Tesis: "Modelos de bianchi"

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MATEUS, Dairo Antonio Cuellar. "Considerações Sobre a Anisotropia em Modelos Bianchi Tipo I". reponame:Repositório Institucional da UNIFEI, 2018. http://repositorio.unifei.edu.br/xmlui/handle/123456789/1149.

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Neste trabalho apresentamos uma introdução matemática ao estudo de modelos cosmológicos espacialmente homogêneos, em especial aos modelos Bianchi tipo I, que são espacialmente planos. Neste caso analisamos como a geometria espacial evolui sob certas condições da anisotropia. Ao fi nal analisamos a possibilidade destes modelos substituirem o modelo Robertson-Walker plano com constante cosmológica.

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2

Fay, Stéphane. "Cosmologies spatialement homogènes en théories tenseur-scalaires". Phd thesis, Université Paris-Diderot - Paris VII, 2004. http://tel.archives-ouvertes.fr/tel-00008063.

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Cette thèse étudie les modèles cosmologiques homogènes mais anisotropes en théories tenseur-scalaire. Son but est de déterminer les propriétés que doivent avoir ces théories afin que ces modèles possèdent asymptotiquement les caractéristiques dynamiques de notre Univers actuel ou apportent une réponse à certains de ses problèmes comme ceux de la constante cosmologique. La première partie de la thèse est consacrée à une introduction historique et à une justification physique des théories tenseur-scalaires de la gravitation et des modèles cosmologiques anisotropes. La seconde partie détaille les notions mathématiques nécessaires à la compréhension de cette thèse, à savoir la classification des cosmologies anisotropes et l'écriture des équations de champs dans le formalisme Lagrangien et Hamiltonien. La troisième partie est composée d'une série de sept articles montrant comment l'on peut parvenir à contraindre les théories tenseur-scalaires à l'aide de solutions exactes, en exigeant que l'Univers possède certains comportements dynamiques (expansion, inflation, etc), soit dépourvu de singularité ou possède une symétrie de Noether. Dans la quatrième partie, le processus d'isotropisation des modèles anisotropes est étudié en détail pour de nombreuses classes de théories tenseur-scalaires. Des contraintes nécessaires à l'isotropisation, les comportements asymptotiques des fonctions métriques et du potentiel au voisinage de cet état sont déterminés et le phénomène de quintessence analysé. Un lien entre les champs scalaires quintessents qui pourraient peupler notre Univers et la matière noire dans les galaxies (1 article) est montré. Les six articles à l'origine de ce chapitre sont reproduits dans la sixième partie qui tient lieu d'appendice. Nous concluons dans la cinquième partie.

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Cheng, A. D. Y. "Supersymmetric quantum Bianchi models". Thesis, University of Cambridge, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.597576.

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This thesis is about the quantum cosmology of supergravity theories, in particular N = 1 supergravity. In chapter 2, the Bianchi-IX model in N = 1 supergravity with a cosmological constant is investigated. This example is also restricted to the case of the k = +1 Friedmann universe. In chapter 3, the most general solution of the Lorentz constraints is found. Using this solution, N = 1 supergravity in the diagonal Bianchi-IX model is studied. The Hamilton-Jacobi equation is derived and completely solved. The Hartie-Hawking and wormhole actions are both found among the solutions. In chapter 4, the relation between the Chern-Simons functional and the no-boundary proposal is considered. The exponential of the Chern-Simons functional is the first known exact solution of quantum general relativity with a cosmological constant, being defined in the Ashtekar variables. However, it has turned out to be possible to show that the Chern-Simons functional and the no-boundary proposal are not related to each other in general relativity and N = 1 supergravity by considering perturbations around the k = +1 Friedmann universe. In chapter 5, the canonical formulation of N = 1 supergravity coupled to supermatter is presented. The supersymmetry and gauge constraints are derived. This model is then studied in the k = +1 Friedmann universe. It is found there are solutions in the case of a scalar multiplet. However, no non-trivial solution exists for a Yang-Mills multiplet, and it is explained why there is no physical state. Chapter 6 describes a brief investigation of the quantum cosmology of N = 2 and N = 4 supergravity theories. The thesis ends with concluding remarks and an indication of directions of future development.

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4

Friedrichsen, James Edward. "Quantization of Bianchi type cosmological models /". Full text (PDF) from UMI/Dissertation Abstracts International, 2000. http://wwwlib.umi.com/cr/utexas/fullcit?p3004268.

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5

Matsas, George Emanuel Avraam [UNESP]. "Estudo do universo primitivo no modelo bianchi IX". Universidade Estadual Paulista (UNESP), 1988. http://hdl.handle.net/11449/132638.

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Matsas, George Emanuel Avraam. "Estudo do universo primitivo no modelo bianchi IX /". São Paulo : [s.n.], 1988. http://hdl.handle.net/11449/132638.

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Yearsley, J. M. "Anisotropic cosmologies and the role of matter". Thesis, University of Sussex, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.259719.

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Hervik, Sigbjørn. "Mathematical cosmology : Bianchi models, asymptotics and extra dimensions". Thesis, University of Cambridge, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.616093.

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Nunes, Thiago Crisóstomo Carlos. "Relevância da dimensionalidade no modelo de Bianconi-Barabási". PROGRAMA DE PÓS-GRADUAÇÃO EM FÍSICA, 2017. https://repositorio.ufrn.br/jspui/handle/123456789/25467.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
Redes sem escala são bastante populares hoje em dia, uma vez que muitos sistemas estão bem representados por tais estruturas. Para estudar esses sistemas, foram propostos vários modelos. No entanto, a maioria deles não levam em conta a distância Euclidiana nó à nó, ou seja, a distância geográ ca. Em redes reais, a distância entre os sítios pode ser muito relevante, por exemplo, os casos em que se pretende minimizar custos. Neste cenário, estudamos o papel da dimensionalidade d no Modelo de Bianconi-Barabási com um crescimento e ligação preferencial envolvendo distâncias Euclidianas. A ligação preferencial neste modelo segue a regra Πi ∝ ηiki/rαA ij (1 ≤ i < j; αA ≥ 0), onde ηi caracteriza a qualidade do i-ésimo sítio e é escolhido aleatoriamente dentro do intervalo (0, 1]. Veri camos que a distribuição de grau P(k) para as dimensões d = 1, 2, 3, 4 são bem ajustadas por P(k) ∝ e −k/κ q , onde e −k/κ q é a função q-exponencial que surge naturalmente da Mecânica Estatística não-extensiva de Tsallis. Determinamos o índice q e κ como funções das quantidades αA e d e veri camos numericamente que ambos apresentam um comportamento universal em relação à variável αA/d. O mesmo comportamento também foi exibido pelo expoente dinâmico β que está associado a taxa que determinado sítio tem em receber ligações.
Scale-free networks are quite popular nowadays since many systems are well represented by such structures. In order to study these systems, several models were proposed. However, most of them do not take into account the node-to-node Euclidean distance, i.e., the geographical distance. In real networks, the distance between sites can be very relevant, e.g., those cases where it is intended to minimize costs. Within this scenario, we studied the role of dimensionality d in the Bianconi-Barabási model with a preferential attachment growth involving Euclidean distances. The preferential attachment in this model follows the rule Πi ∝ ηiki/rαA ij (1 ≤ i < j; αA ≥ 0), where ηi characterizes the tness of the i-th site and is randomly chosen within the (0, 1] interval. We veri ed that the degree distribution P(k) for dimensions d = 1, 2, 3, 4 are well tted by P(k) ∝ e −k/κ q , where e −k/κ q is the q-exponential function naturally emerging within nonextensive statistical mechanics. We determine the index q and κ as functions of the quantities αA and d, and numerically verify that both present a universal behavior with respect to the scaled variable αA/d. The same behavior also has been displayed by the dynamical β exponent which characterizes the steadily growing number of links of a given site.

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10

Pereyra, Pablo Hernán. "Soluções não-planas no modelo cosmológico Bianchi tipo V na teoria 5D-Espaço-Tempo-Massa". reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 1999. http://hdl.handle.net/10183/127585.

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As teorias de gravitação invariante por escala propõem uma variação com relação ao tempo da constante gravitacional ou da massa dos objetos que constituem o universo. Desta forma a intensidade da interação gravitacional também se torna variável, modificando sensivelmente o comportamento do universo. Algumas teorias foram propostas no decorrer do século, porém, descartadas devido a problemas técnicos e de concordância com dados observacionais. trabalho a ser apresentado nesta dissertação está fundamentado em uma teoria de gravitação invariante por escala, a qual vem atualmente sendo desenvolvida e é denominada teoria penta-dimensional Espaço-Tempo-Massa. Tal teoria propõe a quantidade de massa de repouso como uma quantidade extensiva, de maneira a introduzi-la na métrica e torná-la variável. Diversos trabalhos foram realizados com esta teoria, incluindo alguns, o estudo de modelos cosmológicos. Investigaremos aqui a extensão do modelo cosmológico de Bianchi tipo V, que é um dos mais importantes modelos do universo. Duas métricas foram propostas e as soluções das equações de campo da teoria SD-Espaço-Tempo-Massa para tais métricas foram obtidas. Tais soluções correspondem a espaços não-planos. Um estudo sobre singularidades na métrica e na curvatura foi realizado para ambas as métricas, em adição, o tensor de energia-momento induzido foi obtido para as métricas e as suas propriedades investigadas. Através da análise do tensor de Kretschmann verificou-se a ausência de singularidades efetivas nos modelos 5D abordados, sugerindo uma distribuição finita de energia devido a inclusão da massa de repouso.
The scale invariant gravitational theories propose the time variation either in the gravitational constant or in the rest mass of the objects that constitute the universe. By this way the intensity of the gravitational interaction varies as well, changing accordingly the behavior of the universe. Several theories have been proposed in the literature, however most of them have been discharged due to drawbacks in thecnicalities or lack of agreement with observational data. The work conducted here takes into account a 5-dimensional theory called SpaceTime- Mass, which proposes that the rest mass be na extensible quantity that change with time. Severa! investigations have been done so far with this theory, some o f them including cosmological studies. Here we will investigate the 5D extension of the Bianchi type V cosmological model, which is one of the most important model of the universe. Two metrics are proposed and the solution of the corresponding 5D-Spae-Time-Mass field equations are found. Both solutions shown to be non-flat spaces. The singularity behavior of the metric and curvature were done, the induced energy-momentum tensor for both metrics were determined and their properties were investigated. Through the analysis of the Kretschmann tensor, it has been shown that there is no effective singularity in the space, which suggest that there is a finite distribution of energy due to the inclusion of the rest mass variable.

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11

Sandin, Patrik. "Cosmological Models and Singularities in General Relativity". Doctoral thesis, Karlstads universitet, Avdelningen för fysik och elektroteknik, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-8206.

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This is a thesis on general relativity. It analyzes dynamical properties of Einstein's field equations in cosmology and in the vicinity of spacetime singularities in a number of different situations. Different techniques are used depending on the particular problem under study; dynamical systems methods are applied to cosmological models with spatial homogeneity; Hamiltonian methods are used in connection with dynamical systems to find global monotone quantities determining the asymptotic states; Fuchsian methods are used to quantify the structure of singularities in spacetimes without symmetries. All these separate methods of analysis provide insights about different facets of the structure of the equations, while at the same time they show the relationships between those facets when the different methods are used to analyze overlapping areas. The thesis consists of two parts. Part I reviews the areas of mathematics and cosmology necessary to understand the material in part II, which consists of five papers. The first two of those papers uses dynamical systems methods to analyze the simplest possible homogeneous model with two tilted perfect fluids with a linear equation of state. The third paper investigates the past asymptotic dynamics of barotropic multi-fluid models that approach a `silent and local' space-like singularity to the past. The fourth paper uses Hamiltonian methods to derive new monotone functions for the tilted Bianchi type II model that can be used to completely characterize the future asymptotic states globally. The last paper proves that there exists a full set of solutions to Einstein's field equations coupled to an ultra-stiff perfect fluid that has an initial singularity that is very much like the singularity in Friedman models in a precisely defined way.

Status of the paper "Perfect Fluids and Generic Spacelike Singularities" has changed from manuscript to published since the thesis defense.

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12

Bianchi, Lorenzo [Verfasser], Valentina [Akademischer Betreuer] Forini, Jan [Akademischer Betreuer] Plefka y Arkady A. [Akademischer Betreuer] Tseytlin. "Perturbation theory for string sigma models / Lorenzo Bianchi. Gutachter: Valentina Forini ; Jan Plefka ; Arkady A. Tseytlin". Berlin : Mathematisch-Naturwissenschaftliche Fakultät, 2016. http://d-nb.info/1084692643/34.

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13

Holgersson, David. "Lanczos potentialer i kosmologiska rumtider". Thesis, Linköping University, Department of Mathematics, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-2582.

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We derive the equation linking the Weyl tensor with its Lanczos potential, called the Weyl-Lanczos equation, in 1+3 covariant formalism for perfect fluid Bianchi type I spacetime and find an explicit expression for a Lanczos potential of the Weyl tensor in these spacetimes. To achieve this, we first need to derive the covariant decomposition of the Lanczos potential in this formalism. We also study an example by Novello and Velloso and derive their Lanczos potential in shear-free, irrotational perfect fluid spacetimes from a particular ansatz in 1+3 covariant formalism. The existence of the Lanczos potential is in some ways analogous to the vector potential in electromagnetic theory. Therefore, we also derive the electromagnetic potential equation in 1+3 covariant formalism for a general spacetime. We give a short description of the necessary tools for these calculations and the cosmological formalism we are using.

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14

Bianchini, Paolo [Verfasser] y de Ven Glenn [Akademischer Betreuer] van. "The internal kinematics of globular clusters. An intimate view, from models to observations / Paolo Bianchini ; Betreuer: Glenn van de Ven". Heidelberg : Universitätsbibliothek Heidelberg, 2016. http://d-nb.info/1180616642/34.

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15

Eriksson, Daniel. "Perturbative Methods in General Relativity". Doctoral thesis, Umeå : Department of Physics, Umeå University, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-1488.

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16

Camborata, Caterina. "Modello stocastico per la plasticità sinaptica". Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2016. http://amslaurea.unibo.it/12046/.

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Nel sistema nervoso centrale i neuroni comunicano l'uno con l'altro attraverso le connessioni sinaptiche e sono soggetti a centinaia di stimoli, ma hanno la capacità di distinguerli l'uno dall'altro. L'abilità delle sinapsi di interpretare questi cambiamenti morfologici e biochimici è detta \textit{plasticità sinaptica} e l'obiettivo di questa tesi è proprio studiare un modello per le dinamiche di questo affascinante processo, da un punto di vista prima deterministico e poi stocastico. Infatti le reazioni che inducono la plasticità sinaptica sono ben approssimate da equazioni differenziali non lineari, ma nel caso di poche molecole bisogna tener conto delle fluttuazioni e quindi sono necessari dei metodi di analisi stocastici. Nel primo capitolo, dopo aver introdotto gli aspetti fondamentali del sistema biochimico coinvolto e dopo aver accennato ai diversi studi che hanno approcciato l'argomento, viene illustrato il modello basato sull'aggregazione delle proteine (PADP) volto a spiegare la plasticità sinaptica. Con il secondo capitolo si introducono i concetti matematici che stanno alla base dei processi stocastici, strumenti utili per studiare e descrivere la dinamica dei sistemi biochimici. Il terzo capitolo introduce una giustificazione matematica riguardo la modellizzazione in campo medio e vede una prima trattazione del modello, con relativa applicazione, sui moscerini. Successivamente si applica il modello di cui sopra ai mammiferi e se ne studia nel dettaglio la dinamica del sistema e la dipendenza dai parametri di soglia che portano alle varie transizioni di fase che coinvolgono le proteine. Infine si è voluto osservare questo sistema da un punto di vista stocastico inserendo il rumore di Wiener per poi confrontare i risultati con quelli ottenuti dall'approccio deterministico.

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17

Martineau, Killian. "Quelques aspects de cosmologie et de physique des trous noirs en gravitation quantique à boucles Detailed investigation of the duration of inflation in loop quantum cosmology for a Bianchi I universe with different inflaton potentials and initial conditions Some clarifications on the duration of inflation in loop quantum cosmology A first step towards the inflationary trans-Planckian problem treatment in loop quantum cosmology Scalar spectra of primordial perturbations in loop quantum cosmology Phenomenology of quantum reduced loop gravity in the isotropic cosmological sector Primordial Power Spectra from an Emergent Universe: Basic Results and Clarifications Fast radio bursts and the stochastic lifetime of black holes in quantum gravity Quantum fields in the background spacetime of a polymeric loop black hole Quasinormal modes of black holes in a toy-model for cumulative quantum gravity Seeing through the cosmological bounce: Footprints of the contracting phase and luminosity distance in bouncing models Dark matter as Planck relics without too exotic hypotheses A Status Report on the Phenomenology of Black Holes in Loop Quantum Gravity: Evaporation, Tunneling to White Holes, Dark Matter and Gravitational Waves". Thesis, Université Grenoble Alpes (ComUE), 2019. http://www.theses.fr/2019GREAY044.

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Cantonnée à la physique mathématique depuis des décennies, la gravitation quantique entre désormais dans le giron de la science expérimentale. Suivant cette mouvance nous considérons dans cette thèse trois cadres d’application de la gravitation quantique à boucles (LQG) : le système Univers, les trous noirs et les astroparticules. Le troisième n’est qu’esquissé tandis que les deux premiers sont présentés plus en détails.Le secteur cosmologique étant l’un des domaines les plus prometteurs pour tester et contraindre des théories de gravité quantique, le développement de différents modèles tentant d’appliquer les idées de la LQG à l’Univers primordial ne s’est pas fait attendre. Les travaux que nous présentons portent sur la phénoménologie associée à ces modèles; tant dans le secteur homogène (où nous nous focalisons notamment sur la durée de la phase d’inflation), que dans le secteur inhomogène (nous étudions ce coup-ci le devenir des spectres de puissance primordiaux). Ces études combinées nous permettent alors de préciser dans quelle mesure des effets de gravité quantique (à boucles) peuvent être observés dans les anisotropies du fond diffus cosmologique.D’autre part les trous noirs, non contents de faire partie des objets les plus étranges et les plus fascinants de l’Univers, constituent également des sondes privilégiées pour tester des théories de gravitation. Nous développons la phénoménologie associée à différents traitements des trous noirs en gravitation quantique à boucles. Celle-ci intervient sur une grande variété de fronts : de l’évaporation de Hawking aux ondes gravitationnelles, en passant par la matière noire. C’est sans nul doute un domaine riche et vaste.Finalement, l’existence d’une échelle de longueur minimale, prédite par la majorité des théories de gravité quantique, suggère une généralisation du principe d’incertitude de Heisenberg. Partant de ce constat nous présentons également dans ce manuscrit une méthodologie permettant de calculer une nouvelle relation de dispersion de la lumière à partir du principe d’incertitude généralisé le plus couramment répandu
After decades of being confined to mathematical physics, quantum gravity now enters the field of experimental science. Following this trend, we consider throughout this thesis three implementation frameworks of Loop Quantum Gravity (LQG): the Universe as a system, black holes and astroparticles. The last one is only outlined while the first two are presented in more detail.Since the cosmological sector is one of the most promising areas for testing and constraining quantum gravity theories, it was not long before the development of different models attempting to apply the ideas of the LQG to the primordial Universe. The work we present deals with the phenomenology associated with these models; both in the homogeneous sector (where we focus particularly on the duration of the inflation phase), as in the inhomogeneous sector (where this time, we study the fate of the primordial power spectra). These combined studies then allow us to specify to what extent effects of (loop) quantum gravity can be observed in the anisotropies of the cosmic microwave background.On the other hand black holes, not content to be among the strangest and most fascinating objects of the Universe, are also prominent probes to test the theories of gravitation. We develop the phenomenology associated with different treatments of black holes in the loop quantum gravity framework, which intervenes on multiple levels: from the evaporation of Hawking to gravitational waves, including dark matter. This is undoubtedly a rich and vast area.Finally, the existence of a minimal length scale, predicted by the majority of quantum gravity theories, suggests a generalization of the Heisenberg uncertainty principle. On the basis of this observation, we also present in this manuscript a methodology to derive a new relation dispersion of light from the most widely used generalized uncertainty principle

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18

Ren, Lai Yu y 賴祐仁. "Bianchi type II & VIh Models and Brane Cosmology". Thesis, 2008. http://ndltd.ncl.edu.tw/handle/59584305962867137188.

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碩士
國立交通大學
物理研究所
96
In this thesis, we start at John D. Barrow’s paper, the “Anisotropically inflating universes”. We discuss the Bianchi type II & VIh for the Lagrangian density with the quadratic curvature terms, and calculate the energy-momentum tensor by solving the field equation. However, the energy condition is violated. So we introduce the concept of brane and discuss the extra dimension affect the field equation when we consider the 3-brane world. Finally we calculate the energy-momentum tensor of these two cosmology models once again.

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D'Ambroise, Jennie. "Generalized EMP and Nonlinear Schrodinger-type Reformulations of Some Scaler Field Cosmological Models". 2010. https://scholarworks.umass.edu/open_access_dissertations/225.

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We show that Einstein’s gravitational field equations for the Friedmann- Robertson-Lemaître-Walker (FRLW) and for two conformal versions of the Bianchi I and Bianchi V perfect fluid scalar field cosmological models, can be equivalently reformulated in terms of a single equation of either generalized Ermakov-Milne- Pinney (EMP) or (non)linear Schrödinger (NLS) type. This work generalizes or presents an alternative to similar reformulations published by the authors who inspired this thesis: R. Hawkins, J. Lidsey, T. Christodoulakis, T. Grammenos, C. Helias, P. Kevrekidis, G. Papadopoulos and F.Williams. In particular we cast much of these authors’ works into a single framework via straightforward derivations of the EMP and NLS equations from a simple linear combination of the relevant Einstein equations. By rewriting the resulting expression in terms of the volume expansion factor and performing a change of variables, we obtain an uncoupled EMP or NLS equation that is independent of the imposition of additional conservation equations. Since the correspondences shown here present an alternative route for obtaining exact solutions to Einstein’s equations, we reconstruct many known exact solutions via their EMP or NLS counterparts and show by numerical analysis the stability properties of many solutions.

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