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Communication using fiber optics is an integral part of modern societies and one of the most important parts of this is the grating filter of a laser. In this report we introduce both the periodic and the non-periodic grating filter and discuss how there can be resonance in these structures. We then provide an exact method for calculating the spectrum of these grating filters and study three different methods to calculate this approximately. The first one is the \emph{Fourier approximation} which is very simple. For the studied filters the fundamental form of the results for this method is correct, even though the details are not. The second method consists of calculating the spectrum exactly for some values and then use interpolation by splines. This method gives satisfactory results for the types of gratings analysed. Finally a method of perturbation is provided for the periodic grating filter as well as an outline for how this can be extended to the non-periodic grating filter. For the studied filters the results of this method are very promising. The method of perturbations may also give a deeper understanding of how a filter works and we therefore conclude that it would be of interest to study the method of perturbations further, while all the studied methods can be useful for computation of the spectrum depending on the required precision. / Fiberoptisk kommunikation utgör en viktig del i moderna samhällen och en av de grudläggande delarna av detta är Bragg-filter i lasrar. I den här rapporten introducerar vi både det periodiska och det icke-periodiska Bragg-filtret och diskuterar hur resonans kan uppstå i dessa. Vi presenterar sedan en exakt metod för att beräkna spektrumet av dessa filter samt studerar tre approximativa metoder för att beräkna spektrumet. Den första metoden är \emph{Fourier-approximationen} som är väldigt enkel. För de studerade filtrena blir de grundläggande formerna korrekta med Fourier-approximationen, medan detaljerna är fel. Den andra metoden består av att räkna ut spektrumet exakt för några punkter och sedan interpolera med hjälp av splines. Den här metoden ger mycket bra resultat för de studerade filtrena. Till sist presenteras en metod baserad på störningsteori för det periodiska filtret, samt en översikt över hur det här kan utökas till det icke-periodiska filtret. Denna metod ger mycket lovande resulat och den kan även ge djupare insikt i hur ett filter fungerar. Vi sluter oss därför till att det vore intressant att vidare studera metoder med störningar, men även att alla studerade metoder kan vara användabara för beräkningen av spektra beroende på vilken precision som krävs.

An experimental study of several variants of radius and strut angle of the body centered cubic unit cell was performed to determine the mechanical properties and failure mechanisms of the mesostructure. Quasi static compression tests were performed on an Instron® universal testing machine with a 50kN load cell at 0.2mm/min. The test samples were built using a SLM Solutions 125 selective laser melting machine with 316L stainless steel. Test specimens were based on 5mm cubic unit cells, with a strut diameter 10% of the unit cell size, with skins on top and bottom to provide a cantilever boundary constraint. Specimens were inspected for dimensional accuracy using precision calipers and inspected for morphology using a MicroVu® macroscope. The compressive properties of the mesostructure was compared to the compressive properties of macrostructure. The BCC unit cell behaves significantly different at the boundary layer of a constrained lattice. The failure mode at the boundary is characterized by plastic bending within the microstruts while the non boundary layer cells fail via plastic bending at the node. Manufacturing compensation parameters were determined for part shrinkage and droop. Two predictive numerical models were developed, based on the Gibson-Ashby model of cellular solids, as well as a finite element model. Numerical results did not agree well with the experimental results, indicating that the droop observed on the structures significantly affects the mechanical properties of the overall structure. The 25% radius cubic unit cell and 3^3 lattice withstood the greatest stress of all specimens tested and exhibited nearly ideal plastic deformation behavior.

The goal for this research was to reduce the current manufacturing cost of the polycrystalline diamond compact (PDC) inserts utilized in the natural gas and oil drilling industry while not reducing their current performance. Polycrystalline Diamond is added to the tungsten-carbide (WC) substrates commonly utilized in these applications because of its greater wear and thermal resistance. With the current cube cell design for the high-pressure/high-temperature apparatus, it is necessary to bond an extra WC substrate to the polycrystalline diamond insert to achieve the sizes generally ordered by the customers. The problem of bonding the extra WC substrate was solved by increasing the operating volume of the cube cell assembly and changing the heating pattern within the cell while maintaining the temperature and the pressure required for the successful diamond sintering.The new cell design was proposed and tested. The test data were captured and analyzed to prove the hypotheses. The proposed manufacturing methods resulted in reduced cost, processing time, and reduced the need for equipment and operators without diminishing the performance of the PDC insert.

Solid Oxide Fuel Cells (SOFCs) are emerging as a potential breakthrough energy conversion technology for clean and efficient production of electricity and heat from hydrogen and hydrocarbon fuels. Sc0.1Ce0.01ZrO2 electrolytes for Solid Oxide Fuel Cells are very promising materials because their high ionic conductivity in the intermediate temperature range 700°C-800°C. The vibration response of cubic and rhombohedral (β) 10 mol%Sc2O3 - 1 mol%CeO2 - ZrO2(Sc0.1Ce0.01ZrO2 ) both at room and high-temperatures is reported. The in-situ heating experiments and ex-situ indentation experiments were performed to characterize the vibrational behavior of these important materials. A temperature and stress-assisted phase transition from cubic to rhombohedral phase was detected during in-situ Raman spectroscopy experiments. While heating and indentation experiments performed separately did not cause the transition of the cubic phase into the rhombohedral structure under the performed experimental conditions and only broadened or strained peaks of the cubic phase could be detected, the heating of the indented (strained) surface leaded to the formation of the rhombohedral Sc0.1Ce0.01ZrO2. Both temperature range and strained zone were estimated by in situ heating and 2D mapping, where a formation of rhombohedral or retention of cubic phase has been promoted. The mechanical properties, such as Young’s modulus, Vickers hardness, indentation fracture resistance, room and high temperature four point bending strength and SEVNB fracture toughness along with the stress – strain deformation behavior in compression, of 10 mol% Sc2O3 – 1 mol % CeO2 - ZrO2 (ScCeZrO2) ceramics have been studied. The chosen composition of the ScCeZrO2 has very high ionic conductivity and, therefore, is very promising oxygen ion conducting electrolyte for the intermediate temperature Solid Oxide Fuel Cells. Therefore, its mechanical behavior is of importance and is presented in this study.

No / People, systems, and things in the cities generate large amount of data which is considered to be the most scalable asset of any smart city. Linux users are rapidly increased in last few years, and many large multinational organizations are deploying long distance high bandwidth (LDHB) cloud networks for centralizing the data from various smart cities on a central location. TCP is responsible for reliable communication of data in these cloud networks. For reliability communication among various smart cities, a number of TCP congestion control mechanisms have been developed in the past. TCP Compound, TCP Fusion, and TCP CUBIC are the default TCP congestion control mechanisms for Microsoft Windows, Sun Solaris, and Linux operating systems respectively. The response function of TCP CUBIC is higher than the response function of Standard TCP, which is a trademark congestion control mechanism. As a result, TCP CUBIC does not behave friendly with Standard TCP in LDHB cloud networks. The Congestion Window (cwnd) reduction and growth of TCP CUBIC is very aggressive, which causes high packet loss rate and unfair share of available link bandwidth among competing flows from various smart cities. The aim of this research is to design a new TCP congestion control mechanism for Linux operating system to achieve maximum performance in LDHB cloud networks being used by smart cities. In this paper, congestion control module for slow start (CCM-SS) is designed by increasing the lower boundary limit of cwnd size in slow start phase of communication. Congestion control module for loss event (CCM-LE) is designed by increasing the cwnd reduction rate at each packet loss event and finally Advance Response Function for TCP CUBIC (ARFC) is proposed to design a new congestion control mechanism for Linux operating system. NS-2 is used to compare the performance of TCP CUBIC* with TCP CUBIC in short distance high bandwidth (SDHB) and long distance high bandwidth (LDHB) cloud networks. Results show that TCP CUBIC* has outperformed in LDHB networks, at least by a factor of 18% as compared to TCP CUBIC.

Dirichlet process mixture (DPM) has been widely used as exible prior in nonparametric Bayesian literature, and Weighted Dirichlet process mixture (WDPM) can be viewed as extension of DPM which relaxes model distribution assumptions. Meanwhile, WDPM requires to set weight functions and can cause extra computation burden. In this dissertation, we develop more efficient and exible WDPM approaches under three research topics. The first one is semiparametric cubic spline regression where we adopt a nonparametric prior for error terms in order to automatically handle heterogeneity of measurement errors or unknown mixture distribution, the second one is to provide an innovative way to construct weight function and illustrate some decent properties and computation efficiency of this weight under semiparametric stochastic volatility (SV) model, and the last one is to develop WDPM approach for Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) model (as an alternative approach for SV model) and propose a new model evaluation approach for GARCH which produces easier-to-interpret result compared to the canonical marginal likelihood approach. In the first topic, the response variable is modeled as the sum of three parts. One part is a linear function of covariates that enter the model parametrically. The second part is an additive nonparametric model. The covariates whose relationships to response variable are unclear will be included in the model nonparametrically using Lancaster and Šalkauskas bases. The third part is error terms whose means and variance are assumed to follow non-parametric priors. Therefore we denote our model as dual-semiparametric regression because we include nonparametric idea for both modeling mean part and error terms. Instead of assuming all of the error terms follow the same prior in DPM, our WDPM provides multiple candidate priors for each observation to select with certain probability. Such probability (or weight) is modeled by relevant predictive covariates using Gaussian kernel. We propose several different WDPMs using different weights which depend on distance in covariates. We provide the efficient Markov chain Monte Carlo (MCMC) algorithms and also compare our WDPMs to parametric model and DPM model in terms of Bayes factor using simulation and empirical study. In the second topic, we propose an innovative way to construct weight function for WDPM and apply it to SV model. SV model is adopted in time series data where the constant variance assumption is violated. One essential issue is to specify distribution of conditional return. We assume WDPM prior for conditional return and propose a new way to model the weights. Our approach has several advantages including computational efficiency compared to the weight constructed using Gaussian kernel. We list six properties of this proposed weight function and also provide the proof of them. Because of the additional Metropolis-Hastings steps introduced by WDPM prior, we find the conditions which can ensure the uniform geometric ergodicity of transition kernel in our MCMC. Due to the existence of zero values in asset price data, our SV model is semiparametric since we employ WDPM prior for non-zero values and parametric prior for zero values. On the third project, we develop WDPM approach for GARCH type model and compare different types of weight functions including the innovative method proposed in the second topic. GARCH model can be viewed as an alternative way of SV for analyzing daily stock prices data where constant variance assumption does not hold. While the response variable of our SV models is transformed log return (based on log-square transformation), GARCH directly models the log return itself. This means that, theoretically speaking, we are able to predict stock returns using GARCH models while this is not feasible if we use SV model. Because SV models ignore the sign of log returns and provides predictive densities for squared log return only. Motivated by this property, we propose a new model evaluation approach called back testing return (BTR) particularly for GARCH. This BTR approach produces model evaluation results which are easier to interpret than marginal likelihood and it is straightforward to draw conclusion about model profitability by applying this approach. Since BTR approach is only applicable to GARCH, we also illustrate how to properly cal- culate marginal likelihood to make comparison between GARCH and SV. Based on our MCMC algorithms and model evaluation approaches, we have conducted large number of model fittings to compare models in both simulation and empirical study. / Ph. D.

Nonstationary signals are common in many environments such as radar, sonar, bioengineering and power systems. The nonstationary nature of the signals found in these environments means that classicalspectralanalysis techniques are notappropriate for estimating the parameters of these signals. Therefore it is important to develop techniques that can accommodate nonstationary signals. This thesis seeks to achieve this by firstly, modelling each component of the signal as having a polynomial phase and by secondly, developing techniques for estimating the parameters of these components. Several approaches can be used for estimating the parameters of polynomial phase signals, eachwithvarying degrees ofsuccess.Criteria to consider in potential estimation algorithms are (i) the signal-to-noise (SNR) ratio threshold of the algorithm, (ii) the amount of computation required for running the algorithm, and (iii) the closeness of the resulting estimates' mean-square errors to the minimum theoretical bound. These criteria will be used to compare the new techniques developed in this thesis with existing techniques. The literature on polynomial phase signal estimation highlights the recurring trade-off between the accuracy of the estimates and the amount of computation required. For example, the Maximum Likelihood (ML) method provides near-optimal estimates above threshold, but also incurs a heavy computational cost for higher order phase signals. On the other hand, multi-linear techniques such as the high-order ambiguity function (HAF) method require little computation, but have a significantly higher SNR threshold than the ML method. Of the existing techniques, the cubic phase (CP) function method is a promising technique because it provides an attractive SNR threshold and computational complexity trade-off. For this reason, the analysis techniques developed in this thesis will be derived from the CP function. A limitation of the CP function is its inability to accurately process phase orders greater than three. Therefore, the first novel contribution to this thesis develops a broadened class of discrete-time higher order phase (HP)functions to address this limitation.This broadened class is achieved by providing a multi-linear extension of the CP function. Monte Carlo simulations are performed to demonstrate the statistical advantage of the HP functions compared to the HAFs. A first order statistical analysis of the HP functions is presented. This analysis verifies the simulation results. The next novel contribution is a technique called the lower SNR cubic phase function (LCPF)method. It is an extension of the CP function, with the extension enabling performance at lower signal-to-noise ratios (SNRs). The improvement of the SNR threshold's performance is achieved by coherently integrating the CP function over a compact interval in the two-dimensional CP function space. The computation of the new algorithm is quite moderate, especially when compared to the ML method. Above threshold, the LCPF method's parameter estimates are asymptotically efficient. Monte Carlo simulation results are presented and a threshold analysis of the algorithm closely predicts the thresholds observed in these results. The next original contribution to this research involves extending the LCPF method so that it is able to process multicomponent cubic phase signals and higher order phase signals. The LCPF method is extended to higher orders by applying a windowing technique as opposed to adjusting the order of the kernel as implemented in the HP function method. To demonstrate the extension of the LCPF method for processing higher order phase signals and multicomponent cubic phase signals, some Monte Carlo simulations are presented. Finally, these estimation techniques are applied to real-worldscenarios in the fields of Power Systems Analysis, Neuroethology and Speech Analysis.