The fundamental physics and techniques employed in Laplace transform deep level transient spectroscopy (L-DLTS) are reviewed. A Laplace-DLTS system has been constructed. The high resolving power of this system has been demonstrated experimentally. The L-DLTS system was applied to characterize the defects in undoped n-type ZnO thin film grown by the pulsed laser deposition (PLD) method. A 0.3 eV deep trap has been identified. The formations of Ec-0.39eV and Ec-0.20eVcan be enhanced when the sample surface is seriously damaged by high temperature annealing.AnEc-0.25eV trap is identified in the freshly grown samples, but would disappear after the storage of 3 months. Copper doped n-type ZnO thin film samples with low carrier concentration (n~〖10〗^16 〖cm〗^(-3)) were investigated by using both conventional and Laplace DLTS techniques. Positive DLTS signal peaks were detected that are suspected to be contributed by the minority carrier (hole carrier) emission. A physics model involving the inversion layer of a metal-insulator-semiconductor contact has been invoked to interpret the hole carrier concentration existing near the metal-semiconductor interface. Expression for the defect concentration is determined as a function of the temperature of DLTS peaks. AnEv+0.6eV defect with high concentration (N_T~〖10〗^17 〖cm〗^(-3)) was detected. The concentration of Ev+0.6eVcan be enhanced when the annealing temperature was increased from 750 to 900 degree C. / published_or_final_version / Physics / Master / Master of Philosophy

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Orientador: Gerson Francisco / Mestre

Este trabalho focaliza a análise viscoelástica de estruturas laminadas em material compósito de matriz polimérica, propondo o emprego de métodos de inversão numérica da transformada de Laplace numa formulação adaptada ao método dos elementos finitos. Nesta abordagem alternativa, as equações constitutivas viscoelásticas, formuladas no plano complexo da variável de transformação 's', reduzem o problema a uma análise elástica equivalente. As soluções complexas são então retomadas ao plano fisico para o valor de tempo desejado, dispensando processos incrementais. Exemplos de aplicações são executados comparando-se os resultados do Método da Transformada de Laplace com o Método das Variáveis de Estado que trata o problema viscoelástico de forma incremental. / The viscoelastic analysis of laminated structures of polymeric matrix compsite materiais using Laplace transform is the objective of this work. The inverse of the Laplace transform is carried out using numerical methods adapted to a finite element method formulation. In this altemative aproach, as the constitutive equations are formulated on the complex plane in the transformation variable 's', the viscoelastic problem reduces to an equivalent elastic one. The complex solutions are then sent back to the physical plane for the desired time value, dispensing incremental processes. Examples of aplications compamng results obtained with the Laplace Transformation Method and the State Variables Method (that treats the viscoelastic problem in an incremental form) are presented.

Neste trabalho a formulação LTSn para a solução de problemas de ordenadas discretas (Sn) é estendida a duas e três dimensões, considerando meio heterogêneo, espalhamento anisotrópico e modelo de multigrupo. Para tal, o método LTSn e aplicado às equações unidimensionais resultantes da integração das equações Sn multidiomensionais, gerando sistemas lineares para o fluxos angulares médios transformados. A solução desses sistemas fornece a transformada de Laplace da solução procurada, sem que nenhuma aproximação seja feita ao longo da sua obtenção. A posterior aplicação da transformada de Laplace inversa, efetuada através da técnica de expansão de Heaviside, fornece a solução analítica para os fluxos angulares médios e para os fluxos angulares transversos na fronteira do domínio. As soluções geradas através do método LTSn foram comparadas a resultadas numéricos disponíveis na literatura, para problemas bidimensionais com espalhamento isotrópico e anisotrópico em coordenadas cartesianas, considerando meios homogêneos e heterogêneos. Problemas tridimensionais em coordenadas curvilíneas também são considerados. / In this work, the LTSn formulation for the solution of discrete ordinates (Sn) problems is extended to two and three dimensions, considering heterogeneous medium, anisotropic scattering and multigroup model. To this end, the LTSn method is applied to the one-dimensional equations resulting from the integration of the multidimensional Sn resulting from the integration of the multidimensional Sn equations, generating linear systems for the transformed average angular fluxes. Solving theses systems, these systems, the Laplace transform of the solution are obtained, without any approximation along its derivation. Applying the inverse Laplace transform, by the Heaviside expansion technique, furnishes the analytical solution for the average angular fluxes and the transverse angular fluxes on the boundaries of the domain. Solutions generated using LTSn method are compared with numerical results availalre in literature, for two-dimensional problemns in Cartesian coordinates for isotropic and anisotropic scattering, considering homogeneous and heterogeneous media. Three-dimensional problems in curvilinear coordinates are also considered.

Quantile regression (QR) (Koenker and Bassett, 1978), as a comprehensive extension to standard mean regression, has been steadily promoted from both theoretical and applied aspects. Bayesian quantile regression (BQR), which deals with unknown parameter estimation and model uncertainty, is a newly proposed tool of QR. This thesis aims to make some novel contributions to the following three issues related to QR. First, whereas QR for continuous responses has received much attention in literatures, QR for discrete responses has received far less attention. Second, conventional QR methods often show that QR curves crossing lead to invalid distributions for the response. In particular, given a set of covariates, it may turn out, for example, that the predicted 95th percentile of the response is smaller than the 90th percentile for some values of the covariates. Third, mean-based clustering methods are widely developed, but need improvements to deal with clustering extreme-type, heavy tailed-type or outliers problems. This thesis focuses on methods developed over these three challenges: modelling quantile regression with discrete responses, ensuring non-crossing quantile curves for any given sample and modelling tails for collinear data with outliers. The main contributions are listed as below: * The first challenge is studied in Chapter 2, in which a general method for Bayesian inference of regression models beyond the mean with discrete responses is developed. In particular, this method is developed for both Bayesian quantile regression and Bayesian expectile regression. This method provides a direct Bayesian approach to these regression models with a simple and intuitive interpretation of the regression results. The posterior distribution under this approach is shown to not only be coherent to the response variable, irrespective of its true distribution, but also proper in relation to improper priors for unknown model parameters. * Chapter 3 investigates a new kernel-weighted likelihood smoothing quantile regression method. The likelihood is based on a normal scale-mixture representation of an asymmetric Laplace distribution (ALD). This approach benefits of the same good design adaptation just as the local quantile regression (Spokoiny et al., 2014) does and ensures non-crossing quantile curves for any given sample. * In Chapter 4, we introduce an asymmetric Laplace distribution to model the response variable using profile regression, a Bayesian non-parametric model for clustering responses and covariates simultaneously. This development allows us to model more accurately for clusters which are asymmetric and predict more accurately for extreme values of the response variable and/or outliers. In addition to the three major aforementioned challenges, this thesis also addresses other important issues such as smoothing extreme quantile curves and avoiding insensitive to heteroscedastic errors as well as outliers in the response variable. The performances of all the three developments are evaluated via both simulation studies and real data analysis.

We show that the usual variational formulation of the problem of analytic continuation from an arc on the boundary of a plane domain does not lead to a relaxation of this overdetermined problem. To attain such a relaxation, we bound the domain of the functional, thus changing the Euler equations.

Copper (Cu) is an essential trace element in ruminants such as the cow. Its deficiency leads to a number of debilitating symptoms and can eventually cause death. Secondary Cu deficiency is caused by the presence of chemical antagonists such as the thiomolybdates (TMs) (MoOxS4-x2-; x = 0 3). TMs form in the rumen and then form tightly bound insoluble complexes with Cu. These complexes are then excreted and the Cu is unavailable to the animal. The TMs and their effects on ruminant Cu are the focus of this thesis.<p>This study includes three main bodies of work. First, a method for quantifying the composition of TM mixtures in solution was developed. Second, the rate constants of TM interconversions were determined. Third, reactions between Cu and the TMs were studied. This work is part of an ongoing study in the Reid group to model Cu-ligand speciation in the rumen. <p>Thiomolybdates form by successive replacement of molybdate (MoO42-) O ligands with S. This makes synthesis of the uncontaminated compounds difficult. Mixtures of TMs are best analyzed by UV-visible spectroscopy despite the considerable spectral overlap. The combination of these two issues makes the characterization of the spectra difficult. In this study, a method was developed to establish the spectra of the pure TMs despite cross-contamination. Multivariate curve fitting methods were used to establish the composition of synthesized samples simultaneously with the molar absorptivities of the pure TMs. This was done using a Beers Law model. The composition was determined from a fit using assumed molar absorptivities. The absorptivities were then refined using the composition results. These processes were successively reiterated until both were optimized. The optimized absorptivities could then be used to determine the composition of any TM solution mixture. <p>The kinetics of TM formation under biologically relevant conditions were followed by UV-visible spectroscopy. The spectra were then analyzed, using the method developed above, to determine all TM concentrations. Curve fitting methods were used to simultaneously determine the rate constants of all processes that occurred. Integrated rate equations used in the fitting process were developed using the Laplace Transform method. Rate constants were determined at varying pH, ionic strengths and temperatures. From this information it was shown that TM formation and hydrolysis occurs via an associative mechanism. It was also determined that H2S and not HS- was the sulfide nucleophile in TM formation reactions.<p>This study was then extended to include reactions involving Cu and the TMs. First, the UV-visible spectra of the reaction products of Cu with each TM were characterized. This allowed the kinetics of reactions between Cu and the TMs to be followed. This reaction has been found to proceed via an intermediate. Molar absorptivities for this intermediate were optimized along with the appropriate rate constants. This was done using a combination of mathematical simulations and the curve fitting methods used for the TM kinetics. The resulting rate constants can be compared with those obtained previously in the group using a Cu ion selective electrode. <p>These rate constants were used in conjunction with the TM formation rate constants to perform simulations. The results of these simulations provide a picture of what is expected to occur in the rumen. Reactions were also performed in which TM formation occurred in the presence of Cu. This was then extended to mimic bovine feeding habits. Here, portions of the reactions mixture was removed at various time intervals and replaced with fresh reagents. These experiments were used to gain a qualitative picture of Cu speciation in the presence of the TMs over time. The work presented in this thesis provides a crucial step toward understanding the problem of bovine copper deficiency.

Copper (Cu) is an essential trace element in ruminants such as the cow. Its deficiency leads to a number of debilitating symptoms and can eventually cause death. Secondary Cu deficiency is caused by the presence of chemical antagonists such as the thiomolybdates (TMs) (MoOxS4-x2-; x = 0 3). TMs form in the rumen and then form tightly bound insoluble complexes with Cu. These complexes are then excreted and the Cu is unavailable to the animal. The TMs and their effects on ruminant Cu are the focus of this thesis.<p>This study includes three main bodies of work. First, a method for quantifying the composition of TM mixtures in solution was developed. Second, the rate constants of TM interconversions were determined. Third, reactions between Cu and the TMs were studied. This work is part of an ongoing study in the Reid group to model Cu-ligand speciation in the rumen. <p>Thiomolybdates form by successive replacement of molybdate (MoO42-) O ligands with S. This makes synthesis of the uncontaminated compounds difficult. Mixtures of TMs are best analyzed by UV-visible spectroscopy despite the considerable spectral overlap. The combination of these two issues makes the characterization of the spectra difficult. In this study, a method was developed to establish the spectra of the pure TMs despite cross-contamination. Multivariate curve fitting methods were used to establish the composition of synthesized samples simultaneously with the molar absorptivities of the pure TMs. This was done using a Beers Law model. The composition was determined from a fit using assumed molar absorptivities. The absorptivities were then refined using the composition results. These processes were successively reiterated until both were optimized. The optimized absorptivities could then be used to determine the composition of any TM solution mixture. <p>The kinetics of TM formation under biologically relevant conditions were followed by UV-visible spectroscopy. The spectra were then analyzed, using the method developed above, to determine all TM concentrations. Curve fitting methods were used to simultaneously determine the rate constants of all processes that occurred. Integrated rate equations used in the fitting process were developed using the Laplace Transform method. Rate constants were determined at varying pH, ionic strengths and temperatures. From this information it was shown that TM formation and hydrolysis occurs via an associative mechanism. It was also determined that H2S and not HS- was the sulfide nucleophile in TM formation reactions.<p>This study was then extended to include reactions involving Cu and the TMs. First, the UV-visible spectra of the reaction products of Cu with each TM were characterized. This allowed the kinetics of reactions between Cu and the TMs to be followed. This reaction has been found to proceed via an intermediate. Molar absorptivities for this intermediate were optimized along with the appropriate rate constants. This was done using a combination of mathematical simulations and the curve fitting methods used for the TM kinetics. The resulting rate constants can be compared with those obtained previously in the group using a Cu ion selective electrode. <p>These rate constants were used in conjunction with the TM formation rate constants to perform simulations. The results of these simulations provide a picture of what is expected to occur in the rumen. Reactions were also performed in which TM formation occurred in the presence of Cu. This was then extended to mimic bovine feeding habits. Here, portions of the reactions mixture was removed at various time intervals and replaced with fresh reagents. These experiments were used to gain a qualitative picture of Cu speciation in the presence of the TMs over time. The work presented in this thesis provides a crucial step toward understanding the problem of bovine copper deficiency.

During the last two centuries many methods have been proposed to solve the angles-only initial orbit determination problem. As this problem continues to be relevant as an initial estimate is needed before high accuracy orbit determination is accomplished, it is important to perform direct comparisons among the popular methods with the aim of determining which methods are the most suitable (accuracy, robustness) for the most important orbit determination scenarios. The methods tested in this analysis were the Laplace method, the Gauss method (suing the Gibbs and Herrick-Gibbs methods to supplement), the Double R method, and the Gooding method. These were tested on a variety of scenarios and popular orbits. A number of methods for quantifying the error have been proposed previously. Unfortunately, many of these methods can overwhelm the analyst with data. A new method is used here that has been shown in previous research by the author. The orbit error is here quantified by two new general orbit error parameters identifying the capability to capture the orbit shape and the orbit orientation. The study concludes that for nearly all but a few cases, the Gooding method best estimates the orbit, except in the case for the polar orbit for which it depends on the observation interval whether one uses the Gooding method or the Double R method. All the methods were found to be robust with respect to noise and the initial guess (if required by the method). All the methods other than the Laplace method suffered no adverse effects when additional observation sites were used and when the observation intervals were unequal. Lastly for the case when the observer is in space, it was found that typically the Gooding method performed the best if a good estimate is known for the range, otherwise the Laplace method is generally best.