Dynamics at infinity and the existence of singularly degenerate heteroclinic cycles in the Lorenz system

In this paper, by using the Poincare compactification in R(3) we make a global analysis of the Lorenz system, including the complete description of its dynamic behavior on the sphere at infinity. Combining analytical and numerical techniques we show that for the parameter value b = 0 the system presents an infinite set of singularly degenerate heteroclinic cycles, which consist of invariant sets formed by a line of equilibria together with heteroclinic orbits connecting two of the equilibria. The dynamical consequences related to the existence of such cycles are discussed. In particular a possibly new mechanism behind the creation of Lorenz-like chaotic attractors, consisting of the change in the stability index of the saddle at the origin as the parameter b crosses the null value, is proposed. Based on the knowledge of this mechanism we have numerically found chaotic attractors for the Lorenz system in the case of small b > 0, so nearby the singularly degenerate heteroclinic cycles.

PERIODIC PERTURBATION of QUADRATIC SYSTEMS WITH TWO INFINITE HETEROCLINIC CYCLES

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Time-periodic perturbation of a Lienard equation with an unbounded homoclinic loop

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Global dynamics of the Rikitake system

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Bifurcation Analysis of a Van der Pol-Duffing Circuit with Parallel Resistor

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Species diversity of yeast in oral colonization of insulin-treated diabetes mellitus patients

The aim of this study was to investigate oral yeast colonization, antifungal susceptibility and strain diversity in insulin-dependent diabetes mellitus patients (175), as well as to evaluate the influence of dental prostheses. Oral rinse samples were cultured on selective media, in order to isolate, count and identify the yeasts recovered. More than half of the diabetic subjects (53%) carried significant amounts of Candida cells in the buccal cavity and these organisms were recovered at higher densities in diabetics wearing dentures. A total of 93 yeast strains were isolated from these patients, including: Candida spp. (n = 89); Pichia (n = 02); Trichosporon (n = 1), and Geotrichum (n = 1). C. albicans represented 56% of these strains, non-albicans Candida 39.8%, and other genera of yeast 4.3%. C. albicans was prevalent, followed by C. parapsilosis, C. tropicalis, C. glabrata, C. krusei, C. rugosa and C. guilliermondii. Agar disk-diffusion tests of the susceptibility of non-albicans Candida and other genera of yeast to fluconazole showed resistance in 21.9%, mainly in C. rugosa (100%), C. glabrata (57%) and C. krusei (50%). Local oral factors, such as the presence of dentures, in association with diabetes, seemed to have the effect of increasing the amount and variety of Candida species in the oral cavities, mainly those with lower drug susceptibilities.

Artificial satellites orbits in 2:1 resonance: GPS constellation

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Dynamical erosion of asteroid groups in the region of the Phocaea family

In a previous paper, the current state of knowledge of the region containing the Phocaea dynamical family was revised. Here, the dynamical evolution and possible origin of the Phocaea dynamical family and asteroid groups in the region are investigated. First, I study the case of asteroids at high eccentricity (e > 0.31). I find that these objects are unstable because of encounters with Mars on time-scales of up to 270 Myr. The minimum time needed by members of the Phocaea classical family to reach the orbital locations of these objects, 370 Myr, can be used to set a lower limit on the age of the Phocaea family.Next, attention is focused on the chaotic layer previously identified near the nu(6) secular resonance border. Using analytical and numerical tools, I find that the presence of the nu(6) secular resonance forces asteroids with vertical bar g-g(6)vertical bar < 2.55 arcsec yr(-1) to reach eccentricities high enough to allow them to experience deep, close encounters with Mars. Results of the analytical model of Yoshikawa and of my numerical simulations fully explain the low-inclination chaotic region found by Carruba.Finally, I investigate the long-term stability of the minor families and clumps identified in the previous paper, with particular emphasis on a clump only identifiable in the domain of proper frequencies (n, g, g - s) around (6246) Komurotoru. I find that while the clumps identified in the space of proper elements quickly disperse when the Yarkovsky effect is considered, the family around (19536) is still observable for time-scales of more than 50 Myr. The (6246) clump, characterized by its interaction with the nu(5) + nu(16) and 2 nu(6) - nu(16) secular resonances, is robust on time-scales of 50 Myr. I confirm that this group may be the first clump ever detected in the frequency domain that can be associated with a real collisional event.

Dynamical erosion of asteroid groups in the region of the Pallas family

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

The Orbital Dynamics of Synchronous Satellites: Irregular Motions in the 2:1 Resonance

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Qualitative and quantitative characterization of aluminium alloys after corrosion testing

The 2024 and 7050 aluminium alloys used as aircraft components were subjected to laboratory corrosion tests in sodium chloride solution, Light-microscope examinations make it possible to characterise morphological aspects of the localised corrosion. Image analysis was used to determine both depth and width of pits over corroded surfaces. It has been concluded that the annealing could reduce the pit growth in both alloys, by means of grains recrystallization or recovery. The 2024 alloy also tends to present an exfoliation mechanism, mainly throughout non-recrystallized and recrystallized grain boundaries, increasing the width and sustaining the depth of pit cavities during exposition to saline atmosphere. SEM and EDS analysis reveal the morphology and elemental distribution of the corrosion products formed after immersion corrosion test. Some of these products were identified by X-ray diffraction analysis. For 2024, Al(OH)(3), MS(OH)(2) and Cu2O were found. AI(OH)(3) and Cu2O were also found in 7050 samples.

An analysis of the region of the Phocaea dynamical family

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Control aspects in nonlinear Hill's equation

The Hill's equations-even in the linear original version are a describer of phenomenon having chaotic flavor, giving sometimes very unusual situations. The theory of the so called intervals of instability in the equation provides the precise description for most of these phenomena. Considerations on nonlinearities into the Hill's equation is a quite recent task. The linearized version for almost of these systems it reduces to the Hill's classical linear one. In this paper, some indicative facts are pointed out on the possibility of having the linear system stabilizable and/or exactly controllable. As consequence of such an approach we get results having strong classical aspects, like the one talking about location of parameters in intervals of stability. A result for nonlinear proper periodic controls, is considered too. (C) 2010 Elsevier B.V. All rights reserved.

Control Design Applied to a Micro Electro Mechanical System: MEMS Comb drive

This paper presents the linear optimal control technique for reducing the chaotic movement of the micro-electro-mechanical Comb Drive system to a small periodic orbit. We analyze the non-linear dynamics in a micro-electro-mechanical Comb Drive and demonstrated that this model has a chaotic behavior. Chaos control problems consist of attempts to stabilize a chaotic system to an equilibrium point, a periodic orbit, or more general, about a given reference trajectory. This technique is applied in analyzes the nonlinear dynamics in an MEMS Comb drive. The simulation results show the identification by linear optimal control is very effective.

Extraocular muscle fixation to porous polyethylene orbital implants using 2-octyl-cyanoacrylate

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)