Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1983. / Vita. Abstract. Includes bibliographical references (leaves 35-38). Also available via the Internet.

Depuis sa formulation au début du 20ème siècle, la théorie de la Relativité Générale a été vérifiée avec une précision sans cesse croissante. Cette théorie prédit, entre autre, l'existence d'ondes gravitationnelles qui restent à ce jour inobservées, et ce malgré de nombreuses tentatives de détections. Ces ondes sont caractérisées par leur absence de masse. Une des questions qui se pose alors est de savoir si cette absence de masse est une condition nécessaire pour que théorie et observations concordent. Pour répondre à cette question, il est indispensable d'étudier les différents aspects des théories décrivant des ondes gravitationnelles massives. Au-delà de cet intérêt purement théorique, l'étude de ces théories est, entre autre, motivée par de récentes observations cosmologiques. Celles-ci indiquent que l'accord entre la Relativité Générale et les observations n'est possible que si on suppose l'existence de matière et d'énergie noires. Cette thèse est dédiée à une classe de théories décrivant des ondes gravitationnelles massives. Dans un premier temps, nous résumons les différents problèmes qui surgissent lorsqu'on tente de donner une masse aux ondes gravitationnelles. Ensuite, nous introduisons une classe de modèles et étudions certaines de leurs caractéristiques. Le premier aspect étudié concerne l'existence d'une interaction de type instantanée. De telles interactions sont possibles étant donné que l'invariance de Lorentz est spontanément brisée dans les modèles considérés. Celles-ci sont dès lors discutées et un exemple concret est fourni. La présence d'une interaction instantanée dans ces modèles a une conséquence directe sur les solutions "trous noirs" des équations du champ. En effet, on s'attend à ce que l'interaction instantanée puisse propager de l'information à l'extérieur d'un trou noir, ce qui entraînerait une modification de ces solutions par rapport à celles de la Relativité Générale. Cette supposition est confirmée par les solutions "trous noirs" obtenues dans cette thèse. Celles-ci peuvent soit imiter une certaine quantité de matière noire, soit conduire à un champ gravitationnel répulsif. Finalement, les mécanismes de formation des grandes structures de l'Univers (galaxies, amas de galaxies, ... ) sont étudiés pour les théories considérées. Cette dernière discussion démontre que ces modèles reproduisent le comportement prévu par la Relativité Générale et sont, par conséquent, en accord avec les observations.

The aim of this thesis is to summarize some results in two approaches to studying how quantum gravity may be relevant for experiments. The first approach starts off by stating that one of the questions a theory of quantum gravity might address is how a large-scale universe can be constructed from discrete Planck-size elements. Starting from a discussion of the role of causal and foliation structure in causal dynamical triangulations, this approach leads to a formulation of a model based on graphs whose purpose is to uncover what kind organizational principle or structure might be responsible for endowing spacetime with manifold-like properties. Thus in this approach, experimental input used to constrain models for quantum gravity are observations of glaring large-scale properties of the universe such as the dimensionality or total size. The second approach considers the possible effects of quantum gravity on the propagation of particles. In particular, the focus is on understanding the physics of deformed special relativity when this novel symmetry is seen as a residual effect due to a gauge fixing from a higher dimensional system. Thus here the hope is to connect a proposal for quantum gravity phenomenology with precision experiments of particle properties. A synthesis of such complementary approaches would represent a consistent model for quantum gravity phenomenology and is the background goal for the work in this thesis. The extent to which such a synthesis can be described today is presented.

The aim of this thesis is to summarize some results in two approaches to studying how quantum gravity may be relevant for experiments. The first approach starts off by stating that one of the questions a theory of quantum gravity might address is how a large-scale universe can be constructed from discrete Planck-size elements. Starting from a discussion of the role of causal and foliation structure in causal dynamical triangulations, this approach leads to a formulation of a model based on graphs whose purpose is to uncover what kind organizational principle or structure might be responsible for endowing spacetime with manifold-like properties. Thus in this approach, experimental input used to constrain models for quantum gravity are observations of glaring large-scale properties of the universe such as the dimensionality or total size. The second approach considers the possible effects of quantum gravity on the propagation of particles. In particular, the focus is on understanding the physics of deformed special relativity when this novel symmetry is seen as a residual effect due to a gauge fixing from a higher dimensional system. Thus here the hope is to connect a proposal for quantum gravity phenomenology with precision experiments of particle properties. A synthesis of such complementary approaches would represent a consistent model for quantum gravity phenomenology and is the background goal for the work in this thesis. The extent to which such a synthesis can be described today is presented.

We develop a new approach to classical gravity starting from Mach's principles and the idea that the local shape of spatial configurations is fundamental. This new theory, shape dynamics, is equivalent to general relativity but differs in an important respect: shape dynamics is a theory of dynamic conformal 3-geometry, not a theory of spacetime. Equivalence is achieved by trading foliation invariance for local conformal invariance (up to a global scale). After the trading, what is left is a gauge theory invariant under 3d diffeomorphisms and conformal transformations that preserve the volume of space. There is one non-local global Hamiltonian that generates the dynamics. Thus, shape dynamics is a formulation of gravity that is free of the local problem of time. In addition, the symmetry principle is simpler than that of general relativity because the local constraints are linear. Therefore, shape dynamics provides a novel new starting point for quantum gravity. Furthermore, the conformal invariance provides an ideal setting for studying the relationship between gravity and boundary conformal field theories. The procedure for the trading of symmetries was inspired by a technique called best matching. We explain best matching and its relation to Mach's principles. The key features of best matching are illustrated through finite dimensional toy models. A general picture is then established where relational theories are treated as gauge theories on configuration space. Shape dynamics is then constructed by applying best matching to conformal geometry. We then study shape dynamics in more detail by computing its Hamiltonian perturbatively and establishing a connection with conformal field theory.

In this thesis I present a mathematical tool for understanding the spin networks that arise from the study of the loop states of quantum gravity. The spin networks that arise in quantum gravity possess more information than the original spin networks of Penrose: they are embedded within a manifold and thus possess topological information. There are limited tools available for the study of this information. To remedy this I introduce a slightly modi ed mathematical object - Braided Ribbon Networks - and demonstrate that they can be related to spin networks in a consistent manner which preserves the di eomorphism invariant character of the loop states of quantum gravity. Given a consistent de nition of Braided Ribbon Networks I then relate them back to previous trinion based versions of Braided Ribbon Networks. Next, I introduce a consistent evolution for these networks based upon the duality of these networks to simplicial complexes. From here I demonstrate that there exists an invariant of this evolution and smooth deformations of the networks, which captures some of the topological information of the networks. The principle result of this program is presented next: that the invariants of the Braided Ribbon Networks can be transferred over to the original spin network states of loop quantum gravity. From here we represent other advances in the study of braided ribbon networks, accompanied by comments of their context given the consistent framework developed earlier including: the meaning of isolatable substructures, the particular structure of the capped three braids in trivalent braided ribbon networks and their application towards emergent particle physics, and the implications of the existence of microlocal topological structures in spin networks. Lastly we describe the current state of research in braided ribbon networks, the implications of this study on quantum gravity as a whole and future directions of research in the area.

ABSTRACT This paper treats the standing waves formed by two progressive waves possessing same properties but opposite direction in stationary atmosphere and uniform depth. The third-order approximation to two-wave trains interactions obtained by Chen¡]1990¡^is cited. From the solution that can be reduced to the cases such as standing waves, the properties resulted in standing wave due to the nonlinear interactions between two wave trains intersection, particularly, the two peaks of wave pressure, are described clearly. Furthermore, the profile, pressure and angular frequency is also verified in good agreement with the experimental results.

Thesis (Ph. D.)--Lehigh University, 2001. / Includes vita. Includes bibliographical references (leaves 222-231).

Thesis (Ph. D.)--University of Texas at Austin, 2001. / Vita. Includes bibliographical references (leaves 82-96). Available also in a digital version from Dissertation Abstracts.

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