Orbital evolution of the mu and nu dust ring particles of Uranus

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

A note on the horseshoe confinement model: the Poynting-Robertson effect

In the present work we numerically simulated the motion of particles coorbital to a small satellite under the Poynting-Robertson light drag effect in order to verify the symmetry suggested by Dermott et al. (1979, 1980) on their ring confinement model. The results reveal a more complex scenario, especially for very small particles (micrometer sizes), which present chaotic motion. Despite the complexity of the trajectories the particles remain confined inside the coorbital region. However, the dissipative force caused by the solar radiation also includes the radiation pressure component which can change this configuration. Our results show that the inclusion of the radiation pressure, which is not present in the original confinement model, can destroy the configuration in a time much shorter than the survival time predicted for a dust particle in a horseshoe orbit with a satellite.

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).

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.

Electronic states in quantum rings: electric field and eccentricity effects

The polarization effects of in-plane electric fields and eccentricity on electronic and optical properties of semiconductor quantum rings (QRs) are discussed within the effective-mass approximation. As eccentric rings may appropriately describe real (grown or fabricated) QRs, their energy spectrum is studied. The interplay between applied electric fields and eccentricity is analysed, and their polarization effects are found to compensate for appropriate values of eccentricity and field intensity. The importance of applied fields in tailoring the properties of different nanoscale materials and structures is stressed.

The Yang-Lee edge singularity in spin models on connected and non-connected rings

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Aggregates in the strength and gravity regime: Particles sizes in Saturn's rings

Particles in Saturn's main rings range in size from dust to kilometer-sized objects. Their size distribution is thought to be a result of competing accretion and fragmentation processes. While growth is naturally limited in tidal environments, frequent collisions among these objects may contribute to both accretion and fragmentation. As ring particles are primarily made of water ice attractive surface forces like adhesion could significantly influence these processes, finally determining the resulting size distribution. Here, we derive analytic expressions for the specific self-energy Q and related specific break-up energy Q(star) of aggregates. These expressions can be used for any aggregate type composed of monomeric constituents. We compare these expressions to numerical experiments where we create aggregates of various types including: regular packings like the face-centered cubic (fcc), Ballistic Particle Cluster Aggregates (BPCA), and modified BPCAs including e.g. different constituent size distributions. We show that accounting for attractive surface forces such as adhesion a simple approach is able to: (a) generally account for the size dependence of the specific break-up energy for fragmentation to occur reported in the literature, namely the division into "strength" and "gravity" regimes and (b) estimate the maximum aggregate size in a collisional ensemble to be on the order of a few tens of meters, consistent with the maximum particle size observed in Saturn's rings of about 10 m. (c) 2012 Elsevier B.V. All rights reserved.

Reactivity of mesenteric and aortic rings from trained rats fed with high caloric diet

A strong association between the benefits of physical exercise on the cardiovascular disease with an improvement of the endothelium-derived relaxing factor production has been consistently shown. The purpose of this study was to evaluate the effect of exercise training associated with high caloric diet in the reactivity of rat mesenteric and aortic rings. Experimental protocol consisted of 4 weeks of high caloric diet consumption previous to 4 weeks of run training (1.2 km/h, 0% grade, in sessions of 60 min, 5 days/week). Concentrations of triglycerides, glucose, insulin and nitrite/nitrate levels were measured and atherogenic index was calculated. Concentration-response curves to acetylcholine (10 nM-100 mu M), sodium nitroprusside (100 pM-100 nM) and phenylephrine (1 nM-3 mu M) were obtained. Exercise training reduced body mass (6%) and triglyceride levels (about 54%), without changes in glucose and insulin concentrations. An improvement of endothelium-dependent relaxation responses to acetylcholine in mesenteric and aortic rings was observed in trained group. No changes were seen for sodium nitroprusside and phenylephrine. In conclusion, our study is the first to show clearly that run training promotes an improvement of the endothelium-dependent relaxing response in aorta and mesenteric rings from rats fed with high caloric diet and that is associated with increase of NO production. (c) 2006 Elsevier B.V. All rights reserved.

Goppa and Srivastava codes over finite rings

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

Alternant and BCH codes over certain rings

Alternant codes over arbitrary finite commutative local rings with identity are constructed in terms of parity-check matrices. The derivation is based on the factorization of x s - 1 over the unit group of an appropriate extension of the finite ring. An efficient decoding procedure which makes use of the modified Berlekamp-Massey algorithm to correct errors and erasures is presented. Furthermore, we address the construction of BCH codes over Zm under Lee metric.

Stable satellites around extrasolar giant planets

In this work, we study the stability of hypothetical satellites of extrasolar planets. Through numerical simulations of the restricted elliptic three-body problem we found the borders of the stable regions around the secondary body. From the empirical results, we derived analytical expressions of the critical semimajor axis beyond which the satellites would not remain stable. The expressions are given as a function of the eccentricities of the planet, e(P), and of the satellite, e(sat). In the case of prograde, satellites, the critical semimajor axis, in the units of Hill's radius, is given by a(E) approximate to 0.4895 (1.0000 - 1.0305e(P) - 0.2738e(sat)). In the case of retrograde satellites, it is given by a(E) approximate to 0.9309 (1.0000 - 1.0764e(P) - 0.9812e(sat)). We also computed the satellite stability region (a(E)) for a set of extrasolar planets. The results indicate that extrasolar planets in the habitable zone could harbour the Earth-like satellites.

Dynamics of two planets in the 3/2 mean-motion resonance: Application to the planetary system of the pulsar PSR B1257+12

This paper considers the dynamics of two planets, as the planets B and C of the pulsar PSR B1257+12, near a 3/2 mean-motion resonance. A two-degrees-of-freedom model, in the framework of the general three-body planar problem, is used and the solutions are analyzed through surfaces of section and Fourier techniques in the full phase space of the system.

Growth rings in cerrado woody species: occurrence and anatomical markers

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

Effects of varying curvature and width on the electronic states of GaAs quantum rings

Stationary states of an electron in thin GaAs elliptical quantum rings are calculated within the effective-mass approximation. The width of the ring varies smoothly along the centerline, which is an ellipse. The solutions of the Schrödinger equation with Dirichlet boundary conditions are approximated by a product of longitudinal and transversal wave functions. The ground-state probability density shows peaks: (i) where the curvature is larger in a constant-with ring, and (ii) in thicker parts of a circular ring. For rings of typical dimensions, it is shown that the effects of a varying width may be stronger than those of the varying curvature. Also, a width profile which compensates the main localization effects of the varying curvature is obtained.