CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior / Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / O objetivo deste trabalho à estudar a geometria das mÃtricas tipo-Einstein (solitons de Ricci, quase solitons de Ricci e mÃtricas quasi-Einstein). Mais especificamente, vamos obter equaÃÃes de estrutura, exemplos, fÃrmulas integrais e estimativas que permitirÃo caracterizar estas classes de mÃtricas. / The purpose of this work is study the geometric of the like-Einstein metrics (Ricci soliton, almost Ricci solitons and quasi-Einstein metrics). More specifically, we obtain structure equations, examples, integral formulae and estimates that will enable characterize these classes of metrics.

published_or_final_version / Physics / Doctoral / Doctor of Philosophy

published_or_final_version / Mechanical Engineering / Master / Master of Philosophy

No description available.

No description available.

Approved for public release; distribution is unlimited. / The effects of shoaling inner shelf solitons on the bottom boundary layer have been observed and analyzed over a two month summer period at the Monterey Inner Shelf Observatory in Monterey, CA, during 2002. Utilizing CTD data to characterize the temperature field of the water column, Acoustic Doppler Current Profiler (ADCP) data to measure the velocity structure from 3m height above the bed (HAB) to the near surface, and Bistatic Doppler Velocity Sediment Profiler (BDVSP) data to measure the velocity structure and sediment concentration from a range of 60cm to 1cm HAB, solitary internal waves and internal tidal bores were regularly observed at the observation site. These events were characterized by their large isotherm displacements and the sudden change from near surface to near bed stratification as the internal tidal bores passed the observation site. Cross-shore timeseries revealed that the strongest events pushed water onshore near the surface and offshore near the bed, indicating a baroclinic water column during their passage. To analyze their effects on the bottom boundary layer, 3m HAB ADCP and BCDV velocities were compared with backscatter data and surface gravity wave energy at 3m HAB to determine their relative contribution to bed stress and resulting sediment suspension. As the strong internal waves passed, a logarithmic layer formed indicating that shear stress above the bed was occurring. This allowed the friction velocity within the log layer to be estimated. Combining this term with the stress contribution due to the wave energy, the total stress on the bed was then estimated. From this it was determined that typically moderate surface gravity wave forcing at the bed suspended sediment, while solitary internal waves and internal tidal bores continued to transport suspended sediment offshore near the bed. / Ensign, United States Navy

by Yu Wai Kuen. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1993. / Includes bibliographical references (leaves 71-76). / Preface --- p.1 / PART I / Chapter Chapter 1 --- Inverse Scattering Method / Chapter §1 --- Introduction --- p.5 / Chapter §2 --- Rapidly decreasing solutions of the GNLSE --- p.6 / Chapter Chapter 2 --- Modified Inverse Scattering Method / Chapter §1 --- Introduction --- p.25 / Chapter §2 --- Singular solutions of the KdV equation --- p.25 / PART II / Chapter Chapter 3 --- Backlund Transformation Method / Chapter §1 --- Introduction --- p.37 / Chapter §2 --- Solution by Backlund transformation --- p.37 / Chapter §3 --- Clairin's method for finding Backlund transformations --- p.46 / Chapter §4 --- Construction of multi-soliton solutions --- p.48 / Chapter Chapter 4 --- Dressing Method And Hirota Direct Method / Chapter §1 --- Introduction --- p.51 / Chapter §2 --- Zakharov-Shabat's dressing method --- p.52 / Chapter §3 --- Hirota direct method --- p.57 / Chapter Chapter 5 --- Group Reduction Method / Chapter §1 --- Introduction --- p.61 / Chapter §2 --- Method of group reduction --- p.61 / Bibliography --- p.71

Cette thèse a pour objectif l’étude expérimentale de la propagation de solitons sombres temporels aux abords de la longueur d’onde de dispersion nulle d’une fibre optique. Dans un premier temps, nous nous concentrons sur la génération d’ondes dispersives par des solitons sombres. Pour cela, plusieurs techniques de génération de solitons sont mises en oeuvre. La première, basée sur la collision de deux impulsions laser, permet de générer un train de quasi-solitons sombres. Ainsi, en fonction du nombre de solitons composant le train et de la puissance en entrée de la fibre, nous observons l’émission d’une seule ou de plusieurs ondes dispersives ainsi que la génération de supercontinua spectraux. La deuxième technique de génération de solitons sombres mise en place utilise un ensemble de deux façonneurs d’ondes optique. Au moyen de mesures spectrales et de corrélation croisée, nous montrons que celle-ci permet la génération de solitons sombres isolés dont la longueur d’onde, la phase, la profondeur et la durée peuvent être ajustées précisément. Nous montrons alors que la variation de ces paramètres induit une variation de la longueur d’onde des ondes dispersives émises. Nous étudions dans un deuxième temps la collision entre un soliton sombre et une onde dispersive. En réemployant la technique précédente, nous générons simultanément le soliton sombre et l’onde dispersive dans une fibre optique. Nous montrons alors théoriquement, numériquement et expérimentalement, que la collision mène à un décalage en fréquence de l’onde dispersive incidente suivant une relation d’accord de phase spécifique mettant en jeu la profondeur du soliton et la longueur d’onde de l’onde dispersive. / The aim of this thesis is to experimentally study the propagation of temporal dark solitons and their nonlinear dynamics around the zero-dispersion wavelength of an optical fiber. First, we focus on the generation of dispersive waves by dark solitons. For this, several techniques of solitons generation are implemented. The first one, based on the collision of two laser pulses, allows to generate a train of dark quasi-solitons. Depending on the number of solitons in the train and the input power, we observe the emission of one or more dispersive waves, as well as the generation of supercontinua. The second technique to generate dark solitons, uses a set of two waveshapers. By means of spectral and cross-correlation measurements, we show that this technique allows the generation of isolated dark solitons whose wavelength, phase, depth and duration can be precisely adjusted. Thus, we show that the variation of these parameters modifies the wavelength of the emitted dispersive waves. In a second time, we studied the optical collision between a dark soliton with a dispersive wave. Using the previous technique, we generate both the dark soliton and the dispersive wave in an optical fiber. We then show theoretically, numerically and experimentally, that the collision leads to a frequency shift of the incident dispersive wave. According to a specific phase matching, we show that this spectral shift varies as a function of the soliton grayness and also of the dispersive wave wavelength.

This dissertation begins with a review of Calabi-Yau manifolds and their moduli spaces, flux compactification largely tailored to the case of type IIb supergravity, and Coleman-De Luccia vacuum decay. The three chapters that follow present the results of novel research conducted as a graduate student. Our first project is concerned with bubble collisions in single scalar field theories with multiple vacua. Lorentz boosted solitons traveling in one spatial dimension are used as a proxy to the colliding 3-dimensional spherical bubble walls. Recent work found that at sufficiently high impact velocities collisions between such bubble vacua are governed by "free passage" dynamics in which field interactions can be ignored during the collision, providing a systematic process for populating local minima without quantum nucleation. We focus on the time period that follows the bubble collision and provide evidence that, for certain potentials, interactions can drive significant deviations from the free passage bubble profile, thwarting the production of a new patch with different field value. However, for simple polynomial potentials a fine-tuning of vacuum locations is required to reverse the free passage kick enough that the field in the collision region returns to the original bubble vacuum. Hence we deem classical transitions mediated by free passage robust. Our second project continues with soliton collisions in the limit of relativistic impact velocity, but with the new feature of nontrivial field space curvature. We establish a simple geometrical interpretation of such collisions in terms of a double family of field profiles whose tangent vector fields stand in mutual parallel transport. This provides a generalization of the well-known limit in flat field space (free passage). We investigate the limits of this approximation and illustrate our analytical results with numerical simulations. In our third and final project we investigate the distribution of field theories that arise from the low energy limit of flux vacua built on type IIb string theory compactified on the mirror quintic. For a large collection of these models, we numerically determine the distribution of Taylor coefficients in a polynomial expansion of each model's scalar potential to fourth order. We provide an analytic explanation of the proncounced hierarchies exhibited by the random sample of masses and couplings generated numerically. The analytic argument is based on the structure of masses in no scale supergravity and the divergence of the Yukawa coupling at the conifold point in the moduli space of the mirror quintic. Our results cast the superpotential vev as a random element whose capacity to cloud structure vanishes as the conifold is approached.

Orientador: Alvaro de Souza Dutra / Banca: Julio Marny Hoff da Silva / Banca: Bruto Max Pimentel Escobar / Resumo: Neste trabalho, apresentamos uma breve introdução ao estudo dos sólitons. Além disso, introduzimos uma nova classe de configurações oscilantes do tipo lump e do tipo kink. Tais configurações são obtidas de forma analítica e exata, como conseqüência somos capazes de fazer a análise da estabilidade das soluções apresentadas. Por fim, apresentamos no último capítulo soluções de estados ligados de férmions na presença das novas configurações de campo que estamos apresentando neste trabalho / Abstract: In this work we present a brief introduction to the study of solitons. Furthermore, we introduce a new class of oscillating Lorentz covariant configurations for the evolution of the domain walls which are analytically obtained in diverse dimensions. As a consequence, we are able to perform the analysis of the stability of the presented solutions. Finally, in the last chapter, we present analytical solutions of fermion bound states on the background of kinks of a class of asymmetrical scalar field / Mestre