Radiação e detetores de Unruh - DeWitt

Pós-graduação em Física - IFT

Um estuo dos modelos da geometria hiperbólica

Pós-graduação em Matemática Universitária - IGCE

Hiperbolicidade seccional em dimensões arbitrárias

Pós-graduação em Matemática - IBILCE

Fundamentos de geometria hiperbólica

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Continuity of Dynamical Structures for Nonautonomous Evolution Equations Under Singular Perturbations

In this paper we study the continuity of invariant sets for nonautonomous infinite-dimensional dynamical systems under singular perturbations. We extend the existing results on lower-semicontinuity of attractors of autonomous and nonautonomous dynamical systems. This is accomplished through a detailed analysis of the structure of the invariant sets and its behavior under perturbation. We prove that a bounded hyperbolic global solutions persists under singular perturbations and that their nonlinear unstable manifold behave continuously. To accomplish this, we need to establish results on roughness of exponential dichotomies under these singular perturbations. Our results imply that, if the limiting pullback attractor of a nonautonomous dynamical system is the closure of a countable union of unstable manifolds of global bounded hyperbolic solutions, then it behaves continuously (upper and lower) under singular perturbations.

Robust tori-like Lagrangian coherent structures

In general the term "Lagrangian coherent structure" (LCS) is used to make reference about structures whose properties are similar to a time-dependent analog of stable and unstable manifolds from a hyperbolic fixed point in Hamiltonian systems. Recently, the term LCS was used to describe a different type of structure, whose properties are similar to those of invariant tori in certain classes of two-dimensional incompressible flows. A new kind of LCS was obtained. It consists of barriers, called robust tori that block the trajectories in certain regions of the phase space. We used the Double-Gyre Flow system as the model. In this system, the robust tori play the role of a skeleton for the dynamics and block, horizontally, vortices that come from different parts of the phase space. (C) 2012 Elsevier B.V. All rights reserved.

Use of ground-penetrating radar to map subsurface features at the Lapa do Santo archaeological site (Brazil)

In this article we present some results of ground-penetrating radar (GPR) studies carried out at the Lapa do Santo archaeological site. This cave is within the Lagoa Santa karstic region, Minas Gerais State, Brazil. Results from 44 GPR profiles obtained with 400 MHz shielded antennas indicated anomalous hyperbolic reflections and areas with high sub-horizontal reflection amplitude suggesting archaeological and geological potential targets, respectively. These results were encouraging and were used to guide excavations at this site. Excavation of test units (metre by metre) allowed identifying an anthropogenic feature, e.g., a fire hearth structure and natural features, such as a stalagmite and top of bedrock. Results also indicated the importance of the GPR survey as a tool for orienting archaeological researches, increasing the probability of finding archaeological interest targets in an excavation program in an area of environmental protection.

Differential geometry of grassmannians and the Plucker map

Using the Plucker map between grassmannians, we study basic aspects of classic grassmannian geometries. For 'hyperbolic' grassmannian geometries, we prove some facts (for instance, that the Plucker map is a minimal isometric embedding) that were previously known in the 'elliptic' case.

Representation and analysis of control surface freeplay nonlinearity

Different representations for a control surface freeplay nonlinearity in a three degree of freedom aeroelastic system are assessed. These are the discontinuous, polynomial and hyperbolic tangent representations. The Duhamel formulation is used to model the aerodynamic loads. Assessment of the validity of these representations is performed through comparison with previous experimental observations. The results show that the instability and nonlinear response characteristics are accurately predicted when using the discontinuous and hyperbolic tangent representations. On the other hand, the polynomial representation fails to predict chaotic motions observed in the experiments. (c) 2012 Elsevier Ltd. All rights reserved.

Characterization of Stability Region for General Autonomous Nonlinear Dynamical Systems

The existing characterization of stability regions was developed under the assumption that limit sets on the stability boundary are exclusively composed of hyperbolic equilibrium points and closed orbits. The characterizations derived in this technical note are a generalization of existing results in the theory of stability regions. A characterization of the stability boundary of general autonomous nonlinear dynamical systems is developed under the assumption that limit sets on the stability boundary are composed of a countable number of disjoint and indecomposable components, which can be equilibrium points, closed orbits, quasi-periodic solutions and even chaotic invariant sets.

A continuously differentiable upwinding scheme for the simulation of fluid flow problems

This paper deals with the numerical solution of complex fluid dynamics problems using a new bounded high resolution upwind scheme (called SDPUS-C1 henceforth), for convection term discretization. The scheme is based on TVD and CBC stability criteria and is implemented in the context of the finite volume/difference methodologies, either into the CLAWPACK software package for compressible flows or in the Freeflow simulation system for incompressible viscous flows. The performance of the proposed upwind non-oscillatory scheme is demonstrated by solving two-dimensional compressible flow problems, such as shock wave propagation and two-dimensional/axisymmetric incompressible moving free surface flows. The numerical results demonstrate that this new cell-interface reconstruction technique works very well in several practical applications. (C) 2012 Elsevier Inc. All rights reserved.

Modeling and simulation of severe slugging with mass transfer effects

A mathematical model and numerical simulations are presented to investigate the dynamics of gas, oil and water flow in a pipeline-riser system. The pipeline is modeled as a lumped parameter system and considers two switchable states: one in which the gas is able to penetrate into the riser and another in which there is a liquid accumulation front, preventing the gas from penetrating the riser. The riser model considers a distributed parameter system, in which movable nodes are used to evaluate local conditions along the subsystem. Mass transfer effects are modeled by using a black oil approximation. The model predicts the liquid penetration length in the pipeline and the liquid level in the riser, so it is possible to determine which type of severe slugging occurs in the system. The method of characteristics is used to simplify the differentiation of the resulting hyperbolic system of equations. The equations are discretized and integrated using an implicit method with a predictor-corrector scheme for the treatment of the nonlinearities. Simulations corresponding to severe slugging conditions are presented and compared to results obtained with OLGA computer code, showing a very good agreement. A description of the types of severe slugging for the three-phase flow of gas, oil and water in a pipeline-riser system with mass transfer effects are presented, as well as a stability map. (C) 2011 Elsevier Ltd. All rights reserved.

Stability boundary characterization of nonlinear autonomous dynamical systems in the presence of saddle-node equilibrium points

A dynamical characterization of the stability boundary for a fairly large class of nonlinear autonomous dynamical systems is developed in this paper. This characterization generalizes the existing results by allowing the existence of saddle-node equilibrium points on the stability boundary. The stability boundary of an asymptotically stable equilibrium point is shown to consist of the stable manifolds of the hyperbolic equilibrium points on the stability boundary and the stable, stable center and center manifolds of the saddle-node equilibrium points on the stability boundary.

Cube Complexes and Virtual Fibering of 3-Manifolds.

Una 3-varietà si dice virtualmente fibrata se ammette un rivestimento finito che è un fibrato con base una circonferenza e fibra una superficie. In seguito al lavoro di geometrizzazione di Thurston e Perelman, la generica 3-varietà risulta essere iperbolica; un recente risultato di Agol afferma che una tale varietà è sempre virtualmente fibrata. L’ingrediente principale della prova consiste nell’introduzione, dovuta a Wise, dei complessi cubici nello studio delle 3-varietà iperboliche. Questa tesi si concentra sulle proprietà algebriche e geometriche di queste strutture combinatorie e sul ruolo che esse hanno giocato nella dimostrazione del Teorema di Fibrazione Virtuale.

Bestimmung mechanischer Eigenschaften dünner Polymerfilme mittels AFM-Kraft-Abstands-Kurven

In der vorliegenden Arbeit wurden AFM-Kraft-Abstands-Kurven benutzt, um die mechanischen Eigenschaften dünner Polymerfilme verschiedener Schichtdicken (2 - 400 nm) auf einem sehr viel steiferen Substrat (mechanische Doppelschichten) zu untersuchen. Die mechanischen Eigenschaften einer solchen Probe setzen sich aus den mechanischen Eigenschaften der Bestandteile, d.h. Polymer und Substrat, zusammen. Der Beitrag der Bestandteile hängt von der Schichtdicke und von der Auflagekraft ab. Es wurden existierende Modelle für die Auswertung von an Doppelschichten gemessenen Deformationskurven überprüft und festgestellt, dass kein Modell befriedigende Ergebnisse erzielt. Dies zeigte die Notwendigkeit einer neuen semiempirischen Theorie zur Beschreibung der Deformationskurven von mechanischen Doppelschichten. In dieser Arbeit wird der hyperbolische Fit zu diesem Zweck eingeführt. Die Validität des hyperbolischen Fit wurde anhand von drei Experimenten gezeigt. Alle experimentellen Kurven konnten sehr gut durch den hyperbolischen Fit beschrieben werden. Die Elastizitätsmoduln der Bestandteile konnten in Übereinstimmung mit den Literaturwerten berechnet werden. Die Schichtdicken der Proben konnten in allen Fällen mit großer Exaktheit bestimmt werden. Es wurde zudem die Möglichkeit der Auswertung einzelner Kraft-Abstands-Kurven untersucht. Damit konnte die Schichtdicke der untersuchten Doppelschichten ortsaufgelöst im Submikrometerbereich bestimmt werden und ein verstecktes Substrat detektiert werden. Die Adhäsion an der Grenzfläche Polymer/Substrat hat einen fundamentalen Einfluss auf die mechanischen Eigenschaften der Doppelschicht, der qualitativ im letzten Teil der Doktorarbeit gezeigt werden konnte.