Very fine discretizations of differential operators often lead to large, sparse matrices A, where the condition number of A is large. Such ill-conditioning has well known effects on both solving linear systems and eigenvalue computations, and, in general, computing solutions with relative accuracy independent of the condition number is highly desirable. This dissertation is divided into two parts. In the first part, we discuss a method of preconditioning, developed by Ye, which allows solutions of Ax=b to be computed accurately. This, in turn, allows for accurate eigenvalue computations. We then use this method to develop discretizations that yield accurate computations of the smallest eigenvalue of the biharmonic operator across several domains. Numerical results from the various schemes are provided to demonstrate the performance of the methods. In the second part we address the role of the condition number of A in the context of multigrid algorithms. Under various assumptions, we use rigorous Fourier analysis on 2- and 3-grid iteration operators to analyze round off errors in floating point arithmetic. For better understanding of general results, we provide detailed bounds for a particular algorithm applied to the 1-dimensional Poisson equation. Numerical results are provided and compared with those obtained by the schemes discussed in part 1.

Agrichemical spray drift is an issue of concern for the orcharding industry. Shelterbelts surrounding orchard blocks can significantly reduce spray drift by intercepting droplets from the airflow. At present, there is little information available with which to predict drift deposits downwind, particularly in the case of a fully-sheltered orchard block. In this thesis, we develop a simple mathematical model for the transport of airborne drifting spray droplets, including the effects of droplet evaporation and interception by a shelterbelt. The object is for the model to capture the major features of the droplet transport, yet be simple enough to determine an analytic solution, so that the deposit on the ground may be easily calculated and the effect of parameter variations observed. We model the droplet transport using an advection-dispersion equation, with a trapping term added to represent the shelterbelt. In order to proceed analytically, we discretise the shelterbelt by dividing it into a three-dimensional array of blocks, with the trapping in each block concentrated to the point at its centre. First, we consider the more straightforward case where the droplets do not evaporate; solutions are presented in one, two and three dimensions, along with explicit expressions for the total amount trapped and the deposit on the ground. With evaporation, the model is more difficult to solve analytically, and the solutions obtained are nestled in integral equations which are evaluated numerically. In both cases, examples are presented to show the deposition profile on the ground downwind of the shelterbelt, and the corresponding reduction in deposit from the same scenario without the shelterbelt.

As disturbed binocular functions in small children may lead to severe amblyopia it is of interest to detect it as early as possible. Most tests for binocular functions, however, demand active cooperation and may be unreliable in children up to 4-5 years of age. This study therefore aims to employ visual evoked potentials (VEP) to enable the examiner to evaluate the binocular function in a subject without need of active cooperation from the subject. Initially we studied the relation of suprathreshold contrast to the latency of the transient pattern VEP (tpVEP). Although suprathreshold contrast independently influenced the tpVEP latency, interindividual variation was too large to suggest tpVEP as a possible method for objectively measuring contrast sensitivity in a subject. The tpVEP latency in normal and microstrabismic adult subjects was examined. It was significantly shorter with binocular viewing in normals, but not in the microstrabismic group. Contrast sensitivity and tpVEP latency was examined in adults, both with normal binocularity and with microstrabismus, using both luminance (black-and-white) contrast and colour contrast patterns. The tpVEP latency to colour contrast, like that to luminance contrast, is shorter in normal subjects who view the stimulus binocularly. Interindividual variation or overlap between the normal and microstrabismic groups did not improve with colour contrast. The most significant features of the tpVEP are amplitude and latency. Depending on stimulus conditions, the response may show variations in configuration, amplitude and, to a lesser degree, latency. To decrease the influence of such variations steady-state VEP (ssVEP) can be used. The stimulus is presented in a fast repetitive manner, yielding a VEP response shaped as a continuous curve. The frequency components of this curve can be analysed using Fast Fourier Analysis. Fast Fourier analysis of ssVEP in children aged 8-15 years with normal binocularity and with microstrabismus showed that the power of the second harmonic (the double frequency of stimulus frequency) of the response with binocular viewing was larger than with monocular viewing, both in normals and microstrabismic subjects. For higher stimulus frequencies, microstrabismic subjects showed a significantly lower power of the second harmonic compared with subjects with normal binocularity, when the stimulus was presented binocularly. Finally, Fast Fourier analysed ssVEP in pre-school children aged 4-5 years was studied. A normal group was compared with a group with microstrabismus and a group with significant amblyopia. Amblyopic subjects had significant interocular differences in the first harmonic. We confirmed the significant difference found between microstrabismic subjects and subjects with normal binocularity regarding the second harmonic’s power with higher temporal frequency binocular stimulation, although at a slightly lower frequency than for older children. A low power of the second harmonic in the ssVEP to a binocular stimulus with high temporal frequency is a strong indicator of disturbed binocular function. / För att förhindra amblyopi (ensidig synsvaghet) hos barn är det viktigt att upptäcka störningar i samsynsfunktionerna så tidigt som möjligt. Samsynstester kräver dock aktiv medverkan och kan ge osäkra resultat hos barn upp till 4-5 års ålder. Den här avhandlingen studerar möjligheterna att utifrån tidsmässiga (temporala) egenskaper hos visual evoked potentials (VEP) undersöka samsynsfunktioner objektivt, utan att den undersökte behöver medverka aktivt. Första delstudien visar att ett synstimulus kontrastnivå i relation till kontrastkänslighetströskeln oberoende påverkar latensen i VEP, men variationer mellan individer gör metoden olämplig som objektiv kontrastkänslighetstest. Andra delstudien jämför latensen i VEP hos individer med normal samsyn med den hos personer med mikroskelning. Stimulering av båda ögonen gav signifikant kortare latens än stimulering av ett öga hos normala, men inte hos mikroskelare. I den tredje delstudien jämfördes känslighet för luminanskontrast och färgkontrast hos individer med normal samsyn och personer med mikroskelning. Både luminansmönster (svart-vita) och färgkontrastmönster upptäcktes vid lägre kontrast om båda ögonen stimulerades istället för ett i taget hos normalseende. Mikroskelare uppfattade mönstren sämre med båda ögonen än med ett öga (det dominanta). Latensen i VEP mättes i båda grupperna för både luminans- och färgkontrastmönster. Båda typerna av kontrast gav förkortning av latensen när båda ögonen stimulerades vid normal samsyn, men denna förkortning uteblev hos mikroskelare. Både luminans- och färgkontrast gav för varierande resultat för att utnyttja metoden för objektiv undersökning av samsynen. Fourier-analys innebär att en kurvform delas upp i sinuskurvor med olika frekvens, amplitud och fas. Om ett stimulus växlar hastigt får man ett steady-state VEP (ssVEP), dvs en kontinuerligt vågformad VEP-kurva, som kan delas upp i delsinuskurvor med Fourieranalys. Detta gör att man särskilt kan studera frekvenser som är relaterade till stimuleringsfrekvensen, till exempel grundton och övertoner (multipler av grundtonsfrekvensen). Barn 8-15 år gamla, med normal samsyn och med mikroskelning undersöktes med ssVEP i det fjärde delarbetet. Den första övertonen (= ”second harmonic”) var statistiskt signifikant svagare hos mikroskelare jämfört med normala individer, när stimuleringsfrekvensen var hög. Det femte och sista delarbetet undersökte ssVEP hos 4-5 år gamla förskolebarn på motsvarande sätt. I denna studie deltog också en grupp barn med amblyopi (synsvaghet) på ena ögat. På en något lägre stimuleringsfrekvens bekräftades den svagare första övertonen hos barnen med mikroskelning jämfört med barnen med normal samsyn. De amblyopa barnen visade tydligast förändringar vid lägre stimuleringsfrekvenser och i ssVEP:s grundtonsfrekvens (= ”first harmonic” eller ”fundamental harmonic”). Resultaten i de olika grupperna är så pass åtskilda att metoden verkar lämpa sig för objektiv undersökning av samsynsfunktioner, i det att en svag första överton i binokulärt ssVEP utlöst av hög stimuleringsfrekvens inger en stark misstanke om störd samsyn, medan en stor skillnad i grundtonens styrka i höger respektive vänster ögas ssVEP tyder på amblyopi.

We prove several inequalities involving the Fourier transform of functions which are compactly supported. The constraint that the functions have compact support is a simplifying feature which is desirable in applications, but there is a trade-off in control of other relevant quantities-- such as the mass of the function. With applications in mind, we prove inequalities which quantify these types of trade-offs. / text

In this thesis, a capacitor semi-active hybrid energy storage system for electric vehicle is proposed. A DC-to-DC bi-directional converter is required to couple the supercapacitor to the system DC bus. Through literature reviews, it was decided that a dual-bridge resonant converter with HF transformer isolation is best suited for the hybrid energy storage application. First, a dual-bridge series resonant converter with capacitive output filter is proposed. Modified gating scheme is applied to the converter instead of the 50% duty cycle gating scheme. Comparing to the 50% duty cycle gating scheme where only four switches work in ZVS, The modified gating scheme allows all eight switches working in ZVS at design point with high load level, and seven switches working in ZVS under other conditions. Next, a dual-bridge LCL-type series resonant converter with capacitive output filter is proposed. Similarly, the modified gating scheme is applied to the converter. This converter shows further improvement in ZVS ability. Operating principles, design examples, simulation results and experimental results of the two newly proposed converters are also presented. In the last part of the thesis, a capacitor semi-active hybrid energy storage system is built to test if the proposed converters are compatible to the system. The dual-bridge LCL-type series resonant converter is placed in parallel to the supercapacitor. The simulation and experimental results of the hybrid energy storage system match closely to the theoretical waveforms. / Graduate

Achieving a believable gait pattern for a virtual quadrupedal character requires a significant time investment from an animator. This thesis presents a prototype system for creating a foundational layer of natural-looking animation to serve as a starting point for an animator. Starting with video of an actual horse walking, joints are animated over the footage to create a rotoscoped animation. This animation represents the animal’s natural motion. Joint angle values for the legs are sampled per frame of the animation and conditioned for Fourier analysis. The Fast Fourier Transform provides frequency information that is used to create mathematical descriptions of each joint’s movement. A model representing the horse’s overall gait pattern is created once each of the leg joints has been analyzed and defined. Lastly, a new rig for a virtual quadruped is created and its leg joints are animated using the gait pattern model derived through the analysis.

Diss. (sammanfattning) Linköping : Linköpings universitet, 2006. / Härtill 5 uppsatser.

Thesis (M.Sc.) - Carleton University, 2005. / Includes bibliographical references (p. 125-130). Also available in electronic format on the Internet.

Thesis (Ph. D.)--University of Washington, 1997. / Vita. Includes bibliographical references (leaves [216]-217).

Orientador: Chang Hung Kiang / Banca: Paulo Milton Barbosa Landim / Banca: Alexandre Campane Vidal / Resumo: Esse trabalho apresenta os resultados obtidos com o monitoramento detalhado de nível d'água, realizado no período de 2002 a 2005 em poços no Aqüífero Rio Claro. Os problemas encontrados durante a coleta de dados dos poços de monitoramento foram solucionados por meio de programas desenvolvidos para este fim. Em seguida, os dados já tratados serviram à avaliação qualitativa dos fenômenos observados e comparados com aqueles encontrados na literatura. Por fim, foram aplicadas técnicas de análise de séries temporais (Análise de Fourier, Correlação Cruzada e Análise R/S) a esses dados, a fim de se verificar as periodicidades de alguns fenômenos naturais, como os ciclos sazonais e de maré terrestre, bem como estimar a relação temporal entre a pluviometria e a recarga, e avaliar o grau de persistência e auto-correlação das variações de nível d'água. Os resultados obtidos mostram que o monitoramento detalhado é capaz de fornecer informações que, além de contribuírem para um melhor conhecimento das características do aqüífero, podem auxiliar em processos de remediação, através da melhor caracterização da variação do nível d'água e seu conseqüente transporte vertical de contaminantes. / Abstract: This work presents the results of detailed water level monitoring in the course of 2002 to 2005 in monitoring in wells on Rio Claro Aquifer. Problems found during data aquisition were solved by specific programs developed for this purpose. Qualitative evaluation of observed phenomena was made, comparing it with those from literature and, at the end, methods to time-series analysis were applied on data (Fourier Analysis, Cross-Correlation and R/S Analysis), in order to verify the periodicities of natural phenomena, like those resulting from seasonal cycles and earth-tides, to estimate temporal relationship between rainfall and well recovering, and evaluate the persistence and degree of auto-correlation of water levels variations. The results shows that detailed monitoring process gives important information that leads to a better knowledge on the aquifer characteristics, and it can help remediation process through a better characterization of water level variations and its consequent vertical transport of contaminants. / Mestre