Dissertations / Theses on the topic 'Gravity Tensor'
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Davies, Trevor Bamidelé. "Quadratic scalar-tensor gravity." Thesis, University of Aberdeen, 2017. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=234075.
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This thesis develops novel analytic models of scalar-tensor theories with quadratic coupling. In this framework, the coupling strength between scalar and matter is regulated in a way that allows the vacuum expectation value to vanish for low matter densities while becoming non-vanishingly large in the high-density regime. This results in significant deviations from the predictions of General Relativity in the strong-gravity regime. In astrophysics, we addressed the core-collapse supernova problem to account for the apparently missing energy required to explain the observed powerful explosions. We assumed a small, massless scalar gravitational field, thus allowing General Relativity to be recovered in the weak-gravity asymptotic limit. The non-trivial effects coming from the coupling function in the presence of a high-density field were analyzed at the instant of neutron star formation. Our results show that the scalar gravitational field evolves from a cosmological value to a new equilibrium via a Higgs-like mechanism. Additionally, the calculations associated with the gravitational binding energy shift and relevant relaxation timescale are explicitly shown. The full theory space of the model was also investigated for positive values of the coupling parameter. We studied a mechanism to address the stalled shock issue in core-collapse scenarios, which involved the application of sufficiently large positive values to the coupling parameter. Our results show that pulsating neutron stars act like optical cavities in which resonant scalar waves are parametrically amplified. It implies that the surface of a neutron star acts like an anti-phase reflector, releasing traveling scalar gravitational waves similar to an optical laser. In cosmology, the same framework was applied to a generic Friedman-Robertson-Walker universe involving general metric coupling and scalar potential functions. In cosmology, the same framework was applied to a generic Friedman-Robertson-Walker universe involving general metric coupling and scalar potential functions. We developed a mechanism which allowed the scalar field to be dynamically trapped, thus generating a potential capable of driving primordial inflation. Our results show that a trapped scalar field produces non-trivial dynamical consequences when applied to standard cosmology. Additionally, our analytic solutions for the generic inflationary behaviour, produce acceptable duration and e-foldings, thus recovering the Hubble parameter which is consistent with the present-day value. A feature of our cosmological model is that the universe can undergo several accelerating or decelerating phases, even though the scalar potential and metric coupling are monotonic functions overall. As this is important for the current dark energy problem, the quasi-static motion of the gravitational field induced by the scalar potential in the early universe, is investigated for a small value of the scalar field with normalized metric at the present time. Our results show that a variable Lambda Cold Dark Matter universe emerges naturally from the quadratic model.
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Wands, David Graham. "Cosmology of scalar-tensor gravity." Thesis, University of Sussex, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.335537.
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Delepouve, Thibault. "Quartic Tensor Models." Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLS085/document.
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Les modèles de tenseurs sont des mesures de probabilité sur des espaces de tenseurs aléatoires. Ils généralisent les modèles de matrices et furent développés pour l’étude de la géométrie aléatoire en dimension arbitraire. De plus, ils sont fortement liés aux théories de gravité quantique car, en plus des modèles standards très simples, ils incluent les théories de champs sur groupes, qui constituent l’approche « intégrale fonctionnelle » de la gravité quantique à boucle. Dans cette thèse, nous étudions le cas restreint des modèles tensoriels quartiques, pour lesquels un plus grand nombre de résultats mathématiques rigoureux ont pu être démontrés. Grâce à la transformation de champ intermédiaire, les modèles quartiques peuvent être ré-écrits sous forme de modèles de matrices multiples, et leurs développements perturbatifs peuvent être indexés par des cartes combinatoires. En utilisant divers développement en cartes, nous démontrons d’importants résultats d’analycité ainsi que des bornes pour les cumulants du modèle tensoriel standard le plus général et de rang arbitraire, ainsi que du plus simple modèle renormalisable de rang 3. Ensuite, nous introduisons une nouvelle famille de modèles, les modèles améliorés, dont le développement perturbatif se comporte de manière nouvelle, différente du comportement « melonique » qui caractérise les modèles tensoriels précédemment étudiésTensor models are probability measures for random tensors. They generalise matrix models and were developed to study random geometry in arbitrary dimension. Moreover, they are strongly connected to quantum gravity theories as, additionally to the standard bare-bones models, they encompass the field theoretical approach to loop quantum gravity known as group field theory.In the present thesis, we focus on the restricted case of quartic tensor models, for which a far greater number of rigorous mathematical results have been proven. Quartic models can be re-written as multi-matrix models using the intermediate field representation, and their perturbative expansions can be written as series expansions over combinatorial maps. Using a variety of map expansions, we prove analyticity results and useful bounds for the cumulants of various tensor models : the most general standard quartic model at any rank and the simplest renormalisable tensor field theory at rank 3. Then, we introduce a new class of models, the enhanced models, which perturbative expansions display new behaviour, different to the so called melonic behaviour that characterise most known tensor models so far
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Da, Silva Caroline Dos Santos. "Cosmic strings and scalar tensor gravity." Thesis, Durham University, 1999. http://etheses.dur.ac.uk/4577/.
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This thesis is concerned with the study of cosmic strings. We studied the values for the Higgs mass and string coupling for which the gravitational effect of an infinite cosmic string in the context of the Einstein theory is not only locally but also globally weak. We conclude this happens for strings formed at scales less or equal to the Planck one with Higgs mass being less or equal to the boson vectorial mass. Then we examined the metric of an isolated self-gravitating abelian-Higgs vortex in dilatonic gravity for arbitrary coupling of the vortex fields to the dilaton. We looked for solutions in both massless and massive dilaton gravity. We compared our results to existing metrics for strings in Einstein and .Jordan-Brans-Dicke theories. We explored the generalisation of Bogomolnyi arguments for our vortices and commented on the effects on test particles. We then included the presence of an axion field and examined the metric of an isolated self-gravitating axionic-dilatonic string. Finally we studied dilatonic strings through black hole solutions in string theory. We concluded that the horizon of non-extreme charged black holes supports the long-range fields of the Nielsen-Olesen string that can be considered as black hole hair and whose gravitational effect is in general the production of a conical deficit into the metric of the black hole background. We also concluded that the effect of the dilaton on the horizon of these black holes is to generate an additional charge.
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Oreta, Timothy. "Vector-Galileon-Tensor theories of gravity." Master's thesis, University of Cape Town, 2016. http://hdl.handle.net/11427/20925.
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A detailed study of the cosmological evolution in a particular vector-tensor theory of gravity with a potential and a Galileon-motivated interaction terms is presented. The evolution of vector field self interactions that are relatively related to Galileon fields throughout the expansion history of the universe is considered and a classification of the parameters M (mass term) and H (Hubble parameter) according to the behaviour of the field in each cosmological epoch is carried out. In particular, we obtain conditions for the parameters so that the field grows exponentially or oscillates with decreasing amplitude. We also obtain an autonomous system for the inflationary case. The general features of the phasemaps are given and the critical point is appropriately characterised. It is not possible to obtain an autonomous system for radiation and matter dominated epochs hence, we consider other analytical methods. We obtain eigenvalues and hence, phasemaps. The general features of the phasemaps are given and the point to which the trajectories on the phasemaps converge is appropriately characterised. Therefore, we show that it is possible to obtain a wide variety of behaviours or interesting phenomenologies for the cosmological evolution of vector field self-interactions that are relatively related to Galileon fields by choosing suitable values for the parameters M and H of given conditions.
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Bourhrous, Hassan. "CMB tensor anisotropies in f(R) gravity." Master's thesis, University of Cape Town, 2014. http://hdl.handle.net/11427/4866.
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Dartois, Stephane. "Random Tensor models : Combinatorics, Geometry, Quantum Gravity and Integrability." Thesis, Sorbonne Paris Cité, 2015. http://www.theses.fr/2015USPCD104/document.
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Dans cette thèse nous explorons différentes facettes des modèles de tenseurs aléatoires. Les modèles de tenseurs aléatoires ont été introduits en physique dans le cadre de l'étude de la gravité quantique. En effet les modèles de matrices aléatoires, qui sont un cas particuliers de modèles de tenseurs, en sont une des origines. Ces modèles de matrices sont connus pour leur riche combinatoire et l'incroyable diversité de leurs propriétés qui les font toucher tous les domaines de l'analyse, la géométrie et des probabilités. De plus leur étude par les physiciens ont prouvé leur efficacité en ce qui concerne l'étude de la gravité quantique à deux dimensions. Les modèles de tenseurs aléatoires incarnent une généralisation possible des modèles de matrices. Comme leurs cousins, les modèles de matrices, ils posent questions dans les domaines de la combinatoire (comment traiter les cartes combinatoires d dimensionnelles ?), de la géométrie (comment contrôler la géométrie des triangulations générées ?) et de la physique (quel type d'espace-temps produisent-ils ? Quels sont leurs différentes phases ?). Cette thèse espère établir des pistes ainsi que des techniques d'études de ces modèles. Dans une première partie nous donnons une vue d'ensemble des modèles de matrices. Puis, nous discutons la combinatoire des triangulations en dimensions supérieures ou égales à trois en nous concentrant sur le cas tridimensionnelle (lequel est plus simple à visualiser). Nous définissons ces modèles et étudions certaines de leurs propriétés à l'aide de techniques combinatoires permettant de traiter les cartes d dimensionnelles. Enfin nous nous concentrons sur la généralisation de techniques issues des modèles de matrices dans le cas d'une famille particulières de modèles de tenseurs aléatoires. Ceci culmine avec le dernier chapitre de la thèse donnant des résultats partiels concernant la généralisation de la récurrence topologique de Eynard et Orantin à cette famille de modèles de tenseursIn this thesis manuscript we explore different facets of random tensor models. These models have been introduced to mimic the incredible successes of random matrix models in physics, mathematics and combinatorics. After giving a very short introduction to few aspects of random matrix models and recalling a physical motivation called Group Field Theory, we start exploring the world of random tensor models and its relation to geometry, quantum gravity and combinatorics. We first define these models in a natural way and discuss their geometry and combinatorics. After these first explorations we start generalizing random matrix methods to random tensors in order to describes the mathematical and physical properties of random tensor models, at least in some specific cases
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Wu, Chun-Hsien. "Quantum fluctuations of the stress tensor /." Thesis, Connect to Dissertations & Theses @ Tufts University, 2002.
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Thesis (Ph.D.)--Tufts University, 2002.Adviser: L. H. Ford. Submitted to the Dept. of Physics. Includes bibliographical references (leaves 161-165). Access restricted to members of the Tufts University community. Also available via the World Wide Web;
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Schiappacasse, Enrico D. "Beyond Semiclassical Gravity| Quantum Stress Tensor Fluctuations in the Vacuum." Thesis, Tufts University, 2018. http://pqdtopen.proquest.com/#viewpdf?dispub=10812605.
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Large vacuum fluctuations of a quantum stress tensor can be described by the asymptotic behavior of its probability distribution. Here we focus on stress tensor operators which have been averaged with a sampling function in time. The Minkowski vacuum state is not an eigenstate of the time-averaged operator, but can be expanded in terms of its eigenstates. We calculate the probability distribution and the cumulative probability distribution for obtaining a given value in a measurement of the time-averaged operator taken in the vacuum state. In these calculations, we use the normal ordered square of the time derivative of a massless scalar field in Minkowski spacetime as an example of a stress tensor operator. We analyze the rate of decrease of the tail of the probability distribution for different temporal sampling functions, such as compactly supported functions and the Lorentzian function. We find that the tails decrease relatively slowly, as exponentials of fractional powers, in agreement with previous work using the moments of the distribution. Our results lead additional support to the conclusion that large vacuum stress tensor fluctuations are more probable than large thermal fluctuations, and may have observable effects.
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Holden, Damien James. "Generalised Brans-Dicke cosmology." Thesis, University of Portsmouth, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.247071.
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Parsons, Paul. "Scalar-field models of the early universe." Thesis, University of Sussex, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.390077.
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Domenech, Fuertes Guillem. "Inflationary Cosmology in Scalar-Tensor Theories." Kyoto University, 2017. http://hdl.handle.net/2433/227579.
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Vlasov, Igor. "Reference frames and equations of motion in the first PPN approximation of scaler-tensor and vector-tensor theories of gravity." Diss., Columbia, Mo. : University of Missouri-Columbia, 2006. http://hdl.handle.net/10355/4372.
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Thesis (Ph. D.)--University of Missouri-Columbia, 2006.The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file viewed on (Mar. 1, 2007). Vita. Includes bibliographical references.
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Lehebel, Antoine. "Objets astrophysiques compacts en gravité modifiée." Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLS204/document.
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Vingt années se sont écoulées depuis la découverte de l'expansion accélérée de l'Univers, ravivant l'intérêt pour les théories alternatives de la gravité. Ajouter un champ scalaire à la métrique habituelle de la relativité générale est l'une des manières les plus simples de modifier notre théorie de la gravité. En parallèle, nos connaissances sur les trous noirs et les étoiles à neutrons sont en plein essor, grâce notamment au développement de l'astronomie par ondes gravitationnelles. Cette thèse se situe au carrefour entre les deux domaines : elle étudie les propriétés des objets compacts dans les théories tenseur-scalaire généralisées. Je commence par rappeler les théorèmes d'unicité essentiels établis depuis les années soixante-dix. Après avoir présenté le théorème d'unicité pour les trous noirs en théorie de Horndeski, je l'étends aux étoiles. La deuxième partie de cette thèse détaille les différentes manières de contourner ce théorème. Parmi elles, je présente des solutions où la dépendance temporelle du champ scalaire permet de le raccorder à une solution cosmologique, mais aussi des trous noirs statiques et asymptotiquement plats. Dans la troisième partie, j'établis un critère important pour la stabilité de ces solutions, qui s'appuie sur leur structure causale. C'est aussi l'occasion d'étudier la propagation des ondes gravitationnelles au voisinage de trous noirs, et de sélectionner les théories dans lesquelles les ondes gravitationnelles se propagent à la même vitesse que la lumièreTwenty years have passed since the discovery of the accelerated expansion of the Universe, reviving the interest for alternative theories of gravity. Adding a scalar degree of freedom to the usual metric of general relativity is one of the simplest ways to modify our gravitational theory. In parallel, our knowledge about black holes and neutron stars is booming, notably thanks to the advent of gravitational wave astronomy. This thesis is at the crossroads between the two fields, investigating the properties of compact objects in extended scalar-tensor theories. I start by reviewing essential no-hair results established since the seventies. After discussing the no-hair theorem proposed for black holes in Horndeski theory, I present its extension to stars. The second part of the thesis investigates in detail the various ways to circumvent this theorem. These notably include solutions with a time-dependent scalar field in order to match cosmological evolution, but also static and asymptotically flat configurations. In a third part, I establish an important stability criterion for these solutions, based on their causal structure. It is also the occasion to study the propagation of gravitational waves in black hole environments, and to select the theories where gravitational waves travel at the same speed as light
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Kutluay, Emir. "Identification Of Inertia Tensor Of Vehicles." Master's thesis, METU, 2007. http://etd.lib.metu.edu.tr/upload/3/12608796/index.pdf.
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The aim of this thesis is to develop a methodology for obtaining mass properties of a vehicle using specific test rig. Investigated mass properties are the mass, location of center of gravity and the inertia tensor. Accurate measurement of mass properties of vehicles is crucial for vehicle dynamics research. The test rig consists of a frame on which the vehicle is fixed and which is suspended from the ceiling of the laboratory using steel cables. Mass and location of center of gravity are measured using the data from the test rig in equilibrium position and basic static equations. Inertia tensor is measured using the data from
dynamical response of the system. For this purpose an identification routine which employs prediction error method is developed using the built&ndashin functions from the System Identification Toolbox of MATLAB®
. The experiment was also simulated using Simmechanics Toolbox of MATLAB®
. Identification code is verified using the results of the experiment simulations for various cases.
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Edwards, David Craig. "Theoretical considerations in the use of scalar-tensor theories of gravity in inflationary models." Thesis, University of Edinburgh, 2018. http://hdl.handle.net/1842/31404.
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The inflationary paradigm is one which was designed to answer questions that arose from classical Hot Big Bang cosmology. The period of rapid expansion in the early Universe provides a mechanism to solve the flatness, horizon and relic problems. More importantly, since the theory was first introduced it has been realised that it also provides a mechanism to generate the initial perturbations from which structure in the Universe can grow. In the zoo of potential inflationary models there is a dominant class: slow-roll inflation. The idea that the energy density of the inflationary field is dominated by its potential highly simplifies the calculations required to predict observable quantities. This simplification relies on all the information required to know the subsequent dynamics of the field to be encoded in the space Φ-Φ̇; it must be an effective phase space. I show that Φ-Φ̇ can be considered to be such a space for the most general scalar-tensor theory which gives second-order equations of motion: Horndeski theory. There are theoretical issues associated with this reduction that are illuminated through specific examples in which they occur. A theoretical issue with inflation is that there is an overabundance of models, with some capable of predicting any value of the possible observables. The second block of work in this thesis looks at a particular set of models that make the same observational prediction. These 'attractor' models utilise a non-minimal coupling between the inflationary fields and gravity and are studied in depth, both in the case of one and several fields. Firstly, I examine the Universal Attractors, a single field subset of these models. I show, in detail, the observational prediction such a model makes in the case of a strong non-minimal coupling and then examine the constraints it would be possible to put on such a coupling if a confirmed detection of primordial gravitational waves was made. Despite the discussion existing in the literature there is a small deviation of the Universal Attractor models from the predictions of the Starobinsky model. Furthermore, the coupling, ξ is found to be constrained so that |ξ| < 1 in the case where there a level of detectable primordial tensor modes. While the attractor models have an effective one-field description in reality there are several other fields that are assumed to be fixed during the inflationary phase. This claim requires careful examination as the field-space of the models generally is not flat. This curvature can cause a destabilising effect with certain parameters and so I investigate how susceptible the α-attractors and related models are to the destabilisation. A key result of this chapter is to highlight how important it is to not rely on the slow-roll approximation when assessing the effect of the instability, as the region where the effect begins to become large corresponds with the region where slow-roll begins to break down. Assuming the slow-roll approximation is valid leads to an over-estimation of the effect that the instability mechanism has. Despite this, some of the models considered are seen to experience the instability for certain ranges of model parameters. Making the assumption that any occurrence of the instability will, at the very least, move the observational prediction of the model outside the currently constrained range allows a constraint on the model parameter in question which directly translates to a theoretical lower bound on the tensor-scalar ratio, r > 0.0005.
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Mimoso, Jose Pedro. "Cosmological models of the early universe." Thesis, University of Sussex, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.358557.
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Ferrari, Angelo Giuseppe. "Cosmological effects of the Galileon term in scalar-tensor theories." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2020. http://amslaurea.unibo.it/20760/.
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In questa tesi studiamo un'estensione con un termine di interazione cubica di tipo Galileone della lagrangiana dei più semplici modelli scalari-tensoriali, come gravità indotta (IG) e il modello Jordan-Brans-Dicke esteso con un potenziale (eJBD). Ne analizziamo gli effetti cosmologici sia a livello di background che di perturbazioni lineari. Il lavoro si suddivide in una parte analitica ed una numerica: nella parte analitica vengono ricavate le equazioni del moto del modello sia a livello omogeneo che per le perturbazioni lineari e si ottiene una classe di soluzioni analitiche in assenza di materia. La parte numerica, che ha richiesto l'implementazione delle equazioni della teoria in un codice Einstein-Boltzmann dedicato, ci ha permesso di studiare più nel dettaglio l'evoluzione della cosmologia omogenea e fare predizioni sulle anisotropie dello spettro di potenza angolare della radiazione cosmica di fondo (CMB) e dello spettro di potenza della materia, confrontando tali risultati con quelli ottenuti in IG e nel modello cosmologico standard ΛCDM.
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Delporte, Nicolas. "Tensor Field Theories : Renormalization and Random Geometry." Thesis, université Paris-Saclay, 2020. http://www.theses.fr/2020UPASP011.
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Cette thèse se scinde en deux volets, avec vue sur la renormalisation de théorie quantique des champs.Le premier volet traite de trois modèles tensoriels en trois dimensions, un quartique fermionique de rang 3 et deux sextiques bosonique, de rangs 3 et 5. On se base sur l'expansion melonique à grand N des théories tensorielles. Pour le premier modèle, invariant sous le groupe U(N)³, on calcule le flot du groupe de renormalisation des deux couplages meloniques et on dresse le diagramme des phases du vide de la théorie, en étudiant sa reformulation par un champ intermédiaire matriciel diagonalisable. Observant une brisure spontanée de la symétrie discrète chirale, la comparaison avec le modèle de Gross-Neveu tri-dimensionel est faite. Au-delà de la phase symétrique U(N)³ sans masse, on note aussi une phase massive de même symétrie et une autre où la symétrie est brisée vers U(N²) x U(N/2) x U(N/2). Un modèle matriciel de symétrie U(N) x U(N²), présentant les mêmes caractéristiques, est aussi considéré.Dans les deux autres modèles tensoriels, de groupes de symétrie U(N)³ et O(N)⁵, un couplage non-melonique (la ``roue") adjoint d'une puissance de N optimale nous conduit à une expansion melonique généralisée. Les termes cinétiques sont pris de courte ou longue portée et on étudie, à grand N, perturbativement les différents groupes de renormalisation des couplages d'ordre 6, jusqu'à quatre boucles. Tandis que le modèle de rang 5 ne présente pas de point fixe non-trivial, celui de rang 3 possède deux points fixes non-triviaux réels de type Wilson-Fisher dans le cas à courte portée et une ligne de points fixes dans l'autre. On obtient enfin les dimensions conformes réelles des opérateurs primaires bilinéaires en le champ fondamental.Le second volet établit les premiers résultats de renormalisation constructive multi-échelle pour un modèle scalaire quartique sur des arbres de Galton-Watson critiques, avec un terme cinétique à longue portée. Au point critique, l'émergence d'une spine infinie fournit un espace de dimension effective 4/3 sur lequel calculer des fonctions de corrélations moyennées. Cela formalise la notion de théorie des champs sur une géométrie aléatoire. Nous utilisons dans notre approche des bornes probabilistes sur le noyau de la chaleur dans un graphe aléatoire. On esquisse pour terminer l'extension du formalisme à des fermions et à une spine compactifiéeThis thesis divides into two parts, focusing on the renormalization of quantum field theories. The first part considers three tensor models in three dimensions, a fermionic quartic with tensors of rank-3 and two bosonic sextic, of ranks 3 and 5. We rely upon the large-N melonic expansion of tensor models. For the first model, invariant under U(N)³, we compute the renormalization group flow of the two melonic couplings and establish the vacuum phase diagram, from a reformulation with a diagonalizable matrix intermediate field. Noting a spontaneous symmetry breaking of the discrete chiral symmetry, the comparison with the three-dimensional Gross-Neveu model is made. Beyond the massless U(N)³ symmetric phase, we also observe a massive phase of same symmetry and another where the symmetry breaks into U(N²) x U(N/2) x U(N/2). A matrix model invariant under U(N) x U(N²), sharing the same properties, is also studied.For the two other tensor models, with symmetry groups U(N)³ and O(N)⁵, a non-melonic coupling (the ``wheel") with an optimal scaling in N drives us to a generalized melonic expansion. The kinetic terms are taken of short and long range, and we analyze perturbatively, at large-N, the renormalization group flows of the sextic couplings up to four loops. While the rank-5 model doesn't present any non-trivial fixed point, that of rank 3 displays two real non-trivial Wilson-Fisher fixed points in the short-range case and a line of fixed points in the other. We finally obtain the real conformal dimensions of the primary operators bilinear in the fundamental field.In the second part, we establish the first results of constructive multi-scale renormalization for a quartic scalar field on critical Galton-Watson trees, with a long-range kinetic term. At the critical point, an emergent infinite spine provides a space of effective dimension 4/3 on which to compute averaged correlation fonctions. This approach formalizes the notion of a quantum field theory on a random geometry. We use known probabilistic bounds on the heat-kernel on a random graph. At the end, we sketch the extension of the formalism to fermions and to a compactified spine
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Veraguth, Olivier J. "Conformal loop quantum gravity : avoiding the Barbero-Immirzi ambiguity with a scalar-tensor theory." Thesis, University of Aberdeen, 2017. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=236513.
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In the construction of Canonical Loop Quantum Gravity, General Relativity is rewritten in terms of the Ashtekar variables to simplify its quantisation. They consist of a densitised triad and a connection terms. The latter depends by definition and by construction on a free parameter β, called the Barbero–Immirzi parameter. This freedom is passed on to the quantum theory as it appears in the expressions of certain operators. Their discreet spectra depend on the arbitrary value of this parameter β, meaning that the scale of those spectra is not uniquely defined. To get around this ambiguity, we propose to consider a theory of Conformal Loop Quantum Gravity, by imposing a local conformal symmetry through the addition of a scalar field. We construct our theory starting from the usual Einstein–Hilbert action for General Relativity to which we add the action for the massless scalar field and rewrite it in terms of a new set of Ashtekar-like variables. They are constructed through a set of canonical transformations, which allow to move the Barbero–Immirzi parameter from the connection to the scalar variable. We then show that the theory can be quantised by fulfilling the conditions for a Dirac quantisation. Finally, we present some first elements of the quantum formalism. It is expected that with such a scalar-tensor theory, the quantum operators should not depend on the free parameter directly but rather on the dynamical scalar field, solving therefore the ambiguity.
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Panassiti, Antonio. "General relativity limit of Brans-Dicke gravity." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/23344/.
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In Brans-Dicke gravity a scalar field non-minimally coupled with the curvature acts as a new gravitational degree of freedom in addition to the usual metric field of General Relativity. Usually, when the coupling ω of the scalar field diverges, the latter approaches a constant and the solutions of the theory reduce to those generated by the Einstein equations with the same energy-momentum tensor as source. However, in the limit ω → ∞, the static and spherically symmetric vacuum solutions, called Brans solutions, do not reduce to the Schwarzschild metric, the only solution of General Relativity with the same type of symmetry. In this work we test their limit with a new method. Unlike the usual way, we use the Brans solutions to take the limit at the level of the equations. Since these are non-linear field equations depending on ω, in principle our procedure could lead to a different outcome. In particular, we take advantage of the Einstein frame formulation of the Brans-Dicke theory and we check if the solutions are able to satisfy the equations of the so called Minimal Geometric Deformation approach. Namely, we study if they can be seen as a geometric deformation - due to the Brans-Dicke scalar - of the Schwarzschild solution. Indeed, the peculiar feature of the geometric deformation is that it is built in such a way to guarantee a clear limit to the vacuum equations of General Relativity. However, we find that the Brans solutions do not meet all the requirements imposed by the structure of the Minimal Geometric Deformation approach. This result supports the conclusion that there is no simple limiting procedure in which the complete Brans-Dicke theory just reduces to General Relativity.
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Beiki, Majid. "New Techniques for Estimation of Source Parameters : Applications to Airborne Gravity and Pseudo-Gravity Gradient Tensors." Doctoral thesis, Uppsala universitet, Geofysik, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-143015.
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Gravity gradient tensor (GGT) data contains the second derivatives of the Earth’s gravitational potential in three orthogonal directions. GGT data can be measured either using land, airborne, marine or space platforms. In the last two decades, the applications of GGT data in hydrocarbon exploration, mineral exploration and structural geology have increased considerably. This work focuses on developing new interpretation techniques for GGT data as well as pseudo-gravity gradient tensor (PGGT) derived from measured magnetic field. The applications of developed methods are demonstrated on a GGT data set from the Vredefort impact structure, South Africa and a magnetic data set from the Särna area, west central Sweden. The eigenvectors of the symmetric GGT can be used to estimate the position of the causative body as well as its strike direction. For a given measurement point, the eigenvector corresponding to the maximum eigenvalue points approximately toward the center of mass of the source body. For quasi 2D structures, the strike direction of the source can be estimated from the direction of the eigenvectors corresponding to the smallest eigenvalues. The same properties of GGT are valid for the pseudo-gravity gradient tensor (PGGT) derived from magnetic field data assuming that the magnetization direction is known. The analytic signal concept is applied to GGT data in three dimensions. Three analytic signal functions are introduced along x-, y- and z-directions which are called directional analytic signals. The directional analytic signals are homogenous and satisfy Euler’s homogeneity equation. Euler deconvolution of directional analytic signals can be used to locate causative bodies. The structural index of the gravity field is automatically identified from solving three Euler equations derived from the GGT for a set of data points located within a square window with adjustable size. For 2D causative bodies with geometry striking in the y-direction, the measured gxz and gzz components of GGT can be jointly inverted for estimating the parameters of infinite dike and geological contact models. Once the strike direction of 2D causative body is estimated, the measured components can be transformed into the strike coordinate system. The GGT data within a set of square windows for both infinite dike and geological contact models are deconvolved and the best model is chosen based on the smallest data fit error.Felaktigt tryckt som Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 730
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Moslehi, Sadegh. "Mach’s principle and modified gravity." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2018.
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It was after the discussion about the nature of matter and space among scientists and philosophers,meanwhile Newton presented more accurate theories based on his equations. Newton believed that time and space are absolute, and he based his principles upon this belief.After him many scientists presented sometimes complementary or different theories.Mach was one of the famous scientists who had another ideas different from Newton, that later used and considered by Einstein as the completion of general relativity and named it Mach's principle. Although later Einstein rejected some subjects of this principle such as the reference frame. He succeeded to explain the relation between space and time according to the field equation which extracted from his theory and pull over the Newton’s absolute space
In fact Mach's theories and thoughts had such a significant impact on change the point of view of scientists towards substance in universe. Today we dare to say that students are less aware of his attempts in evolution and revolutions that happened in physics early by Newton and then by Einstein.In recent years and probably less than half a century, scientists that proved general relativity theory due to the experiments (about the investigation of substance's nature and space and the influence of gravity on them) decided to create a unified theory between the four main forces in nature.Therefore, gravity was always the main reason that left all the efforts unfinished.This was the reason that scientists decided to modify the gravity which clearly affects the Einstein field equation,which maybe can create a new approach to unify the gravity force with other main forces in nature.In this thesis I tried to investigate one of these efforts for modified gravity and show its role in couple of matter and space in a format by using several theories and hypotheses (such as f(R) gravity,Pressuron etc.) raised in recent years. Although there is still a long way to reach the main answer
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Ragozzine, Brett. "Modeling the Dark Matter of Galaxy Clusters Using the Tensor-Vector-Scalar Theory of Alternate Gravity." Ohio University / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1364229568.
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Rossi, Massimo. "Dark energy as a scalar field non-minimally coupled to gravity." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/12825/.
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The cosmological constant is not the only possibility in order to describe the accelerated expansion of the Universe. A different approach is to modify the gravitational sector of the Einstein equations. In scalar-tensor theories the gravitational interaction is affected by both a scalar and a tensor field. The dependence of gravity from the scalar field is obtained through a non-minimal coupling function which multiplies the Ricci scalar in the Lagrangian. In this thesis we consider a specific shape of the coupling function that reduces to the minimal coupling case and to the induced gravity case for specific choices of the parameters.
We consider two shapes for the potential: one leads to an effectively massless Klein-Gordon equation while the other is motivated by the fact that it is a viable potential for the chaotic inflation in superconformal theory. For the former we consider also the conformal coupling case, which is the required coupling in order to obtain a conformally invariant theory.
We derive the fundamental equation at the background and linear perturbations level and then we recover the initial condition for the perturbations.
In order to study the evolution for the background and linear fluctuations within non-minimally coupling we modified the publicly available Einstein-Boltzmann code CLASS.
The evolution of the dark energy density parameter and the equation of state are shown. Furthermore we pay attention to the actual value of the post-Newtonian parameters in order to see which choices of the parameters satisfies the Solar System constraints.
We present the results obtained for CMB anisotropies, linear matter power spectrum, metric and scalar field perturbations. As for the background we confront them with the ΛCDM model for both the potential considered.
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Pereira, Bomfim Everton. "THE USE OF THE GOCE MISSION DATA FOR CHARACTERIZATIONS AND IMPLICATIONS ON THE DENSITY STRUCTURE OF THE SEDIMENTARY BASINS OF AMAZON AND SOLIMOES, BRASIL." Doctoral thesis, Università degli studi di Trieste, 2012. http://hdl.handle.net/10077/9910.
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2010/2011Em geral, verifica-se que as bacias têm um estado isostático anômalo, se for considerada a clássica hipótese isostática que postula que as cargas topográficas e sedimentares são sustentadas pelo espessamento ou afinamento da crosta. Em alguns casos, a alta densidade do material na crosta inferior ou no manto superior tem sido um componente importante na formação das bacias sedimentares de larga escala e na contribuição para o equilíbrio isostático. A maneira mais direta de detectar as anomalias da densidade é pelo estudo do potencial gravitacional e de suas derivadas. A disponibilidade global e a boa resolução dos dados do satélite GOCE, aliadas à disponibilidade de dados de gravimetria terrestre, são ideais para a comparação e classificação das bacias de larga escala, como as bacias sedimentares do Solimões e do Amazonas, no que diz respeito à sua estrutura de densidade litosférica, determinadas por meio de uma modelagem 3D da distribuição de densidades usando as geometrias do embasamento e da descontinuidade de Moho admitidas conhecidas como vínculo inicial. Além disso, por esta técnica pode ser obtido um modelo isostático fisicamente independente do modelo de densidades, bem como outras grandezas associadas ao campo de gravidade como o geóide, a distribuição da anomalia da gravidade e das componentes do tensor gradiente gravimétrico, grandezas importantes para o modelamento e o estudo destas estruturas.
I bacini sedimentari di Amazon e Solimões sembrano avere uno stato anomalo isostatico se si considera l’ipotesi classica dell’isostasia, che presuppone che i carichitopografici e sedimentari siano sostenuti da un ispessimento della crosta terrestre o da un assottigliamento. In alcuni casi, la densità delle rocce nella crosta inferiore o mantello superiore è presumibilmente una componente importante nella formazione dei bacini sedimentari a grande scala, contribuedo all’equilibrio isostatico. Il modo più diretto per rilevare le variazioni di densità è lo studio del campo potenziale di gravità e delle sue derivate. La disponibilità globale e buona risoluzione dei dati della missione satellitare GOCE, unitamente alla disponibilità di dati gravitazionali terrestri sono l'ideale per intraprendere la comparazione e classificazione dei due grandi bacini sedimentari Amazon e Solimões. La struttura della densità della litosfera è stata studiata attraverso una modellazione 3D della distribuzione di densità utilizzando la geometria del basamento e della discontinuità Moho, conosciuti come vincolo iniziale. Poi, un modello isostatico per crosta inferiore o mantello superiore è stato ottenuta. Inoltre, abbiamo preso in considerazione il geoide, e le componenti del tensore gradiente, che sono quantità importanti per la modellazione e lo studio di queste strutture.
In general the basins appear to have an anomalous isostatic state if the classic isostatic hypothesis is considered, which assumes that the topographic and sedimentary loads are sustained by crustal thickening or thinning. In some cases, the high density of the material in the lower crust or upper mantle has been supposedly an important component in the formation of large scale sedimentary basins and in contributing to the isostatic equilibrium. The most direct way to detect density anomalies is the study of the gravity potential field and its derivatives. The global availability and good resolution of the GOCE satellite data mission coupled with the availability of terrestrial gravity data are ideal for the scope of intercomparison and classification of the two large-scale Amazon and Solimoes sedimentary basins. The lithospheric density structure has been studied through a 3D modelling of density distribution using the geometry of basement and Moho discontinuity, assumed to be known as initial constraint. Furthermore, an isostatic model for lower crust or upper mantle has been obtained. Also, we considered others gravity field as geoid, gravity anomaly and gravity gradient tensor components, which are important quantities for modelling and studying these structures.
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Kuntz, Adrien. "Testing gravity with the two-body problem." Thesis, Aix-Marseille, 2020. http://www.theses.fr/2020AIXM0206.
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Les ondes gravitationnelles sont une nouvelle sonde pour le régime de champ fort de la gravité. Il est donc essentiel d’identifier les prédictions de la Relativité Générale sur la nature du problème à deux corps et de les contraster à des théories alternatives. Cette thèse se propose de comparer les prédictions de la Relativité Générale et des théories tenseur-scalaires sur les observables gravitationnelles en utilisant des techniques de théories effectives des champs. Dans une première partie, on montrera comment de simples théories tenseur-scalaire peuvent être intégrées dans l’approche "Relativité Générale Non Relativiste" du problème à deux corps, et on soulignera leurs propriétés essentielles. De plus, l’effet d’un couplage disforme du scalaire sur la dynamique à deux corps sera étudié et une technique de resommation sera introduite. Ce nouveau formalisme "Tenseur- Scalaire Non Relativiste" formera les bases de l’étude du mécanisme de Vainshtein dans le cadre du problème à deux corps qui est au coeur de la seconde partie de cette thèse. Enfin, dans une dernière partie on introduira une nouvelle théorie effective des champs adaptée à l’étude de la génération d’ondes gravitationnelles dans les théories prédisant des "cheveux scalaires" autour de trous noirs, dans l’approximation d’un rapport de masse extrêmeGravitational waves provide a new probe into the strong-field regime of gravity. It is thus essential to identify the predictions of General Relativity on the nature of the two-body problem, and to contrast them to alternative theories. This thesis aims at comparing the predictions of General Relativity and scalar-tensor theories on gravitational observables using Effective Field Theory techniques. In a first part, we show how simple scalar-tensor theories can be embedded in the Non-Relativistic General Relativity approach to the two-body problem and highlight their essential features. Furthermore, we study the effects of a disformal coupling of the scalar on the two-body dynamics and introduce a resummation technique. This new Non-Relativistic Scalar-Tensor formalism will provide a basis for the study of the Vainshtein mechanism in two-body configurations which is at the core of the second part of this thesis. Finally, in a last part we devise an Effective Field Theory formalism adapted to gravitational wave generation in theories featuring scalar hair, in the extreme mass ratio regime
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Sepehrmanesh, Mahnaz. "APPLICATION OF THE KALMAN FILTER ON FULL TENSOR GRAVITY GRADIOMETRY DATA AROUND THE VINTON SALT DOME, LOUISIANA." UKnowledge, 2014. http://uknowledge.uky.edu/ees_etds/26.
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Full tensor gravity (FTG) data are known for their high resolution but also for higher noise in its components due to the dynamic nature of the platform used for data acquisition. Although a review of the literature suggests steady increase in the success of gravity gradiometry, we still cannot take advantage of the full potential of the method, mostly because of the noise with the same amplitude and wavenumber characteristics as the signal that affects these data. Smoothing from common low pass filters removes small wavelength features and makes it difficult to detect structural features and other density variations of interest to exploration. In Kalman filtering the components of the FTG are continuously updated to calculate the best estimation of the state. The most important advantage of the Kalman filter is that it can be applied on gravity gradiometry components simultaneously. In addition, one can incorporate constraints. We use the Laplace’s equation that is the most meaningful constraint for potential field data to extract signal from noise and improve the detection and continuity of density variations. We apply the Kalman filter on the FTG data acquired by Bell Geospace over the Vinton salt dome in southwest Louisiana.
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Umiltà, Caterina. "Cosmological predictions for a scalar tensor dark energy model by a dedicated Einstein-Boltzmann code." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2014. http://amslaurea.unibo.it/6580/.
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Majid, Shahn, and Andreas Cap@esi ac at. "Riemannian Geometry of Quantum Groups and Finite Groups with." ESI preprints, 2000. ftp://ftp.esi.ac.at/pub/Preprints/esi902.ps.
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Braglia, Matteo. "Initial conditions for cosmological perturbations in scalar-tensor dark-energy models." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/13860/.
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We discuss the evolution and imprints of isocurvature initial conditions for the scalar field in scalar tensor extensions of Einstein gravity. We consider the simplest models of scalar tensor theories, as Induced gravity (IG, which can be recasted in form of Jordan-Brans-Dicke theory by a redefinition of the scalar field) or non-minimally coupled (NMC) scalar fields in which the acceleration of the Universe is connected to a variation of the effective Planck mass. After introducing the fundamental ideas of cosmological perturbation theory and scalar tensor theories of gravity, we give the evolution equations for matter, metric and scalar field fluctuations in synchronous gauge. We use this set of equations for both the IG and the NMC models to find a new isocurvature solution in which the scalar field fluctuations compensate for the relativistic components respectively. We also show how we can generalize the well known isocurvature modes in Einstein GR to these models. We show the different evolution of cosmological fluctuations for these isocurvature initial conditions compared to the standard adiabatic one. After that, we compute the CMB angular power spectrum for these solutions in the IG model, with the help of a modified Einstein-Boltzmann CLASS code. In particular the CMB power spectrum is computed separately for adiabatic and isocurvature initial conditions, i.e. for totally uncorrelated modes, and with arbitrary correlations leading to an interesting explanation of the lack of power in the low multipoles region of the CMB temperature power spectrum. Finally we show how a simple model of double inflation in IG could explain the generation of the new isocurvature mode.
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Henz, Tobias [Verfasser], and Jan Martin [Akademischer Betreuer] Pawlowski. "Physics on all Scales : Scalar-Tensor Theories of Quantum Gravity in Particle Physics and Cosmology / Tobias Henz ; Betreuer: Jan Martin Pawlowski." Heidelberg : Universitätsbibliothek Heidelberg, 2016. http://d-nb.info/1180614623/34.
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Lionni, Luca. "Colored discrete spaces : Higher dimensional combinatorial maps and quantum gravity." Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLS270/document.
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On considère, en deux dimensions, une version euclidienne discrète de l’action d’Einstein-Hilbert, qui décrit la gravité en l’absence de matière. À l’intégration sur les géométries se substitue une sommation sur des surfaces triangulées aléatoires. Dans la limite physique de faible gravité, seules les triangulations planaires survivent. Leur limite en distribution, la carte brownienne, est une surface fractale continue dont l’importance dans le contexte de la gravité quantique en deux dimensions a été récemment précisée. Cet espace est interprété comme un espace-temps quantique, obtenu comme limite à grande échelle d’un ensemble statistique de surfaces discrètes aléatoires. En deux dimensions, on peut donc étudier les propriétés fractales de la gravité quantique via une approche discrète. Il est bien connu que les généralisations directes en dimensions supérieures échouent à produire des espace-temps quantiques aux propriétés adéquates : en dimension D>2, la limite en distribution des triangulations qui survivent dans la limite de faible gravité est l’arbre continu aléatoire, ou polymères branchés en physique. Si en deux dimensions on parvient aux mêmes conclusions en considérant non pas des triangulations, mais des surfaces discrètes aléatoires obtenues par recollements de 2p-gones, nous savons depuis peu que ce n’est pas toujours le cas en dimension D>2. L’apparition de nouvelles limites continues dans le cadre de théories de gravité impliquant des espaces discrets aléatoires reste une question ouverte. Nous étudions des espaces obtenus par recollements de blocs élémentaires, comme des polytopes à facettes triangulaires. Dans la limite de faible gravité, seuls les espaces qui maximisent la courbure moyenne survivent. Les identifier est cependant une tâche ardue dans le cas général, pour lequel les résultats sont obtenus numériquement. Afin d’obtenir des résultats analytiques, une coloration des (D-1)-cellules, les facettes, a été introduite. En toute dimension paire, on peut trouver des familles d’espaces discrets colorés de courbure moyenne maximale dans la classe d’universalité des arbres – convergeant vers l’arbre continu aléatoire, des cartes planaires – convergeant vers la carte brownienne, ou encore dans la classe de prolifération des bébé-univers. Cependant, ces résultats sont obtenus en raison de la simplicité de blocs élémentaires dont la structure uni ou bidimensionnelle ne rend pas compte de la riche diversité des blocs colorés en dimensions supérieures. Le premier objectif de cette thèse est donc d’établir des outils combinatoires qui permettraient une étude systématique des blocs élémentaires colorés et des espaces discrets qu’ils génèrent. Le principal résultat de ce travail est l’établissement d’une bijection entre ces espaces et des familles de cartes combinatoires, qui préserve l’information sur la courbure locale. Elle permet l’utilisation de résultats sur les surfaces discrètes et ouvre la voie à une étude systématique des espaces discrets en dimensions supérieures à deux. Cette bijection est appliquée à la caractérisation d’un certain nombre de blocs de petites tailles ainsi qu’à une nouvelle famille infinie. Le lien avec les modèles de tenseurs aléatoires est détaillé. Une attention particulière est donnée à la détermination du nombre maximal de (D-2)-cellules et de l’action appropriée du modèle de tenseurs correspondant. Nous montrons comment utiliser la bijection susmentionnée pour identifier les contributions à un tout ordre du développement en 1/N des fonctions à 2n points du modèle SYK coloré, et appliquons ceci à l’énumération des cartes unicellulaires généralisées – les espaces discrets obtenus par recollement d’un unique bloc élémentaire – selon leur courbure moyenne. Pour tout choix de blocs colorés, nous montrons comment réécrire la théorie d’Einstein-Hilbert discrète correspondante comme un modèle de matrices aléatoires avec traces partielles, dit représentation en champs intermédiairesIn two dimensions, the Euclidean Einstein-Hilbert action, which describes gravity in the absence of matter, can be discretized over random triangulations. In the physical limit of small Newton's constant, only planar triangulations survive. The limit in distribution of planar triangulations - the Brownian map - is a continuum fractal space which importance in the context of two-dimensional quantum gravity has been made more precise over the last years. It is interpreted as a quantum continuum space-time, obtained in the thermodynamical limit from a statistical ensemble of random discrete surfaces. The fractal properties of two-dimensional quantum gravity can therefore be studied from a discrete approach. It is well known that direct higher dimensional generalizations fail to produce appropriate quantum space-times in the continuum limit: the limit in distribution of dimension D>2 triangulations which survive in the limit of small Newton's constant is the continuous random tree, also called branched polymers in physics. However, while in two dimensions, discretizing the Einstein-Hilbert action over random 2p-angulations - discrete surfaces obtained by gluing 2p-gons together - leads to the same conclusions as for triangulations, this is not always the case in higher dimensions, as was discovered recently. Whether new continuum limit arise by considering discrete Einstein-Hilbert theories of more general random discrete spaces in dimension D remains an open question.We study discrete spaces obtained by gluing together elementary building blocks, such as polytopes with triangular facets. Such spaces generalize 2p-angulations in higher dimensions. In the physical limit of small Newton's constant, only discrete spaces which maximize the mean curvature survive. However, identifying them is a task far too difficult in the general case, for which quantities are estimated throughout numerical computations. In order to obtain analytical results, a coloring of (D-1)-cells has been introduced. In any even dimension, we can find families of colored discrete spaces of maximal mean curvature in the universality classes of trees - converging towards the continuous random tree, of planar maps - converging towards the Brownian map, or of proliferating baby universes. However, it is the simple structure of the corresponding building blocks which makes it possible to obtain these results: it is similar to that of one or two dimensional objects and does not render the rich diversity of colored building blocks in dimensions three and higher.This work therefore aims at providing combinatorial tools which would enable a systematic study of the building blocks and of the colored discrete spaces they generate. The main result of this thesis is the derivation of a bijection between colored discrete spaces and colored combinatorial maps, which preserves the information on the local curvature. It makes it possible to use results from combinatorial maps and paves the way to a systematical study of higher dimensional colored discrete spaces. As an application, a number of blocks of small sizes are analyzed, as well as a new infinite family of building blocks. The relation to random tensor models is detailed. Emphasis is given to finding the lowest bound on the number of (D-2)-cells, which is equivalent to determining the correct scaling for the corresponding tensor model. We explain how the bijection can be used to identify the graphs contributing at any given order of the 1/N expansion of the 2n-point functions of the colored SYK model, and apply this to the enumeration of generalized unicellular maps - discrete spaces obtained from a single building block - according to their mean curvature. For any choice of colored building blocks, we show how to rewrite the corresponding discrete Einstein-Hilbert theory as a random matrix model with partial traces, the so-called intermediate field representation
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Carrozza, Sylvain. "Tensorial methods and renormalization in Group Field Theories." Thesis, Paris 11, 2013. http://www.theses.fr/2013PA112147/document.
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Cette thèse présente une étude détaillée de la structure de théories appelées GFT ("Group Field Theory" en anglais),à travers le prisme de la renormalisation. Ce sont des théories des champs issues de divers travaux en gravité quantique, parmi lesquels la gravité quantique à boucles et les modèles de matrices ou de tenseurs. Elles sont interprétées comme desmodèles d'espaces-temps quantiques, dans le sens où elles génèrent des amplitudes de Feynman indexées par des triangulations,qui interpolent les états spatiaux de la gravité quantique à boucles. Afin d'établir ces modèles comme des théories deschamps rigoureusement définies, puis de comprendre leurs conséquences dans l'infrarouge, il est primordial de comprendre leur renormalisation. C'est à cette tâche que cette thèse s'attèle, grâce à des méthodes tensorielles développées récemment,et dans deux directions complémentaires. Premièrement, de nouveaux résultats sur l'expansion asymptotique (en le cut-off) des modèles colorés de Boulatov-Ooguri sont démontrés, donnant accès à un régime non-perturbatif dans lequel une infinité de degrés de liberté contribue. Secondement, un formalisme général pour la renormalisation des GFTs dites tensorielles (TGFTs) et avec invariance de jauge est mis au point. Parmi ces théories, une TGFT en trois dimensions et basée sur le groupe de jauge SU(2) se révèle être juste renormalisable, ce qui ouvre la voie à l'application de ce formalisme à la gravité quantiqueIn this thesis, we study the structure of Group Field Theories (GFTs) from the point of view of renormalization theory.Such quantum field theories are found in approaches to quantum gravity related to Loop Quantum Gravity (LQG) on the one hand,and to matrix models and tensor models on the other hand. They model quantum space-time, in the sense that their Feynman amplitudes label triangulations, which can be understood as transition amplitudes between LQG spin network states. The question of renormalizability is crucial if one wants to establish interesting GFTs as well-defined (perturbative) quantum field theories, and in a second step connect them to known infrared gravitational physics. Relying on recently developed tensorial tools, this thesis explores the GFT formalism in two complementary directions. First, new results on the large cut-off expansion of the colored Boulatov-Ooguri models allow to explore further a non-perturbative regime in which infinitely many degrees of freedom contribute. The second set of results provide a new rigorous framework for the renormalization of so-called Tensorial GFTs (TGFTs) with gauge invariance condition. In particular, a non-trivial 3d TGFT with gauge group SU(2) is proven just-renormalizable at the perturbative level, hence opening the way to applications of the formalism to (3d Euclidean) quantum gravity
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Bomfim, Everton Pereira. "O uso dos dados da missão GOCE para a caracterização e a investigação das implicações na estrutura de densidade das Bacias Sedimentares do Amazonas e Solimões, Brasil." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/14/14132/tde-21062013-003455/.
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A maneira mais direta de detectar as anomalias da densidade é pelo estudo do potencial gravitacional e de suas derivadas. A disponibilidade global e a boa resolução dos dados do satélite GOCE, aliadas à disponibilidade de dados de gravimetria terrestre, são ideais para a comparação e classificação das bacias de larga escala, como as bacias sedimentares do Solimões e do Amazonas dentro do Craton amazônico. Foram processados um conjunto de dados, produtos GOCE EGG_TRF_2 Level 2, ao longo das trajetórias do satélite para remover o ruído (shift/drift) nos gradientes da gravidade a partir da técnica crossover (XO). Calculamos a redução das massas topográfica a fim de obter os componentes do gradiente da gravidade e anomalia da gravidade usando modelagem direta com prismas esféricos a partir do modelo de elevação digital, ETOPO1. Desta maneira, a comparação dos dados somente do satélite GOCE com as reduções das massas topográficas referentes aos componentes do gradiente da gravidade permitiram estimar quantidades invariantes que trouxeram uma melhoria na interpretação dos dados do tensor de gravidade. Além disso, comparamos dados terrestres do campo de gravidade com dados do campo de gravidade dos modelos geopotenciais EGM2008 e GOCE, uma vez que os dados terrestres podem ser afetados por erros em longos comprimentos de onda devido a erros de nivelamento, diferentes referenciais de altitudes, e aos problemas em interligar diferentes campanhas de medidas da gravidade. Portanto, estimamos uma melhora e uma nova representação dos mapas das anomalias de gravidade e do tensor gradiente da gravidade nas áreas inacessíveis do Craton Amazônico. As observações forneceram novas entradas para determinar campos regionais a partir dados brutos pre-processados (gradiente de gravidade EGG_TRF_2 L2), bem como a partir de um modelo geopotencial mais recente até grau e ordem 250 dos harmonicos esféricos derivados de dados somente do satélite GOCE para a representação do campo de gravidade como geóide, anomalias da gravidade e os componentes tensor da gravidade, os quais foram quantidades importantes para interpretação, modelagem e estudo dessas estruturas. Finalmente, obtivemos um modelo isostático considerando a estrutura de densidade litosférica estudada através de uma modelagem direta 3D da distribuição de densidade por prismas esféricos usando a geometria do embasamento e descontinuidade do Moho. Além do que, constatamos através da modelagem direta das soleiras de diabásios dentro dos sedimentos mostramos que somente as soleiras dentro da Bacia do Amazonas não são as únicas responsáveis pela anomalia de gravidade positiva que coincide aproximadamente com as espessuras máximas dos sedimentos da Bacia. Talvez, isso possa ser também um resultado de movimentos relativos do Escudo das Guianas situado ao norte da Bacia, e o Escudo Brasileiro situado ao sul. Embora isso seja apenas uma evidência adicional preliminar, não podemos confirmá-las a partir das estimativas do campo da gravidade. Portanto, é necessário outros tipos de dados geofísicos, como por exemplo, evidências mais claras advindas do paleomagnetismo.The most direct way to detect density anomalies is the study of the gravity potential field and its derivatives. The global availability and good resolution of the GOCE mission coupled with the availability of terrestrial gravity data are ideal for the scope of intercomparison and classification of the two large-scale Amazon and Solimoes sedimentary basins into area of the Amazon Craton. The GOCE data set obtained in satellite tracks were processed from EGG_TRF_2 Level 2 Products generated with the correction needed to remove the noise (shift/drift), and so, to recover the individual components of the gravity gradient tensor using the crossover (XO) points technique. We calculated the topographic masses reductions in order to obtain the gravity gradient components and gravity anomaly (vertical component) using forward modelling from tesseroids from Digital Elevation Model, ETOPO1. Thus, the comparison of the only-satellite GOCE data with the reductions of the topographic masses for the gradient components allowed to estimate invariants quantities for bring an improvement in the interpretation of the gravity tensor data. Furthermore, we compared the terrestrial data gravity field with EGM2008 and GOCE-deduced gravity field because the terrestrial fields may be affected by errors at long wavelengths due to errors in leveling, different height references, and problems in connecting different measurement campaigns. However, we have estimated an improvement and new representations of the gravity anomalies maps and gravity gradient tensor components primary in inaccessible areas of the Amazon Craton. GOCE observations provide new inputs to determine the regional fields from the preprocessed raw data (EGG_TRF_2 L2 gravity gradients), as well from the most recent global geopotential model available up to degree and order 250 developed in spherical harmonics derived only-satellite GOCE data for representing of geoid and others gravity field as gravity anomaly and gravity gradient tensor components, which are important quantities for modelling and studying these structures. Finally, we obtained the isostatic model considering the lithospheric density structure studied through a 3D direct modelling of density distribution using the geometry of basement and Moho discontinuity, assumed to be known as initial constraint. In addition, we found through direct modeling sills and sediment has shown that the diabase sills are not the only ones responsible for positive gravity anomaly map that transects the Amazon Basin, roughly coincident with the maximum thickness of sedimentary rocks or the trough of the basin. Maybe, this could be the result of the relative movements of the Guiana Shield, situated at the north of the Amazon basin, and the Brazilian Shield, situated at the south. Although this is only a preliminary additional evidence, we cannot confirm it only from the data of gravity. It is necessary others types of geophysical data, for example, more clear evidences obtained from paleomagnetism.
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Lanči, Jaroslav. "Návrh zařízení pro měření tenzoru setrvačnosti vozidla." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2012. http://www.nusl.cz/ntk/nusl-230309.
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The aim of this thesis was to design a device allowing to measure the moments of inertia of a motor vehicle around several intersecting axes. Next, a three dimensional model of the proposed device was created in programme Pro/ENGINEER. Stress analysis of individual components was performed using the finite element method (FEM) in programme ANSYS.
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Gucci, Federica. "Experimental and numerical investigation of turbulence in Stable Boundary Layer flows." Doctoral thesis, Università degli studi di Trento, 2023. https://hdl.handle.net/11572/371127.
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The present work combines experimental and numerical analyses to improve current understanding of turbulence in stably stratified flows. An extensive literature review is presented on the mechanisms governing turbulence under stratified conditions, with a special focus on the Richardson number parameter, as it is often adopted as a switch to turn turbulence modelling on/off. Anisotropization of turbulence is investigated, as it is found to be an important mechanism for turbulence survival at any Richardson number, but usually overlooked in turbulence parameterizations.
For this purpose, an experimental dataset previously collected over an Alpine glacier is used, with a focus on the anisotropy of the Reynolds stress tensor, as the scientific community has recently shown improvements in the description of the atmospheric surface layer by taking this aspect into account. Different sources leading stresses to deviate from the isotropic limit are explored, as well as energy exchanges across scales and between kinetic and potential reservoirs, in order to identify the main processes that should be included in turbulence parameterizations to properly represent anisotropic turbulence under stable conditions. High-resolution numerical simulations are then performed with the Weather Research and Forecasting (WRF) model to evaluate different PBL parameterizations in reproducing specific stable atmospheric conditions developing over complex terrain, and their influence on the local circulation. For this purpose, two wintertime case studies in a basin-like area of an Alpine valley are investigated. Both are fair-weather episodes with weak synoptic forcing and well-developed diurnal local circulations, differing by the thermal stratification in the basin. In particular, the influence of thermal stratification on the outbreak of a valley-exit wind coming from a tributary valley is investigated, and the influence of such type of flows on turbulence anisotropy in stably stratified conditions is discussed for future investigations.
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Almeida, Tony Silva. "Teoria escalar-tensorial: Uma abordagem geométrica." Universidade Federal da Paraíba, 2014. http://tede.biblioteca.ufpb.br:8080/handle/tede/9531.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
In this cool thesis, we consider an approach to Brans-Dicke theory of gravity in which the scalar eld has a geometrical nature. By postulating the Palatini variation, we nd out that the role played by the scalar eld consists in turning the space-time geometry into a Weyl integrable manifold. This procedure leads to a scalar-tensor theory that di ers from the original Brans-Dicke theory in many aspects and presents some new features. We also consider the Weyl integrable geometry to investigate gravity in (2+1)-dimensions. We show that, in addition to leading to a Newtonian limit, WIST in (2+1) dimensions presents some interesting properties that are not shared by Einstein theory, such as geodesic deviation between particles in a dust distribution. Finally, taking advantage of the duality between the geometrical scalar-tensor theory and general relativity coupled with a massless scalar eld we study naked singularities and wormholes.
Esta tese trata de tópicos relacionados às teorias escalares-tensoriais e a geometria de Weyl integrável. Nossa abordagem será no sentido de indicar a geometria de Weyl integr ável como sendo um ambiente natural para a introdução de teorias escalares-tensorias. Nossa discussão será em torno da teoria de Brans-Dicke, considerada o protótipo das teorias escalares tensoriais, no entanto a discussão é facilmente estendida para essas versões mais gerais. Fazemos isso em dois momentos. Primeiro, indicando, no âmbito da teoria de Brans-Dicke, que na estrutura geométrica e de campos adotadas pela teoria existe uma relação estreita com a geometria de Weyl, inclusive associando o efeito descrito na literatura como "quinta força"(que violaria o princípio de equivalência) com o movimento geodésico da geometria de Weyl integrável, reformulando o postulado geodésico. E, num segundo momento, usando o método variacional de Palatini, acabamos por formular uma nova teoria escalar-tensorial, agora com ingredientes completamente geométricos, ambientada numa geometria de Weyl integrável. Estudamos ainda soluções no vazio do problema estático de uma distribuição de massa esfericamente simétrica, onde surgem objetos de interesse astrofísico como singularidades nuas e buracos de minhoca. Também formulamos a teoria conhecida por WIST (Weyl Integrable Spacetimes) em (2 + 1)D, o que resulta numa teoria consistente, não sofrendo das falhas associadas à teoria da relatividade geral nessa dimensionalidade
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Kuyrukcu, Halil. "Kaluza-klein Reduction Of Higher Curvature Gravity Models." Phd thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/3/12611748/index.pdf.
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The standard Kaluza-Klein theory is reviewed and its basic equations are rewritten in an anholonomic basis. A five dimensional Yang-Mills type quadratic
and cubic curvature gravity model is introduced. By employing the Palatini variational principle, the field equations and the stress-energy tensors of these models are presented. Unification of gravity with electromagnetism is achieved
through the Kaluza-Klein reduction mechanism. Reduced curvature invariants,field equations and stress-energy tensors in four dimensional space-time are obtained. The structure of interactions among the gravitational, electromagnetic
and massless scalar fields are demonstrated in detail. It is shown that in addition to a set of generalized Maxwell and Yang-Mills type gravity equations the
Lorentz force also emerges from this theory. Solutions of the standard Kaluza-Klein theory are explicitly demonstrated to be intrinsically contained in the quadratic model.
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Zhang, Ying. "Coalescence of Sessile Drops: the Role of Gravity, Interfacial Tension and Surface Wettability." Research Showcase @ CMU, 2016. http://repository.cmu.edu/dissertations/994.
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Coalescence of liquid drops is important in many natural and industrial processes, such as raining, inkjet printing and coating applications. The coalescence for sessile drops is more complicated due to the additional interplay between the drops and solid surface. This work examines the impact of gravity, interfacial tensions and wetting properties on both the static and dynamic aspects of the coalescence of sessile drops. In the presence of gravity, seven dimensionless parameters are identified to describe the axisymmetric configuration of a compound sessile drop after coalescence. A stability criterion is established based on the perturbation of Laplacian shape and the stability criterion is numerically evaluated in the zero Bond number limit. Surface Evolver simulations and experiments are performed for compound sessile drops at small and intermediate Bond numbers. Both simulations and experiments agree closely with the zero Bond number analysis, exhibiting a small discrepancy at intermediate Bond number. For the dynamics of sessile drop coalescence, experiments are performed for miscible fluids with similar surface tensions but different densities and viscosities. The coalescence behavior shows three distinctive stages with well separated timescales: an initial stage of fast bridge healing process, an intermediate stage of advective motion for fluids with different densities, and a final stage of diffusion. A dimensional analysis shows that the flow behavior for the advective motion resembles gravity current. A more detailed analytical model based on the lubrication approximation is conducted and demonstrates good qualitative agreement with the advective motion during the sessile drop coalescence.
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King, Andrew A. "The effects of surface tension and gravity on a liquid film lining a tube." Thesis, University of Nottingham, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.423970.
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Ward, Nicholas Rhys. "The rate-limiting mechanism for the heterogeneous burning of iron in normal gravity and reduced gravity." Queensland University of Technology, 2007. http://eprints.qut.edu.au/16673/.
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This thesis presents a research project in the field of oxygen system fire safety relating to the heterogeneous burning of iron in normal gravity and reduced gravity. Fires involving metallic components in oxygen systems often occur, with devastating and costly results, motivating continued research to improve the safety of these devices through a better understanding of the burning phenomena. Metallic materials typically burn in the liquid phase, referred to as heterogeneous burning. A review of the literature indicates that there is a need to improve the overall understanding of heterogeneous burning and better understand the factors that influence metal flammability in normal gravity and reduced gravity. Melting rates for metals burning in reduced gravity have been shown to be higher than those observed under similar conditions in normal gravity, indicating that there is a need for further insight into heterogeneous burning, especially in regard to the rate-limiting mechanism. The objective of the current research is to determine the cause of the higher melting rates observed for metals burning in reduced gravity to (a) identify the rate-limiting mechanism during heterogeneous burning and thus contribute to an improved fundamental understanding of the system, and (b) contribute to improved oxygen system fire safety for both ground-based and space-based applications. In support of the work, a 2-s duration ground-based drop tower reduced-gravity facility was commissioned and a reduced-gravity metals combustion test system was designed, constructed, commissioned and utilised. These experimental systems were used to conduct tests involving burning 3.2-mm diameter cylindrical iron rods in high-pressure oxygen in normal gravity and reduced gravity. Experimental results demonstrate that at the onset of reduced gravity, the burning liquid droplet rapidly attains a spherical shape and engulfs the solid rod, and that this is associated with a rapid increase in the observed melting rate. This link between the geometry of the solid/liquid interface and melting rate during heterogeneous burning is of particular interest in the current research. Heat transfer analysis was performed and shows that a proportional relationship exists between the surface area of the solid/liquid interface and the observed melting rate. This is confirmed through detailed microanalysis of quenched samples that shows excellent agreement between the proportional change in interfacial surface area and the observed melting rate. Thus, it is concluded that the increased melting rates observed for metals burning in reduced gravity are due to altered interfacial geometry, which increases the contact area for heat transfer between the liquid and solid phases. This leads to the conclusion that heat transfer across the solid/liquid interface is the rate-limiting mechanism for melting and burning, limited by the interfacial surface area. This is a fundamental result that applies in normal gravity and reduced gravity and clarifies that oxygen availability, as postulated in the literature, is not rate limiting. It is also established that, except for geometric changes at the solid/liquid interface, the heterogeneous burning phenomenon is the same at each gravity level. A conceptual framework for understanding and discussing the many factors that influence heterogeneous burning is proposed, which is relevant to the study of burning metals and to oxygen system fire safety in both normal-gravity and reduced-gravity applications.
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Ward, Nicholas Rhys. "The rate-limiting mechanism for the heterogeneous burning of iron in normal gravity and reduced gravity." Thesis, Queensland University of Technology, 2007. https://eprints.qut.edu.au/16673/1/Nicholas_Ward_Thesis.pdf.
Full textAbstract:
This thesis presents a research project in the field of oxygen system fire safety relating to the heterogeneous burning of iron in normal gravity and reduced gravity. Fires involving metallic components in oxygen systems often occur, with devastating and costly results, motivating continued research to improve the safety of these devices through a better understanding of the burning phenomena. Metallic materials typically burn in the liquid phase, referred to as heterogeneous burning. A review of the literature indicates that there is a need to improve the overall understanding of heterogeneous burning and better understand the factors that influence metal flammability in normal gravity and reduced gravity. Melting rates for metals burning in reduced gravity have been shown to be higher than those observed under similar conditions in normal gravity, indicating that there is a need for further insight into heterogeneous burning, especially in regard to the rate-limiting mechanism. The objective of the current research is to determine the cause of the higher melting rates observed for metals burning in reduced gravity to (a) identify the rate-limiting mechanism during heterogeneous burning and thus contribute to an improved fundamental understanding of the system, and (b) contribute to improved oxygen system fire safety for both ground-based and space-based applications. In support of the work, a 2-s duration ground-based drop tower reduced-gravity facility was commissioned and a reduced-gravity metals combustion test system was designed, constructed, commissioned and utilised. These experimental systems were used to conduct tests involving burning 3.2-mm diameter cylindrical iron rods in high-pressure oxygen in normal gravity and reduced gravity. Experimental results demonstrate that at the onset of reduced gravity, the burning liquid droplet rapidly attains a spherical shape and engulfs the solid rod, and that this is associated with a rapid increase in the observed melting rate. This link between the geometry of the solid/liquid interface and melting rate during heterogeneous burning is of particular interest in the current research. Heat transfer analysis was performed and shows that a proportional relationship exists between the surface area of the solid/liquid interface and the observed melting rate. This is confirmed through detailed microanalysis of quenched samples that shows excellent agreement between the proportional change in interfacial surface area and the observed melting rate. Thus, it is concluded that the increased melting rates observed for metals burning in reduced gravity are due to altered interfacial geometry, which increases the contact area for heat transfer between the liquid and solid phases. This leads to the conclusion that heat transfer across the solid/liquid interface is the rate-limiting mechanism for melting and burning, limited by the interfacial surface area. This is a fundamental result that applies in normal gravity and reduced gravity and clarifies that oxygen availability, as postulated in the literature, is not rate limiting. It is also established that, except for geometric changes at the solid/liquid interface, the heterogeneous burning phenomenon is the same at each gravity level. A conceptual framework for understanding and discussing the many factors that influence heterogeneous burning is proposed, which is relevant to the study of burning metals and to oxygen system fire safety in both normal-gravity and reduced-gravity applications.
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Sakr, Ziad. "Cosmology beyond ΛCDM model in the light of cluster abundance tension." Thesis, Toulouse 3, 2018. http://www.theses.fr/2018TOU30346.
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Le modèle ΛCDM permet de décrire avec une grande précision la plupart des présentes observations cosmologiques. Cependant, l'un de ses paramètres, σ 8, mesurant l'amplitude de fluctuations de la matière, présente une discordance entre sa valeur contrainte par le spectre de puissance angulaire du CMB de la mission Planck, les Cls, et celle déterminée à partir des amas SZ dans l'univers proche. Dans le présent travail on explore divers extensions du modèle ΛCDM comme origines possibles de cette anomalie. Pour tester les effets de ces extensions, nous avons effectué une analyse Monte Carlo on l'on compare les contraintes sur σ 8 à partir de ΛCDM avec celles résultantes de ces extensions, et ceci en utilisant principalement le spectre de puissance CMB seul ou combiné avec des comptages d'amas. Ces derniers sont basés sur différentes relations masse observables et couvrent différents redshift : des amas de rayons X dans l'univers local, des amas de la mission SZ Planck dans l'univers proche ou une estimation des amas détectés par leur richesse photométrique à partir du la future mission Euclid. Du fait qu'une mauvaise détermination de l'étalonnage de la masse des amas pourrait également être la raison de cette divergence, notre approche consistait, lorsqu'on combinait les deux sondes issues des amas et du CMB, à laisser le facteur d'étalonnage libre afin qu'il soit contraint comme les autres paramètres cosmologiques par les deux données. Dans le cas d'introduction de trois neutrinos massifs dégénérés, nous avons trouvé qu'ils n'ont aucun effet significatif sur la correction de l'écart entre les contraintes issues de comptage CMB et ceux issues des Xray ou SZ cluster. Nous avons ensuite permis à l'indice de croissance ƴ de varier. Nous trouvons une corrélation entre ƴ et le paramètre de calibration masse-observable des amas détectés par rayons X qui n'est pas affecté par la présence ou non des neutrinos massifs. [...]The ΛCDM model has proved successful in describing to a high precision most of nowadays cosmological observations. However, one of its parameters, σ 8, measuring the present matter amplitude fluctuations, constrained from CMB angular power spectrum, the Cls, was found by the Planck mission, in significant tension with value constrained by SZ galaxy cluster counts in the near universe. In the present work we investigate extensions to ΛCDM model as possible origins behind this discrepancy. To test these extensions, we performed a Monte Carlo analysis to compare constraints on σ 8 in ΛCDM with constraints under these extensions, using mainly CMB Cls combined with cluster counts sample. The later were based on different mass observables relations and covered different redshift ranges: X-ray cluster in the local universe, SZ Planck mission clusters from the near universe or photometric richness estimated detected clusters from future high redshift upcoming Euclid alike mission. Because an improper determination of the calibration of cluster mass function could also be behind this discrepancy, our approach was, when combined with CMB, to leave the calibration factor free to vary and be constrained by data. Introducing three degenerate massive neutrinos, we found that they have no significant effect on fixing the discrepancy between CMB and Xray or SZ cluster counts. We then allowed the growth index ƴ to vary. We find a correlation in the confidence space between ƴ and the X-ray mass observable factor not affected by the presence of massive neutrinos, indicating that a modifying gravity is favored over massive neutrinos as a way to alleviate the tension. However, when a SZ cluster sample covering a larger redshift range was used, we found that the correlation between ƴ and the calibration factor, is constrained by the evolution of the growth through redshift and limited to a region where it cannot fix the discrepancy. [...]
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Cericola, Davide. "Rapporto tensore su scalare con gravità indotta: analisi dell’approssimazione di slow-roll nei frames di Jordan e Einstein." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2016. http://amslaurea.unibo.it/11506/.
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L’obbiettivo di questa tesi è quello di analizzare le conseguenze della scelta del frame (Jordan o Einstein) nel calcolo delle proprietà degli spettri primordiali generati dall’inflazione ed in particolare dell’osservabile r (rapporto tensore su scalare) al variare del potenziale del campo che genera l’espansione accelerata.
Partendo dalla descrizione della teoria dell’inflazione in relatività generale, focalizzando l’attenzione sui motivi che hanno portato all’introduzione di questa teoria, vengono presentate le tecniche di utilizzo comune per lo studio della dinamica omogenea (classica) inflazionaria e di quella disomogenea (quantistica). Una particolare attenzione viene rivolta ai metodi di approssimazione che è necessario adottare per estrarre predizioni analitiche dai modelli inflazionari per poi confrontarle con le osservazioni. Le tecniche introdotte vengono poi applicate ai modelli di inflazione con gravità indotta, ovvero ad una famiglia di modelli con accoppiamento non minimale tra il campo scalare inflatonico e il settore gravitazionale. Si porrà attenzione alle differenze rispetto ai modelli con accoppiamento minimale, e verrà studiata la dinamica in presenza di alcuni potenziali derivanti dalla teoria delle particelle e diffusi in letteratura. Il concetto di “transizione tra il frame di Jordan e il frame di Einstein” viene illustrato e le sue conseguenze nel calcolo approssimato del rapporto tensore su scalare sono discusse.
Infine gli schemi di approssimazione proposti vengono analizzati numericamente. Risulterà che per due dei tre potenziali presentati i metodi di approssimazione sono più accurati nel frame di Einstein, mentre per il terzo potenziale i due frames portano a risultati analitici similmente accurati.
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NOVAK, JEROME. "Etude numerique de sources de rayonnement gravitationnel en theorie tenseur-scalaire de la gravite." Paris 7, 1998. http://www.theses.fr/1998PA077115.
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Afin de tester la relativite generale, il faut comparer cette derniere a des theories alternatives. Les theories tenseur-scalaire sont en ce sens non seulement alternatives, mais representent egalement une generalisation de la relativite generale, motivee par les tentatives d'unification des forces. Un des moyens les plus interessants de les contraindre est de prevoir le signal gravitationnel emis dans le cadre de ces theories lors de catastrophes astrophysiques, et de detecter ou non ce signal par les observatoires gravitationnels actuellement en cours de construction. Les sources etudiees dans cette these touchent toutes aux etoiles a neutrons, que ce soient les oscillations de ces astres, leur effondrement en trou noir ou leur formation a partir de naine blanche ou lors d'une explosion de supernova de type ii. Les techniques numeriques employees pour modeliser ces phenomenes sont les methodes pseudo-spectrales de decomposition des fonctions sur une base de polynomes de tchebychev, qui sont tres precises tant que les quantites decrites restent continues. Dans le cas de l'etude de l'explosion menant a la formation d'une etoile a neutrons (presence de choc) ces methodes ont ete associees avec succes aux methodes aux differences finies, capables de traiter ces discontinuites. Les resultats donnent une estimation des formes et amplitudes attendues des signaux gravitationnels produits, lors de ces effondrements gravitationnels, en fonction des parametres de la theorie.
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Sebastianutti, Marco. "Geodesic motion and Raychaudhuri equations." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/18755/.
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The work presented in this thesis is devoted to the study of geodesic motion in the context of General Relativity. The motion of a single test particle is governed by the geodesic equations of the given space-time, nevertheless one can be interested in the collective behavior of a family (congruence) of test particles, whose dynamics is controlled by the Raychaudhuri equations. In this thesis, both the aspects have been considered, with great interest in the latter issue. Geometric quantities appear in these evolution equations, therefore, it goes without saying that the features of a given space-time must necessarily arise. In this way, through the study of these quantities, one is able to analyze the given space-time. In the first part of this dissertation, we study the relation between geodesic motion and gravity. In fact, the geodesic equations are a useful tool for detecting a gravitational field. While, in the second part, after the derivation of Raychaudhuri equations, we focus on their applications to cosmology. Using these equations, as we mentioned above, one can show how geometric quantities linked to the given space-time, like expansion, shear and twist parameters govern the focusing or de-focusing of geodesic congruences. Physical requirements on matter stress-energy (i.e., positivity of energy density in any frame of reference), lead to the various energy conditions, which must hold, at least in a classical context. Therefore, under these suitable conditions, the focusing of a geodesics "bundle", in the FLRW metric, bring us to the idea of an initial (big bang) singularity in the model of a homogeneous isotropic universe. The geodesic focusing theorem derived from both, the Raychaudhuri equations and the energy conditions acts as an important tool in understanding the Hawking-Penrose singularity theorems.
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Lachaume, Xavier. "Des équations de contrainte en gravité modifiée : des théories de Lovelock à un nouveau problème de σk-Yamabe." Thesis, Tours, 2017. http://www.theses.fr/2017TOUR4018/document.
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Cette thèse est consacrée au problème d’évolution des théories de gravité modifiée : après avoir rappelé ce qu’il en est pour la Relativité Générale (RG), nous exposons le formalisme n + 1 des théories ƒ(R), Brans-Dicke et tenseur-scalaire et redémontrons un résultat connu : le problème de Cauchy est bien posé pour ces théories, et les équations de contrainte se réduisent à celles de la RG avec un champ de matière. Puis nous effectuons la même décomposition n + 1 pour les théories de Lovelock et, ce qui est nouveau, ƒ(Lovelock). Nous étudions ensuite les équations de contrainte des théories de Lovelock et montrons qu’elles sont, dans le cas conformément plat et symétrique en temps, la prescription d’une somme de σk-courbures. Afin de résoudre cette équation de prescription, nous introduisons une nouvelle famille de polynômes semi-symétriques homogènes et développons des résultats de concavité pour ces polynômes. Nous énonçons une conjecture qui, si elle était avérée, nous permettrait de résoudre l’équation de prescription dans de nombreux cas : ∀ P;Q ∈ ℝ[X], avec deg P = deg Q = p, P et Q sont scindés => p ∑ k=0 P(k) Q(p-k) est scindéThis thesis is devoted to the evolution problem for modified gravity theories. After having explained this problem for General Relativity (GR), we present the n + 1 formalism for ƒ(R) theories, Brans-Dicke and scalar-tensor theories. We recall a known result: the Cauchy problem for these theories is well-posed, and the constraint equations are reduced to those of GR with a matter field. Then we proceed to the same n+1 decomposition for Lovelock and ƒ(Lovelock) theories, the latter being an original result. We show that in the locally conformally flat timesymmetric case, they can be written as the prescription of a sum of σk-curvatures. In order to solve the prescription equation, we introduce a new family of homogeneous semisymmetric polynomials and prove some concavity results for those polynomials. We express the following conjecture: if this is true, we are able to solve the prescription equation in many cases. ∀ P;Q ∈ ℝ[X], avec deg P = deg Q = p, P and Q are real-rooted => p ∑ k=0 P(k) Q(p-k) is real-rooted:
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Maurice, Michel. "Participation à la construction d'un spectromètre RMN in vivo : application à la mesure des variations de volume de l'eau au niveau du vertex chez l'homme en microgravité simulée." Lyon 1, 1991. http://www.theses.fr/1991LYO1T009.
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Autard, Laurent. "Etude de la liaison entre la tension du vent à la surface et les propriétés des champs de vagues de capillarité-gravité developpés." Aix-Marseille 2, 1995. http://www.theses.fr/1995AIX22084.
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La teledetection radar de la surface de la mer en mode diffusiometre s'appuie sur l'existence d'une liaison entre la tension du vent a la surface et la couverture de l'interface air/mer en vagues de capillarite-gravite. Pour preciser cette liaison, nous avons examine tout d'abord les proprietes des champs de vagues courtes en soufflerie pour des fetchs et des vitesses de vent variees. La transformation en ondelettes des signaux de vagues mesures simultanement en deux points a permis de distinguer: des vagues courtes generees directement par le vent dont les paquets se deplacent librement a la surface ; des vagues courtes demeurant attachees aux cretes des vagues de gravite qui les ont generees par des mecanismes d'instabilite. Pour des vitesses de vent croissantes, l'energie des vagues de capillarite-gravite augmente comme le cube de la vitesse de frottement dans l'air sans que la repartition de l'energie entre les deux classes de petites vagues ne soit modifiee. On observe ainsi une loi d'equilibre spectral en puissance moins sept tiers de la frequence. Nous avons ensuite observe la reponse d'un champ de vagues de capillarite-gravite bien developpe a une acceleration brutale du vent obtenue en contractant la veine d'air. L'energie du champ de vagues courtes augmente alors aussi rapidement que la vitesse du vent. Simultanement une couche limite interne se developpe dans l'air sous les effets combines de l'acceleration du vent et du changement de rugosite de la surface lie a l'apparition de vagues de capillarite-gravite supplementaires. Un modele analytique decrivant ce phenomene montre que meme en conditions inhomogenes, l'energie des vagues courtes demeure liee instantanement a la tension du vent a la surface