Semiclassical scaling functions of sine-Gordon model

We present an analytic study of the finite size effects in sine-Gordon model, based on the semi-classical quantization of an appropriate kink background defined on a cylindrical geometry. The quasi-periodic kink is realized as an elliptic function with its real period related to the size of the system. The stability equation for the small quantum fluctuations around this classical background is of Lame type and the corresponding energy eigenvalues are selected inside the allowed bands by imposing periodic boundary conditions. We derive analytical expressions for the ground state and excited states scaling functions, which provide an explicit description of the flow between the IR and UV regimes of the model. Finally, the semiclassical form factors and two-point functions of the basic field and of the energy operator are obtained, completing the semiclassical quantization of the sine-Gordon model on the cylinder. (C) 2004 Elsevier B.V. All rights reserved.

Spatially-antisymmetric localization of matter wave in a bichromatic optical lattice

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

Distant stable direct orbits around the Moon

In the present work we explore regions of distant direct stable orbits around the Moon. First, the location and size of apparently stable regions are searched for numerically, adopting the approach of temporary capture time presented in Vieira Neto & Winter (2001). The study is made in the framework of the planar, circular, restricted three-body problem, Earth-Moon-particle. Regions of the initial condition space whose trajectories are apparently stable are determined. The criterion adopted was that the trajectories do not escape from the Moon during an integration period of 10(4) days. Using Poincare surface of sections the reason for the existence of the two stable regions found is studied. The stability of such regions proved to be due to two families of simple periodic orbits, h1 and h2, and the associated quasi-periodic orbits that oscillate around them. The robustness of the stability of the larger region, h2, is tested with the inclusion of the solar perturbation. The size of the region decreases, but it is still significant in size and can be useful in spacecraft missions.

Time analysis for temporary gravitational capture - Stable orbits

In a previous work, Vieira Neto & Winter (2001) numerically explored the capture times of particles as temporary satellites of Uranus. The study was made in the framework of the spatial, circular, restricted three-body problem. Regions of the initial condition space whose trajectories are apparently stable were determined. The criterion adopted was that the trajectories do not escape from the planet during an integration of 10(5) years. These regions occur for a wide range of orbital initial inclinations (i). In the present work it is studied the reason for the existence of such stable regions. The stability of the planar retrograde trajectories is due to a family of simple periodic orbits and the associated quasi-periodic orbits that oscillate around them. These planar stable orbits had already been studied (Henon 1970; Huang & Innanen 1983). Their results are reviewed using Poincare surface of sections. The stable non-planar retrograde trajectories, 110 degrees less than or equal to i < 180, are found to be tridimensional quasi-periodic orbits around the same family of periodic orbits found for the planar case (i = 180 degrees). It was not found any periodic orbit out of the plane associated to such quasi-periodic orbits. The largest region of stable prograde trajectories occurs at i = 60 degrees. Trajectories in such region are found to behave as quasi-periodic orbits evolving similarly to the stable retrograde trajectories that occurs at i = 120 degrees.

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.

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.

Numerical study of low-cost alternative orbits around the Moon

In this paper, we have investigated a region of direct stable orbits around the Moon, whose stability is related to the H2 Family of periodic orbits and to the quasi-periodic orbits that oscillate around them. The stability criteria adopted was that the path did not escape from the Moon during an integration period of 1000 days (remaining with negative two-body Moon-probe orbital energy during this period). Considering the three-dimensional four-body Sun-Earth-Moon-probe problem, we investigated the evolution of the size of the stability region, taking into account the eccentricity of the Earth's orbit, the eccentricity and inclination of the Moon's orbit, and the solar radiation pressure on the probe. We also investigated the evolution of the region's size and its location by varying the inclination of the probe's initial osculating orbit relative to the Moon's orbital plane between 0 degrees and 180 degrees. The size of the stability region diminishes; nevertheless, it remains significant for 0 <= i <= 25 degrees and 35 degrees <= i <= 45 degrees. The orbits of this region could be useful for missions by space vehicles that must remain in orbit around the Moon for periods of up to 1000 days, requiring low maintenance costs. (c) 2005 COSPAR. Published by Elsevier Ltd. All rights reserved.

A contribution for nonlinear structural dynamics characterization of cantilever beams

Successful experiments in nonlinear vibrations have been carried out with cantilever beams under harmonic base excitation. A flexible slender cantilever has been chosen as a convenient structure to exhibit modal interactions, subharmonic, superharmonic and chaotic motions, and others interesting nonlinear phenomena. The tools employed to analyze the dynamics of the beam generally include frequency- and force-response curves. To produce force-response curves, one keeps the excitation frequency constant and slowly varies the excitation amplitude, on the other hand, to produce frequency-response curves, one keeps the excitation amplitude fixed and slowly varies the excitation frequency. However, keeping the excitation amplitude constant while varying the excitation frequency is a difficult task with an open-loop measurement system. In this paper, it is proposed a closed-loop monitor vibration system available with the electromagnetic shaker in order to keep the harmonic base excitation amplitude constant. This experimental setup constitutes a significant improvement to produce frequency-response curves and the advantages of this setup are evaluated in a case study. The beam is excited with a periodic base motion transverse to the axis of the beam near the third natural frequency. Modal interactions and two-period quasi-periodic motion are observed involving the first and the third modes. Frequency-response curves, phase space and Poincaré map are used to characterize the dynamics of the beam.

Localization of a Bose-Einstein condensate in a bichromatic optical lattice

By direct numerical simulation of the time-dependent Gross-Pitaevskii equation, we study different aspects of the localization of a noninteracting ideal Bose-Einstein condensate (BEC) in a one-dimensional bichromatic quasiperiodic optical-lattice potential. Such a quasiperiodic potential, used in a recent experiment on the localization of a BEC, can be formed by the superposition of two standing-wave polarized laser beams with different wavelengths. We investigate the effect of the variation of optical amplitudes and wavelengths on the localization of a noninteracting BEC. We also simulate the nonlinear dynamics when a harmonically trapped BEC is suddenly released into a quasiperiodic potential, as done experimentally in a laser speckle potential. We finally study the destruction of the localization in an interacting BEC due to the repulsion generated by a positive scattering length between the bosonic atoms. © 2009 The American Physical Society.

Stable regions around Pluto

In a previous work, GiuliattiWinter et al. found several stable regions for test particles in orbit around Pluto associated with families of periodic orbits obtained in the circular, restricted three-body problem. They have shown that a possible eccentricity of the Pluto-Charon binary slightly reduces but does not destroy any of these stable regions. In thiswork, we extended their results by analysing the cases with the orbital inclination (I) equal to zero and considering the argument of pericentre (w) equal to 90°, 180° and 270°. We explore the influence of the orbital inclination of the particles in these stable regions. In this case, the initial inclination varies from 10° to 170° in steps of 10°. We also present a sample of results for the longitude of the ascending node Ω = 90°, considering the cases I = 20°, 50°, 130° and 180°. Our results show that stable regions are present in all of the inclined cases, except when the initial inclination of the particles is equal to 110°. A sample of 3D trajectories of quasi-periodic orbits were found related to the periodic orbits obtained in the planar case by Giuliatti Winter et al. © 2013 The Authors. Published by Oxford University Press on behalf of the Royal Astronomical Society.

Dinâmica caótica e sincronização de fase em mapas acoplados

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Comportamento dinâmico de suspensão eletromecânica: análise da resposta devido ao amortecimento e à rigidez não linear

Pós-graduação em Engenharia Elétrica - FEB

Deformation and tidal evolution of close-in planets and satellites using a Maxwell viscoelastic rheology

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

Characterization of Stability Region for General Autonomous Nonlinear Dynamical Systems

The existing characterization of stability regions was developed under the assumption that limit sets on the stability boundary are exclusively composed of hyperbolic equilibrium points and closed orbits. The characterizations derived in this technical note are a generalization of existing results in the theory of stability regions. A characterization of the stability boundary of general autonomous nonlinear dynamical systems is developed under the assumption that limit sets on the stability boundary are composed of a countable number of disjoint and indecomposable components, which can be equilibrium points, closed orbits, quasi-periodic solutions and even chaotic invariant sets.

Age models and stable isotope ratios from the Mid-Miocene

Mid-Miocene pelagic sedimentary sections can be correlated using intermediate and high resolution oxygen and carbon isotopic records of benthic foraminifera. Precision of a few tens of thousands of years is readily achievable at sites with high sedimentation rates, for example, Deep Sea Drilling Project sites 289 and 574. The mid-Miocene carbon isotope records are characterized by an interval of high d13C values between 17 and 13.5 Ma (the Monterey Excursion of Vincent and Berger 1985) upon which are superimposed a series of periodic or quasi-periodic fluctuations in d13C values. These fluctuations have a period of approximately 440 kyr, suggestive of the 413 kyr cycle predicted by Milankovitch theory. Vincent and Berger proposed that the Monterey Excursion was the result of increased organic carbon burial in continental margins sediments. The increased d13C values (called 13C maxima) superimposed on the generally high mid-Miocene signal coincide with increases in d18O values suggesting that periods of cooling and/or ice buildup were associated with exceptionally rapid burial of organic carbon and lowered atmospheric CO2 levels. It is likely that during the Monterey Excursion the ocean/atmosphere system became progressively more sensitive to small changes in insolation, ultimately leading to major cooling of deep water and expansion of continental ice. We have assigned an absolute chronology, based on biostratigraphic and magneto-biostratigraphic datum levels, to the isotope stratigraphy and have used that chronology to correlate unconformities, seismic reflectors, carbonate minima, and dissolution intervals. Intervals of sediment containing 13C maxima are usually better preserved than the overlying and underlying sediments, indicating that the d13C values of TCO2 in deep water and the corrosiveness of seawater are inversely correlated. This again suggests that the 13C maxima were associated with rapid burial of organic carbon and reduced levels of atmospheric CO2. The absolute chronology we have assigned to the isotopic record indicates that the major mid-Miocene deepwater cooling/ice volume expansion took 2 m.y. and was not abrupt as had been reported previously. The cooling appears abrupt at many sites because the interval is characterized by a number of dissolution intervals. The cooling was not monotonic, and the 2 m.y. interval included an episode of especially rapid cooling as well as a brief return to warmer conditions before the final phase of the cooling period. The increase in d18O values of benthic foraminifera between 14.9 and 12.9 Ma was greatest at deeper water sites and at sites closest to Antarctica. The data suggest that the d18O value of seawater increased by no more than about 1.1 per mil during this interval and that the remainder of the change in benthic d18O values resulted from cooling in Antarctic regions of deepwater formation. Equatorial planktonic foraminifera from sites 237 and 289 exhibit a series of 0.4 per mil steplike increases in d13C values. Only one of these increases in planktonic d13C is correlated with any of the features in the mid-Miocene benthic carbon isotope record.