimensional electron systems subject to low temperature and high perpendicular magnetic field. The phenomenology of these two effects is rich and provides interesting insight into quantum physics. We present two experimental studies of phenomena in the fractional quantum Hall regime. The first examines the tunneling conductance of quasiparticles at filling factor 5/2. This state is of significant interest because it lies outside the traditional Jain hierarchy of fractional quantum Hall states and because it may be the first physical system found to exhibit non-abelian particle statistics. A quantum point contact is used to bring edge states on opposite sides of the system in proximity to each other, allowing quasiparticles to tunnel between the edge states. By annealing the gates forming the quantum point contact at different voltages we control the tunneling strength for fixed temperature and bias. We demonstrate a transition from strong to weak tunneling controlled in this manner. In the weak tunneling regime, the DC bias and temperature dependence of the tunneling conductance is fit to a theoretical form, resulting in values for the quasiparticle charge \(e*\) and the interaction parameter \(g\). The values of these parameters are used to help distinguish between proposed candidate states for the 5/2 wave function. Quantitative and qualitative results are most consistent with the abelian 331 state. Our second main focus is the breakdown of the fractional quantum Hall states at filling factors 4/3 and 5/3. Breakdown of integer and fractional quantum Hall states is known to occur when the Hall and longitudinal resistances deviate from their ideal values at nonzero critical currents. Although multiple studies of breakdown in the integer quantum Hall regime have been reported, corresponding results for the fractional regime are scarce. We observe breakdown over a range of integer states that is consistent with previous results. However, breakdown in the fractional regime is found to exhibit markedly different behavior. In particular, the magnitude of the critical current decreases with increased sample width. This behavior is opposite that observed for integer filling factors and does not seem to be explicable based on current theories of breakdown. / Physics

Keliami uždaviniai: GARCH modelių klasės taikymas ilgo periodo finansiniams duomenims: modelių parametrų paieška, jų vertinimas, testavimas ir taikymas. Ilga atmintis sąlyginiame variantiškume yra viena iš empirinių savybių, kurią turi daugelis finansinių laiko eilučių. Viena modelių klasė, kuri atvaizduoja šį elgesį yra vadinama Dalinai Integruotu GARCH (Baillie, Bollerslev ir Mikkelsen 1996). Dalinės integracijos idėją pateikė ir ją pritaikė GARCH struktūrai Granger (1980) ir Hosking (1981). Šiame darbe bus surastos analitinės FIGARCH proceso antros eilės logaritminės tikėtinumo funkcijos išvestinės. Ilgo diapazono priklausomybė bus apskaičiuota parametriniu dalinai integruotu GARCH modeliu. Finansinių laiko eilučių duomenys bus įvertinti GARCH (CGARCH(1), CGARCH(2)) ir FIGARCH(1,d,1)) modeliais maksimalaus tikėtinumo metodu. Taip pat bus sukurtas NASDAQ- NYSE santykinio stiprumo indikatorius bei patikrintos jo panaudojimo sąlygos. Iiustracija yra pateikta 5 akcijų indeksais, 2 valiutų santykiais, aukso bei NNSS duomenims. / The paper deals with the problems of applying GARCH model/framework to a long term financial data, the search of the models, their evaluation, testing/validation and application. Long memory in conditional variance is one of the empirical features exhibited by many financial time series. One class of models that was suggested to capture this behavior is the so-called Fractionally Integrated GARCH (Baillie, Bollerslev and Mikkelsen 1996) in which the ideas of fractional integration originally introduced by Granger (1980) and Hosking (1981) for processes of the mean are applied to GARCH framework. In this paper we derive analytic expressions for the second-order derivatives of the log-likelihood function of FIGARCH processes. Long-range dependence is assessed through the parametric fractionally integrated GARCH model. Financial time series data will be estimated Component GARCH (CGARCH(1), CGARCH(2)) and FIGARCH models maximum likelihood method. Also we built NASDAQ- NYSE relative strength indicator and tested its usage conditions. An illustration is provided on 2 exchange rate, 5 stock index, gold and NNSS data.

This was a qualitative study carried out with learners from a grade twelve Standard Grade mathematics class from a South Durban school in the province of KwaZulu-Natal, South Africa. The main purpose of this study was to explore learners‟ understanding of the concept of the derivative. The participants comprised one class of twenty seven learners who were enrolled for Standard Grade mathematics at grade twelve level. Learners‟ responses to May and August examinations were examined. The examination questions that were highlighted were those based on the concept of the derivative. Additionally semi-structured interviews were carried out with a smaller sample of four of the twenty seven learners to gauge their perceptions of the derivative. The learners‟ responses to the examination questions and semi-structured interviews were exhaustively analysed. Themes that ran across the data were identified and further categorised in a bid to provide answers to the main research question. It was found that most learners‟ difficulties with the test items were grounded in their difficulties with algebraic manipulation skills. A further finding was that learners overwhelmingly preferred working out items that involved applying the rules. Although the Higher and Standard grade system of assessing learners‟ mathematical abilities has been phased out, with the advent of the new curriculum, the findings of this study is still important for learners, teachers, curriculum developers and mathematics educators because calculus forms a large component of the new mathematics curriculum. / Thesis (M.Ed.)-University of KwaZulu-Natal, Durban, 2008.

Iterative rounding has been an increasingly popular approach to solving network design optimization problems ever since Jain introduced the concept in his revolutionary 2-approximation for the Survivable Network Design Problem (SNDP). This paper looks at several important iterative rounding approximation algorithms and makes improvements to some of their proofs. We generalize a matrix restatement of Nagarajan et al.'s token argument, which we can use to simplify the proofs of Jain's 2-approximation for SNDP and Fleischer et al.'s 2-approximation for the Element Connectivity (ELC) problem. Lau et al. show how one can construct a (2,2B + 3)-approximation for the degree bounded ELC problem, and this thesis provides the proof. We provide some structural results for basic feasible solutions of the Prize-Collecting Steiner Tree problem, and introduce a new problem that arises, which we call the Prize-Collecting Generalized Steiner Tree problem.

Buvo parodyta, kaip gali būti naudojama JAHN programa darbui su atominėmis ir branduolinėmis būsenos funkcijomis izosukinio bazėje. Visa informacija apie atomines ar konfigūracines būsenos funkcijas gali būti pateikta įprastame formate. Tokia tvarka leistų greitą priėjimą prie reikiamų duomenų ir paprastą komandų valdymą. Būsenos funkcijų klasifikacijas izosukinio bazėje, viendalelius kilminius koeficientus CFP, dvidalelius kilminius koeficientus CFGP, transformacijos matricas iš LS ryšio į izosukinio ryšio bazę galima surasti naudojant atitinkamas komandas, kurių sintaksė yra analogiška literatūroje naudojamiems žymėjimams. Trumpas ir efektyvus sluoksnių ir konfigūracinių būsenų įvedimas daro programą atsparesnę klaidoms ir leidžia vartotojui sukurti atskiras koeficientų lenteles tam tikriems sluoksnių būsenų termams izosukinio bazėje. Tokios lentelės gaunamos vienos komandinės eilutės pagalba. Tikimasi, kad JAHN programa padės smulkiau analizuoti įvairių fizikinių operatorių matricinius elementus izosukinio bazėje. Komandos jj ryšiui, analogiškai kaip ir LS ryšiui, yra pateikiamos kuo mažiau nutolstant nuo jų užrašymo formos knygose ar straipsniuose. Įvedant nesudėtingas komandas nustatome sluoksnio charakteristikas. CFGP reikšmės irgi randamos JAHN programa, kas gerokai sutaupo laiko, kadangi jų nereikia ieškoti spausdinamose lentelėse. / We have shown how JAHN has been used for dealing with atomic or nuclear state functions within an isospin basis. All information about the atomic or the configuration state functions can be stored in a suitable format in order to allow a fast access and manipulation. Apart from the classification of the shell states in an isospin basis the coefficients of fractional parentage, the coefficients of fractional grandparentage, the transformation matrices for going from LS – coupled to an isospin – coupled basis can be calculated interactively. A short and powerful notation has been introduced for the shell and configuration states which makes the program less prone to errors and which enables the user to create an electronic table of shell state terms or CFP in isospin basis within only a single command line. The JAHN program will support a more detailed analysis of the matrix elements of various physical operators by using an isospin basis. The algorithms for jj coupling is analogous with LS coupling and they are presented in the way, which is commonly used in printed books and articles. We define layer characteristics from ordinary commands. CFGP values are also calculated with JAHN program, which is very convenient for saving the time that is needed to look up for those values in the printed tables.

Climate change is being observed through increased average temperatures world-wide, as well as through increased frequency of extreme events, such as floods and droughts. As climate is an uncontrollable yet essential input in the agriculture industry, the impact of climate change may have on crop production in Saskatchewan is of importance. The main objective of this study is to investigate how farmers adapt to climate change by switching their crop mix, and how this crop mix may change under future climate change scenarios. A fractional multinomial logit (FMNL) model was used to assess how total area of cropland has changed over a thirty year time period. The panel data included variables to represent the land characteristics of Saskatchewan (i.e. the three major soil zones - Black, Dark Brown and Brown), climatic variables to represent average monthly temperature and precipitation, and price and policy variables in order to assess how average seeded area of each crop group changed. With these results, a simple simulation model was developed to evaluate how the area of each crop group in a base year comparison (2000) would change under future climate scenarios for each soil zone. The results from the FMNL model indicate that crop allocation depends largely on the price of other crop groups and temperatures in the spring (April) and summer (July). Climate plays and important role in the major crop groups, such as wheat, canola and pulses. Cool, dry springs are the ideal conditions when choosing nearly all crops, while hot, wet summers increase the choice to leave land to summerfallow. Policy and the different soil zones also play a significant role in area allocation decisions. Changes in policies such as the removal of the Crow’s Nest Pass Agreement, and the removal of oats from the Canadian Wheat Board (CWB) marketing, had a negative impact on the choice to grow wheat, as expected. The different soil zones in Saskatchewan played an important role in area allocation for a majority of the crops, having a negative effect on the choice of wheat over every other crop group except pulses and summerfallow. Three climate change scenarios were simulated for each soil zone and compared to a base area (year 2000 area seeded) of crop groups. The findings from the projected changes in climate indicate that the area allocated to wheat will continue to decrease into the future, following current trends. The average projected decline in wheat area from the base years by 2099 ranges between 3.5% to 4.6% in the Black soil zone, between 2.7% and 2.9% in the Dark Brown and 2.7% to 4% in the brown soil zone, depending on climate change scenario. Interestingly, the area left to summerfallow is projected to increase over the future climate change scenarios. The choice of wheat is preferred over pulses, feed and forages, while the choice of specialty oilseeds (flaxseed, mustard seed and canary seed) are projected to become preferred over wheat in the future. The major conclusion from this research are: (i) following current trends, the area devoted to spring wheat and durum wheat would continue to decline into the future; (ii) Area devoted to wheat remains a preferred choice over pulses, feed and forages while specialty oilseeds represent a viable alternative choice to wheat and (iii) most significantly, summerfallow area would increase. This is in contrast to the current trend of declining summerfallow area as a result of tighter crop rotations. This finding was observed throughout all three soil zones as well as for all three climate change projection periods. This will have major implications on individual farmers as well as the economy in Saskatchewan, as summerfallow does not produce a crop in the year it is chosen. It is therefore important to determine a possible new crop mix that would benefit from the projected change in climate. This study could be improved by including a measure of profitability for each crop group and introducing a new crop group that is better suited to the projected change in climate in Saskatchewan.