Mawson Lakes is a new suburban housing development, situated 12 kms from the city of Adelaide in South Australia. The developers, the Mawson Lakes Joint Venture (MLJV), and the local council, the City of Salisbury, intend to capture all stormwater entering the site and recondition all wastewater. The water will then be supplied to residents and businesses for non-potable usage. Modelling the behaviour of the Mawson Lakes catchment under extreme conditions such as drought and prolonged periods of high rainfall will allow the project team to determine optimal water management strategies for the catchment. -- abstract / Thesis (PhDMathematics)--University of South Australia, 2004.

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Despite the vast amount of delivered theoretical results, regarding the topic of controller design, more than 90% of the controllers used in industry (petro-chemical, pulp and paper, steel, mining, etc) are of PID type (P, PI, PII, PD). This shows the importance of progressing in the elaboration of methods that consider restricted complexity controllers for practical applications, and that are computationally simple. Iterative Feedback Tuning (IFT) stands out as a new solution that takes into account both constraints. It belongs to the family of model-free controller tuning methods. It was developed at Cesame in the nineties and, since then, many real applications of IFT have been reported. This algorithm minimizes a cost function by means of a stochastic gradient descent scheme. In spite of the fact that the method has had an unexpected success in the tuning of real processes, a number of issues had not been fully covered yet. This thesis focuses on two aspects of this set of uncovered theoretical points: the convergence rate of the algorithm and a robust estimation of its gradient. Optimal prefilters, left as a degree of freedom for the user in the first formulation of IFT, are computed at each experiment. Their application allows a reduction in the covariance of the gradient estimate. Depending on what particular aspect the user is interested in improving, one optimal prefilter is selected. Monte-Carlo simulations have shown an enhancement with regards to a constant prefilter. A flexible arm set-up mounted in our robotics laboratory is used as a test bed to compare a model-based controller design algorithm with a model-free controller tuning method. The comparison is performed with some specifications defined beforehand. The same set-up plus a couple of air-jets serves as a tester for our theoretical results, when the rejection of a perturbation is the ultimate objective. Both cases have confirmed the predicted good behaviour offered by IFT.

From the beginning of 20th century many studies proved randomness in price evolution of investment instruments. Therefore models respecting this randomness must be used in portfolio management. This thesis' aim is to provide basic theory regarding some of the stochastic methods and show their practical use in real situations.

Le bruit généré par l'impact du sillage de la soufflante avec les aubes du redresseur est une source prédominante des turboréacteurs en conditions d'approche, et la composante à large bande contribue fortement au niveau sonore global. Une méthode numérique basée sur un code CAA résolvant les équations d Euler est développée dans cette thèse afin d'estimer le bruit d'interaction entre un sillage turbulent et un aubage de géométrie quelconque. Le sillage amont est modélisé à l'aide d'une méthode stochastique supposant un spectre de turbulence homogène isotrope et une représentation spatiale simplifiée du champ de vitesse. Ces fluctuations de vitesse sont injectées dans le code CAA via des conditions aux limites adéquates. La méthode ainsi mise en place est validée dans un premier temps sur des cas d'interaction avec une plaque plane en comparant les résultats numériques aux solutions du modèle d'Amiet. Un chaınage avec une méthode intégrale est aussi réalisé pour estimer le rayonnement acoustique. La méthode numérique est ensuite mise en œuvre pour simuler la réponse acoustique d'un profil isolé avec un bord d'attaque ondulé conçu et testé dans la soufflerie de l'ISVR dans le cadre du projet européen FLOCON. Enfin, la méthodologie est étendue à des configurations de grilles d'aubes annulaires en conduit. Après une étape de validation sur des cas monofréquentiels issus d'un benchmark CAA, des simulations large bande sont réalisées, tout d'abord sur une configuration de grille d'aubes sans incidence (écoulement axial uniforme) testée en soufflerie au LMFA, puis sur une configuration plus complexe de grille d'aubes non chargée en écoulement tournant proposée par Atassi / Noise generation due to the rotor wakes impinging the stator vanes is a dominant turbofan source at approach conditions, and the broadband noise component is significantly contributing to the overall level. A numerical method based on a CAA code solving the Euler equations is developped in this thesis in order to simulate the interaction noise between a turbulent wake and a vane row without geometry restrictions. The upstream turbulent flow is synthesized using a stochastic approach by considering an homogeneous isotropic turbulence spectrum model and a simplified spatial representation of the velocity field. These velocity gusts are injected in the CAA code by implementing a suited boundary condition. The present methodology is first va- lidated against turbulence-flat plate interaction cases, by comparing the numerical predictions to Amiet model solutions. A chaining with an integral formulation is also performed to assess the acoustic far-field. Then, the method is used to estimate the acoustic response of an isolated airfoil with a wavy leading egde, designed and tested in ISVR wind tunnel in the framework of European FLOCON project. Finally, the computations are extended to ducted annular grid configurations. After a validation step on single-frequency cases described in a CAA benchmark, broadband noise simulations are performed, firstly on a flat-plate annular grid in a uniform axial flow tested in the LMFA wind tunnel, and then on a more complex configuration related to an unloaded grid in a swirling mean flow proposed by Atassi

Nesta tese, mostramos que o modelo estocástico binário para expressão gênica, por um gene auto-regulado, possui solução completa. A solução dependente do tempo é escrita via expansão em termos das funções de Heun confluentes. Apresentamos um exemplo de dinâmica estocástica desse gene. Para tal, desenvolvemos uma relação de recorrência entre derivadas arbitrárias das funções de Heun confluentes. Mostramos também que o regime estacionário deste modelo possui simetria de Lie SO(2, 1) tipo Lorentz. Esta simetria é análoga à simetria do momento angular, porém com um sinal errado. O invariante desta álgebra define a meia-vida relativa do regime dinâmico do gene. O equivalente do momento angular azimutal é uma medida indireta do nível de atividade do gene. Os operadores levantamento e abaixamento conectam diferentes processos estocásticos de expressão proteínica. As flutuações destes processos estocásticos são classificadas em termos das relações entre os etiquetadores de um elemento da representação da álgebra. No arcabouço da teoria dos grupos, o modelo estocástico para um gene externamente regulado aparece como um caso particular do modelo para um gene auto-regulado. Mostramos, por fim, uma comparação entre estas duas estratégias de regulação. Demonstramos que um gene auto-regulado pode expressar proteínas em regimes sub Poisson, Poisson ou super Poisson. Por seu turno, o gene externamente regulado somente expressa proteínas em regimes Poisson ou super Poisson. Portanto, num processo estocástico, a auto-regulação mostra-se como uma forma de controle mais precisa. Também mostramos que a dinâmica de genes auto-regulados possui meia-vida mais curta que a de genes externamente regulados. Ou seja, a auto-regulação permite respostas mais rápidas à perturbações externas. / In this thesis we show that the stochastic binary model to protein synthesis by na auto-regulated gene is completely solvable. The time-dependent solution is written in terms of the confluent Heun functions. We present an example of probability dynamics to this gene. To get that, we developed a recurrence relation between arbitrary derivatives of the confluent Heun functions. We also show the existence of a Lorentz-like Lie symmetry SO(2, 1). This is an analogous to the angular momentum symmetry but presenting one wrong sign in its preserved form. This invariant defines the relative half-life of the dynamical regime of the gene. The equivalent of the azimuth angular momentum measures indirectly the activity level of the gene. The ladder operators connect distinct stochastic processes of protein synthesis. The fluctuations of these processes are classified in terms of the relation between labeling numbers of a representation of the algebra. In the group theory formalism, the stochastic model to an externally regulated gene is a particular case of the model to an auto-regulated gene. We compare these two gene regulation strategies, and show that the auto-regulated gene can synthesize proteins into the super Poisson, Poisson, and sub Poisson fluctuating regimes. The externally regulated gene only presents the super Poisson and Poisson regimes. Therefore, the auto-regulation is responsible for a more precise control of gene expression. We also show that the dynamics of the auto-regulated genes has a shorter half-life. Thus, the auto-regulation permits faster responses of the system to external perturbation.

Conselho Nacional de Desenvolvimento Científico e Tecnológico / O estudo dos diferentes fenômenos de separação tem sido cada vez mais importante para os diferentes ramos da indústria e ciência. Devido à grande capacidade computacional atual, é possível modelar e analisar os fenômenos cromatográficos a nível microscópico. Os modelos de rede vêm sendo cada vez mais utilizados, para representar processos de separação por cromatografia, pois através destes pode-se representar os aspectos topológicos e morfológicos dos diferentes materiais adsorventes disponíveis no mercado. Neste trabalho visamos o desenvolvimento de um modelo de rede tridimensional para representação de uma coluna cromatográfica, a nível microscópico, onde serão modelados os fenômenos de adsorção, dessorção e dispersão axial através de um método estocástico. Também foram utilizadas diferentes abordagens com relação ao impedimento estérico Os resultados obtidos foram comparados a resultados experimentais. Depois é utilizado um modelo de rede bidimensional para representar um sistema de adsorção do tipo batelada, mantendo-se a modelagem dos fenômenos de adsorção e dessorção, e comparados a sistemas reais posteriormente. Em ambos os sistemas modelados foram analisada as constantes de equilíbrio, parâmetro fundamental nos sistemas de adsorção, e por fim foram obtidas e analisadas isotermas de adsorção. Foi possível concluir que, para os modelos de rede, os fenômenos de adsorção e dessorção bastam para obter perfis de saída similares aos vistos experimentalmente, e que o fenômeno da dispersão axial influência menos que os fenômenos cinéticos em questão / The study of different phenomena of separation has been most important for the different areas of industry and science. Due to the large computational available, we can model and analyze the chromatographic phenomena at the microscopic level. The network model has been most used to represent processes of separation by chromatography, because through them we are able represent the topological and morphological aspects of different adsorbent materials available on the market. In this work we aim at studying the dynamics of percolation chromatography through the phenomenology of adsorption, desorption and axial dispersion. In this work we aim to develop a three-dimensional network model representation of a chromatographic column, microscopic level, which will model the phenomena of adsorption, desorption and axial dispersion through a stochastic method. After that, a two-dimensional network model is used to represent a system of adsorption in batch, keeping the modeling of the adsorption / desorption, and then compare to real systems. In both systems modeled are analyzed the equilibrium constant, the basic parameter in the adsorption systems, and at the end are obtained and analyzed adsorption isotherms. We concluded for the network models the phenomena of adsorption and desorption were sufficient to obtain output profiles similar to those seen experimentally, the phenomenon of axial dispersion effect unless the kinetic phenomena in question.

The generation of multigroup neutron cross sections is usually the first step in the solution of reactor physics problems. This typically includes generating condensed cross section sets, collapsing the scattering kernel, and within the context of diffusion theory, computing diffusion coefficients that capture transport effects as accurately possible. Although the calculation of multigroup parameters has historically been done via deterministic methods, it is natural to think of using the Monte Carlo method due to its geometric flexibility and robust computational capabilities such as continuous energy transport. For this reason, a stochastic cross section generation method has been implemented in the Mont Carlo code MCNP5 (Brown et al, 2003) that is capable of computing macroscopic material cross sections (including angular expansions of the scattering kernel) for transport or diffusion applications. This methodology includes the capability of tallying arbitrary-order Legendre expansions of the scattering kernel. Furthermore, several approximations of the diffusion coefficient have been developed and implemented. The accuracy of these stochastic diffusion coefficients within the multigroup framework is investigated by examining a series of simple reactor problems.

Mawson Lakes is a new suburban housing development, situated 12 kms from the city of Adelaide in South Australia. The developers, the Mawson Lakes Joint Venture (MLJV), and the local council, the City of Salisbury, intend to capture all stormwater entering the site and recondition all wastewater. The water will then be supplied to residents and businesses for non-potable usage. Modelling the behaviour of the Mawson Lakes catchment under extreme conditions such as drought and prolonged periods of high rainfall will allow the project team to determine optimal water management strategies for the catchment. One of the problems facing the team is the prediction of future rainfall patterns and the typical form of extreme events. In this thesis I have used historical records to construct synthetic rainfall data that will allow the project team to investigate a wide range of typical behaviour. The Gamma distribution has been widely used to approximate the probability density function (PDF) of monthly rainfall totals. However, there is no natural way to extend this method directly to obtain a joint PDF for rainfall densities associated with two or more months, unless the monthly totals are independent. I propose a modified method to construct a suitable PDF using parameters from the maximum likelihood estimate for a marginal Gamma distribution and a series of associated Laguerre polynomials. This series of special functions allows us to match the correlation between monthly totals and to match the observed moments with any level of precision needed. The joint PDF for two months is constructed using a sum of products of associated Laguerre polynomials. In order to get an analytic expression for the marginal distributions and the associated cumulative probabilities, it is convenient to use a weighted total and a weighted proportion contributed from the first month. The method makes extensive use of well-known formulae from the theory of special functions. The cumulative marginal probability density for the weighted total and the cumulative conditional probability density for the weighted proportion are used to generate simulated rainfall totals for each month in a two month period. In theory the simulated data is statistically identical to the observed data. In practice we apply standard statistical methods to check that the simulated data is consistent with the observed data. This method can be extended to the general case of any number of months, but computationally is restricted to only three. For this reason an alternative method is proposed to generate synthetic data for more than three months, which uses groups and subgroups of months, but still retains the characteristics of the original PDF. Although the series method could also be used to model a sequence of days, I propose an alternative method using Markov processes. This method will match a sequence of daily totals, generated from a probability transition matrix, to the monthly total generated by the series method. This methodology allows the research team to simulate certain special cases such as droughts and prolonged periods of high rainfall. These unusual events are of great interest in catchment planning and management. / thesis (PhDMathematics)--University of South Australia, 2004.

Conselho Nacional de Desenvolvimento Científico e Tecnológico / O estudo dos diferentes fenômenos de separação tem sido cada vez mais importante para os diferentes ramos da indústria e ciência. Devido à grande capacidade computacional atual, é possível modelar e analisar os fenômenos cromatográficos a nível microscópico. Os modelos de rede vêm sendo cada vez mais utilizados, para representar processos de separação por cromatografia, pois através destes pode-se representar os aspectos topológicos e morfológicos dos diferentes materiais adsorventes disponíveis no mercado. Neste trabalho visamos o desenvolvimento de um modelo de rede tridimensional para representação de uma coluna cromatográfica, a nível microscópico, onde serão modelados os fenômenos de adsorção, dessorção e dispersão axial através de um método estocástico. Também foram utilizadas diferentes abordagens com relação ao impedimento estérico Os resultados obtidos foram comparados a resultados experimentais. Depois é utilizado um modelo de rede bidimensional para representar um sistema de adsorção do tipo batelada, mantendo-se a modelagem dos fenômenos de adsorção e dessorção, e comparados a sistemas reais posteriormente. Em ambos os sistemas modelados foram analisada as constantes de equilíbrio, parâmetro fundamental nos sistemas de adsorção, e por fim foram obtidas e analisadas isotermas de adsorção. Foi possível concluir que, para os modelos de rede, os fenômenos de adsorção e dessorção bastam para obter perfis de saída similares aos vistos experimentalmente, e que o fenômeno da dispersão axial influência menos que os fenômenos cinéticos em questão / The study of different phenomena of separation has been most important for the different areas of industry and science. Due to the large computational available, we can model and analyze the chromatographic phenomena at the microscopic level. The network model has been most used to represent processes of separation by chromatography, because through them we are able represent the topological and morphological aspects of different adsorbent materials available on the market. In this work we aim at studying the dynamics of percolation chromatography through the phenomenology of adsorption, desorption and axial dispersion. In this work we aim to develop a three-dimensional network model representation of a chromatographic column, microscopic level, which will model the phenomena of adsorption, desorption and axial dispersion through a stochastic method. After that, a two-dimensional network model is used to represent a system of adsorption in batch, keeping the modeling of the adsorption / desorption, and then compare to real systems. In both systems modeled are analyzed the equilibrium constant, the basic parameter in the adsorption systems, and at the end are obtained and analyzed adsorption isotherms. We concluded for the network models the phenomena of adsorption and desorption were sufficient to obtain output profiles similar to those seen experimentally, the phenomenon of axial dispersion effect unless the kinetic phenomena in question.