Polychlorinated dibenzo-p-dioxins (PCDDs) and dibenzofurans (PCDFs), two groups of structurally related chlorinated aromatic hydrocarbons, are of high concern due to their global distribution and extreme toxicity. Since they occur at very low levels, their analysis is complex, challenging and hence there is a need for efficient, reliable and rapid alternative analytical methods. Developing such methods was the aim of the project this thesis is based upon. During the first years of the project the focus was on the first parts of the analytical chain (extraction and clean-up). A selective pressurized liquid extraction (SPLE) procedure was developed, involving in-cell clean-up to remove bulk co-extracted matrix components from sample extracts. It was further streamlined by employing a modular pressurized liquid extraction (M-PLE) system, which simultaneously extracts, cleans up and isolates planar PCDD/Fs in a single step. Both methods were validated using a wide range of soil, sediment and sludge reference materials. Using dichloromethane/n-heptane (DCM/Hp; 1/1, v/v) as a solvent, results statistically equivalent to or higher than the reference values were obtained, while an alternative, less harmful non-chlorinated solvent mixture - diethyl ether/n-heptane (DEE/Hp; 1/2, v/v) – yielded data equivalent to those values. Later, the focus of the work shifted to the final instrumental analysis. Six gas chromatography (GC) phases were evaluated with respect to their chromatographic separation of not just the 17 most toxic congeners (2,3,7,8-substituted PCDD/Fs), but all 136 tetra- to octaCDD/Fs. Three novel ionic liquid columns performed much better than previously tested commercially available columns. Supelco SLB-IL61 offered the best overall performance, successfully resolving 106 out of the 136 compounds, and 16 out of the 17 2,3,7,8-substituted PCDD/Fs. Another ionic liquid (SLB-IL111) column provided complementary separation. Together, the two columns separated 128 congeners. The work also included characterization of 22 GC columns’ selectivity and solute-stationary phase interactions. The selectivities were mapped using Principal Component Analysis (PCA) of all 136 PCDD/F’s retention times on the columns, while the interactions were probed by analyzing both the retention times and the substances’ physicochemical properties.

Magister Scientiae - MSc / In recent years, two estimators have been proposed to correct the bias exhibited by the leastsquares (LS) estimator of the lagged dependent variable (LDV) coefficient in dynamic regression models when the sample is finite. They have been termed as ‘mean-unbiased’ and ‘medianunbiased’ estimators. Relative to other similar procedures in the literature, the two locationbased estimators have the advantage that they offer an exact and uniform methodology for LS estimation of the LDV coefficient in a first order autoregressive model with or without exogenous regressors i.e. ARX(1). However, no attempt has been made to accurately establish and/or compare the statistical properties among these estimators, or relative to those of the LS estimator when the LDV coefficient is restricted to realistic values. Neither has there been an attempt to  compare their performance in terms of their mean squared error (MSE) when various forms of the exogenous regressors are considered. Furthermore, only implicit confidence intervals have been given for the ‘medianunbiased’ estimator. Explicit confidence bounds that are directly usable for inference are not available for either estimator. In this study a new estimator of the LDV coefficient is proposed; the ‘most-probably-unbiased’ estimator. Its performance properties vis-a-vis the existing estimators are determined and compared when the parameter space of the LDV coefficient is restricted. In addition, the following new results are established: (1) an explicit computable form for the density of the LS estimator is derived for the first time and an efficient method for its numerical evaluation is proposed; (2) the exact bias, mean, median and mode of the distribution of the LS estimator are determined in three specifications of the ARX(1) model; (3) the exact variance and MSE of LS estimator is determined; (4) the standard error associated with the determination of same quantities when simulation rather than numerical integration method is used are established and the methods are compared in terms of computational time and effort; (5) an exact method of evaluating the density of the three estimators is described; (6) their exact bias, mean, variance and MSE are determined and analysed; and finally, (7) a method of obtaining the explicit exact confidence intervals from the distribution functions of the estimators is proposed. The discussion and results show that the estimators are still biased in the usual sense: ‘in expectation’. However the bias is substantially reduced compared to that of the LS estimator. The findings are important in the specification of time-series regression models, point and interval estimation, decision theory, and simulation. / South Africa

Magister Scientiae - MSc / This study examines the behaviour of the South African financial markets with regards to the Geometric Brownian motion process. It uses the daily, weekly, and monthly stock returns time series of some major securities trading in the South African financial market, more specifically the US dollar/Euro, JSE ALSI Total Returns Index, South African All Bond Index, Anglo American Corporation, Standard Bank, Sasol, US dollar Gold Price , Brent spot oil price, and South African white maize near future. The assumptions underlying the Geometric Brownian motion in finance, namely the stationarity, the normality and the independence of stock returns, are tested using both graphical (histograms and normal plots) and statistical test (Kolmogorov-Simirnov test, Box-Ljung statistic and Augmented Dickey-Fuller test) methods to check whether or not the Brownian motion as a model for South African financial markets holds. The Hurst exponent or independence index is also applied to support the results from the previous test. Theoretically, the independent or Geometric Brownian motion time series should be characterised by the Hurst exponent of ½. A value of a Hurst exponent different from that would indicate the presence of long memory or fractional Brownian motion in a time series. The study shows that at least one assumption is violated when the Geometric Brownian motion process is examined assumption by assumption. It also reveals the presence of both long memory and random walk or Geometric Brownian motion in the South African financial markets returns when the Hurst index analysis is used and finds that the Currency market is the most efficient of the South African financial markets. The study concludes that although some assumptions underlying the rocess are violated, the Brownian motion as a model in South African financial markets can not be rejected. It can be accepted in some instances if some parameters such as the Hurst exponent are added. / South Africa

Dans cette thèse nous étudions le comportement asymptotique de systèmes de particules en interaction de type champ moyen en espace discret, systèmes pour lesquels l'interaction a lieu par l'intermédiaire de la mesure empirique. Dans la première partie de ce mémoire, nous nous intéressons aux systèmes de particules de type Fleming-Viot: les particules se déplacent indépendamment suivant une dynamique markovienne jusqu'au moment où l'une d'entre elles touche un état absorbant. A cet instant, la particule absorbée choisit uniformément une autre particule et saute sur sa position. L'ergodicité du processus est établie dans le cadre de marches aléatoires sur N avec dérive vers l'origine et pour une dynamique proche de celle du graphe complet. Pour ce dernier, nous obtenons une estimation quantitative de la convergence en temps long à l'aide de la courbure de Wasserstein. Nous montrons de plus la convergence de la distribution empirique stationnaire vers une unique distribution quasi-stationnaire, quand le nombre de particules tend vers l'infini. Dans la deuxième partie de ce mémoire, nous nous intéressons au comportement en temps long et quand le nombre de particules devient grand, d'un système de processus de naissance et mort pour lequel les particules interagissent à chaque instant par le biais de la moyenne de leurs positions. Nous établissons l'existence d'une limite macroscopique, solution d'une équation non linéaire ainsi que le phénomène de propagation du chaos avec une estimation quantitative et uniforme en temps / In this thesis we study the asymptotic behavior of particle systems in mean field type interaction in discrete space, where the system acts over one fixed particle through the empirical measure of the system. In the first part of this thesis, we are interested in Fleming-Viot particle systems: the particles move independently of each other until one of them reaches an absorbing state. At this time, the absorbed particle jumps instantly to the position of one of the other particles, chosen uniformly at random. The ergodicity of the process is established in the case of random walks on N with a dirft towards the origin and on complete graph dynamics. For the latter, we obtain a quantitative estimate of the convergence described by the Wasserstein curvature. Moreover, under the invariant measure, we show the convergence of the empirical measure towards the unique quasi-stationary distribution as the size of the system tends to infinity. In the second part of this thesis, we study the behavior in large time and when the number of particles is large of a system of birth and death processes where at each time a particle interacts with the others through the mean of theirs positions. We establish the existence of a macroscopic limit, solution of a non linear equation and the propagation of chaos phenomenon with quantitative and uniform in time estimate

L’adaptation de maillage est un outil puissant pour l’obtention de simulations aérodynamiques précises à coût limité. Dans le cas particulier des simulations visant au calcul de fonctions aérodynamiques (efforts, moments, rendements...), plusieurs méthodes dites de raffinement ciblé (ou, en anglais, « goal-oriented ») basées sur le vecteur adjoint de la fonction d’intérêt ont été proposées. L’objectif de la thèse est l’extension d’une méthode de ce type basée sur la dérivée totale dJ/dX de la grandeur aérodynamique d’intérêt, J, par rapport aux coordonnées du maillage volumique, X. Les trois méthodes usuelles de calcul de gradient discret – la méthode de différentiation directe, la méthode adjointe-"paramètres" et la méthode adjointe-"maillage" évaluant dJ/dX – ont tout d’abord été étudiées et codées dans le logiciel elsA de l’ONERA pour des maillages non-structurés, pour des écoulements compressibles de fluide parfait et des écoulements laminaires. La seconde étape du travail a consisté à créer un senseur local θ basé sur dJ/dX qui identifie les zones du maillage volumique où la position des nœuds a une forte incidence sur l’évaluation de la fonction J. Ce senseur sert d’indicateur pour l’adaptation de différents maillages, pour différents régimes d’écoulement (subsonique, transsonique, supersonique), pour des configurations d’aérodynamique interne (aube et tuyère) et externe (profil d’aile). La méthode proposée est comparée à une méthode de raffinement ciblée très populaire (Venditti et Darmofal, 2001) et à une méthode de raffinement basée sur les caractéristiques de l’écoulement (ou, en anglais, « feature-based ») ; elle conduit à des résultats très satisfaisants. / Mesh adaptation is a powerful tool to obtain accurate aerodynamic simulations with limited cost. In the specific case of computation of aerodynamic functions (forces, moments, efficiency ...), goal-oriented methods based on the adjoint vector have been proposed. The aim of the thesis is the extension of a method of this type based on the total derivative dJ/dX of the aerodynamic output of interest, J, with respect to the volume mesh coordinates, X. The three common methods for calculating discrete gradient – the direct differentiation method, the parameter-adjoint method and mesh-adjoint method evaluating dJ/dX – have been studied first and coded in the elsA ONERA software for unstructured grids, for compressible inviscid and laminar flows. The second part of this work was has been to define a local sensor θ based on dJ/dX in order to identify zones where the volume mesh nodes position has a strong impact on the evaluation of the function J. This sensor is the selected indicator for different mesh adaptations for different flow regimes (subsonic, transonic, supersonic) for internal (blade and nozzle) and external (wing profile) aerodynamic configurations. The proposed method is compared to a well-known goal-oriented method (Darmofal and Venditti, 2001) and to a feature-based method ; it leads to very consistent results. very consistent results.

No description available.

Highly-loaded turbomachine blades can stall under off-design conditions. In this regime, the flow can separate close to the leading edge of the blade in a periodic manner that can lead to blade vibrations, commonly referred to as stall flutter. Prior experimental studies on stall flutter have been at large Re (Re ~ 106). In the present work, motivated by applications in Unmanned Air Vehicles (UAV) and Micro Air Vehicles (MAV), we study experimentally the forces and flow fields around an oscillating blade at low Re (Re ~ 3 x 104). At these low Re, the flow even over the stationary blade can be quite different. We experimentally study the propensity of an isolated symmetric and cambered blade (with chord c) to undergo self-excited oscillations at high angles of attack and at low Reynolds numbers (Re ~ 30, 000). We force the blade, placed at large mean angle of attack, to undergo small amplitude pitch oscillations and measure the unsteady loads on the blade. From the measured loads, the direction and magnitude of energy transfer to/from the blade is calculated. Systematic measurements have been made for varying mean blade incidence angles and for different excitation amplitudes and frequencies (f). These measurements indicate that post stall there is a possibility of excitation of the blade over a range of Strouhal Numbers (St = fc/U) with the magnitude of the exciting energy varying with amplitude, frequency and mean incidence angles. In particular, the curves for the magnitude of the exciting energy against Strouhal number (St) are found to shift to higher St values as the mean angle of attack is increased. We perform the same set of experiments on two different blade shapes, namely NACA 0012 and a compressor blade profile, SC10. Both blade profiles show qualitatively similar phenomena. The flow around both the stationary and oscillating blades is studied through Particle Image Velocimetry (PIV). PIV measurements on the stationary blade show the gradual shift of the flow separation point towards the leading edge with increasing angle of attack, which occurs at these low Re. From PIV measurements on an oscillating blade near stall, we present the flow field around the blade at different phases of the blade oscillation. These show that the boundary layer separates from the leading edge forming a shear layer, which flaps with respect to the blade. As the Strouhal number is varied, the phase between the flapping shear layer and the blade appears to change. This is likely to be the reason for the observed change in the sign of the energy transfer between the flow and the blade that is responsible for stall flutter.

For time-varying signals such as speech and audio, short-time analysis becomes necessary to compute specific signal attributes and to keep track of their evolution. The standard technique is the short-time Fourier transform (STFT), using which one decomposes a signal in terms of windowed Fourier bases. An advancement over STFT is the wavelet analysis in which a function is represented in terms of shifted and dilated versions of a localized function called the wavelet. A specific modeling approach particularly in the context of speech is based on short-time linear prediction or short-time Wiener filtering of noisy speech. In most nonstationary signal processing formalisms, the key idea is to analyze the properties of the signal locally, either by first truncating the signal and then performing a basis expansion (as in the case of STFT), or by choosing compactly-supported basis functions (as in the case of wavelets). We retain the same motivation as these approaches, but use polynomials to model the signal on a short-time basis (“short-time polynomial representation”). To emphasize the local nature of the modeling aspect, we refer to it as “local polynomial modeling (LPM).” We pursue two main threads of research in this thesis: (i) Short-time approaches for speech enhancement; and (ii) LPM for enhancing smooth signals, with applications to ECG, noisy nonuniformly-sampled signals, and voiced/unvoiced segmentation in noisy speech. Improved iterative Wiener filtering for speech enhancement A constrained iterative Wiener filter solution for speech enhancement was proposed by Hansen and Clements. Sreenivas and Kirnapure improved the performance of the technique by imposing codebook-based constraints in the process of parameter estimation. The key advantage is that the optimal parameter search space is confined to the codebook. The Nonstationary signal enhancement solutions assume stationary noise. However, in practical applications, noise is not stationary and hence updating the noise statistics becomes necessary. We present a new approach to perform reliable noise estimation based on spectral subtraction. We first estimate the signal spectrum and perform signal subtraction to estimate the noise power spectral density. We further smooth the estimated noise spectrum to ensure reliability. The key contributions are: (i) Adaptation of the technique for non-stationary noises; (ii) A new initialization procedure for faster convergence and higher accuracy; (iii) Experimental determination of the optimal LP-parameter space; and (iv) Objective criteria and speech recognition tests for performance comparison. Optimal local polynomial modeling and applications We next address the problem of fitting a piecewise-polynomial model to a smooth signal corrupted by additive noise. Since the signal is smooth, it can be represented using low-order polynomial functions provided that they are locally adapted to the signal. We choose the mean-square error as the criterion of optimality. Since the model is local, it preserves the temporal structure of the signal and can also handle nonstationary noise. We show that there is a trade-off between the adaptability of the model to local signal variations and robustness to noise (bias-variance trade-off), which we solve using a stochastic optimization technique known as the intersection of confidence intervals (ICI) technique. The key trade-off parameter is the duration of the window over which the optimum LPM is computed. Within the LPM framework, we address three problems: (i) Signal reconstruction from noisy uniform samples; (ii) Signal reconstruction from noisy nonuniform samples; and (iii) Classification of speech signals into voiced and unvoiced segments. The generic signal model is x(tn)=s(tn)+d(tn),0 ≤ n ≤ N - 1. In problems (i) and (iii) above, tn=nT(uniform sampling); in (ii) the samples are taken at nonuniform instants. The signal s(t)is assumed to be smooth; i.e., it should admit a local polynomial representation. The problem in (i) and (ii) is to estimate s(t)from x(tn); i.e., we are interested in optimal signal reconstruction on a continuous domain starting from uniform or nonuniform samples. We show that, in both cases, the bias and variance take the general form: The mean square error (MSE) is given by where L is the length of the window over which the polynomial fitting is performed, f is a function of s(t), which typically comprises the higher-order derivatives of s(t), the order itself dependent on the order of the polynomial, and g is a function of the noise variance. It is clear that the bias and variance have complementary characteristics with respect to L. Directly optimizing for the MSE would give a value of L, which involves the functions f and g. The function g may be estimated, but f is not known since s(t)is unknown. Hence, it is not practical to compute the minimum MSE (MMSE) solution. Therefore, we obtain an approximate result by solving the bias-variance trade-off in a probabilistic sense using the ICI technique. We also propose a new approach to optimally select the ICI technique parameters, based on a new cost function that is the sum of the probability of false alarm and the area covered over the confidence interval. In addition, we address issues related to optimal model-order selection, search space for window lengths, accuracy of noise estimation, etc. The next issue addressed is that of voiced/unvoiced segmentation of speech signal. Speech segments show different spectral and temporal characteristics based on whether the segment is voiced or unvoiced. Most speech processing techniques process the two segments differently. The challenge lies in making detection techniques offer robust performance in the presence of noise. We propose a new technique for voiced/unvoiced clas-sification by taking into account the fact that voiced segments have a certain degree of regularity, and that the unvoiced segments do not possess any smoothness. In order to capture the regularity in voiced regions, we employ the LPM. The key idea is that regions where the LPM is inaccurate are more likely to be unvoiced than voiced. Within this frame-work, we formulate a hypothesis testing problem based on the accuracy of the LPM fit and devise a test statistic for performing V/UV classification. Since the technique is based on LPM, it is capable of adapting to nonstationary noises. We present Monte Carlo results to demonstrate the accuracy of the proposed technique.

The flow field and forces on an isolated oscillating NACA 0012 airfoil in a uniform flow is studied using viscous vortex particle method. The simulations are carried out at very low chord (c) based Reynolds number (Re=1000), motivated by the current interest in development of Micro Air Vehicles (MAV). The airfoil is forced to oscillate in both heave and pitch at different normalized oscillation frequencies (f), which is represented by the non-dimensional reduced frequency fc/U).( From the unsteady loading on the airfoil, the net energy transfer to the airfoil is calculated to determine the propensity for the airfoil to undergo self-induced oscillations or flutter at these very low Reynolds numbers. The simulations are carried out using a viscous vortex particle method that utilizes discrete vortex elements to represent the vorticity in the flow field. After validation of the code against test cases in the literature, simulations are first carried out for the stationary airfoil at different angles of attack, which shows the stall characteristics of the airfoil at this very low Reynolds numbers. For the airfoil oscillating in heave, the airfoil is forced to oscillate at different reduced frequencies at a large angle of attack in the stall regime. The unsteady loading on the blade is obtained at different reduced frequencies. This is used to calculate the net energy transfer to the airfoil from the flow, which is found to be negative in all cases studied. This implies that stall flutter or self-induced oscillations are not possible under the given heave conditions. The wake vorticity dynamics is presented for the different reduced frequencies, which show that the leading edge vortex dynamics is progressively more complex as the reduced frequency is increased from small values. For the airfoil oscillating in pitch, the airfoil is forced to oscillate about a large mean angle of attack corresponding to the stall regime. The unsteady moment on the blade is obtained at different reduced frequencies, and this is used to calculate the net energy transfer to the airfoil from the flow, which is found to be positive in all cases studied. This implies that stall flutter or self-induced oscillations are possible in the pitch mode, unlike in the heave case. The wake vorticity dynamics for this case is found to be relatively simple compared to that in heave. The results of the present simulations are broadly in agreement with earlier stall flutter studies at higher Reynolds numbers that show that stall flutter does not occur in the heave mode, but can occur in the pitch mode. The main difference in the present very low Reynolds number case appears to be the broader extent of the excitation region in the pitch mode compared to large Re cases studied earlier. region in the pitch mode compared to large Re cases studied earlier.

Après une présentation des notations usuelles de la théorie des graphes, on étudie l'ensemble des fonctions harmoniques sur les graphes, c'est à dire des fonctions dont le laplacien est nul. Ces fonctions forment un espace vectoriel et sur un graphe uniformément localement fini, on montre que cet espace vectoriel est soit de dimension un, soit de dimension infinie. Lorsque le graphe comporte une infinité de cycles, ce résultat tombe en défaut et on exhibe des exemples qui montrent qu'il existe un graphe sur lequel les harmoniques forment un espace vectoriel de dimension n, pour tout n. Un exemple de graphe périodique est également traité. Ensuite, toujours pour le laplacien, on étudie plus précisément sur les arbres uniformément localement finis les valeurs propres dont l'espace propre est de dimension infini. Dans ce cas, il est montré que l'espace propre contient un sous-espace isomorphe à l'ensemble des suites réelles bornées. Une inégalité concernant le spectre est donnée dans le cas spécial où les arêtes sont de longueur un. Des exemples montrent que ces inclusions sont optimales. Dans le chapitre suivant, on étudie le comportement asymptotique des valeurs propres pour des opérateurs elliptiques d'ordre 2 quelconques sous des conditions de Kirchhoff dynamiques. Après réécriture du problème sous la forme d'un opérateur de Sturm-Liouville, on écrit le problème de façon matricielle. Puis on trouve une équation caractéristique dont les zéros correspondent aux valeurs propres. On en déduit une formule pour l'asymptotique des valeurs propres. Dans le dernier chapitre, on étudie la stabilité de solutions stationnaires pour certains problèmes de réaction-diffusion où le terme de non linéarité est polynomial. / After a quick presentation of usual notations for the graph theory, we study the set of harmonic functions on graphs, that is, the functions whose laplacian is zero. These functions form a vectorial space. On a uniformly locally finite tree, we shaw that this space has dimension one or infinity. When the graph has an infinite number of cycles, this result change and we describe some examples showing that there exists a graph on which the harmonic functions form a vectorial space of dimension n, for all n. We also treat the case of a particular periodic graph. Then, we study more precisely the eigenvalues of infinite dimension. In this case, the eigenspace contains a subspace isomorphic to the set of bounded sequences. An inequality concerning the spectral is given when edges length is equal to one. Examples show that these inclusions are optimal. We also study the asymptotic behavior of eigenvalues for elliptic operators under dynamical Kirchhoff node conditions. We write the problem as a Sturm-Liouville operator and we transform it in a matrix problem. Then we find a characteristic equation whose zeroes correspond to eigenvalues. We deduce a formula for the asymptotic behavior. In the last chapter, we study the stability of stationary solutions for some reaction-diffusion problem whose the non-linear term is polynomial.