Dynamic portrait of the planetary 2/1 mean-motion resonance - I. Systems with a more massive outer planet

We analyse the global structure of the phase space of the planar planetary 2/1 mean-motion resonance in cases where the outer planet is more massive than its inner companion. Inside the resonant domain, we show the existence of two families of periodic orbits, one associated to the librational motion of resonant angle (sigma-family) and the other related to the circulatory motion of the difference in longitudes of pericentre (Delta pi-family). The well-known apsidal corotation resonances (ACR) appear as intersections between both families. A complex web of secondary resonances is also detected for low eccentricities, whose strengths and positions are dependent on the individual masses and spatial scale of the system. The construction of dynamical maps for various values of the total angular momentum shows the evolution of the families of stable motion with the eccentricities, identifying possible configurations suitable for exoplanetary systems. For low-moderate eccentricities, several different stable modes exist outside the ACR. For larger eccentricities, however, all stable solutions are associated to oscillations around the stationary solutions. Finally, we present a possible link between these stable families and the process of resonance capture, identifying the most probable routes from the secular region to the resonant domain, and discussing how the final resonant configuration may be affected by the extension of the chaotic layer around the resonance region.

THE ROLE OF DIFFUSIVITY QUENCHING IN FLUX-TRANSPORT DYNAMO MODELS

In the nonlinear phase of a dynamo process, the back-reaction of the magnetic field upon the turbulent motion results in a decrease of the turbulence level and therefore in a suppression of both the magnetic field amplification (the alpha-quenching effect) and the turbulent magnetic diffusivity (the eta-quenching effect). While the former has been widely explored, the effects of eta-quenching in the magnetic field evolution have rarely been considered. In this work, we investigate the role of the suppression of diffusivity in a flux-transport solar dynamo model that also includes a nonlinear alpha-quenching term. Our results indicate that, although for alpha-quenching the dependence of the magnetic field amplification with the quenching factor is nearly linear, the magnetic field response to eta-quenching is nonlinear and spatially nonuniform. We have found that the magnetic field can be locally amplified in this case, forming long-lived structures whose maximum amplitude can be up to similar to 2.5 times larger at the tachocline and up to similar to 2 times larger at the center of the convection zone than in models without quenching. However, this amplification leads to unobservable effects and to a worse distribution of the magnetic field in the butterfly diagram. Since the dynamo cycle period increases when the efficiency of the quenching increases, we have also explored whether the eta-quenching can cause a diffusion-dominated model to drift into an advection-dominated regime. We have found that models undergoing a large suppression in eta produce a strong segregation of magnetic fields that may lead to unsteady dynamo-oscillations. On the other hand, an initially diffusion-dominated model undergoing a small suppression in eta remains in the diffusion-dominated regime.

Shielding of ionic interactions by sulfur dioxide in an ionic liquid

The effect of adding SO(2) on the structure and dynamics of 1-butyl-3-methylimidazolium bromide (BMIBr) was investigated by low-frequency Raman spectroscopy and molecular dynamics (MD) simulations. The MD simulations indicate that the long-range structure of neat BMIBr is disrupted resulting in a liquid with relatively low viscosity and high conductivity, but strong correlation of ionic motion persists in the BMIBr-SO(2) mixture due to ionic pairing. Raman spectra within the 5 < omega < 200 cm(-1) range at low temperature reveal the short-time dynamics, which is consistent with the vibrational density of states calculated by MD simulations. Several time correlation functions calculated by MD simulations give further insights on the structural relaxation of BMIBr-SO(2).