Short Lyapunov time: a method for identifying confined chaos

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Analysing the new Saturnian rings, R/2004 S1 and R/2004 S2

The Cassini-Huygens arrival into the Saturnian system brought a large amount of data about the satellites and rings. Two diffuse rings were found in the region between the A ring and Prometheus. R/2004 S1 is coorbital to Atlas and R/2004 S2 is close to Prometheus. In this work we analysed the closest approach between Prometheus and both rings. As a result we found that the satellite removes particles from R/2004 S2 ring. Long-term numerical simulations showed that some particles can cross the F ring region . The well known region of the F ring, where small satellites are present and particles are being taking from the ring, gains a new insight with the presence of particles from R/2004 S2 ring. The computation of the Lyapunov Characteristic Exponent reveled that the R/2004 S2 ring lies in a chaotic region while R/2004 S1 ring and Atlas are in a stable region. Atlas is responsible for the formation of three regimes in the R/2004 S1 ring, as expected for a satellite embedded in a ring.

The strands of the F ring disturbed by its closest satellites

Some Voyager images showed that the F ring of Saturn is composed of at least four separate, non-intersecting, strands covering about 45 degrees in longitude. According to Murray et al. [Murray, C.D., Gordon, M., Giuliatti Winter, S.M. Unraveling the strands of Saturn's F ring. Icarus 129, 304, 1997.] this structure may be caused by undetected satellites embedded in the gaps.Due to precession, the satellites Prometheus and Pandora and the ring particles can experience periodic close encounters. Giuliatti Winter et al. [Giuliatti Winter, S.M, Murray, C.D., Gordon, M. Perturbations to Saturn's F-ring strands at their closest approach to Prometheus. Plan. Space Sciences, 48, 817, 2000.] analysed the behaviour of these four strands at closest approach with the satellite Prometheus. Their work suggests that Prometheus can induce the ring particles to scatter in the direction of the planet, thus increasing the population of small bodies in this region.In this work we analysed the effects of Prometheus on the radial structure of Saturn's F ring during the Voyager and early Cassini epochs. Our results show that at Voyager epoch Prometheus, and also Pandora, had a negligible influence in the strands. However, during the Cassini encounter Prometheus could affect the strands significantly, scattering particles of the inner strand in the direction of the planet. This process can contribute to the replenishment of material in the region between the F ring and the A ring, where two rings have recently been discovered [Porco, C. et al. Cassini imaging science. Initial results on Saturn's rings and small Satellites. Science, 307, 1226, 2005].We also analyse the behaviour of undetected satellites under the effects of these two satellites by computing the Lyapunov Characteristic Exponent. Our results show that these satellites have a chaotic behaviour which leads to a much more complex scenario. The new satellite S/2004 S6 also presents a chaotic behaviour with can alter the dynamic of the system, since this satellite crosses the orbit of the strands. (C) 2006 COSPAR. Published by Elsevier Ltd. All rights reserved.

Peculiar trajectories around the Lagrangian equilateral points

In the present work we analyse the behaviour of a particle under the gravitational influence of two massive bodies and a particular dissipative force. The circular restricted three body problem, which describes the motion of this particle, has five equilibrium points in the frame which rotates with the same angular velocity as the massive bodies: two equilateral stable points (L-4, L-5) and three colinear unstable points (L-1, L-2, L-3). A particular solution for this problem is a stable orbital libration, called a tadpole orbit, around the equilateral points. The inclusion of a particular dissipative force can alter this configuration. We investigated the orbital behaviour of a particle initially located near L4 or L5 under the perturbation of a satellite and the Poynting-Robertson drag. This is an example of breakdown of quasi-periodic motion about an elliptic point of an area-preserving map under the action of dissipation. Our results show that the effect of this dissipative force is more pronounced when the mass of the satellite and/or the size of the particle decrease, leading to chaotic, although confined, orbits. From the maximum Lyapunov Characteristic Exponent a final value of gamma was computed after a time span of 10(6) orbital periods of the satellite. This result enables us to obtain a critical value of log y beyond which the orbit of the particle will be unstable, leaving the tadpole behaviour. For particles initially located near L4, the critical value of log gamma is -4.07 and for those particles located near L-5 the critical value of log gamma is -3.96. (c) 2006 Elsevier B.V. All rights reserved.

Análise da região do anel F de Saturno

Pós-graduação em Física - FEG

The Liapunov exponent as a tool for exploring phase space

We have used the Liapunov exponent to explore the phase space of a dynamical system. Considering the planar, circular restricted three-body problem for a mass ratio mu = 10(-3) (close to the Jupiter/Sun case), we have integrated similar to 16,000 starting conditions for orbits started interior to that of the perturber and we have estimated the maximum Liapunov characteristic exponent for each starting condition. Despite the fact that the integrations, in general, are for only a few thousand orbital periods of the secondary, a comparative analysis of the Liapunov exponents for various values of the 'cut-off' gives a good overview of the structure of the phase space. It provides information about the diffusion rates of the various chaotic regions, the location of the regular regions associated with primary resonances and even details such as the location of secondary resonances that produce chaotic regions inside the regular regions of primary resonances.

Management of vomplex systems: Modeling the biological pest control

The aim of this paper is to study the cropping system as complex one, applying methods from theory of dynamic systems and from the control theory to the mathematical modeling of the biological pest control. The complex system can be described by different mathematical models. Based on three models of the pest control, the various scenarios have been simulated in order to obtain the pest control strategy only through natural enemies' introduction. © 2008 World Scientific Publishing Company.

Avrami exponent of crystallization in tellurite glasses

Nucleation process and crystal growth for three samples of the (20-x)Li(2)O-80TeO(2)-xWO(3) glass system were studied using X-ray diffraction and differential scanning calorimetry techniques. X-ray diffraction data confirmed the amorphous characteristic of the as-quenched samples and indicated the growth of crystalline phases formed due to the thermal treatment for annealed samples. These results reveal the presence of three distinct gamma-TeO(2), alpha-TeO(2) and alpha-Li(2)Te(2)O(5) crystalline phases in the TL sample, and two distinct alpha-TeO(2) and gamma-TeO(2) crystalline phases in the TLW5 and TLW10 samples. The activation energy and the Avrami exponent were determined from DSC measurements. The activation energy values X-ray diffraction data of the TLW10 glass sample suggest that gamma-TeO(2) phase occur before the alpha-TeO(2). The results obtained for the Avrami exponent point to that the nucleation process is volumetric and that the crystal growth is two or three-dimensional.

Scaling properties of the fermi-ulam accelerator model

The chaotic low energy region (chaotic sea) of the Fermi-Ulam accelerator model is discussed within a scaling framework near the integrable to non-integrable transition. Scaling results for the average quantities (velocity, roughness, energy etc.) of the simplified version of the model are reviewed and it is shown that, for small oscillation amplitude of the moving wall, they can be described by scaling functions with the same characteristic exponents. New numerical results for the complete model are presented. The chaotic sea is also characterized by its Lyapunov exponents.

Sensitivity, specificity and predictive values of linear and nonlinear indices of heart rate variability in stable angina patients

Background: Decreased heart rate variability (HRV) is related to higher morbidity and mortality. In this study we evaluated the linear and nonlinear indices of the HRV in stable angina patients submitted to coronary angiography. Methods. We studied 77 unselected patients for elective coronary angiography, which were divided into two groups: coronary artery disease (CAD) and non-CAD groups. For analysis of HRV indices, HRV was recorded beat by beat with the volunteers in the supine position for 40 minutes. We analyzed the linear indices in the time (SDNN [standard deviation of normal to normal], NN50 [total number of adjacent RR intervals with a difference of duration greater than 50ms] and RMSSD [root-mean square of differences]) and frequency domains ultra-low frequency (ULF) ≤ 0,003 Hz, very low frequency (VLF) 0,003 - 0,04 Hz, low frequency (LF) (0.04-0.15 Hz), and high frequency (HF) (0.15-0.40 Hz) as well as the ratio between LF and HF components (LF/HF). In relation to the nonlinear indices we evaluated SD1, SD2, SD1/SD2, approximate entropy (-ApEn), α1, α2, Lyapunov Exponent, Hurst Exponent, autocorrelation and dimension correlation. The definition of the cutoff point of the variables for predictive tests was obtained by the Receiver Operating Characteristic curve (ROC). The area under the ROC curve was calculated by the extended trapezoidal rule, assuming as relevant areas under the curve ≥ 0.650. Results: Coronary arterial disease patients presented reduced values of SDNN, RMSSD, NN50, HF, SD1, SD2 and -ApEn. HF ≤ 66 ms§ssup§2§esup§, RMSSD ≤ 23.9 ms, ApEn ≤-0.296 and NN50 ≤ 16 presented the best discriminatory power for the presence of significant coronary obstruction. Conclusion: We suggest the use of Heart Rate Variability Analysis in linear and nonlinear domains, for prognostic purposes in patients with stable angina pectoris, in view of their overall impairment. © 2012 Pivatelli et al.; licensee BioMed Central Ltd.

Growth evolution of ZnO thin films deposited by RF magnetron sputtering

We study the surface morphology evolution of ZnO thin films grown on glass substrates as a function of thickness by RF magnetron sputtering technique. The surface topography of the samples is measured by atomic force microscopy (AFM). All AFM images of the films are analyzed using scaling concepts. The results show that the surface morphology is initially formed by a small grains structure. The grains increase in size and height with growth time resulting in the formation of a mounds-like structure. The growth exponent, beta, and the exponent defining the evolution of the characteristic wavelength of the surface, p, amounted to beta = 0.76 +/- 0.08 and p = 0.3 +/- 0.05. From these exponents, the surface morphology is determined by the nonlocal shadowing effects, that is the dominant mechanism, due to the incident deposition particles during film growth.

Artificial satellites orbits in 2:1 resonance: GPS constellation

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

Chaotic diffusion caused by close encounters with several massive asteroids The (4) Vesta case

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Parameter-dependent Lyapunov functions for state-derivative feedback control in polytopic linear systems

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On certain curves of genus three in characteristic two

We study curves of genus 3 over algebraically closed fields of characteristic 2 with the canonical theta characteristic totally supported in one point. We compute the moduli dimension of such curves and focus on some of them which have two Weierstrass points with Weierstrass directions towards the support of the theta characteristic. We answer questions related to order sequence and Weierstrass weight of Weierstrass points and the existence of other Weierstrass points with similar properties.