O comportamento critico de sistemas unidimensionais de spin do tipo Z(N) na ausência de campos magnéticos, é estudado sob a luz da teoria do grupo de renormalização. Os modelos são resolvidos exatamente pelo método da matriz de transferência e expressões para as funções de correlação e susceptibilidade (a campo zero) por si tio são também calculadas. As transformações do grupo de renormalização são efetuadas através de um traço parcial na função de partição, obtendo- se um conjunto de relações de recorrência que podem ser escritas de maneira simples para qualquer valor inteiro do fator de reescala espacial, mediante o uso de campos de escala convenientes. Tirando vantagem de um ponto fixo inteiramente atrativo, calculamos uma expressão para a energia livre por sitio, exata para T ¢ O. Analisamos o comportamento de nossos modelos no espaço de parâmetros, onde identificamos em particular as ~s ferro e antiferromagnéticas. O problema de correções às previsões de escala em termos de campos de escala não lineares é discutido. Aventamos também a possibilidade de calcular os auto valores da matriz de transferência através dos campos não lineares / In this work we study the criticai behaviour of one dimensional Z(N) spin systems in zero magnetic fields, using the approach of the renormalization group (RG) theory. The models are solved by the transfer matrix method and expressions for the correlation functions and zero field susceptibility per site are found. The RG transformations are carried out via a partial trace over the partition function and one obtains a set of recursion relations which, with the use of a convenient set of scaling fields, are written out in a simple manner for any integer value of the spatial rescaling factor. Using a totaly attractive fixed point we calculate an expression for the free energy per site, valid exactly for non zero values of the temperature. We analyse the behaviour of our models in the space of parameters, identifying in particular ferro and antiferromagnetic regions. The problem of corrections to scaling in terms of nonlinear scaling fields is discussed and a possibility of finding the eigen values of the transfer matrix from such fields is contemplated

O entendimento de quebra espontânea de simetria é um problema importante para o estudo de fenômenos na evolução de sistemas abertos, tanto em física quanto em química, como também na biologia. Aqui estudamos um método a mais para este tipo de análise, usando conceitos de sistemas dinâmicos com simetria. O sistema dinâmico escolhido é discreto, isto é, realizado por iteração de um difeomorfismo equivariante sob a ação de um grupo compacto, neste caso um grupo finito do tipo Dm. Especificamente, investigamos o comportamento de atratores caóticos sob a variação dos parâmetros. / The understanding of spontaneous symmetry breaking is an important problem in the study of phenomena in the evolution of open systems, in physics and chemistry as well as in biology. Here we study another method for this kind of analysis, using concepts from dynamical systems with symmetry. The chosen dynamical system is discrete, that is, realized by iteration of an equivariant diffeomorphism under the action of a compact group, in this case one of the finite groups of type Dm. Specifically, we investigate the behavior of chaotic attractors under variation of the parameters.

Apresentamos um estudo do setor da quebra espontânea de simetria da teoria eletrofraca através do formalismo de lagrangianas quirais, analisando os operadores que geram vértices anômalos genuinamente quárticos entre os bósons de gauge, os quais podem ser sondados pela próxima geração de aceleradores: LHC e NLC. Com o objetivo de obter vínculos aos acoplamentos anômalos relativos a esses operadores, estudamos as reações e POT. +e POT. - W POT. + W POT. Z e e POT. +e POT. - ZZZ no NLC operando com energias no centro de massa de s = 0.5 TeV e 1 TeV, estendendo as nossas análises para a colisão com o feixe de elétrons polarizado. Avaliamos também o impacto desses mesmos acoplamentos ao processo pp VV + 2 jatos (V = W±, Z) no LHC. No intuito de desenvolver cálculos realísticos, todas as amplitudes de espalhamento das reações estudadas foram determinadas sem qualquer tipo de aproximação. / We present a study of electroweak symmetry breaking sector in the framework or chiral Lagrangians, analyzing the operators that lead to genuine quartic gauge boson couplings, which could be probed by the next generation accelerators; LHC and NLC. In order to get bounds on the anomalous couplings related to these operators, we studied the reactions e+e- W+W-Z and e+e- ZZZ at the NLC operating with center-or-mass energy of s = 0.5 TeV and 1 TeV, extending our analysis to polarized electron beam collisions. We also estimate the impact of these couplings to the process pp VV + 2 jets (V = W±, Z) at the LHC. In order to develop realistic calculations, all the scattering amplitudes considered have been determined without any kind of approximation.

Orientador: Marco Antonio Teixeira / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-13T09:38:10Z (GMT). No. of bitstreams: 1 Mereu_AnaCristinadeOliveira_D.pdf: 1463250 bytes, checksum: 9bbe3e5b625f68effb7acc05409359ea (MD5) Previous issue date: 2009 / Resumo: Este trabalho é voltado ao estudo de existência e persistência de órbitas periódicas e órbitas homoclínicas em perturbações de sistemas dinamicos reversíveis. Primeiramente, rompemos a reversibilidade de centros no plano e em dimensões superiores e detectamos condições para a existência de ciclos limites e toros invariantes. A seguir, estudamos a existência de soluções periódicas simétricas de perturbações de uma família de equações diferencias reversíveis. A existência e persistência de órbitas homoclínicas em tais equações também foram discutidas. / Abstract: In this work we study the existence and persistence of some minimal sets in perturbations of reversible systems. First we make non reversible perturbations of centers in R2 and R4 and we detect conditions for the existence of limit cycles and invariant tori. We study the existence of periodic solutions of the perturbations of a family of di_erential equations expressed by x(2n) + a (2n-2)/2 +¿+ a1x(2) + x = 0 ; for n = 2; 3. The existence and persistence of homoclinic orbits in such equations are also discussed. / Doutorado / Geometria e Topologia / Doutor em Matemática

O termo sigma do núcleon, $sigma_N$, pode ser extraído dos dados experimentais e permite testar teorias e modelos que buscam descrever os efeitos da quebra explícita de simetria quiral sobre o núcleon. A teoria de perturbação quiral é considerada atualmente a teoria efetiva da cromodinâmica quântica, sendo destinada a descrever o regime de baixas energias das interações fortes. Neste contexto, a expansão do termo sigma do núcleon em função da massa do píon depende das chamadas constantes de baixa energia, que devem ser extraídas da experiência. Neste trabalho apresentamos um modelo em que se elimina este tipo de dependência e fornece valores para $sigma_N$ e o termo sigma da delta, $sigma_Delta$, a partir de parâmetros conhecidos. No caso deste último, este procedimento é particularmente importante, porque não é possível extrair $sigma_Delta$ a partir da experiência, apesar desta grandeza ser fundamental para a obtenção de amplitudes na teoria de perturbação quiral, quando a delta aparece como grau de liberdade explícito. Variando as constantes de acoplamento entre os bárions e o píon, obtivemos resultados nos intervalos 43~MeV~$leq sigma_N leq$~49~MeV e 28~MeV~$leq sigma^R_Delta leq$~32~MeV, compatíveis com resultados de outros grupos. Pela possibilidade da delta decair, o seu termo sigma possui uma parte imaginária, a qual usamos para testar a consistência dos nossos resultados. Analisamos também a contagem de potências e o limite quiral, que mostraram o acordo entre a nossa expansão e a tirada da teoria de perturbação quiral. / The nucleon sigma term, $sigma_N$, may be extracted from experimental data and allows theories and models aimed at describing chiral symmetry breaking effects to be tested. At present, chiral perturbation theory is considered the effective theory of quantum chromodynamics at low energies. With this theory, one can obtain an expansion of $sigma_N$ in terms of the pion mass, involving low energy constants, which must be obtained from experiment. In this work we present a model that yields values for both $sigma_N$ and the delta sigma term, $sigma_Delta$, as functions of known parameters only. In the case of $sigma_Delta$, this procedure is particularly relevant, because $sigma_Delta$ is an important quantity in the evaluation of theoretical amplitudes and it is impossible to take it from experimental data. Several choices for pion-baryon coupling constants were used and our results lie in the intervals 43~MeV~$leq sigma_N leq$~49~MeV e 28~MeV~$leq sigma^R_Delta leq$~32~MeV, which are compatible with values produced by other groups. As the delta can decay, its sigma term has an imaginary part that we used to test the consistency of our calculations. The power counting in the chiral limit of our results is consistent with chiral perturbation theory.

Dans cette thèse, nous étudions la structure asymptotique de la gravité à trois dimensions d’espace-temps avec et sans constante cosmologique.La première partie de la thèse présente en détails les propriétés fondamentales de la gravité à trois dimensions pour des espaces à constante cosmologique négative, ou espaces de types Anti-de Sitter (AdS). Nous introduisons le formalisme de Chern-Simons pour la gravité en utilisant la formulation dite du premier ordre pour cette dernière. Nous présentons également les conditions aux bords dites de Brown-Henneaux et le calcul associé de l’algèbre des charges de surface. Enfin, nous décrivons les étapes de la réduction du modèle de Chern-Simons à un modèle de Wess-Zumino-Witten puis à celui d’une théorie de Liouville. La relevance de cette théorie dans le calcul microscopique de l’entropie d’un trou noir à trois dimensions est également discutée.La seconde partie de la thèse contient les contributions originales. Tout d’abord, nous étendons l’analyse de la dynamique asymptotique de la supergravité à trois dimensions au cas d’une constante cosmologique nulle. Nous montrons que l’algèbre des charges de surface associée est une extension supersymétrique de l’algèbre BMS, et construisons la théorie bidimensionnelle située au bord de l’espace-temps qui possède cette symétrie. Le second résultat est l’obtention d’une symétrie de dimension infinie au voisinage de l’horizon d’événements d’un trou noir tridimensionnel non extrême. Troisièmement, nous discutions le cas d’une constante cosmologique positive et montrons l’existence d’une théorie de Liouville euclidienne duale à la gravité d’Einstein avec des conditions aux bords de Dirichlet dans le patch statique. Enfin, nous explorons un autre cadre dans lequel des symétries de dimension infinie apparaissent pour des espaces temps qui non sont pas du type Anti-de Sitter. Nous considérons pour cela des déformations de ces derniers, connus sous le nom d’espaces-temps Warped Anti-de Sitter. Nous montrons que ces déformations admettent une algèbre de surface donnée par une somme semi-direct entre une algèbre de Virasoro et une algèbre affine de Kac-Moody, avec extensions centrales non nulles. Nous montrons que les configurations du trou noir hôte des espaces-temps Warped s’organisent en termes de deux algèbres de Virasoro. Nous identifions les générateurs associés qui décrivent les représentations de la théorie duale et, en appliquant une formule de Cardy, nous prouvons qu’un calcul microscopique reproduit correctement l’entropie de ces trous noirs. Nous étendons ce résultat à des conditions aux bords plus générales qui incluent de nouvelles solutions associés à des degrés de liberté locaux, des gravitons massifs contenus dans le volume d’espace-temps. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

In current mammography practice, radiologists typically view mammograms in a symmetric, side-by-side, configuration in the belief that abnormalities will be made salient because they break the perceived symmetry. The literature on the use of symmetry as an aid to signal detection is limited and this thesis has taken a psychophysical approach to investigate the radiologist’s task of detecting a small mass (a blob) in paired mammogram backgrounds. Initial experiments used Gaussian white noise and synthetic mammogram backgrounds to test observer performance for the radiologist’s task using symmetric (side-by-side) displays and animated (the two images of a pair alternated sequentially in the same location) displays. The use of animated displays was then tested using real mammogram backgrounds in the subsequent experiments. The results showed that side-by-side presentation of paired images does not provide any benefit for the detection of a blob, whereas, alternated presentation enabled the observer to use the correlation present between the paired images to improve detection performance. The effect of alternation was not evident when applied to the task of detecting a small mass in real mammogram pairs and subsequent investigation suggested that the loss of effect resulted from the lack of scale invariance of real images. This meant that, regardless of the level of global correlation between two images, the localised correlation, at a region size reflecting the visual angle subtended by the fovea, was much lower. Thus, decorrelation by the visual system was ineffective and performance for the detection of a blob in the paired images was also ineffective. This thesis suggests that, whilst animated displays can be a powerful tool for the identification of differences between paired images, the underpinning mechanism of decorrelation makes them unsuited for mammograms where scale invariance means that correlation at local levels is a fraction of the global correlation level.

Group Representation Theory is the mathematical language best suited to describing the symmetry properties of a structure, and a structural analysis can utilises Group Representation Theory to provide the most efficient and systematic method of exploiting the full symmetry properties of any symmetric structure. Group Representation Theory methods currently exist for the Stiffness Niethod of structural analysis, where the stiffness matrix of a structure is block-diagonalised into a number of independent submatrices, each of which relates applied loads and displacements with a particular type of symmetry. This dissertation extends the application of Group Representation Theory to the equilibrium and compatibility matrices which are commonly used in the Force Method of structural analysis. Group Representation Theory is used to find symmetry-adapted coordinate systems for both the external vector space which is suitable for representing the loads applied to a structure, and the internal vector space wh",t-k is-suitable for representing the internal forces. Using these symmetry-adapted coordinate systems the equilibrium matrix is block-diagonalised into a number of independent submatrix blocks, thus decomposing the analysis into a number of subproblems which require less computational effort. Each independent equilibrium submatrix block relates applied loads and internal forces with particular symmetry properties, and hence any states of self-stress or inextensional mechanisms in one of these equilibrium submatrix blocks will necessarily have ~rresponding symmetry properties. Thus, a symmetry analysis provides valuable insight into the behaviour of symmetric structures by helping to identify and classif:)'. any states of self-stress .or inextensional mechanisms present in a structure. In certain cases it is also possible for a symmetry analysis to identify when a structure contains a :ijnite rather than infinitesimal mechanism. To do this a symmetry analysis must b~ carried out using the symmetry properties of the inextensional mechanism of interest. If the analysis shows that any states of self-stress which exist in the structure have "lesser" symmetry properties, then the states of self-stress exist independently from the mechanism and cannot prevent its finite motion.

Scalar fields are used to represent physical quantities measured over a domain of interest. Study of symmetric or repeating patterns in scalar fields is important in scientific data analysis because it gives deep insights into the properties of the underlying phenomenon. This thesis proposes three methods to detect symmetry in scalar fields. The first method models symmetry detection as a subtree matching problem in the contour tree, which is a topological graph abstraction of the scalar field. The contour tree induces a hierarchical segmentation of features at different scales and hence this method can detect symmetry at different scales. The second method identifies symmetry by comparing distances between extrema from each symmetric region. The distance is computed robustly using a topological abstraction called the extremum graph. Hence, this method can detect symmetry even in the presence of significant noise. The above methods compare pairs of regions to identify symmetry instead of grouping the entire set of symmetric regions as a cluster. This motivates the third method which uses a clustering analysis for symmetry detection. In this method, the contours of a scalar field are mapped to points in a high-dimensional descriptor space such that points corresponding to similar contours lie in close proximity to each other. Symmetry is identified by clustering the points in the descriptor space. We show through experiments on real world data sets that these methods are robust in the presence of noise and can detect symmetry under different types of transformations. Extraction of symmetry information helps users in visualization and data analysis. We design novel applications that use symmetry information to enhance visualization of scalar field data and to facilitate their exploration.

Dissipative spots are found in physical experiments of many branches of natural science. In this thesis we use three-component reaction-diffusion systems on two-dimensional domains in order to generate these patterns. Using a dynamical system approach we proceed with a Fourier analysis on a linearized reaction-diffusion system in order to provide the bifurcation conditions for a given homogeneous state. We validate our results and establish it's limitations through numerical experiments. We report very interesting behavior during these simulations, notably hysteresis and multi-stability. We will then turn our attention to the relatively unexplored phenomenon of rotating spots. Based on previous work done for spiral waves, we investigate the effect of translational symmetry-breaking on a rotating spot mainly through careful numerical analysis.