Thema der Dissertation ist die Untersuchung von asymptotischen Eigenschaften im Wechselspiel von Diffusion und Wellenausbreitung. Es geht um diskrete, zufällige Schrödingeroperatoren, die in die diskrete Wärmeleitungsgleichung eingefügt werden. Das Ensemble der Lösungen kann mit der vom diskreten Laplace erzeugten Irrfahrt in kontinuierlicher Zeit und der Feynman-Kac-Formel stochastisch interpretiert werden. So werden Methoden aus der Theorie der großen Abweichungen anwendbar. Neben dem stochastischen Zugang können die Schrödingeroperatoren auch spektraltheoretisch untersucht werden. In der Dissertation wird das Wechselspiel dieser beiden Herangehensweisen im Hinblick auf die asymptotischen Eigenschaften der Momente, der integrierten Zustandsdichte und der Korrelationsfunktion betrachtet.

Magistro darbe sprendėme diferencialinę difuzijos lygtį naujais metodais. Išanalizavę standartinius kintamo difuzijos koeficiento parabolinių lygčių sprendimo metodus, mes šiame darbe pasiūlėme spręsti šias lygtis naudojant vadinamąsias „tilto“ funkcijas. Išbandėme dviejų rūšių „tilto“ funkcijas: hiperbolinio tangento ir trigonometrinio. Diferencialinės lygties sprendinio ieškojome per „tilto“ funkcijų ir polinomų sandaugų sumą: trigonometrinei „tilto“ funkcijai ir hiperbolinei tangento „tilto“ funkcijai. Gavome kompiuterinius sprendinius ir nustatėme tų sprendinių paklaidas. Palyginę trigonometrinio bei hiperbolinio tangento „tilto“ funkcijos paklaidų standartinius nuokrypius gavome, kad tikslesnis yra hiperbolinio tangento „tilto“ funkcijos metodas. / Master thesis solved differential equation of diffusion of new techniques methods. Having analyzed the standard variable diffusion coefficient parabolic equation solution methods suggested in this work we solve these equations using the so-called "bridge" function. Tried two types of "bridge" functions: tangent hyperbolic and trigonometric. Differential equation, the solution we were looking for a "bridge" function and the amount of products of powers of polynomials: trigonometry "bridge" function and hyperbolic tangent of a "bridge" function. We have received computer-based solutions and the solutions found at the margins. A comparison of hyperbolic tangent trigonometric "bridge" function of the error standard deviations have received, the more accurate the hyperbolic tangent of a "bridge" function approach.

<p>In recent years, there has been a great interest towards the higher order numerical methods for singularly perturbed problems. As compared to their lower order counterparts, they provide better accuracy with fewer mesh points. Construction and/or implementation of direct higher order methods is usually very complicated. Thus a natural choice is to use some convergence acceleration techniques, e.g., Richardson extrapolation, defect correction, etc. In this thesis, we will consider various classes of problems described by singularly perturbed ordinary and partial differential equations. For these problems, we design some novel numerical methods and attempt to increase their accuracy as well as the order of convergence. We also do the same for existing numerical methods in some instances. We &macr / nd that, even though the Richardson extrapolation technique always improves the accuracy, it does not perform equally well when applied to different methods for certain classes of problems. Moreover, while in some cases it improves the order of convergence, in other cases it does not. These issues are discussed in this thesis for linear and nonlinear singularly perturbed ODEs as well as PDEs. Extrapolation techniques are analyzed thoroughly in all the cases, whereas the limitations of the defect correction approach for certain problems is indicated at the end of the thesis</p>

Baigiamajame magistro darbe suprojektuotos ir pagamintos dviejų rūšių šviesos koncentratorinės sistemos: jungtinė parabolinė ir sistema su Frenelio lęšiu. Atlikta saulės elementų efektyvumo analizė, išnagrinėtos šviesą koncentruojančių sistemų rūšys bei aptarti jų optiniai parametrai. Frenelio lęšis ir koncentratorinių sistemų laikančiosios konstrukcijos pagamintos vakuuminio formavimo būdu, ieškant pigesnės gamybos technologijos. Baigiamajame darbe atlikti optinio pralaidumo ir lūžio rodiklio, matomos šviesos bangų ilgių ruože, tyrimai bei saulės elementų, esančių šviesos koncentratorinėse sistemose,voltamperinių ir voltvatinių charakteristikų tyrimai. Iš tyrimų rezultatų nustatyti šviesos koncentravimo laipsniai. Darbe diskutuojama apie pigių optinių sistemų galimus pritaikymus ir jų tobulinimo būdus. Išnagrinėjus teorinę ir praktinę dalis, pateiktos išvados ir pasiūlymai. Darbą sudaro 8 dalys: įvadas, saulės elementų efektyvumo ribos, saulės šviesos koncentratoriai ir jų panaudojimas fotoelektrinėse sistemose, eksperimentinių tyrimų metodika, prototipų gamyba, eksperimentiniai tyrimai, išvados, literatūros sąrašas. Darbo apimtis – 82 p. teksto be priedų, 95 pav., 13 lent., 22 bibliografiniai šaltiniai. Atskirai pridedami darbo priedai. / Concentrated PV systems (compound parabolic and Fresnel CPV) have been designed and investigated. The efficiency of solar cells and the types of light concentrated systems have been analyzed and their optical parameters have been discussed. Fresnel lens and the CPV system holding structure have been fabricated by means of vacuum forming machine in this way making the technology of production less expensive. Optical transmittance and refractive index of Fresnel lens were measured in the range of visible light wavelengths. Current-voltage and voltage-power characteristics of solar cells built inside the CPV systems were investigated, based on results the degree of light concentration by Fresnel lens and compound parabolic CPV has been determined. Some discussions regarding possible applications of concentrated PV systems containing the Fresnel lens as well as possible ways of CPV design improvements are given in current work. After analysed theoretical and practical parts, conclusions and suggestions are proposed. Thesis structure: introduction, theoretical and experimental parts, results of experiments, conclusions and references. Thesis consist of: 82 p. text without appendixes, 95 pictures, 13 tables, 22 bibliographical entries. Appendixes included.

Multipath remains a dominant error source in Global Positioning System (GPS) applications that require high accuracy. With the use of differential techniques it is possible to remove many of the common-mode error sources, but the error effects of multipath have proven much more difficult to mitigate. The research aim of this work is to enhance the understanding of multipath propagation and its effects in GPS terrestrial applications, through the modelling of signal propagation behaviour and the resultant error effects. Multipath propagation occurs when environmental features cause combinations of reflected and/or diffracted replica signals to arrive at the receiving antenna. These signals, in combination with the original line-of-sight (LOS) signal, can cause distortion of the receiver correlation function and ultimately the discrimination function and hence errors in range estimation. To date, a completely satisfactory mitigation strategy has yet to be developed. In the search for such a mitigation strategy, it is imperative that a comprehensive understanding of the multipath propagation environment and the resultant error effects exists. The work presented here, provides a comprehensive understanding through the use of new modelling and simulation techniques specific to GPS multipath. This dissertation unites the existing theory of radio frequency propagation for the GPS L1 signal into a coherent treatment of GPS propagation in the terrestrial environment. To further enhance the understanding of the multipath propagation environment and the resultant error effects, this dissertation also describes the design and development of a new parabolic equation (PE) based propagation model for analysis of GPS multipath propagation behaviour. The propagation model improves on previous PE-based models by incorporating terrain features, including boundary impedance properties, backscatter and time-domain decomposition of the field into a multipath impulse response. The results provide visualisation as well as the defining parameters necessary to fully describe the multipath propagation behaviour. These resultant parameters provide the input for a correlation and discrimination model for visualisation and the generation of resultant receiver error measurements. Results for a variety of propagation environments are presented and the technique is shown to provide a deterministic methodology against real GPS data. The unique and novel combined modelling of multipath propagation and reception, presented in this dissertation, provides an effective set of tools that have enhanced the understanding of the behaviour and effect of multipath in GPS applications, and ultimately should aid in providing a solution to the GPS multipath mitigation problem.

Domestic solar hot water units, if properly designed, are capable of providing all hot water needs in an environmentally friendly and cost-effective way. Despite 50 years of development, commercial technology has not yet achieved substantial market penetration compared to mainstream electric and gas options. Therefore, alternate designs are warranted if they can offer similar or greater performance for a comparable cost to conventional units. This study proved that such alternatives are possible by designing and testing two novel solar hot water systems (SHWS). The first system used compound parabolic collector (CPC) panels to concentrate solar energy and produce steam. The steam moved from a rooftop downward into a heat exchange pipe within a ground level water tank, heating the water, condensing and falling into a receptacle. The operation was entirely passive, since the condensate was pulled up due to the partial vacuum that occurred after system cooling. Efficiencies of up to 40% were obtained. The second system used an air heater panel. Air was circulated in open and closed loop configuration (air recycling) by means of a fan/blower motor and was forced across a compact heat exchanger coupled to a water tank. This produced a natural thermosiphon flow heating the water. Air recycling mode provided higher system efficiencies: 34% vs. 27%. The concurrent development of an analytical model that reasonably predicted heat transfer dynamics of these systems allowed 1) performance optimisation for specific input/starting operating conditions and 2) virtual design improvements. The merit of this model lay in its acceptable accuracy in spite of its simplicity. By optimising for operating conditions and parameter design, both systems are capable of providing over 30 MJ of useful domestic hot water on clear days, which equates roughly to an increase of 35°C in a 200 L water tank. This will satisfy, on average, daily hot water requirements for a 4-person household, particularly in low-latitude regions (eg. Queensland). Preliminary costing for these systems puts them on par with conventional units, with the passive, remotely coupled, low maintenance, CPC SHWS comparable to higher end models. The air heater SHWS, by contrast, was much more economical and easier to build and handle, but at the trade-off cost of 1) the need for an active system, 2) increased maintenance and running costs and 3) the requirement for a temperature control mechanism that would protect the panel body by dumping hot air trapped inside if stagnation were to occur.

Localisation, which is a mechanism for discovering the spatial relationship between objects, is an area that has received considerable research and development in recent times. A common name given to localisation operations based on the absolute reference frame of Earth is Geolocation. One important example of geolocation research is E-911, where wireless carriers in the United States must provide the location of 911 callers. The operation of E-911 can be based on either a network configuration, or the Global Positioning System (GPS). With the importance of localisation being acknowledged, a review concerning the vulnerability of the Global Navigation Satellite System (GNSS) is provided as background and motivation for this research. With the current vulnerability of GNSS, this dissertation presents the results of a research program undertaken with the objective of developing an electromagnetic localisation technique that can determine the relative position of GPS Radio Frequency Interference (RFI) sources. Intended for operation in a hostile environment, blind and passive localisation methodologies must be incorporated into the developed model. In performing localisation research, a background of current techniques is provided in addition to a review of current electromagnetic propagation models. From the review of propagation models, the Parabolic Equation Model (PEM) was chosen for investigation concerning localisation. The selection of PEM is due to model properties that are required for blind/passive localisation. The localisation system developed in this research program is based on the integration of inverse diffraction propagation (IDP) within the parabolic equation model. The title chosen for the localisation method is Inverse Diffraction Parabolic Equation Localisation System (IDPELS). This thesis presents the simulation and field trial results of IDPELS. Under simulation, the terrain or obstacle profiles were not based on any geodetic datum. Any estimate provided by IDPELS under simulation is therefore a "Localisation" solution. In the field trials however, IDPELS operation is referred to as "Geolocation" as geodetic datum's where used to determine the receiver's position. Under simulation analysis, IDPELS operation was considered to provide good promise as it could simultaneously perform localisation on multiple transmission sources. In each investigated simulation scenario, a display of signals amplitude (dB units) is displayed over the entire region. By determining the field convergence regions, a localisation estimate of IDPELS is provided. By defining the convergence regions as areas having the greatest signal amplitude values (i.e. ≥ 99%), elliptical areas as low as 3.2m² were considered to indicate an excellent localisation capability. With the theoretical validity of IDPELS operation in electromagnetics having been established under simulation, further investigation into the practical feasibility of the IDPELS was performed. The field trials positioned a continuous-wave (CW) transmission source at a known location. By measuring signal phasors along a straight section of road, the geodetic spatial-phase profile was used as the input signal for IDPELS. Road sections used were cross-wise to the transmitter's boresight. Many data sets were recorded, each being made over a sixty second time period. Different regions and ranges where used to continuously measure the spatial-phase profile of the signal with fixed antennas in a moving vehicle. Such a measurement process introduced an analogy with Synthetic Aperture Radar (SAR) processes. In quantitating the accuracy of the IDPELS geolocation estimate in field trials, the linear error of range and cross-range components was analysed. A free-space PEM model was chosen for development of IDPELS and hence, data sets demonstrating properties of a free-space environment were able to be considered suitable for testing of the geolocation method. Data sets demonstrating free-space propagation characteristics were measured at the base of the Mt Lofty ranges in South Australia, where the range and cross-range error are respectively 3.14m, and 0.15m. Such low error values clearly demonstrate the practical feasibility of IDPELS geolocation. With the practical feasibility of IDPELS having been established in this research program, a novel contribution to electromagnetic geolocation methodologies is provided. An important characteristic of any geolocation technique concerns its robustness to operate in a wide variety of possible environments. With continued development of IDPELS, the robustness of this passive/blind geolocation technique can be enhanced. Further assistance with geolocation of multiple transmission sources is also indicated to be available by IDPELS, as shown in the simulation analysis.

Cette thèse contient quatre travaux sur le modèle d'Agrégation Limitée par Diffusion Interne (iDLA), qui est un modèle de croissance pour la construction récursive d'ensembles aléatoires. Le premier travail concerne la dimension 1 et étudie le cas où les marches aléatoires formant l'agrégat évoluent dans un milieu aléatoire. L'agrégat normalisé converge alors non pas vers une forme limite déterministe comme dans le cas de marches aléatoires simples mais converge en loi vers un segment contenant l'origine dont les extrémités suivent la loi de l'Arcsinus. Dans le deuxième travail, on considère le cas où l'agrégat est formé par des marches aléatoires simples en dimension d > 1. On donne alors des résultats de convergence et de fluctuations sur la fonction odomètre introduite par Levine et Peres, qui compte en chaque point le nombre de passages des marches ayant formé l'agrégat. Dans le troisième travail, on s'intéresse au cas où l'agrégat est formé par des marches aléatoires multidimensionnelles qui ne sont pas centrées. On montre que sous une normalisation appropriée, l'agrégat converge vers une forme limite qui s'identifie à une vraie boule de chaleur. Nous répondons ainsi à une question ouverte en analyse concernant l'existence d'une telle boule bornée. Le quatrième travail concerne le cas particulier où une borne intérieure est connue pour l'agrégat. On donne alors des conditions suffisantes sur le graphe ainsi que sur la nature de cette borne pour qu'elle implique une borne extérieure. Ce résultat est appliqué au cas de marches évoluant sur un amas de percolation par arêtes surcritique, complétant ainsi un résultat de Shellef. / This thesis contains four works on the Internal Diffusion Limited Aggregation model (iDLA), which is a growth model that recursively builds random sets. The first work is set in dimension 1 and studies the case where the random walks that build the aggregate evolve in a random environment. The normalised aggregate then does not converges towards a deterministic limiting shape as it is the case for simple random walks, but converges in law towards a segment that contains the origin and which extremal points follow the Arcsine law. In the second work, we consider the case where the aggregate is built by simple random walks in dimension d > 1. We give convergence and fluctuation results on the odometer function introduced by Levine and Peres, which counts at each point the number of visits of walkers throughout the construction of the aggregate. In the third work, we examine the case where the aggregate is built using multidimensional drifted random walks. We show that under a suitable normalisation, the aggregate converges towards a limiting shape which is identified as a true heat ball. We thus give an answer to an open question in analysis concerning the existence of such a bounded shape. The last work deals with the special case where an interior bound is known for the aggregate. We give a set of conditions on the graph and on the nature of this interior bound that are sufficient to imply an outer bound. This result is applied to the case of random walks on the supercritical bond percolation cluster, thus completing a result by Shellef.

Absolicon Solar Collector AB in Härnösand, Sweden, develops concentrating solar collectors with a parabolic trough. In the solar collector trough, there is thermal loss due to convection. A convection suppressor was made and used as a method to reduce thermal loss due to convection in the trough. The objective of the project was to evaluate the convection suppressor for solar collectors with a parabolic trough and its impact on the performance (thermal loss characteristics) in two different orientations of the trough, horizontal and inclined. The performance of the solar collector was first measured without the convection suppressor; these results were compared to two previous quasi-dynamical tests of the solar collector performance made by two different institutes, Research Institute of Sweden and SPF Institut für Solartechnik (Switzerland). The comparison was made to validate the test results from the tests without the convection suppressor, which matched. Secondly, when the convection suppressor was made and tested in the two different orientations, the results of the performance with and without the convection suppressor was evaluated as well as the convection suppressor itself. The results showed a significant improvement of the solar collector performance in the aspect of reduced thermal loss when the convection suppressor was used, hence higher efficiency. / Absolicon Solar Collector AB I Härnösand, Sverige, utvecklar koncentrerande solfångare med ett paraboliskt tråg. I solfångarens tråg uppstår termiska förluster som en följd av konvektion. En konvektionsreducerare tillverkades och användes som metod för att minska de termiska förlusterna i tråget. Målet med projektet var att testa och utvärdera konvektionsreduceraren för koncentrerande solfångare med ett paraboliskt tråg samt dess inverkan på verkningsgraden i två olika positioner för tråget, horisontell och lutande. För att kunna mäta konvektionsreducerarens inverkan på solfångaren mättes först solfångarens prestanda utan konvektionsreduceraren i de två olika positionerna, detta resultat användes som referens efter validering. Valideringen gjordes genom att resultatet jämfördes sedan med två andra prestandamätningar (quasi-dynamical test) av solfångaren gjorda av två olika institut, Research Institute of Sweden och SPF Institut für Solartechnik (Schweiz). Därefter, när konvektionsreduceraren var tillverkat och testad i de olika positionerna på samma sätt som mätningarna utan konvektionsreducerare, jämfördes resultaten med och utan konvektionsreducerareet samt att en utvärdering gjordes av dess inverkan. Resultatet visade en signifikant förbättring av solfångarens prestanda i form av minskade termiska förluster när konvektionsreduceraren användes och därav ökad verkningsgrad.

[pt] Os efeitos da difração na propagação de ondas de rádio sobre terreno irregular em VHF e outras bandas a ser usado por futuras aplicações da TV digital são normalmente estimados usando um dos muitos modelos clássicos. Nesta dissertação é feita uma comparação dos erros cometidos na previsão do sinal recebido por três modelos de propagação computacionalmente intensivos. Os resultados da presente comparação indicarão se os esforços computacionais envolvidos na aplicação destes métodos são capazes de diminuir o valor médio e desvio padrão das diferenças entre as medidas e predições determinadas pelos métodos clássicos. / [en] Diffraction effects on the propagation of radio wave over irregular terrain in the VHF and other bands to be used by future digital TV applications are normally estimated using one of many classical models. In this dissertation is made a comparison of the errors committed prediction of signal received by three propagation models computationally-intensive. The results of the present comparison will indicate whether the computational efforts involved on the application of these methods are capable of decreasing the mean value and the standard deviation of the difference between measurements and predictions determined by the classical methods.