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31	Dynamics of few-cluster systems. Lekala, Mantile Leslie 30 November 2004 (has links) The three-body bound state problem is considered using configuration-space Faddeev equations within the framework of the total-angular-momentum representation. Different three-body systems are considered, the main concern of the investigation being the i) calculation of binding energies for weakly bounded trimers, ii) handling of systems with a plethora of states, iii) importance of three-body forces in trimers, and iv) the development of a numerical technique for reliably handling three-dimensional integrodifferential equations. In this respect we considered the three-body nuclear problem, the 4He trimer, and the Ozone (16 0 3 3) system. In practice, we solve the three-dimensional equations using the orthogonal collocation method with triquintic Hermite splines. The resulting eigenvalue equation is handled using the explicitly Restarted Arnoldi Method in conjunction with the Chebyshev polynomials to improve convergence. To further facilitate convergence, the grid knots are distributed quadratically, such that there are more grid points in regions where the potential is stronger. The so-called tensor-trick technique is also employed to handle the large matrices involved. The computation of the many and dense states for the Ozone case is best implemented using the global minimization program PANMIN based on the well known MERLIN optimization program. Stable results comparable to those of other methods were obtained for both nucleonic and molecular systems considered. / Physics / D.Phil. (Physics) Three-body bound state Configuration space Faddeev equations Total-angular- momentum representation Three-body forces Orthogonal spline collocation Weakly bounded trimers. 530.14 Three-body problem Configuration space Orthogonalization methods
32	Dynamics of few-cluster systems. Lekala, Mantile Leslie 30 November 2004 (has links) The three-body bound state problem is considered using configuration-space Faddeev equations within the framework of the total-angular-momentum representation. Different three-body systems are considered, the main concern of the investigation being the i) calculation of binding energies for weakly bounded trimers, ii) handling of systems with a plethora of states, iii) importance of three-body forces in trimers, and iv) the development of a numerical technique for reliably handling three-dimensional integrodifferential equations. In this respect we considered the three-body nuclear problem, the 4He trimer, and the Ozone (16 0 3 3) system. In practice, we solve the three-dimensional equations using the orthogonal collocation method with triquintic Hermite splines. The resulting eigenvalue equation is handled using the explicitly Restarted Arnoldi Method in conjunction with the Chebyshev polynomials to improve convergence. To further facilitate convergence, the grid knots are distributed quadratically, such that there are more grid points in regions where the potential is stronger. The so-called tensor-trick technique is also employed to handle the large matrices involved. The computation of the many and dense states for the Ozone case is best implemented using the global minimization program PANMIN based on the well known MERLIN optimization program. Stable results comparable to those of other methods were obtained for both nucleonic and molecular systems considered. / Physics / D.Phil. (Physics) Three-body bound state Configuration space Faddeev equations Total-angular- momentum representation Three-body forces Orthogonal spline collocation Weakly bounded trimers. 530.14 Three-body problem Configuration space Orthogonalization methods
33	Improvements in Genetic Approach to Pole Placement in Linear State Space Systems Through Island Approach PGA with Orthogonal Mutation Vectors Cassell, Arnold 01 January 2012 (has links) This thesis describes a genetic approach for shaping the dynamic responses of linear state space systems through pole placement. This paper makes further comparisons between this approach and an island approach parallel genetic algorithm (PGA) which incorporates orthogonal mutation vectors to increase sub-population specialization and decrease convergence time. Both approaches generate a gain vector K. The vector K is used in state feedback for altering the poles of the system so as to meet step response requirements such as settling time and percent overshoot. To obtain the gain vector K by the proposed genetic approaches, a pair of ideal, desired poles is calculate first. Those poles serve as the basis by which an initial population is created. In the island approach, those poles serve as a basis for n populations, where n is the dimension of the necessary K vector. Each member of the population is tested for its fitness (the degree to which it matches the criteria). A new population is created each “generation” from the results of the previous iteration, until the criteria are met, or a certain number of generations have passed. Several case studies are provided in this paper to illustrate that this new approach is working, and also to compare performance of the two approaches. Thesis University of North Florida UNF Parallel algorithms -- Testing Orthogonalization methods -- Testing Genetic algorithms -- Testing Linear systems Pole Placement Genetic Algorithm State Space Orthogonal Mutation Controls and Control Theory
34	Contribution à la théorie des ondelettes : application à la turbulence des plasmas de bord de Tokamak et à la mesure dimensionnelle de cibles / Contribution to the wavelet theory : Application to edge plasma turbulence in tokamaks and to dimensional measurement of targets Scipioni, Angel 19 November 2010 (has links) La nécessaire représentation en échelle du monde nous amène à expliquer pourquoi la théorie des ondelettes en constitue le formalisme le mieux adapté. Ses performances sont comparées à d'autres outils : la méthode des étendues normalisées (R/S) et la méthode par décomposition empirique modale (EMD).La grande diversité des bases analysantes de la théorie des ondelettes nous conduit à proposer une approche à caractère morphologique de l'analyse. L'exposé est organisé en trois parties.Le premier chapitre est dédié aux éléments constitutifs de la théorie des ondelettes. Un lien surprenant est établi entre la notion de récurrence et l'analyse en échelle (polynômes de Daubechies) via le triangle de Pascal. Une expression analytique générale des coefficients des filtres de Daubechies à partir des racines des polynômes est ensuite proposée.Le deuxième chapitre constitue le premier domaine d'application. Il concerne les plasmas de bord des réacteurs de fusion de type tokamak. Nous exposons comment, pour la première fois sur des signaux expérimentaux, le coefficient de Hurst a pu être mesuré à partir d'un estimateur des moindres carrés à ondelettes. Nous détaillons ensuite, à partir de processus de type mouvement brownien fractionnaire (fBm), la manière dont nous avons établi un modèle (de synthèse) original reproduisant parfaitement la statistique mixte fBm et fGn qui caractérise un plasma de bord. Enfin, nous explicitons les raisons nous ayant amené à constater l'absence de lien existant entre des valeurs élevées du coefficient d'Hurst et de supposées longues corrélations.Le troisième chapitre est relatif au second domaine d'application. Il a été l'occasion de mettre en évidence comment le bien-fondé d'une approche morphologique couplée à une analyse en échelle nous ont permis d'extraire l'information relative à la taille, dans un écho rétrodiffusé d'une cible immergée et insonifiée par une onde ultrasonore / The necessary scale-based representation of the world leads us to explain why the wavelet theory is the best suited formalism. Its performances are compared to other tools: R/S analysis and empirical modal decomposition method (EMD). The great diversity of analyzing bases of wavelet theory leads us to propose a morphological approach of the analysis. The study is organized into three parts. The first chapter is dedicated to the constituent elements of wavelet theory. Then we will show the surprising link existing between recurrence concept and scale analysis (Daubechies polynomials) by using Pascal's triangle. A general analytical expression of Daubechies' filter coefficients is then proposed from the polynomial roots. The second chapter is the first application domain. It involves edge plasmas of tokamak fusion reactors. We will describe how, for the first time on experimental signals, the Hurst coefficient has been measured by a wavelet-based estimator. We will detail from fbm-like processes (fractional Brownian motion), how we have established an original model perfectly reproducing fBm and fGn joint statistics that characterizes magnetized plasmas. Finally, we will point out the reasons that show the lack of link between high values of the Hurst coefficient and possible long correlations. The third chapter is dedicated to the second application domain which is relative to the backscattered echo analysis of an immersed target insonified by an ultrasonic plane wave. We will explain how a morphological approach associated to a scale analysis can extract the diameter information Ondelettes Principe d'incertitude de Heisenberg Pavage temps-Fréquence Moments Régularité Support compact Fonction d'échelle Fonction d'ondelette Approximations Détails Résolution Filtre QMF Coefficients de Daubechies Analyse Reconstruction Précurseur Algorithme de Mallat Convolution Décimation Symétrisation Orthogonalisation Gram Schmidt Filtres frontières Complexité Décomposition modale empirique Méthode R/S Analyse des fluctuations redressées Fractal Auto-Similarité Plasma Bruit Gaussien fractionnaire Mouvement Brownien fractionnaire Ultrason Wavelets Heisenberg uncertainty principle Time-Frequency tiles Vanishing moments Regularity Compact support Scaling function Wavelet function Approximations Details Resolution QMF filters Daubechies coefficients Analysis Reconstruction Precursor Mallat algorithm Convolution Decimation Mirroring Orthogonalization Gram Schmidt Boundary filters Complexity Empirical Modal Decomposition R/S method Detrended fluctuations Analysis Fractal Self-Similarity Plasma Fractional Gaussian noise Fractional Brownian motion Ultrasound 530.44 515.243 3

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