This thesis aims to determine the distribution of the relative permittivity for random mixtures of material using electromagnetic simulations. The algorithm used in the simulations is the FDTD method which solves Maxwell's equations numerically in the time-domain. The material is modeled as randomly shaped particles with radius 12 ± 10 micrometre in x- and y-direction and radius 3 ± 1 micrometre in zdirection. The scattering parameters from the transmitted and reflected electric field when a plane wave interacts with the material are measured. The relative permittivity is determined from the scattering parameters using the iterative Baker-Jarvis method. The simulations shows that both the distribution and the value of the relative permittivity is low when the particles have non conducting layers to force interruptions to prevent percolation, a conducting path between the particles. The most important result is of the kind where the simulations do not have any boundaries to prevent percolation. These simulations reflects how the relative permittivity distributes in real measurements. It is established that the value of the relative permittivity has a large distribution and also that percolation occurs because of the periodic structures.

This thesis focuses on optimization on a generic objective function based on reflected Brownian motion (RBM). We investigate in several approaches including the partial differential equation approach where we write our objective function in terms of a Hamilton-Jacobi-Bellman equation using the dynamic programming principle and the gradient descent approach where we use two different gradient estimators. We provide extensive numerical results with the gradient descent approach and we discuss the difficulties and future study opportunities for this problem.

Mass media has long been thought to have a detrimental effect on an adolescent’s values and behaviors. Many social ills including violence, misogyny and negative health behaviors, as well as egoistic cultural values have been attributed to mass media’s influence. Yet the media is not all powerful, nor are its powers unable to be combated. In this manuscript, I analyze the Educational Longitudinal Study data from 2002 to 2006 to determine the real effects mass media has on adolescents in comparison to other influences. I find that not all media is equal in influence. Television and video games have different relationships with a teenager’s values and behaviors in comparison to internet use. Additionally, I find that when parents are involved with their children as significant others, they do not negate, but can typically counteract many negative effects of media.

This dissertation studies three classes of estimators for the asymptotic variance parameter of a stationary stochastic process. All estimators are based on the concept of data "re-use" and all transform the output process into functions of an approximate Brownian motion process. The first class of estimators consists folded standardized time series area and Cramér-von Mises (CvM) estimators. Detailed expressions are obtained for their expectation at folding levels 0 and 1; those expressions explain the puzzling increase in small-sample bias as the folding level increases. In addition, we use batching and linear combinations of estimators from different levels to produce estimators with significantly smaller variance. Finally, we obtain very accurate approximations of the limiting distributions of batched folded estimators. These approximations are used to compute confidence intervals for the mean and variance parameter of the underlying stochastic process. The second class --- folded overlapping area estimators --- are computed by averaging folded versions of the standardized time series corresponding to overlapping batches. We establish the limiting distributions of the proposed estimators as the sample size tends to infinity. We obtain statistical properties of these estimators such as bias and variance. Further, we find approximate confidence intervals for the mean and variance parameter of the process by approximating the theoretical distributions of the proposed estimators. In addition, we develop algorithms to compute these estimators with only order-of-sample-size work. The third class --- reflected area and CvM estimators --- are computed from reflections of the original sample path. We obtain the expected values and variance of individual estimators. We show that it is possible to obtain linear combinations of reflected estimators with smaller variance than the variance of each constituent estimator, often at no cost in bias. A quadratic optimization problem is solved to find an optimal linear combination of estimators that minimizes the variance of the linearly combined estimator. For all classes of estimators, we provide Monte Carlo examples to show that the estimators perform as well in practice as advertised by the theory.

Thesis (MEng)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: Large close range environmental reflections or poor isolation between the transmit and receive paths of an FMCW radar can overload the receiver. The In phase and Quadrature phase (IQ) Reflected Power Canceller (RPC) provides a solution to the problem by cancelling any close range reflections. In this study a procedure to optimise the design of an RPC is developed and the performance limits of a practical RPC is investigated in depth. There are four focus areas in the evaluation and design of the IQ Reflected Power Canceller. First, an analysis was performed on a theoretical IQ Reflected Power Canceller, which provided insight into how the system functioned and made it possible to identify practical application issues that would arise during the design. The next focus area was the IQ Reflected Power Canceller’s dynamic range. Equations, based on the power and noise characteristics of each component in the canceller, were derived. From these equations, a system, with an optimised dynamic range, could be developed. Next, the IQ Reflected Power Canceller’s feedback loop stability was investigated. The canceller is an active negative feedback control system but, in order to obtain the negative feedback, the feedback signal has to be phase shifted by 180 degrees to the phase of the input signal. An analysis of the canceller’s RF phase contribution resulted in an equation that can be used to manage the nett RF phase in the feedback loop. The evaluation model of the IQ Reflected Power Canceller produced favourable results. The tests performed on the system included measuring the level of cancellation that can be achieved, whether the dynamic range corresponds to the predicted values and the amount of RF phase error that can be introduced in the feedback path while maintaining a stable system. The IQ Reflected Power Canceller was found to perform well in the evaluation. It provided a cancellation of more than 45 dB for close range reflections and the canceller remained stable across a wide range of RF centre frequencies (1 GHz). This means that the FMCW radar’s frequency modulation bandwidth will not be limited because of the IQ Reflected Power Canceller. The evaluation clearly showed that the modulator in the feedback loop is the critical element that determines the dynamic range of the radar with an RPC. / AFRIKAANSE OPSOMMING: Onvoldoende isolasie tussen die sender en ontvanger van ’n Frekwensie Gemoduleerde Kontinu Golf radar, sowel as groot weerkaatsings vanaf voorwerpe in die omgewing van die radar, veroorsaak dat die ontvanger versadig. Hierdie beperking veroorsaak dat die radar ’n verminderde dinamiese bereik het, en daarmee ook dat die radar se maksimum teiken-afstand verminder word. Die IQ Gereflekteerde Drywingskanselleerder kan as ’n oplossing gebruik word teen hierdie ongewenste refleksies. Hierdie navorsing poog om ’n kanselleerder te evalueer met die eind doel gestel daarop om ’n praktiese stelsel aanmekaar te sit. Die kanselleerder word geëvalueer deur na vier fokus areas te kyk. Eerstens word ’n ideale model opgestel, wat ’n beter begrip van die kanselleerder bewerkstellig. Uit hierdie ideale model, is daar praktiese oorwegings wat die kanselleerder affekteer, geïdentifiseer. Ten einde die dinamiese bereik van die radar ontvanger te verbeter, word ’n metode afgelei wat gebruik word om die kanselleerder se dinamiese bereik te optimeer. Hierdie metode neem die maksimum drywingsbeperkinge van die komponente in die kanselleerder in ag. Die kanselleerder is ’n aktiewe terugvoer beheerstelsel, en aangesien ’n sommeerder in die terugvoer lus gebruik word, moet die fase deur die lus met 180 grade geskuif word om sodoende ’n kansellerende sein by die ontvangde sein te tel. Die RF fase foute in die kanselleerder word geanaliseer deur ’n nie-ideale model van die kanselleerder op te stel. Hierdie nie-ideale model maak dit moontlik om die effek van ’n RF fase fout op die kanselleerder se stabiliteit te ondersoek. ’n Praktiese kanselleerder is ontwerp uit die inligting wat versamel is gedurende die evaluasie, en ’n werkende stelsel is aanmekaar gesit. Met hierdie praktiese kanselleerder is die hoeveelheid drywing-onderdrukking wat bereik kan word, gemeet. Die dinamiese bereik van die kanselleerder is ook bepaal en vergelyk met die teoreties berekende waardes. Die aannames oor die effek van die RF fase fout in die kanselleerder, is bevestig deur metings te neem. Goeie resultate is met die kanselleerder behaal. ’n Kansellasie van meer as 45 dB is gemeet vir naby-geleë refleksies. Die kanselleerder het ook stabiel gebly oor ’n wye band van senter-frekwensies (1 GHz). Dus sal die Frekwensie Gemoduleerde Kontinu Golf radar se modulasie bandwydte nie beperk word as gevolg van die kanselleerder nie. Uit die evaluasie is daar gevind dat die modulator die kritieke element in the kanselleerder se terugvoer lus is, dus bepaal die modulator die dinamiese bereik van die radar met ’n kanselleerder.

L'inversion des formes d'onde (full waveform inversion, FWI) a suscité un intérêt dans le monde entier pour sa capacité à estimer de manière précise et détaillée les propriétés physiques du sous-sol. La FWI est généralement formulée sous la forme d'un problème d'ajustement des données par moindres carrés et résolus par une approche linéarisée utilisant des méthodes d'optimisation locales. Cependant, la FWI est bien connue de souffrir du problème de saut de phase rendant les résultats fortement dépendant de la qualité des modèles initiaux. L'inversion des formes d'ondes des arrivées réfléchies (reflection waveform inversion, RWI) a récemment été proposée pour atténuer ce problème en supposant une séparation d'échelle entre le modèle de vitesse lisse et le modèle de réflectivité à haut nombre d'onde. La formulation de RWI considère explicitement les ondes réfléchies afin d'extraire de ces ondes une information sur les variations lisses de vitesse des zones profondes. Cependant, la méthode néglige les ondes transmises qui contraignant les informations lisses de vitesse en proche surface.Dans cette thèse, une étude de la sensibilité en nombre d'ondes des méthodes de FWI et RWI a d'abord été revisitée dans le cadre de la tomographie en diffraction et des décompositions orthogonales. A partir de cette analyse, je propose une nouvelle méthode, à savoir l'inversion jointe des formes d'ondes transmises et réfléchies (joint full waveform inversion, JFWI). La méthode propose une formulation unifiée pour combiner la FWI des transmissions et la RWI pour les réflexions, donnant naturellement une sensibilité commune aux petits nombres d'onde venant des arrivées grand-angle et réfléchies. Les composantes à hauts nombres d'onde sont naturellement atténuées par la formulation. Pour satisfaire l'hypothèse de séparation d'échelle, j'utilise une paramétrisation du sous-sol basée sur la vitesse des ondes de compression et l'impédance acoustique. La complexité temporelle de cette approche est le double de la méthode de FWI classique et la requête mémoire reste la même.Une procédure d'inversion est ensuite proposée, permettant d'estimer alternativement le modèle de la vitesse du sous-sol par JFWI et l'impédance inversion de formes d'ondes réfléchies. Un exemple synthétique réaliste du modèle de Valhall est d'abord utilisé avec des données de streamer et à partir d'un modèle initial très lisse. Dans ce cadre, alors que la FWI converge vers un minimum local, la JFWI réussit à reconstruire un modèle de vitesse lisse de bonne qualité. La prise en compte des ondes tournante par la JFWI montre un fort intérêt pour la qualité de reconstruction superficielle, comparée à la méthode RWI seule. Cela se traduit ensuite par une reconstruction améliorée en profondeur. Le modèle de vitesse lisse construit par JFWI peut ensuite être considéré comme modèle initial pour la FWI classique, afin d'injecter le contenu en haut nombres d'onde tout en évitant le problème de saut de phase.Les avantages et limites de l'approche de JFWI sont ensuite étudiés dans une application sur données réelles, venant d'un profil 2D de données de fond de mer (OBC) recoupant un nuage de gaz au dessus d'un réservoir. Plusieurs modèles initiaux et stratégies d'inversion sont testés afin de minimiser le problème de saut de phase, tout en construisant des modèles de sous-sol avec une résolution suffisante. Sous réserve de mettre en œuvre des stratégies limitant le problème de saut de phase, la JFWI montre qu'elle peut produire un modèle de vitesse acceptable, injectant les bas nombres d'onde dans le modèle de vitesse. L'amélioration de l'éclairage en angles de diffraction fournie par des acquisitions 3D devrait permettre de pouvoir commencer l'inversion par JFWI à partir de modèle encore moins bien définis. / Full waveform inversion (FWI) has attracted worldwide interest for its capacity to estimate the physical properties of the subsurface in details. It is often formulated as a least-squares data-fitting procedure and routinely solved by linearized optimization methods. However, FWI is well known to suffer from cycle skipping problem making the final estimations strongly depend on the user-defined initial models. Reflection waveform inversion (RWI) is recently proposed to mitigate such cycle skipping problem by assuming a scale separation between the background velocity and high-wavenumber reflectivity. It explicitly considers reflected waves such that large-wavelength variations of deep zones can be extracted at the early stage of inversion. Yet, the large-wavelength information of the near surface carried by transmitted waves is neglected.In this thesis, the sensitivity of FWI and RWI to subsurface wavenumbers is revisited in the frame of diffraction tomography and orthogonal decompositions. Based on this analysis, I propose a new method, namely joint full waveform inversion (JFWI), which combines the transmission-oriented FWI and RWI in a unified formulation for a joint sensitivity to low wavenumbers from wide-angle arrivals and short-spread reflections. High-wavenumber components are naturally attenuated during the computation of model updates. To meet the scale separation assumption, I also use a subsurface parameterization based on compressional velocity and acoustic impedance. The temporal complexity of this approach is twice of FWI and the memory requirement is the same.An integrated workflow is then proposed to build the subsurface velocity and impedance models in an alternate way by JFWI and waveform inversion of the reflection data, respectively. In the synthetic example, JFWI is applied to a streamer seismic data set computed in the synthetic Valhall model, the large-wavelength characteristics of which are missing in the initial 1D model. While FWI converges to a local minimum, JFWI succeeds in building a reliable velocity macromodel. Compared with RWI, the involvement of diving waves in JFWI improves the reconstruction of shallow velocities, which translates into an improved imaging at greater depths. The smooth velocity model built by JFWI can be subsequently taken as the initial model for conventional FWI to inject high-wavenumber content without obvious cycle skipping problems.The main promises and limitations of the approach are also reviewed in the real-data application on the 2D OBC profile cross-cutting gas cloud.Several initial models and offset-driven strategies are tested with the aim to manage cycle skipping while building subsurface models with sufficient resolution. JFWI can produce an acceptable velocity model provided that the cycle skipping problem is mitigated and sufficient low-wavenumber content is recovered at the early stage of inversion. Improved scattering-angle illumination provided by 3D acquisitions would allow me to start from cruder initial models.

This diploma thesis analyses the occurrence of synonymy in the texts of academic prose and fiction. The topic of synonymy has been in the centre of attention for a long time and it still deserves much attention. The aim of this thesis is to approach to the topic from a different perspective. Theoretical part describes the theoretical background of synonymy from the upper layers of the system of language. These theories are used as analytical tool in analysing the collected samples with the focus on similarities and differences in connotation of pairs of synonyms. The diploma thesis should particularly contribute to study of partial synonymy and the components of associative meaning that vary in dependence on functional style. This thesis should also marginally refer to the topic of absolute synonymy. The frequency of the components of associative meaning and findings are described in the conclusion of the thesis.

This thesis consists of three self-contained parts, each with its own abstract, body, references and page numbering. Part I, 'Potential theory, path integrals and the Laplacian of the indicator', finds the transition density of absorbed or reflected Brownian motion in a d-dimensional domain as a Feynman-Kac functional involving the Laplacian of the indicator, thereby relating the hitherto unrelated fields of classical potential theory and path integrals. Part II, 'The problem of alternatives', considers parallel investment in alternative technologies or drugs developed over time, where there can be only one winner. Parallel investment accelerates the search for the winner, and increases the winner's expected performance, but is also costly. To determine which candidates show sufficient performance and/or promise, we find an integral equation for the boundary of the optimal continuation region. Part III, 'Optimal support for renewable deployment', considers the role of government subsidies for renewable technologies. Rapidly diminishing subsidies are cheaper for taxpayers, but could prematurely kill otherwise successful technologies. By contrast, high subsidies are not only expensive but can also prop up uneconomical technologies. To analyse this trade-off we present a new model for technology learning that makes capacity expansion endogenous. There are two reasons for this standalone structure. First, the target readership is divergent. Part I concerns mathematical physics, Part II operations research, and Part III policy. Readers interested in specific parts can thus read these in isolation. Those interested in the thesis as a whole may prefer to read the three introductions first. Second, the separate parts are only partially interconnected. Each uses some theory from the preceding part, but not all of it; e.g. Part II uses only a subset of the theory from Part I. The quickest route to Part III is therefore not through the entirety of the preceding parts. Furthermore, those instances where results from previous parts are used are clearly indicated.

Title: Solar Wind Modification in the Earth Foreshock Author: Jaroslav Urbář Department: Department of Surface and Plasma Science Supervisor: Prof. Zdeněk Němeček, Department of Surface and Plasma Science Abstract: The thesis presents statistical studies of the solar wind deceleration and deflection in the foreshock and its potential causes. The multi-point observa- tions from the THEMIS mission in the foreshock are compared with a Wind solar wind monitor with motivation to estimate different factors influencing evolution of solar wind speed and its deflection. We have found a systematic deceleration of the solar wind mainly due to its proton component with a decreasing distance to the bow shock that is controlled by the compressibility and the level of magnetic field fluctuations in the ULF wave range associated with the flux of reflected and accelerated particles. We can conclude that the reflected particles excite waves of large amplitudes that decelerate the solar wind protons throughout the foreshock as well as in front of the Moon. Keywords: Earth foreshock; reflected protons; solar wind proton velocity recon- struction; deceleration; ULF waves 1

Shock-tube experiments are typically performed at high temperatures (≥1200K) due to test-time constraints. These test times are usually ~1 ms in duration and the source of this short, test-time constraint is loss of temperature due to heat transfer. At short test times, there is very little appreciable heat transfer between the hot gas and the cold walls of the shock tube and a high test temperature can be maintained. However, some experiments are using lower temperatures (approx. 800K) to achieve ignition and require much longer test times (up to 15 ms) to fully study the chemical kinetics and combustion chemistry of a reaction in a shock-tube experiment. Using mathematical models, analysis was performed studying the effects of temperature, pressure, shock-tube inner diameter, and test-port location at various test times (from 1 - 20 ms) on temperature maintenance. Three models, each more complex than the previous, were used to simulate test conditions in the endwall region behind the reflected shock wave with Ar and N2 as bath gases. Temperature profile, thermal BL thickness, and other parametric results are presented herein. It was observed that higher temperatures and lower pressures contributed to a thicker thermal boundary layer, as did shrinking inner diameter. Thus it was found that a test case such as 800K and 50 atm in a 16.2-cm-diameter shock tube in Argon maintained thermal integrity much better than other cases - pronounced by a thermal boundary layer ≤ 1 mm thick and an average temperature ≥ 799.9 K from 1-20 ms.