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.

Coupling between muscle activities and muscle torques during horizontal-planar arm movements with direction reversal

In this study we investigated the hypothesis that the simple set of rules used to explain the modulation of muscle activities during single-joint movements could also be applied for reversal movements of the shoulder and elbow joints. The muscle torques of both joints were characterized by a triphasic impulse. The first impulse of each joint accelerated the limb to the target and was generated by an initial burst of the muscles activated first (primary mover). The second impulse decelerated the limb to the target, reversed movement direction and accelerated the limb back to the initial position, and was generated by an initial burst of the muscles activated second (secondary movers). A third impulse, in each joint, decelerated the limb to the initial position due to the generation of a second burst of the primary movers. The first burst of the primary mover decreased abruptly, and the latency between the activation of the primary and secondary movers varied in proportion with target distances for the elbow, but not for the shoulder muscles. All impulses and bursts increased with target distances and were well coupled. Therefore, as predicted, the bursts of muscle activities were modulated to generate the appropriate level of muscle torque. (C) 2005 Elsevier Ltd. All rights reserved.

Periodic orbits for a class of reversible quadratic vector field on R-3

For a class of reversible quadratic vector fields on R-3 we study the periodic orbits that bifurcate from a heteroclinic loop having two singular points at infinity connected by an invariant straight line in the finite part and another straight line at infinity in the local chart U-2. More specifically, we prove that for all n is an element of N, there exists epsilon(n) > 0 such that the reversible quadratic polynomial differential systemx = a(0) + a(1y) + a(3y)(2) + a(4Y)(2) + epsilon(a(2x)(2) + a(3xz)),y = b(1z) + b(3yz) + epsilon b(2xy),z = c(1y) +c(4az)(2) + epsilon c(2xz)in R-3, with a(0) < 0, b(1)c(1) < 0, a(2) < 0, b(2) < a(2), a(4) > 0, c(2) < a(2) and b(3) is not an element of (c(4), 4c(4)), for epsilon is an element of (0, epsilon(n)) has at least n periodic orbits near the heteroclinic loop. (c) 2007 Elsevier B.V. All rights reserved.

Obtaining a light-like planar gauge

In the usual and current understanding of planar gauge choices for Abelian and non-Abelian gauge fields, the external defining vector n(mu), can either be space-like (n(2) < 0) or time-like (n(2) > 0) but not light-like (n(2) = 0). In this work we propose a light-like planar gauge that consists of defining a modified gauge-fixing term, L-GF, whose main characteristic is a two-degree violation of Lorentz covariance arising from the fact that four-dimensional space-time spanned entirely by null vectors as basis necessitates two light-like vectors, namely n(mu) and its dual m(mu), with n(2) = m(2) = 0, n . m not equal 0, say, e.g. normalized to n . m = 2.

Erbium-activated HfO2-based waveguides for photonics

Silica-based sol-gel waveguides activated by Er3+ ions are attractive materials for integrated optic devices. 70SiO(2)-30HfO(2) planar waveguides, doped with Er3+ concentrations ranging from 0.01 to 4 mol%, were prepared by sol-get route. The films were deposited on v-SiO2 and silica-on-silicon substrates, using dip-coating technique. The waveguides show a homogeneous surface morphology, high densification degree and uniform refractive index across the thickness. Emission in the C-telecommunication band was observed at room temperature for ill the samples upon excitation at 980 nm. The shape is found to be almost independent on erbium content, with a FWHM between 44 and 48 nm. The I-4(13/2) level decay curves presented a single-exponential profile, with a lifetime ranging between 1.1 and 6.7 ms, depending on the erbium concentration. The waveguide deposited on silica-on-silicon substrate supports one single propagation mode at 1.5 mum with a confinement coefficient of 0.85, and a losses of about 0.8 dB/cm at 632.8 nm. (C) 2003 Elsevier B.V. All rights reserved.

Fold, transcritical and pitchfork singularities for time-reversible systems

This paper deals with a class of singularly perturbed reversible planar vector fields around the origin where the normal hyperbolicity assumption is not assumed. We exhibit conditions for the existence of infinitely many periodic orbits and hetero-clinic cycles converging to singular orbits with respect to the Hausdorf distance. In addition, generic normal forms of such singularities are presented.

Planar membranes interaction

The system of two parallel planar, arbitrarily charged surfaces immersed in a solution containing only one ionic species, the counterions, is completely analyzed under a mean field Poisson-Boltzmann approach. Results for the pressure, reduced potential, and counterionic concentration are graphically displayed for two dissociating membranes and for a dissociating and an adsorbing membrane. The results indicate that the system of two planar parallel dissociating membranes acts as a buffer for pressure values and for counterionic concentration values in regions interior to and far from the membranes. The results are related to properties of planar or quasiplanar structures in biological cells.

Er-doped silica-based waveguides prepared by different techniques: RF-sputtering, sol-gel and ion-exchange

Erbium-activated silica-based planar waveguides were prepared by three different technological routes: RF-sputtering, sol-gel and ion exchange. Various parameters of preparation were varied in order to optimize the waveguides for operation in the NIR region. Particular attention was devoted to the minimization of the losses and the increase of the luminescence efficiency of the metastable I-4(13/2) state of the Er3+ ion. Waveguide properties were determined by m-line spectroscopy and loss measurements. Waveguide Raman and luminescence spectroscopy were used to obtain information about the structure of the prepared films and about the dynamical processes related to the luminescence of the Er3+ ions.

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.

The high-eccentricity asymmetric expansion of the disturbing function for non-planar resonant problems

In this paper we present an extension to the nonplanar case of the asymmetric expansion of the averaged resonant disturbing function of Ferraz-Mello & Sato (1989, A&A 225, 541-547). Comparions with the exact averaged disturbing function are also presented. The expansion gives a good approximation of the exact function in a wide region around the center of expansion.

On non-linear dynamics and a periodic control design applied to the potential of membrane action

The Fitzhugh-Nagumo (fn) mathematical model characterizes the action potential of the membrane. The dynamics of the Fitzhugh-Nagumo model have been extensively studied both with a view to their biological implications and as a test bed for numerical methods, which can be applied to more complex models. This paper deals with the dynamics in the (FH) model. Here, the dynamics are analyzed, qualitatively, through the stability diagrams to the action potential of the membrane. Furthermore, we also analyze quantitatively the problem through the evaluation of Floquet multipliers. Finally, the nonlinear periodic problem is controlled, based on the Chebyshev polynomial expansion, the Picard iterative method and on Lyapunov-Floquet transformation (L-F transformation).

Sol-gel Er-doped SiO(2)-HfO(2) planar waveguides: A viable system for 1.5 mu m application

70SiO(2)-30HfO(2) planar waveguides, doped with Er(3+) concentrations ranging from 0.3 to 1 mol %, were prepared by sol-gel route, using dip-coating deposition on silica glass substrates. The waveguides show high densification degree, effective intermingling of the two components of the film, and uniform surface morphology. Propagation losses of about 1 dB/cm were measured at 632.8 nm. When pumped with 987 or 514.5 nm continuous-wave laser light, the waveguides show the (4)I(13/2)-->(4)I(15/2) emission band with a bandwidth of 48 nm. The spectral features are found independent both on erbium content and excitation wavelength. The (4)I(13/2) level decay curves presented a single-exponential profile, with a lifetime between 2.9 and 5.0 ms, depending on the erbium concentration. (C) 2002 American Institute of Physics.

Periodic collisions between the moon Prometheus and Saturn's F ring

Saturn's F ring, which lies 3,400 km beyond the edge of the main ring system, was discovered by the Pioneer 11 spacecraft(1) in 1979. It is a narrow, eccentric ring which shows an unusual 'braided' appearance in several Voyager 1 images' obtained in 1980, although it appears more regular in images from Voyager 2 obtained nine months later(3). The discovery of the moons Pandora and Prometheus orbiting on either side of the ring provided a partial explanation for some of the observed features(4). Recent observations of Prometheus(5,6) by the Hubble Space Telescope show, surprisingly, that it is lagging behind its expected position by similar to 20 degrees. By modelling the dynamical evolution of the entire Prometheus-F ring-Pandora system, we show here that Prometheus probably encountered the core of the F ring in 1994 and that it may still be entering parts of the ring once per orbit. Collisions with objects in the F ring provide a plausible explanation for the observed lag and imply that the mass of the F ring is probably less than 25% that of Prometheus.