Baigiamajame magistro darbe nagrinėjama dalelių mišinio dinaminė elgsena kvazistatiniame pusiausvyros būvyje. Pagrindinis dėmesys skiriamas mišinio makro- ir mikrobūsenai charakterizuoti. Darbo tikslas – ištirti betono užpildams būdingomis fizinėmis-mechaninėmis savybėmis pasižyminčio sferinių dalelių mišinio struktūrą ir elgseną fliuktuojančioje aplinkoje kvazistatinio pusiausvyros būvio sąlygomis. Dalelių mišinio elgsenos dinaminis modeliavimas atliktas diskrečiųjų elementų metodu (DEM). Modeliuoti viendispersis ir daugiadispersis mišiniai. Pagal gautus rezultatus, mišinio makrobūsena charakterizuojama struktūros užimama tūrio dalimi (tankumu), dalelių kontaktinėmis jėgomis bei koordinacijos skaičiumi. Atskirų mišinio dalelių mikrobūsena charakterizuojama taikant unikalų geometrinį metodą, sukurtą pagal Hamiltono mechanikos, bendrosios reliatyvumo teorijos ir kvantinės gravitacijos teorijų principus. Metodui realizuoti parengtas kompiuterinis algoritmas patvirtino iškeltas hipotezes. / In the Master Thesis an investigation of dynamical behavior of the mixture of particles under quasistatic equilibrium conditions was performed. It focuses on a characterization of the macro- and microstate of the mixture. The purpose of the research is to explore structure and behavior of the mixture of spherical particles, characterized by the typical physical-mechanical properties of concrete aggregates, in a fluctuating environment under quasistatic equilibrium conditions. Dynamic simulation of the behavior of the particles was performed via the discrete element method (DEM). According to the results obtained, the macrostate of the mixture was investigated in view of a volume fraction, contact forces of particles and a coordination number. A characterization of the microstate of distinct particle was done using the unique geometrical method which had been created according to Hamiltonian mechanics, the theory of relativity and the principles of quantum gravity. The developed computer algorithm allowed to confirm the hypotheses of the method.

With the start of the age of the Large Hadron Collider (LHC) two challenges face theoreticians and computational physicists. The first is about understanding theories beyond the Standard Model and producing verifiable predictions that can be tested against what the LHC and subsequent machines would produce. The second is to improve computational methods so that the new experimental precision is matched by a theoretical one. But this improvement is also crucial for the detection of potential deviations from Standard Model predictions and possibly also finding the elusive Higgs. This work tries to address problems in both areas. In the first part we study the effects of adding tension in considering a black-hole on a brane. Such black-holes are predicted by some models as potential phenomena at the LHC. We calculate the effects of adding tension on observable quantities of black-holes, namely, quasinormal mode frequencies and Hawking radiation, and we show how this improves predictions. In the second part we investigate the computational problem of extending the Britto-Cachazo-Feng-Witten (BCFW) method to 1-loop level. The BCFW has been successfully used in recent years to compute scattering amplitudes at tree-level by suitably complex-shifting external momenta and reducing diagrams to simpler ones. In our investigation we establish that the BCFW can be extended to 1-loop, which means that 1-loop integrands can be treated as trees and can be broken down further into even simpler trees using the BCFW. We explicitly look at the effects of the shift for the lowest three n-point cases, but also demonstrate how the result extends to arbitrary n.

Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / A formulaÃÃo e comprovaÃÃo experimental de uma teoria consistente de GravitaÃÃo QuÃntica à um dos maiores desafios da FÃsica atualmente. Entre as candidatas a ocupar este posto està a GravitaÃÃo QuÃntica de LaÃo, ela sugere a reinterpretaÃÃo do espaÃo-tempo que, em escala planckiana, assume a forma de uma rede de pontos espaÃados por um comprimento mÃnimo caracterÃstico da natureza. Neste trabalho tratamos de um modelo recentemente introduzido que incorpora o conceito de comprimento mÃnimo e o aplica no contexto de baixas energias, a MecÃnica QuÃntica PolimÃrica, discutimos a diferenÃa entre a fÃsica deste modelo e dos modelos de incerteza mÃnima, em especial o PrincÃpio de Incerteza Generalizado, onde a discretizaÃÃo espacial e consequÃncia de alteraÃÃes nas relaÃÃes de comutaÃÃo canÃnicas. Usamos o mÃtodo perturbativo para calcular correÃÃes de primeira ordem nos espectros de energia de alguns potenciais conhecidos, observamos atravÃs de grÃficos as escalas de energia envolvidas e comparamos os resultados com outras correÃÃes que surgem no contexto de altas energias. / The formulation and experimental verication of a consistent theory of Quantum Gravitation is one of the greatest challenges in Physics nowadays. Between the candidates for this post is the Loop Quantum Gravity, it suggests a reinterpretation of space-time, that in planckian scale, would assume the form of a net of points spaced by a minimal length characteristic of nature. In this work we deal with a model that incorporates this concept and applies it to the context of low energies, the Polymer Quantum Mechanics, we discuss the dierences on the physics of this model an that of the model on minimal uncertainty, in special the Generalized Uncertainty principle, where the spacial discretization is a consequence of modications in canonical commutation relations. We use the perturbative method to calculate rst order corrections in the energy spectra of some known potentials, we observe through graphics the energy scales involved and compare the results with other corrections that arise in the context of high energies.

Orientador: Patricio Anibal Letelier Sotomayor / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-10T23:13:00Z (GMT). No. of bitstreams: 1 Manoel_JoaoPauloPitelli_M.pdf: 2107794 bytes, checksum: 5fe60d22c5d7bd4e165a24c4c9c6d375 (MD5) Previous issue date: 2008 / Resumo: Espaços-tempos classicamente singulares são estudados utilizando-se partículas quânticas (ao invés de clássicas) obedecendo as equações de Klein-Gordon e Dirac, a fim de determinar se estes espaços permanecem singulares do ponto de vista quântico. Primeiramente é apresentada uma revisão do ferramental matemático necessário para o estudo de singularidades quânticas, cujo principal resultado utilizado é a teoria de índices deficientes devido a von Neumann. No apêndice A é apresentado um primeiro estudo sobre singularidades quânticas em espaços-tempos com defeitos topológicos numa superfície 2-dimensional (paredes cósmicas), em especial superfícies esféricas e cilíndricas. Estes espaços continuam singulares nesta teoria e todas as informações extras (que em mecânica quântica se apresentam sob a forma de condições de contorno) necessárias para se remover a singularidade são encontradas. No apêndice B, é estudado um espaço-tempo 2+1 dimensional com curvatura negativa constante. É mostrado que este espaço permanece singular quando visto pela mecânica quântica e as condições de contorno possíveis são encontradas utilizando-se resultados obtidos no caso plano / Abstract: Classical singular spacetimes are studied using quantum particles (instead of classical ones) obeying Klein-Gordon and Dirac equations, to determine if these spacetimes remain singular in the view of quantum mechanics. First we give a review of the mathematical framework necessary to study quantum singularities, wich the main result to be used later is von Neumann¿s theory of deficient indices. In appendix A, a first work on quantum singularities in spacetimes with topological defects on a 2-dimensional hypersurface (cosmic walls), specifically spherical and cylindrical surfaces, is presented. These spacetimes remain singular in this theory and all extra informations (which in quantum mechanics correspond to boundary conditions) necessary to remove the naked singularity are found. In Apendix B, a 2+1 dimensional spacetime with constant negative curvature is studied. It is shown that this spacetime remains quantum mechanically singular and all possible boundary conditions are found using results obtained in plane case / Mestrado / Relatividade Geral/Gravitação Quantica / Mestre em Matemática Aplicada

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-06-08T15:27:56Z No. of bitstreams: 1 polianedemoraisteixeira.pdf: 833138 bytes, checksum: 6826a43bfd3baaedb0691bb15c3c425e (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-06-26T19:06:07Z (GMT) No. of bitstreams: 1 polianedemoraisteixeira.pdf: 833138 bytes, checksum: 6826a43bfd3baaedb0691bb15c3c425e (MD5) / Made available in DSpace on 2017-06-26T19:06:07Z (GMT). No. of bitstreams: 1 polianedemoraisteixeira.pdf: 833138 bytes, checksum: 6826a43bfd3baaedb0691bb15c3c425e (MD5) Previous issue date: 2016-02-17 / Nessa tese, exploramos diferentes aspectos do grupo de renormalização (GR) em Gravitação Quântica. Especificamente, estudamos o GR aplicado a três diferentes modelos. Começamos por estudar o GR on-shell usando para isso o modelo de gravidade com torção proposto por Cartan, fizemos o tratamento quântico dessa teoria. Em seguida, mostramos em detalhes os cálculos do estudo da teoria semiclássica usando para isso o método da renormalização física, baseada na subtração de momentos. Nesta parte nós damos os detalhes da derivação dos fatores de forma gravitacionais, usando o método do heat kernel para três teorias massivas: campo escalar, campo vetorial e campo fermiônico. O que nos leva ao análogo gravitacional do teorema de desacoplamento de Appelquist e Carazzone. Nessa parte apenas refizemos os cálculos já desenvolvidos em um artigo de Gorbar e Shapiro, mas agora em detalhes minuciosos para cada etapa calculada. E na última parte, uma análise do grupo funcional de renormalização (GFR) foi feita, aplicando essa técnica também ao modelo de gravidade semiclássica, onde a teoria abordada foi a de um campo escalar com acoplamento não-mínimo no espaço-tempo curvo. / On this thesis, we explored differents aspects of the renormalization group (RG) in Quantum Gravity. Specifically, we studied the RG applied to three differents models. We began studying the RG on-shell and we used for that the model of gravity with torsion proposed by Cartan, we made the quantum treatment of this theory. Then, we showed in details the calculations of the study of semi-classical theory, using for that, the method of physical renormalization, based on the momentum subtraction. On this part, we gave the details of the derivation of gravitational form factors, using the method of the heat kernel for three massive theories: scalar field, vector field and fermionic field which leads us to the gravitational analogue of the decoupling theorem from Appelquist and Carazzone. In this part, we just remade the calculations already undertaken in a paper by Gorbar and Shapiro, but now in minute details for each step calculated. On the last part, an analysis of the functional renormalization group (FRG) was made, applying this technique also to the model of semiclassical gravity, where the theory addressed was a theory with a scalar field with non-minimal coupling in curved spacetime.

Submitted by Geandra Rodrigues (geandrar@gmail.com) on 2018-04-11T18:45:14Z No. of bitstreams: 1 jefersondiasgoncalves.pdf: 877599 bytes, checksum: 55b47e460c6f0960d499ee03cfdfbd27 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2018-04-11T19:36:44Z (GMT) No. of bitstreams: 1 jefersondiasgoncalves.pdf: 877599 bytes, checksum: 55b47e460c6f0960d499ee03cfdfbd27 (MD5) / Made available in DSpace on 2018-04-11T19:36:44Z (GMT). No. of bitstreams: 1 jefersondiasgoncalves.pdf: 877599 bytes, checksum: 55b47e460c6f0960d499ee03cfdfbd27 (MD5) Previous issue date: 2018-02-27 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Nesta tese expomos primeiramente um breve histórico-motivacional para a construção de uma teoria de gravitação quântica, bem como, rápidas revisões orientadas sobre elementos de teorias quânticas de campos e sobre a técnica de Schwinger-Dewitt. De posse destas ferramentas, discutimos a dependência de calibre e da parametrização para uma teoria quântica de gravitação em um espaço-tempo de dimensão arbitrária D. Com este objetivo, calculamos explicitamente as correções quânticas a 1-loop, da ação efetiva da teoria, considerando a parametrização mais geral possível para a métrica quântica. Essa parametrização contém inicialmente sete parâmetros, sendo que alguns deles serão fixados através da condição de fixação de calibre, o que torna o nosso cálculo um pouco mais simples. Por fim, para esta teoria, confirmamos a validade de um teorema geral, o qual garante a independência das divergências on-shell, a 1-loop, com respeito às ambiguidades nas escolhas de calibre e de parametrização da métrica quântica. / In this thesis we first present a brief historical-motivational for a construction of a theory of quantum gravitation, as well as quick reviews oriented on elements of quantum field theory and Schwinger- Dewitt technique. In possession of these tools, the gauge and parametrization dependence is discussed in quantum gravity in an arbitrary dimension D. Explicit one-loop calculations are performed within the most general parametrization of quantum metric with seven arbitrary parameters. On the other hand, some of the gauge fixing parameters are fixed to make the calculations relatively simple. We confirm the general theorem stating that the on shell local terms in the one-loop effective action are independent of the gauge and parametrization ambiguity.

Submitted by Biblioteca do Instituto de Física (bif@ndc.uff.br) on 2017-06-05T18:59:28Z No. of bitstreams: 1 Dissertação_Fernanda.pdf: 596584 bytes, checksum: 88a0a09efaf23dc12638307533c93da0 (MD5) / Made available in DSpace on 2017-06-05T18:59:28Z (GMT). No. of bitstreams: 1 Dissertação_Fernanda.pdf: 596584 bytes, checksum: 88a0a09efaf23dc12638307533c93da0 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Neste trabalho, estudamos algumas soluções estáticas e esfericamente simétricas para uma teoria de gravidade induzida por uma teoria de Yang-Mills no regime de baixas energias. Tal estudo foi feito na situação de vácuo e na presença de uma fonte descrita pelo tensor energia-momento para as equações de campo da gravidade induzida e associada a condição de torção nula. Assim, para a situação de vácuo analisamos duas soluções, uma perturbativa e outra exata. Desta forma, encontramos uma solução perturbativa em torno da solução de Schwarzschild-de Sitter, enquanto a solução exata é uma solução de espaço-tempo de de Sitter modificado. Também discutimos sobre as singularidades para este caso. Na presença do tensor energia-momento das equações de campo da gravidade induzida, analisamos uma solução para uma fonte eletricamente carregada e uma solução associada a um tensor energia-momento de um fluido perfeito. Neste caso, encontramos uma solução perturbativa em torno da solução de Reissner - Nordström - de Sitter e expressões perturbativas para as soluções dentro de um modelo de estrela. Por fim, analisando as equações de campo para uma geometria estática e esfericamente simétrica acoplada a um tensor energia-momento de um fluido perfeito, encontramos uma equação de equilíbrio hidrostático para a densidade de energia e pressão. Onde obtemos uma equação perturbativa em torno equação de Tolman - Oppenheimer - Volkoff - de Sitter. / In this work, we study some static and spherically symmetric solutions to a gravity theory induced by a Yang-Mills theory in the low-energy regime. This study was done in vacuum condition and in the presence of a source described by the energy-momentum tensor to the field equations of induced gravity and associated null torsion condition. Thus, for vacuum situation we analyzed two solutions, one perturbative and another exact. In this way, we find a perturbative solution around the Schwarzschild-de Sitter solution. While the exact solution is a solution of spacetime of de Sitter modified. We also discussed about the singularities in this case. In the presence of the energymomentum tensor of the field equations of induced gravity, we analyze a solution to an electrically charged source and a solution associated with an energy-momentum tensor of a perfect fluid. In this case, we find a perturbative solution around the Reissner - Nordström - de Sitter solution and perturbative expressions for the solutions within a star model. Finally, analyzing the field equations for a static and spherically symmetric geometry coupled to an energy-momentum tensor of a perfect fluid, we found a hydrostatic equilibrium equation for the energy density and pressure. Where we get a perturbation equation around equation Tolman- Oppenheimer - Volkoff - de Sitter.

Le problème de la limite continue de la gravitation quantique à boucle est encore ouvert. En effet, la dynamique précise n’est pas connue et nous ne disposons pas des outils nécessaires à l’étude de cette limite le cas échéant. Dans cette thèse, nous étudions quelques méthodes de coarse-graining (étude à gros grains) qui devraient contribuer à cette entreprise. Nous nous concentrons sur deux aspects du flot: la détermination d’observables naturelles à grandes échelles d’un côté et la manière de s’abstraire du problème de la dynamique à graphe variable en la projetant sur des graphes fixes de l'autre.Pour déterminer les observables aux grandes distances, nous étudions le cas des tétraèdres hyperboliques et leur description naturelle dans un langage proche de celui de la gravitation quantique à boucle. Les holonomies de surface en particulier jouent un rôle important. Cela dégage la structure des double spin networks constitués d'un graphe et de son dual, structure qui semble aussi apparaître dans les travaux de Freidel et al. Pour résoudre le problème des graphes variables, nous considérons et définissons les loopy spin networks. Ils encodent par des boucles la courbure locale d'un vertex effectif et permettent ainsi de décrire différents graphes en les masquant via le processus de coarse-graining. De plus, leur définition donne un procédé naturel systématique de coarse-graining pour passer d'une échelle à une autre.Ensemble, ces deux principaux résultats posent le fondement d'un programme de coarse-graining pour les théories invariantes sous difféomorphismes. / The continuum limit of loop quantum gravity is still an open problem. Indeed, no proper dynamics in known to start with and we still lack the mathematical tools to study its would-be continuum limit. In the present PhD dissertation, we will investigate some coarse-graining methods that should become helpful in this enterprise. We concentrate on two aspects of the theory's coarse-graining: finding natural large scale observables on one hand and studying how the dynamics of varying graphs could be cast onto fixed graphs on the other hand.To determine large scale observables, we study the case of hyperbolic tetrahedra and their natural description in a language close to loop quantum gravity. The surface holonomies in particular play an important role. This highlights the structure of double spin networks, which consist in a graph and its dual, which seems to also appear in works from Freidel et al. To solve the problem of varying graphs, we consider and define loopy spin networks. They encode the local curvature with loops around an effective vertex and allow to describe different graphs by hidding them in a coarse-graining process. Moreover, their definition gives a natural procedure for coarse-graining allowing to relate different scales.Together, these two results constitute the foundation of a coarse-graining programme for diffeomorphism invariant theories.

In this thesis, the symmetry structure of gravitational theories at null infinity is studied further, in the case of pure gravity in four dimensions and also in the case of Einstein-Yang-Mills theory in d dimensions with and without a cosmological constant.<p><p>The first part of this thesis is devoted to the presentation of asymptotic methods (symmetries, solution space and surface charges) applied to gravity in the case of the BMS gauge in three and four spacetime dimensions.<p><p>The second part of this thesis contains the original contributions.<p>Firstly, it is shown that the enhancement from Lorentz to Virasoro algebra also occurs for asymptotically flat spacetimes defined in the sense of Newman-Unti. As a first application, the transformation laws of the Newman-Penrose coefficients characterizing solution space of the Newman-Unti approach are worked out, focusing on the inhomogeneous terms that contain the information about central extensions of the theory. These transformations laws make the conformal structure particularly transparent, and constitute the main original result of the thesis.<p>Secondly, asymptotic symmetries of the Einstein-Yang-Mills system with or without cosmological constant are explicitly worked out in a unified manner in $d$ dimensions. In agreement with a recent conjecture, a Virasoro-Kac-Moody type algebra is found not only in three dimensions but also in the four dimensional asymptotically flat case.<p><p>These two parts of the thesis are supplemented by appendices. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

The gauge/string correspondence provides a non-perturbative definition of string theory and hence quantum gravity in some backgrounds, making it possible to translate statements about strongly coupled quantum field theories into results about gravity. <p><p>In this thesis, we focus on the derivation of holographic backgrounds from the field theory, without using any supergravity input. Instead, we rely crucially on the addition of probe D-branes to the stack of D-branes generating the background.<p>From the field theory description of the probe branes in the presence of the background branes, one can compute an effective action for the probes (in a suitable low-energy/near-horizon limit) by integrating out the background branes. Comparing this action with the D-brane probe action in a generic supergravity background then allows to determine the holographic background dual to the considered field theory vacuum.<p><p>In the first part, the required pre-requisites of field and string theory are recalled and this strategy to derive holographic backgrounds is explained in more detail on the basic case of D3-branes in flat space probed by a small number of D-instantons.<p><p>The second part contains the original results of this thesis, obtained by applying this strategy to several specific examples. We first derive the duals to three continuous deformations (Coulomb branch, β and non-commutative deformations) of the basic case, in the limit in which the D-instantons can probe the full geometry. We then derive the enhançon mechanism in a dual to a simple N=2 quiver gauge theory by using a fractional D-instanton as a probe and exploiting recent exact results on the Coulomb branch of N=2 quivers.<p>Finally, we obtain the near-horizon D4-brane geometry by probing the D4-branes with a small number of D0-branes.<p> / Doctorat en Sciences / info:eu-repo/semantics/nonPublished