Um estuo dos modelos da geometria hiperbólica

Pós-graduação em Matemática Universitária - IGCE

Dark energy as a kinematic effect

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Buracos sônicos em superfícies esféricas

Pós-graduação em Física - IFT

Divertor map with freedom of geometry and safety factor profile

An explicit, area-preserving and integrable magnetic field line map for a single-null divertor tokamak is obtained using a trajectory integration method to represent equilibrium magnetic surfaces. The magnetic surfaces obtained from the map are capable of fitting different geometries with freely specified position of the X-point, by varying free model parameters. The safety factor profile of the map is independent of the geometric parameters and can also be chosen arbitrarily. The divertor integrable map is composed of a nonintegrable map that simulates the effect of external symmetry-breaking resonances, so as to generate a chaotic region near the separatrix passing through the X-point. The composed field line map is used to analyze escape patterns (the connection length distribution and magnetic footprints on the divertor plate) for two equilibrium configurations with different magnetic shear profiles at the plasma edge.

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.

Wing geometry of Anopheles darlingi Root (Diptera: Culicidae) in five major Brazilian ecoregions

We undertook geometric morphometric analysis of wing venation to assess this character's ability to distinguish Anopheles darlingi Root populations and to test the hypothesis that populations from coastal areas of the Brazilian Atlantic Forest differ from those of the interior Atlantic Forest, Cerrado, and the regions South and North of the Amazon River. Results suggest that populations from the coastal and interior Atlantic Forest are more similar to each other than to any of the other regional populations. Notably, the Cerrado population was more similar to that from north of the Amazon River than to that collected of south of the River. thus showing no correlation with geographical distances. We hypothesize that environmental and ecological factors may affect wing evolution in An. darlingi. Although it is premature to associate environmental and ecological determinants with wing features and evolution of the species, investigations on this field are promising. (C) 2012 Elsevier B.V. All rights reserved.

Comparison of wing geometry data and genetic data for assessing the population structure of Aedes aegypti

Aedes aegypti is the most important vector of dengue viruses in tropical and subtropical regions. Because vaccines are still under development, dengue prevention depends primarily on vector control. Population genetics is a common approach in research involving Ae. aegypti. In the context of medical entomology, wing morphometric analysis has been proposed as a strong and low-cost complementary tool for investigating population structure. Therefore, we comparatively evaluated the genetic and phenotypic variability of population samples of Ae. aegypti from four sampling sites in the metropolitan area of Sao Paulo city, Brazil. The distances between the sites ranged from 7.1 to 50 km. This area, where knowledge on the population genetics of this mosquito is incipient, was chosen due to the thousands of dengue cases registered yearly. The analysed loci were polymorphic, and they revealed population structure (global F-ST = 0.062; p < 0.05) and low levels of gene flow (Nm = 0.47) between the four locations. Principal component and discriminant analyses of wing shape variables (18 landmarks) demonstrated that wing polymorphisms were only slightly more common between populations than within populations. Whereas microsatellites allowed for geographic differentiation, wing geometry failed to distinguish the samples. These data suggest that microevolution in this species may affect genetic and morphological characters to different degrees. In this case, wing shape was not validated as a marker for assessing population structure. According to the interpretation of a previous report, the wing shape of Ae. aegypti does not vary significantly because it is stabilised by selective pressure. (C) 2011 Elsevier B.V. All rights reserved.

Effect of sample pre-cracking method and notch geometry in plane strain fracture toughness tests as applied to a PMMA resin

The influence of test method factors (notch shape, square or angular, and pre-cracking method, by tapping onto or pressing a razor blade) on the results obtained in plane strain fracture toughness test according to standard ASTM D5045 using SENB specimens made of a commercial PMMA resin were investigated. Results were analyzed quantitatively by comparing the obtained K-IC values and qualitatively by observing their effect on the Moire fringes observed using photoelasticity, showing that, at 95% significance level, the K-IC values are affected by the pre-cracking method, with the most conservative value being obtained when natural pre-cracks were introduced by tapping onto a razor blade (K-IC = 1.15 +/- 0.11 MPa.m(0.5)). This correlates with a perturbation in the stress field close to the pre-crack tip observed in the photoelasticity test sample when it was introduced by pressing the razor blade. Surprisingly, notch geometry only slightly affects the results. (C) 2012 Elsevier Ltd. All rights reserved.

Mapping the hydrodynamic response to the initial geometry in heavy-ion collisions

We investigate how the initial geometry of a heavy-ion collision is transformed into final flow observables by solving event-by-event ideal hydrodynamics with realistic fluctuating initial conditions. We study quantitatively to what extent anisotropic flow (nu(n)) is determined by the initial eccentricity epsilon(n) for a set of realistic simulations, and we discuss which definition of epsilon(n) gives the best estimator of nu(n). We find that the common practice of using an r(2) weight in the definition of epsilon(n) in general results in a poorer predictor of nu(n) than when using r(n) weight, for n > 2. We similarly study the importance of additional properties of the initial state. For example, we show that in order to correctly predict nu(4) and nu(5) for noncentral collisions, one must take into account nonlinear terms proportional to epsilon(2)(2) and epsilon(2)epsilon(3), respectively. We find that it makes no difference whether one calculates the eccentricities over a range of rapidity or in a single slice at z = 0, nor is it important whether one uses an energy or entropy density weight. This knowledge will be important for making a more direct link between experimental observables and hydrodynamic initial conditions, the latter being poorly constrained at present.

Fluoropolymer piezoelectrets with tubular channels: resonance behavior controlled by channel geometry

Ferro- or piezoelectrets are dielectric materials with two elastically very different macroscopic phases and electrically charged interfaces between them. One of the newer piezoelectret variants is a system of two fluoroethylenepropylene (FEP) films that are first laminated around a polytetrafluoroethylene (PTFE) template. Then, by removing the PTFE template, a two-layer FEP structure with open tubular channels is obtained. After electrical charging, the channels form easily deformable macroscopic electric dipoles whose changes under mechanical or electrical stress lead to significant direct or inverse piezoelectricity, respectively. Here, different PTFE templates are employed to generate channel geometries that vary in height or width. It is shown that the control of the channel geometry allows a direct adjustment of the resonance frequencies in the tubular-channel piezoelectrets. By combining several different channel widths in a single ferroelectret, it is possible to obtain multiple resonance peaks that may lead to a rather flat frequency-response region of the transducer material. A phenomenological relation between the resonance frequency and the geometrical parameters of a tubular channel is also presented. This relation may help to design piezoelectrets with a specific frequency response.

Wecken type problems for self-maps of the Klein bottle

We consider various problems regarding roots and coincidence points for maps into the Klein bottle . The root problem where the target is and the domain is a compact surface with non-positive Euler characteristic is studied. Results similar to those when the target is the torus are obtained. The Wecken property for coincidences from to is established, and we also obtain the following 1-parameter result. Families which are coincidence free but any homotopy between and , , creates a coincidence with . This is done for any pair of maps such that the Nielsen coincidence number is zero. Finally, we exhibit one such family where is the constant map and if we allow for homotopies of , then we can find a coincidence free pair of homotopies.

Effects of specimen geometry and loading mode on crack growth resistance curves of a high-strength pipeline girth weld

This work presents an investigation of the ductile tearing properties for a girth weld made of an API 5L X80 pipeline steel using experimentally measured crack growth resistance curves. Use of these materials is motivated by the increasing demand in the number of applications for manufacturing high strength pipes for the oil and gas industry including marine applications and steel catenary risers. Testing of the pipeline girth welds employed side-grooved, clamped SE(T) specimens and shallow crack bend SE(B) specimens with a weld centerline notch to determine the crack growth resistance curves based upon the unloading compliance (UC) method using the single specimen technique. Recently developed compliance functions and η-factors applicable for SE(T) and SE(B) fracture specimens with homogeneous material and overmatched welds are introduced to determine crack growth resistance data from laboratory measurements of load-displacement records.

Topics in geometry, analysis and inverse problems

The thesis consists of three independent parts. Part I: Polynomial amoebas We study the amoeba of a polynomial, as de ned by Gelfand, Kapranov and Zelevinsky. A central role in the treatment is played by a certain convex function which is linear in each complement component of the amoeba, which we call the Ronkin function. This function is used in two di erent ways. First, we use it to construct a polyhedral complex, which we call a spine, approximating the amoeba. Second, the Monge-Ampere measure of the Ronkin function has interesting properties which we explore. This measure can be used to derive an upper bound on the area of an amoeba in two dimensions. We also obtain results on the number of complement components of an amoeba, and consider possible extensions of the theory to varieties of codimension higher than 1. Part II: Differential equations in the complex plane We consider polynomials in one complex variable arising as eigenfunctions of certain differential operators, and obtain results on the distribution of their zeros. We show that in the limit when the degree of the polynomial approaches innity, its zeros are distributed according to a certain probability measure. This measure has its support on the union of nitely many curve segments, and can be characterized by a simple condition on its Cauchy transform. Part III: Radon transforms and tomography This part is concerned with different weighted Radon transforms in two dimensions, in particular the problem of inverting such transforms. We obtain stability results of this inverse problem for rather general classes of weights, including weights of attenuation type with data acquisition limited to a 180 degrees range of angles. We also derive an inversion formula for the exponential Radon transform, with the same restriction on the angle.