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

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Chaotic diffusion caused by close encounters with several massive asteroids: II. the regions of (10) Hygiea, (2) Pallas, and (31) Euphrosyne

Context. Close encounters with (1) Ceres and (4) Vesta, the two most massive bodies in the main belt, are known to be a mechanism of dynamical mobility able to significantly alter proper elements of minor bodies, and they are the main source of dynamical mobility for medium-sized and large asteroids (D > 20 km, approximately). Recently, it has been shown that drift rates caused by close encounters with massive asteroids may change significantly on timescales of 30 Myr when different models (i.e., different numbers of massive asteroids) are considered. Aims. So far, not much attention has been given to the case of diffusion caused by the other most massive bodies in the main belt: (2) Pallas, (10) Hygiea, and (31) Euphrosyne, the third, fourth, and one of the most massive highly inclined asteroids in the main belt, respectively. Since (2) Pallas is a highly inclined object, relative velocities at encounter with other asteroids tend to be high and changes in proper elements are therefore relatively small. It was thus believed that the scattering effect caused by highly inclined objects in general should be small. Can diffusion by close encounters with these asteroids be a significant mechanism of long-term dynamical mobility? Methods. By performing simulations with symplectic integrators, we studied the problem of scattering caused by close encounters with (2) Pallas, (10) Hygiea, and (31) Euphrosyne when only the massive asteroids (and the eight planets) are considered, and the other massive main belt asteroids and non-gravitational forces are also accounted for. Results. By finding relatively small values of drift rates for (2) Pallas, we confirm that orbital scattering by this highly inclined object is indeed a minor effect. Unexpectedly, however, we obtained values of drift rates for changes in proper semi-major axis a caused by (10) Hygiea and (31) Euphrosyne larger than what was previously found for scattering by (4) Vesta. These high rates may have repercussions on the orbital evolution and age estimate of their respective families. © 2013 ESO.

Moonlets wandering on a leash-ring

Since the Voyager flybys, embedded moonlets have been proposed to explain some of the surprising structures observed in Saturn's narrow F ring. Experiments conducted with the Cassini spacecraft support this suggestion. Images of the F ring show bright compact spots, and seven occultations of stars by the F ring, monitored by ultraviolet and infrared experiments, revealed nine events of high optical depth. These results point to a large number of such objects, but it is not clear whether they are solid moonlets or rather loose particle aggregates. Subsequent images suggested an irregular motion of these objects so that a determination of their orbits consistent with the F ring failed. Some of these features seem to cross the whole ring. Here we show that these observations are explained by chaos in the F ring driven mainly by the 'shepherd' moons Prometheus and Pandora. It is characterized by a rather short Lyapunov time of about a few hundred orbital periods. Despite this chaotic diffusion, more than 93 per cent of the F-ring bodies remain confined within the F ring because of the shepherding, but also because of a weak radial mobility contrasted by an effective longitudinal diffusion. This chaotic stirring of all bodies involved prevents the formation of 'propellers' typical of moonlets, but their frequent ring crossings explain the multiple radial 'streaks' seen in the F ring. The related 'thermal' motion causes more frequent collisions between all bodies which steadily replenish F-ring dust and allow for ongoing fragmentation and re-accretion processes (ring recycling).

Controle de dinâmica caótica com toros robustos

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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.

Scaling invariance of the diffusion coefficient in a family of two-dimensional Hamiltonian mappings

We consider a family of two-dimensional nonlinear area-preserving mappings that generalize the Chirikov standard map and model a variety of periodically forced systems. The action variable diffuses in increments whose phase is controlled by a negative power of the action and hence effectively uncorrelated for small actions, leading to a chaotic sea in phase space. For larger values of the action the phase space is mixed and contains a family of elliptic islands centered on periodic orbits and invariant Kolmogorov-Arnold-Moser (KAM) curves. The transport of particles along the phase space is considered by starting an ensemble of particles with a very low action and letting them evolve in the phase until they reach a certain height h. For chaotic orbits below the periodic islands, the survival probability for the particles to reach h is characterized by an exponential function, well modeled by the solution of the diffusion equation. On the other hand, when h reaches the position of periodic islands, the diffusion slows markedly. We show that the diffusion coefficient is scaling invariant with respect to the control parameter of the mapping when h reaches the position of the lowest KAM island. © 2013 American Physical Society.

A family of dissipative two-dimensional mappings: Chaotic, regular and steady state dynamics investigation

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Bifurcation analysis of a new Lorenz-like chaotic system

In this paper we study the local codimension one and two bifurcations which occur in a family of three-dimensional vector fields depending on three parameters. An equivalent family, depending on five parameters, was recently proposed as a new chaotic system with a Lorenz-like butterfly shaped attractor and was studied mainly from a numerical point of view, for particular values of the parameters, for which computational evidences of the chaotic attractor was shown. In order to contribute to the understand of this new system we present an analytical study and the bifurcation diagrams of an equivalent three parameter system, showing the qualitative changes in the dynamics of its solutions, for different values of the parameters. (C) 2007 Elsevier Ltd. All rights reserved.

Development and validation of a stability-indicative agar diffusion assay to determine the potency of linezolid in tablets in the presence of photodegradation products

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

Measurement of oxygen atom diffusion in Nb and Ta by anelastic spectroscopy

Impurity interstitial atoms present in metals with BCC structure can diffuse in the metallic matrix by jumps to energetically equivalent crystallographic sites. Anelastic spectroscopy (internal friction) is based on the measurement of mechanical loss or internal friction as a function of temperature. Due to its selective and nondestructive nature, anelastic spectroscopy is well suited for the study of diffusion of interstitial elements in metals. Internal friction measurements were made using the torsion pendulum technique with oscillation frequency of a few Hz, temperature interval from 300 to 700 K, heating rate of about 1 K/min, and vacuum better than 10-5 mbar. The polycrystalline Nb and Ta samples used were supplied by Aldrich Inc. The results obtained showed thermally activated relaxation structures due to stress-induced ordering of oxygen atoms around the Nb (or Ta) atoms of the metallic matrix. The results were interpreted by three methods and led to activation enthalpy values for the diffusion of oxygen in Nb and Ta of 1.15 eV and 1.10 eV, respectively.

Determination of the oxygen and nitrogen interstitial diffusion coeficient in niobium by mechanical spectroscopy

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

Diffusion of Interstitial Elements in Ti Alloys used as Biomaterials

Titanium alloys are excellent implant materials for orthopedic applications due to their desirable properties, such as good corrosion resistance, low elasticity modulus, and excellent biocompatibility. The presence of interstitial elements (such as oxygen and nitrogen) causes strong changes in the material's mechanical properties, mainly in its elastic properties. Study of the interaction among interstitial elements present in metals began with Snoek's postulate, that a stress-induced ordering of interstitials gives rise to a peak in the mechanical relaxation (internal friction) spectra. In the mechanical relaxation spectra, each species of interstitial solute atom gives rise to a distinct Snoek's peak, whose temperature and position depend on the measurement frequency. This effect is very interesting because its peculiar parameters are directly related to the diffusion coefficient (D) for the interstitial solute. This paper presents a study of diffusion of heavy interstitial elements in Ti-35Nb-7Zr-5Ta alloys using mechanical spectroscopy. Pre-exponential factors and activation energies are calculated for oxygen and nitrogen in theses alloys.

Oxygen diffusion in superconducting oxides

Since the discovery of high-temperature superconductivity of cuprate oxides, it has been clear that it is strongly affected by the oxygen content, which is also a crucial factor to determine other physical properties of high T-c superconductors. Non-stoichiometric (interstitial) oxygen strongly influences the physical properties of various superconducting oxides, in particular by creating conducting holes. It is now ascertained that the amount of holes injected depends not only on the content of interstitial oxygen, but also on its ordering. Rearrangement of the oxygen ordering may occur even below room temperature due to the unusual high mobility of these atoms. This way, mechanical spectroscopy is one of the most adequate techniques for the study of the mobility (diffusion) of oxygen atoms. This technique allows the determination of the jump frequency of an atomic species precisely, regardless of the model or the different possible types of jumps. In order to evaluate the mobility and the effect of oxygen content on these oxides, ceramic samples we prepared and submitted to several oxygen removal cycles alternately with mechanical relaxation measurements. As for SBCO, it was assumed that the peak was due to O(1)-O(5) jumps of oxygen atoms at the chain terminals or in chain fragments in the orthorhombic phase. In the case of BSCCO, the results showed complex anelastic relaxation structures, which were attributed to interstitial oxygen atom jumps between two adjacent CuO planes.

Diffusion of Nitrogen in Ti-13V-11Cr-3Al Alloys

Metals with a bcc crystalline structure such as Ti-13V-11Cr-3Al alloys have their physical properties significantly changed through the addition of interstitial elements such as oxygen and nitrogen. These metals can dissolve substantial amounts of interstitial elements forming solid solutions. Mechanical spectroscopy measurements constitute a powerful tool for studying interactions of these interstitial elements with other elements that make up the alloy. From these measurements, it is possible to obtain information regarding diffusion, interstitial concentration, interaction between interstitials, and other imperfections of the crystalline lattice, In this paper, Ti-13V-11Cr-3Al alloys with several amount of nitrogen, in a solid solution, were studied using mechanical spectroscopy (internal friction) measurements. The results presented complex internal friction spectra which were resolved in a series of constituent Debye peaks corresponding to different interactions and interstitial diffusion coefficients. Pre-exponential factors and activation energies were calculated for nitrogen in theses alloys.

Nitrogen diffusion in the Nb-1.0wt%Zr measured by mechanical spectroscopy

The scientific and technological development in the area of new materials contributed to several applications of niobium and its alloys in nuclear power plants as well as in aerospace, aeronautics, automobile and naval industries. This paper presents the interstitial diffusion coefficients of nitrogen in solid solution in the Nb-1.0wt%Zr alloy using internal friction measurements obtained by mechanical spectroscopy, which uses a torsion pendulum operating at an oscillation frequency between 1.0 Hz and 10.0 Hz. The temperature range varies from 300K to 700K, at a heating rate of 1 K/min and vacuum better than 2 x 10(-6) Torr. The results showed an increase of the interstitial diffusion coefficient of nitrogen that was correlated with configurational considerations for the octahedral interstitials.