No description available.

No description available.

No description available.

No description available.

Submitted by Emanuel Varela Cardoso (emanuel.varela@ufcg.edu.br) on 2018-10-18T19:17:48Z No. of bitstreams: 1 MARIA APARECIDA DOS SANTOS – DISSERTAÇÃO (PPGFísica) 2014.pdf: 628300 bytes, checksum: be5188c733755263bec183578258ca27 (MD5) / Made available in DSpace on 2018-10-18T19:17:48Z (GMT). No. of bitstreams: 1 MARIA APARECIDA DOS SANTOS – DISSERTAÇÃO (PPGFísica) 2014.pdf: 628300 bytes, checksum: be5188c733755263bec183578258ca27 (MD5) Previous issue date: 2014-02 / Capes / Considerando as diferentes abordagens possíveis referentes ao Universo, este trabalho está voltado para o estudo da Cosmologia Padrão e Inflacionária utilizando campos escalares para descrever a fase de expansão acelerada do Universo. Assim, através da Teoria da Gravitação proposta pela Relatividade Geral é possível determinar as equações de Friedmann e utilizando a Teoria de Campos em Cosmologia podemos obter uma equação de movimento que descreve a evolução temporal de um campo escalar chamado ínflaton, responsável pela inflação. Nesse sentido, propomos como alternativa a utilização de alguns modelos de potenciais já existentes, dentre os quais: V ( ) =12m2 2 (quadr atico), V ( ) = C cos2 (tipo cosseno), V ( ) = C sin2 (tipo seno), V ( ) = (t) 4 e o potencial constante V = V0. Buscando dessa forma descrever a evolução temporal do fator de escala a(t) e o comportamento do parâmetro de desaceleração q(t) com o objetivo de analisar a fase inflacionária, identi cando regiões de aceleração e desaceleração do Universo nos cenários dos espaços plano e curvo. / Taking into consideration the set of di erent approaches to the Universe existent today this work focuses on standard cosmology and in ationary expansion of the said using scalar elds to describe the expansion acceleration rate. Therefore, through a gravitation theory proposed by General Relativity is possible to set Friedmann`s equations and using Field Theory applied to Cosmology to obtain an equation of motion which describes the temporal evolution of a scalar eld called in action, which is responsible for the in ationary process. In this sense, we propose as alternative some models whose potentials are already established, among them: V ( ) = 12m2 2 (quadratic), V ( ) = C cos2 (cosinelike) , V ( ) = C sin2 (sinelike), V ( ) = (t) 4 and the constant potential V = V0 . We seek with this to describe the temporal evolution of the scale factor a(t) and how the decelerating parameter behaves and then analyze the in ationary faze, indentifying periods when the Universe was accelerating or decelerating given curve or plane space scenarios.

Submitted by Emanuel Varela Cardoso (emanuel.varela@ufcg.edu.br) on 2018-11-07T19:11:33Z No. of bitstreams: 1 ELISAMA ERALDENE MARQUES LIMA – DISSERTAÇÃO (PPGFísica) 2014.pdf: 760068 bytes, checksum: 6115401533b8caeb632c4666b961caa1 (MD5) / Made available in DSpace on 2018-11-07T19:11:33Z (GMT). No. of bitstreams: 1 ELISAMA ERALDENE MARQUES LIMA – DISSERTAÇÃO (PPGFísica) 2014.pdf: 760068 bytes, checksum: 6115401533b8caeb632c4666b961caa1 (MD5) Previous issue date: 2014-09-26 / CNPq / Neste trabalho, estudamos as propriedades termodinâmicas da condensação de Bose-Einstein (CBE) para um gás de bósons relativísticos no contexto da teoria quântica de campos não-comutativa. Tais teorias foram introduzidas como uma generalização da mecânica quântica em um espaço-tempo não-comutativo. Nosso principal objetivo é investigar em que regimes de temperatura e/ou energia a não-comutatividade pode caracterizar algum comportamento distinto nas propriedades de um condensado de Bose-Einsteindes-crito por um gás bosônico relativístico. Usamos uma teoria baseada no conceito de campos não-comutativos, são introduzidos os parâmetros θ e σ que atuam como reguladores para a teoria, ambos desempenham um papel fundamental na modificação das relações de dispersão do campo bosônico não-comutativo em estudo, o que leva a possíveis consequências fenomenológicas. Expressões analíticas para a fração de partículas no condensado, energia interna, pressão e calor específico do sistema são obtidas através de aproximações baseadas em expansões nos parâmetros não-comutativos, cujos resultados são comparados com os obtidos através de cálculos numéricos. Os efeitos da não comutatividade nas propriedades do sistema são discutidos, então é encontrado que as modificações introduzidas nessa teorias e tornam mais relevantes no regime de altas temperaturas. / In this work, we study the thermo dynamic properties of the Bose-Einstein condensation (BEC) for a relativistic Bose gas in the context of the non commutative quantum field theory. Such theories was introduced as a generalization of quantum mechanics on a non commutative space time. Our main goal is to investigate in which temperature and/or energy regimes the non commutativity can characterize some influence in the properties of Bose-Einstein condensation described by a relativistic bosonic gas. We use a non com- mutative bosonic field theory introducing the non commutative parameters θ and σ. Both parameters play a key role in the modified dispersion relations of the non commutative bosonic field, leading to possibles triking consequences for phenomenology. Analytical expressions for the condensate fraction, internal energy, pressure and specifiche at of the system are obtained by expanding in a power series of the non commutative parameters. These results are compared with that one get by numerical methods. The non commuta- tive effects in the thermo dynamic properties of the system are discussed, then is found that the non commutativity exhibit caracteristics important at high temperature.

Made available in DSpace on 2015-05-14T12:13:59Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 989729 bytes, checksum: 3e97939bd59206a6ed90c89ca0467d17 (MD5) Previous issue date: 2011-05-20 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Cosmological models involving scalar fields allow the description of a phase of accelerated cosmic expansion and thus appear as a promising alternative for the study of the cosmic inflation and dark energy. We are interested here in analyzing these cosmological models. In particular, we will explore cosmological solutions based on the first order formalism. The inclusion of this method favors the search for analytic solutions with scalar fields in cosmology, and this is particularly important when we consider the component of nonrelativistic matter (dust) in the presence of dark energy, in order to construct a cosmological model capable of explaining, in good agreement with observational data, the current phase of cosmic acceleration. Considering a regime of Lorentz violation, the use of this method allowed us to verify that new considerations must be implemented so that the inflationary regime can now solve the problem of initial conditions. Another question of interest, which can be addressed with the aid of the first order formalism, takes into account the possibility of the dark energy equation of state parameter to be a constant other than −1 and in this case we get that a lot of fine-tuning is needed, which should be interpreted as strong evidence in favor of a dynamic model of dark energy. We also introduce the so-called deformation method on the slow-roll inflationary models, and we explore this framework in applications of current interest to this branch of research. / Modelos cosmológicos envolvendo campos escalares permitem a descrição de uma fase de expansão cósmica acelerada e, portanto, se apresentam como uma alternativa promissora no estudo da inflação cósmica e da energia escura. Estamos aqui interessados em analisar esses modelos cosmológicos; em especial, vamos explorar soluções cosmológicas baseadas no formalismo de primeira ordem. A inclusão desse método favorece a busca por soluções analíticas na cosmologia com campos escalares e isso é particularmente interessante no caso em que consideramos o componente de matéria não relativística (poeira) na presença da energia escura, afim de construir um modelo cosmológico capaz de explicar, em bom acordo com os dados observacionais, a atual fase de aceleração cósmica. Considerando um regime de violação de Lorentz, a utilização desse método nos permitiu verificar que novas considerações devem ser implementadas, para que o regime inflacionário possa resolver o problema das condições iniciais. Outra questão de interesse, que pode ser analisada com auxílio do formalismo de primeira ordem, leva em conta a possibilidade da equação de estado da energia escura ser um constante qualquer diferente de −1 e, nesse caso, obtemos que uma grande quantidade de ajuste fino é necessária, o que deve ser interpretado como uma forte evidência em favor de um modelo dinâmico de energia escura. Também introduzimos o chamado método de deformação a modelos inflacionários sob o regime de rolagem lenta e exploramos essa ferramenta em aplicações de corrente interesse na literatura.

Made available in DSpace on 2015-05-14T12:14:03Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 3752182 bytes, checksum: 63a51d4864db299b4b98e396d8d6e622 (MD5) Previous issue date: 2012-03-13 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work we do an investigation of new features of so-called k-defects, which are topological defects with non-canonical kinetic term. Specifically, we study a class of k-defects in models of scalar field theories distinct from standard theory but discribing, case to case, the very same defect structure with the very same energy density as that described by the theory governed by standard Lagrange density. In teories which presents such relationships, distinct models support the same topological structure; why call them of twinlike models. We then build a model of twin theory, which we call ALTW model, and find the relationships between them, including relations between the potentials of both, which, although distinct, they present minima that are connected by the same field solution, for the case of static and stable configurations. The results are ilustrated with several examples. In order to distinguish between theories, we analyze the situation in which the component T11 of the energy-momentum tensor is nonzero, which is equivalent to breaking the pressureless condition required to ensure stability of static solutions. With the same purpose of distinction, we did a study of linear stability of defects and we found that, although representing the same defect structure, case to case, a theory is not a simple reparametrization of the other. We also made an extension of the twin nature between more general models of real scalar field theries and an application to braneworld scenario. We also investigated the behavior twin between standard and tachyonic models in FRW cosmology, where the scalar field evolves over time. / No presente trabalho fazemos uma investigação de novas características dos chamados kdefeitos, que são defeitos topológicos com termo cinético não-canônico. Especificamente, estudamos uma classe de k-defeitos em modelos de teorias de campos escalares distintos da teoria padrão mas que descrevem, caso a caso, o mesmo defeito com a mesma densidade de energia daquele descrito pela teoria governada pela densidade lagrangiana padrão. Em teorias que apresentam tais relações, modelos distintos suportam a mesma estrutura topológica; daí chamá-los de modelos gêmeos. Construímos, então, um modelo de teoria gêmea, que denominamos modelo ALTW, e encontramos as relações existentes entre eles, incluindo as relações entre os potenciais de ambos, que, embora distintos, apresentam mínimos conectados pelo mesmo campo solução, para o caso de configurações estáticas e estáveis. Os resultados são ilustrados com vários exemplos. Com a finalidade de distinguir as teorias, analisamos a situação em que a componente T11 do tensor energia-momento é não-nula, o que é equivalente a quebrar a condição de pressão nula necessária para garantir a estabilidade das soluções estáticas. Com o mesmo objetivo de distinção, fizemos um estudo da estabilidade linear dos defeitos e obtivemos que, embora representem o mesmo defeito, caso a caso, uma teoria não é uma simples reparametrização da outra. Fizemos ainda uma extensão da natureza gêmea entre modelos mais gerais de teorias de campo escalar real e uma aplicação ao cenário de brana. Investigamos também o comportamento gêmeo entre os modelos padrão e taquiônico em cosmologia FRW, onde o campo escalar evolui com o tempo.

Scalar fields occur quite commonly in several application areas in both static and time-dependent forms. Hence a proper visualization of scalar fieldsneeds to be equipped with tools to extract and focus on important features of the data. Similarity detection and pattern search techniques in scalar fields present a useful way of visualizing important features in the data. This is done by isolating these features and visualizing them independently or show all similar patterns that arise from a given search pattern. Topological features are ideal for this purpose of isolating meaningful patterns in the data set and creating intuitive feature descriptors. The Merge Tree is one such topological feature which has characteristics ideally suited for this purpose. Subtrees of merge trees segment the data into hierarchical regions which are topologically defined. This kind of feature-based segmentation is more intelligent than pure data based segmentations involving windows or bounding volumes. In this thesis, we explore several different techniques using subtrees of merge trees as features in scalar field data. Firstly, we begin with a discussion on static scalar fields and devise techniques to compare features - topologically segmented regions given by the subtrees of the merge tree - against each other. Second, we delve into time-dependent scalar fields and extend the idea of feature comparison to spatio-temporal features. In this process, we also come up with a novel approach to track features in time-dependent data considering the entire global network of likely feature associations between consecutive time steps.The highlight of this thesis is the interactivity that is enabled using these feature-based techniques by the real-time computation speed of our algorithms. Our techniques are implemented in an open-source visualization framework Inviwo and are published in several peer-reviewed conferences and journals. / <p>QC 20171020</p>

Scalar fields are used in many disciplines to represent scalar quantities over some spatial domain. Their versatility and the potential to model a variety of real-world phenomena has made scalar fields a key part of modern data analysis. Examples range from modeling scan results in medical applications (e.g. Magnetic Resonance Imaging or Computer Tomography), measurements and simulations in climate and weather research, or failure criteria in material sciences. But one thing that all applications have in common is that the data is always affected by errors. In measurements, potential error sources include sensor inaccuracies, an unevenly sampled domain, or unknown external influences. In simulations, common sources of error are differences between the model and the simulated phenomenon or numerical inaccuracies. To incorporate these errors into the analysis process, the data model can be extended to include uncertainty. For uncertain scalar fields that means replacing the single value that is given at every location with a value distribution. While in some applications, the influence of uncertainty might be small, there are a lot of cases where variations in the data can have a large impact on the results. A typical example is weather forecasts, where uncertainty is a crucial part of the data analysis. With increasing access to large sensor networks and extensive simulations, the complexity of scalar fields often grows to a point that makes analysis of the raw data unfeasible. In such cases, topological analysis has proven to be a useful tool for reducing scalar fields to their fundamental properties. Scalar field topology studies structures that do not change under transformations like scaling and bending but only depend on the connectivity and relative value differences between the points of the domain. While a lot of research has been done in this area for deterministic scalar fields, the incorporation of uncertainty into topological methods has only gained little attention so far. In this thesis, several methods are introduced that deal with the topological analysis of uncertain scalar fields. The main focus lies on providing fundamental research on the topic and to drive forward a rigorous analysis of the influence of uncertainty on topological properties. One important property that has a strong influence on topological features are stochastic dependencies between different locations in the uncertain scalar field. In the first part of this thesis, we provide a method for extracting regions that show linear dependency, i.e. correlation. Using a combination of point-cloud density estimation, clustering, and scalar field topology, our method extracts a hierarchical clustering. Together with an interactive visualization, the user can explore the correlation information and select and filter the results. A major benefit of our approach is the comprehensive handling of correlation. This also includes global correlation between distant points and inverse correlation, which is often only partially handled by existing methods. The second part of this thesis focuses on the extraction of topological features, such as critical points or hills and valleys of the scalar field. We provide a method for extracting critical points in uncertain scalar fields and track them over multiple realizations. Using a novel approach that operates in the space of all possible realizations, our method can find all critical points deterministically. This not only increases the reliability of the results but also provides complete knowledge that can be used to study the relation and behavior of critical points across different realizations. Through a combination of multiple views, we provide a visualization that can be used to analyze critical points of an uncertain scalar field for real-world data. In the last part, we further extend our analysis to more complex feature types. Based on the well-known contour tree that provides an abstract view on the topology of a deterministic scalar field, we use an approach that is similar to our critical point analysis to extract and track entire regions of the uncertain scalar field. This requires solving a series of new challenges that are associated with tracking features in the multi-dimensional space of all realizations. As our research on the topic falls under the category of fundamental research, there are still some limitations that have to be overcome in the future. However, we provide a full pipeline for extracting topological features that ranges from the data model to the final interactive visualization. We further show the applicability of our methods to synthetic and real-world data. / Skalarfelder sind Funktionen, die jedem Punkt eines Raumes einen skalaren Wert zuweisen. Sie werden in vielen verschiedenen Bereichen zur Analyse von skalaren Messgrößen mit räumlicher Information eingesetzt. Ihre Flexibilität und die Möglichkeit, viele unterschiedliche Phänomene der realen Welt abzubilden, macht Skalarfelder zu einem wichtigen Werkzeug der modernen Datenanalyse. Beispiele reichen von medizinischen Anwendungen (z.B. Magnetresonanztomographie oder Computertomographie) über Messungen und Simulationen in Klima- und Wetterforschung bis hin zu Versagenskriterien in der Materialforschung. Eine Gemeinsamkeit all dieser Anwendungen ist jedoch, dass die erfassten Daten immer von Fehlern beeinflusst werden. Häufige Fehlerquellen in Messungen sind Sensorungenauigkeiten, ein ungleichmäßig abgetasteter Betrachtungsbereich oder unbekannte externe Einflussfaktoren. Aber auch Simulationen sind von Fehlern, wie Modellierungsfehlern oder numerischen Ungenauigkeiten betroffen. Um die Fehlerbetrachtung in die Datenanalyse einfließen lassen zu können, ist eine Erweiterung des zugrunde liegenden Datenmodells auf sogenannte \emph{unsicheren Daten} notwendig. Im Falle unsicherer Skalarfelder wird hierbei statt eines festen skalaren Wertes für jeden Punkt des Definitionsbereiches eine Werteverteilung angegeben, die die Variation der Skalarwerte modelliert. Während in einigen Anwendungen der Einfluss von Unsicherheit vernachlässigbar klein sein kann, gibt es viele Bereiche, in denen Schwankungen in den Daten große Auswirkungen auf die Resultate haben. Ein typisches Beispiel sind hierbei Wettervorhersagen, bei denen die Vertrauenswürdigkeit und mögliche alternative Ausgänge ein wichtiger Bestandteil der Analyse sind. Die ständig steigende Größe verfügbarer Sensornetzwerke und immer komplexere Simulationen machen es zunehmend schwierig, Daten in ihrer rohen Form zu verarbeiten oder zu speichern. Daher ist es wichtig, die verfügbare Datenmenge durch Vorverarbeitung auf für die jeweilige Anwendung relevante Merkmale zu reduzieren. Topologische Analyse hat sich hierbei als nützliches Mittel zur Verarbeitung von Skalarfeldern etabliert. Die Topologie eines Skalarfeldes umfasst all jene Merkmale, die sich unter bestimmten Transformationen, wie Skalierung und Verzerrung des Definitionsbereiches, nicht verändern. Hierzu zählen beispielsweise die Konnektivität des Definitionsbereiches oder auch die Anzahl und Beziehung von Minima und Maxima. Während die Topologie deterministischer Skalarfelder ein gut erforschtes Gebiet ist, gibt es im Bereich der Verarbeitung von Unsicherheit im topologischen Kontext noch viel Forschungspotenzial. In dieser Dissertation werden einige neue Methoden zur topologischen Analyse von unsicheren Skalarfeldern vorgestellt. Der wesentliche Teil dieser Arbeit ist hierbei im Bereich der Grundlagenforschung angesiedelt, da er sich mit der theoretischen und möglichst verlustfreien Verarbeitung von topologischen Strukturen befasst. Eine wichtige Eigenschaft, die einen starken Einfluss auf die Struktur eines unsicheren Skalarfeldes hat, ist die stochastische Abhängigkeit zwischen verschiedenen Punkten. Im ersten Teil dieser Dissertation wird daher ein Verfahren vorgestellt, das das unsichere Skalarfeld auf Regionen mit starker linearer Abhängigkeit, auch \emph{Korrelation} genannt, untersucht. Durch eine Kombination aus hochdimensionaler Punktwolkenanalyse, Clusterbildung und Skalarfeldtopologie extrahiert unsere Methode eine Hierarchie von Clustern, die die Korrelation des unsicheren Skalarfeldes repräsentiert. Zusammen mit einer interaktiven, visuellen Aufbereitung der Daten wird dem Nutzer so ein explorativer Ansatz zur Betrachtung der stochastischen Abhängigkeiten geboten. Anzumerken ist hierbei, dass unser Verfahren auch globale und inverse Korrelation abdeckt, welche in vielen verwandten Arbeiten oft nicht vollständig behandelt werden. Der zweite Teil dieser Dissertation widmet sich der Analyse und Extraktion von topologischen Merkmalen, wie kritischen Punkten oder ganzen Hügeln oder Tälern im Funktionsgraphen des Skalarfeldes. Hierzu wird ein Verfahren zur Berechnung von kritischen Punkten vorgestellt, das diese auch über viele verschiedene Realisierungen des unsicheren Skalarfeldes identifizieren und verfolgen kann. Dies wird durch einen neuen Ansatz ermöglicht, der den Raum aller möglichen Realisierungen nach geometrischen Strukturen untersucht und somit kritische Punkte deterministisch berechnen kann. Dadurch, dass mit diesem Verfahren keine kritischen Punkte ausgelassen werden, steigt nicht nur die Vertrauenswürdigkeit der Resultate, sondern es wird außerdem möglich, Beziehungen zwischen kritischen Punkten zu untersuchen. Zu diesen Beziehungen gehört beispielsweise das Wandern von kritischen Punkten über verschiedene Positionen oder auch die Entstehung von Skalarwerthügeln oder -tälern. Um die Resultate visuell zu untersuchen, stellen wir mehrere verknüpfte Ansichten bereit, die eine Analyse von kritischen Punkten auch in realen Daten ermöglichen. Im letzten Teil dieser Arbeit erweitern wir die Betrachtung der Topologie von kri\-ti\-schen Punkten auf komplexere Strukturen. Basierend auf dem \emph{Konturbaum}, der eine abstrakte Repräsentation der Topologie eines deterministischen Skalarfeldes ermöglicht, untersuchen wir, wie ganze Regionen des Skalarfeldes von Unsicherheit betroffen sind. Dies führt zu einer Reihe von neuen theoretischen und auch praktischen Herausforderungen, wie der stark steigenden Komplexität der notwendigen Berechnungen oder Inkonsistenzen bei der Verfolgung von topologischen Strukturen über mehrere Realisierungen. Auch wenn zur Anwendung unserer Verfahren auf reale Daten aufgrund des großen Möglichkeitsraumes von unsicheren Skalarfeldern noch Einschränkungen notwendig sind, sind viele der theoretischen Erkenntnisse allgemeingültig. Zur Betrachtung der Ergebnisse werden verschiedene Visualisierungen genutzt, um die extrahierten topologischen Strukturen anhand von synthetischen und realen Daten zu zeigen.