Sudden changes in chaotic attractors and transient basins in a model for rattling in gearboxes

We consider a model for rattling in single-stage gearbox systems with some backlash consisting of two wheels with a sinusoidal driving; the equations of motions are analytically integrated between two impacts of the gear teeth. Just after each impact, a mapping is used to obtain the dynamical variables. We have observed a rich dynamical behavior in such system, by varying its control parameters, and we focus on intermittent switching between laminar oscillations and chaotic bursting, as well as crises, which are sudden changes in the chaotic behavior. The corresponding transient basins in phase space are found to be riddled-like, with a highly interwoven fractal structure. (C) 2004 Elsevier Ltd. All rights reserved.

Control and chaos for vibro-impact and non-ideal oscillators

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

Suppressing grazing chaos in impacting system by structural nonlinearity

In this note we investigate the influence of structural nonlinearity of a simple cantilever beam impacting system on its dynamic responses close to grazing incidence by a means of numerical simulation. To obtain a clear picture of this effect we considered two systems exhibiting impacting motion, where the primary stiffness is either linear (piecewise linear system) or nonlinear (piecewise nonlinear system). Two systems were studied by constructing bifurcation diagrams, basins of attractions, Lyapunov exponents and parameter plots. In our analysis we focused on the grazing transitions from no impact to impact motion. We observed that the dynamic responses of these two similar systems are qualitatively different around the grazing transitions. For the piecewise linear system, we identified on the parameter space a considerable region with chaotic behaviour, while for the piecewise nonlinear system we found just periodic attractors. We postulate that the structural nonlinearity of the cantilever impacting beam suppresses chaos near grazing. (C) 2007 Elsevier Ltd. All rights reserved.

The non-twist standard map with robust tori

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

Robust tori in a double-waved Hamiltonian model

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

Robust tori-like Lagrangian coherent structures

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

Labyrinthic standard non-twist map

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

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.

Magnetic Field Line Escape: Comparison with Mean Free Path

In the present work, we determine the fraction of magnetic field lines that reach the tokamak wall leaving the plasma surrounded by a chaotic layer created by resonant perturbations at the plasma edge. The chaotic layer arises in a scenario where an integrable magnetic field with reversed magnetic shear is perturbed by an ergodic magnetic limiter. For each considered line, we calculate its connection length, i.e. the number of toroidal turns that the field lines complete before reaching the wall. We represent the results in the poloidal section in which the initial coordinates are chosen. We also estimate the radial profile of the fraction of field lines, for different temperatures, whose connection lengths are smaller than the electron collisional mean free path.

Decay of energy and suppression of Fermi acceleration in a dissipative driven stadium-like billiard

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

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

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A combined method for evaluating radon and progeny in waters and its use at Guarani aquifer, São Paulo State, Brazil

A combined method for evaluating radon (Rn-222) and progeny (Pb-214 and Bi-214) in water was developed by using inexpensive alpha scintillation Counting and gamma ray spectrometry through NaI(Tl) scintillation detectors. A groundwater sample collected at the Pocos de Caldas alkaline massif in Brazil was submitted to the technique in order to assure its applicability by comparing the volumetric activities by different methods. Similar volumetric activity was determined for Pb-214 and Bi-214 in the sample analyzed that is compatible with the expected condition of radioactive equilibrium between these nuclides. The combined method was successfully used to analyze groundwater samples from Guarani aquifer in S (a) over tildeo Paulo State, Brazil, and the results of the measurements indicated that Pb-214 and Bi-214 provide useful information concerning the evaluation of the drinking water quality in terms of radiological aspects. This is because they are directly identified in the water samples, without the need of requiring the assumption of the establishment of the transient equilibrium condition with its parent Rn-222. (c) 2005 Elsevier Ltd. All rights reserved.

Implications of groundwater weathered profile interactions to the mobilization of radionuclides

This study reports the nature and extent of open-system interaction between groundwater and a weathered profile developed in the high grade thorium and REE ore body in Morro do Ferro, Pocos de Caldas plateau. The radioelement mobility in the shallow oxidizing environment was considered by using chemical data in conjunction with U-234/U-238, Ra-226/Th-230, Th-230/U-234, Th-228/Th-232, Ra-228/Th-232 and Th-230/Ra-228 activity ratios (AR's) for borehole spoil and groundwater samples.Recharging groundwater from the studied borehole has low salinity values, with total dissolved solids content of 14.7 mg/l and total ionic strength of 0.00018. The ratio of the weight of dissolved radioelement per unit volume of solution to the weight of radioelement in solid phase per unit weight of solid phase showed that the radioelement solubility in the studied waters varied according to the following order: radium> uranium >thorium.U-234/U-238 AR's less than 1 were measured in solid phase and can justify the enhancement of U-234 in solution. Ra-226/Th-230 AR's greater than 1 and Th-230/U-234 AR'S less than 1 were evaluated between 20 and 27 m in depth, where a 2.1-m thick magnetite dike was intersected. These ratios could be justified by deposition of U and Ra associated with Fe-Mn oxides and kaolinite, where mineral saturation indices evaluated from the available data confirm this possibility. Covariations among disequilibria involving Th-228/(228) Ra and Ra-228/Th-232 AR's showed the preferential removal of Ra-228 relative to Tn isotopes, Th-228 and Th-232. The recent deposition of radium within the timescale of at least the last 35 years also is suggested. (C) 1998 Elsevier B.V. Ltd. All rights reserved.

Differential proteomic analysis of Acidithiobacillus ferrooxidans cells maintained in contact with bornite or chalcopyrite: Proteins involved with the early bacterial response

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)