Dynamics of a spacecraft and normalization around Lagrangian points in the Neptune-Triton system

The problem of a spacecraft orbiting the Neptune-Triton system is presented. The new ingredients in this restricted three body problem are the Neptune oblateness and the high inclined and retrograde motion of Triton. First we present some interesting simulations showing the role played by the oblateness on a Neptune's satellite, disturbed by Triton. We also give an extensive numerical exploration in the case when the spacecraft orbits Triton, considering Sun, Neptune and its planetary oblateness as disturbers. In the plane a x I (a = semi-major axis, I = inclination), we give a plot of the stable regions where the massless body can survive for thousand of years. Retrograde and direct orbits were considered and as usual, the region of stability is much more significant for the case of direct orbit of the spacecraft (Triton's orbit is retrograde). Next we explore the dynamics in a vicinity of the Lagrangian points. The Birkhoff normalization is constructed around L-2, followed by its reduction to the center manifold. In this reduced dynamics, a convenient Poincare section shows the interplay of the Lyapunov and halo periodic orbits, Lissajous and quasi-halo tori as well as the stable and unstable manifolds of the planar Lyapunov orbit. To show the effect of the oblateness, the planar Lyapunov family emanating from the Lagrangian points and three-dimensional halo orbits are obtained by the numerical continuation method. Published by Elsevier Ltd. on behalf of COSPAR.

Phase Transition in Dynamical Systems: Defining Classes of Universality for Two-Dimensional Hamiltonian Mappings via Critical Exponents

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Finding critical exponents for two-dimensional Hamiltonian maps

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Effect of robust torus on the dynamical transport

In the present work, we quantify the fraction of trajectories that reach a specific region of the phase space when we vary a control parameter using two symplectic maps: one non-twist and another one twist. The two maps were studied with and without a robust torus. We compare the obtained patterns and we identify the effect of the robust torus on the dynamical transport. We show that the effect of meandering-like barriers loses importance in blocking the radial transport when the robust torus is present.

Blocking Radial Diffusion in a Double-Waved Hamiltonian Model

A non-twist Hamiltonian system perturbed by two waves with particular wave numbers can present Robust Tori, barriers created by the vanishing of the perturbing Hamiltonian at some defined positions. When Robust Tori exist, any trajectory in phase space passing close to them is blocked by emergent invariant curves that prevent the chaotic transport. We analyze the breaking up of the RT as well the transport dependence on the wave numbers and on the wave amplitudes. Moreover, we report the chaotic web formation in the phase space and how this pattern influences the transport.

Stickiness in a bouncer model: A slowing mechanism for Fermi acceleration

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Scaling investigation for the dynamics of charged particles in an electric field accelerator

Some dynamical properties of an ensemble of trajectories of individual (non-interacting) classical particles of mass m and charge q interacting with a time-dependent electric field and suffering the action of a constant magnetic field are studied. Depending on both the amplitude of oscillation of the electric field and the intensity of the magnetic field, the phase space of the model can either exhibit: (i) regular behavior or (ii) a mixed structure, with periodic islands of regular motion, chaotic seas characterized by positive Lyapunov exponents, and invariant Kolmogorov-Arnold-Moser curves preventing the particle to reach unbounded energy. We define an escape window in the chaotic sea and study the transport properties for chaotic orbits along the phase space by the use of scaling formalism. Our results show that the escape distribution and the survival probability obey homogeneous functions characterized by critical exponents and present universal behavior under appropriate scaling transformations. We show the survival probability decays exponentially for small iterations changing to a slower power law decay for large time, therefore, characterizing clearly the effects of stickiness of the islands and invariant tori. For the range of parameters used, our results show that the crossover from fast to slow decay obeys a power law and the behavior of survival orbits is scaling invariant. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4772997]

Contrasting fluvial styles of the Paraguay River in the northwestern border of the Pantanal wetland, Brazil

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

Quantitative fidelity of recent freshwater mollusk assemblages from the Touro Passo River, Rio Grande do Sul, Brazil

O presente estudo teve como objetivo apresentar uma das primeiras contribuições ao conhecimento sobre a fidelidade quantitativa de associações de moluscos recentes em rios subtropicais. Tanatocenoses e biocenoses foram estudadas em seções retilínea e meandrante tendendo a anastomosada, no curso médio do rio Touro Passo, um tributário de 4ª ordem do rio Uruguai, localizado no extremo oeste do Rio Grande do Sul. As amostragens foram realizadas por meio de quadrats de 5 m², cinco em cada seção, amostrando-se um total de 50 m². Também foram feitas amostragens em um ambiente lêntico, com comunicação intermitente com o Touro Passo, objetivando detectar a existência de transporte de comunidades lênticas para o interior do rio. Os resultados obtidos mostram que, apesar da freqüente oscilação do nível da água, a biocenose do Touro Passo apresenta uma alta fidelidade ecológica e sofre pouca influência de espécies de ambientes lênticos. A composição taxonômica e características de estrutura de comunidades, especialmente as espécies dominantes, refletem, ainda, diferenças ecológicas relacionadas às duas seções amostradas, como a maior complexidade de habitats da estação meandrante. Quanto à fidelidade quantitativa, 60% das espécies encontradas vivas também foram encontradas mortas e 47,3% das espécies encontradas mortas também foram encontras vivas em escala de rio. Porém, 72% dos exemplares coletados mortos são representantes de espécies encontradas vivas. Essa percentagem alta pode estar relacionada à boa correlação entre o ranking de dominância das associações vivas e mortas e, conseqüentemente, as espécies dominantes das tanatocenoses podem ser utilizadas para inferir características ecológicas das biocenoses. Todos os índices analisados variaram muito em escala local (quadrat) e seus valores são mais aproximados aos de outros, registrados em estudos prévios, apenas quando analisados em escala mais ampla (seção, área total).

Caustics of the restricted three-body problem

Trajectories of the planar, circular, restricted three-body problem are given in the configuration space through the caustics associated to the invariant tori of quasi-periodic orbits. It is shown that the caustics of trajectories librating in any particular resonance display some features associated to that resonance. This method can be considered complementary to the Poincare surface of section method, because it provides information not accessible by the other method.

Hopf-zero bifurcations of reversible vector fields

We study the dynamics of a class of reversible vector fields having eigenvalues (0, alphai, -alphai) around their symmetric equilibria. We give a complete list of all normal forms for such vector fields, their versal unfoldings, and the corresponding bifurcation diagrams of the codimensional-one case. We also obtain some important conclusions on the existence of homoclinic and heteroclinic orbits, invariant tori and symmetric periodic orbits.

The defocusing mechanism of isochronous resonances

We present a numerical study concerning the defocusing mechanism of isochronous resonance island chains in the presence of two permanent robust tori. The process is initialized and concluded through bifurcations of fixed points located on the robust tori. Our approach is based on a Hamiltonian system derived from the resonant normal form. Choosing a convenient parameter in this system, we are able to depict a comprehensive analysis of the dynamics of the problem. (c) 2004 Elsevier B.V. All rights reserved.

Classical and quantal aspects of resonant normal forms

The Birkhoff-Gustavson normal form is employed to study separately chaos and resonances in a system with two degrees of freedom. In the integrable regime, tunnelling effects are appreciable when the nearest level spacings show oscillations. Tunnelling among states in the libration and rotation tori regions is also observed. The regularity of avoided crossings due to tunnelling indicates a collective effect and is associated with an isolated resonance. The spectral fluctuations also show a strong level correlation. The Husimi distribution, on the other hand, is insensitive to avoided crossings. An integrable approximation to the overlap of resonances is obtained and a theoretical description is given for an isolated cubic resonance plus a complex orbit. In the non-integrable regime chaos is stronger after overlapping and preferentially at low energies.

Nova contribuiçao ao conhecimento da formação Rio Claro (T) na Folha Rio Claro (SP)

The Rio Claro Formation mainly occurs in the county of Rio Claro (SP) lying unconformably on Paleozoic and Mesozoic rocks. Its thickness is 30-40 m. It shows fine to coarse, regular to poor sorted, Triable sandstones and conglomerates with quartzite and quartz clasts in the base. Thin layers of mudstone occur interbeded. Stratigraphic maps had been elaborated in recent analyses allowing to improve the knowledge about the formation. The biggest thicknesses occur on the east part of the studied area. The coarse/fine clastic ratio map demonstrates that fine sediments are concentrated in the east side, and suggests the existence of barriers which conditioned perennial water body (or bodies) where decantation took place (east, south and southeast sides). The structural contour map of the Rio Claro Formation base indicates a NW/SE trough which was the main depositional axis. The integrated analysis demonstrates that the formation is formed by lacustrine, fluvial and debris flows deposits whose source area was located on NW side, with coalescent alluvial fans from where braided to psamitic meandering fluvial channels came. The location of the source area suggests no link with the Corumbataf River paleo-terraces.

Caracterização geométrica de um sistema fluvial, formação Ttaquaquecetuba, Terciário da Bacia de São Paulo

The objective of this study is the geometric characterization of a fluvial system, exemplified by the Itaquaquecetuba Formation. The studied area is a quarry located in Itaquaquecetuba, distant 35 km from the city of São Paulo, which is inserted in the context of São Paulo Basin. Fluvial systems are important hydrocarbon reservoirs, and this study may contribute with an analogue for ancient reservoirs. It was elaborated ten facies logs along a distance of 200 m (log spacing of 20 m), with a vertical column (thickness) of 40 m for each log. Eight facies cycles, and its lateral chrono-correlation allowed to map the potential reservoir and non-reservoir facies within each cycle. Regarding the depositional model for the studied section, it is assumed an alluvial fan system composed of meandering and ribbon-type fluvial channels.