HD60532, a planetary system in a 3:1 mean motion resonance

In a recent paper it was reported a planetary system around the star HD60532, composed by two giant planets in a possible 3:1 mean motion resonance, that should be confirmed within the next decade. Here we show that the analysis of the global dynamics of the system allows to confirm this resonance. The present best fit to data already corresponds to this resonant configuration and the system is stable for at least 5Gry. The 3:1 resonance is so robust that stability is still possible for a wide variety of orbital parameters around the best fit solution and also if the inclination of the system orbital plane with respect to the plane of the sky is as small as 15 deg. Moreover, if the inclination is taken as a free parameter in the adjustment to the observations, we find an inclination ~ 20 deg, which corresponds to M_b =3.1 M_Jup and M_c = 7.4 M_Jup for the planetary companions.Comment: 4 Pages, 4 Figures, accepted by A&

On the equilibrium rotation of Earth-like extra-solar planets

The equilibrium rotation of tidally evolved "Earth-like" extra-solar planets is often assumed to be synchronous with their orbital mean motion. The same assumption persisted for Mercury and Venus until radar observations revealed their true spin rates. As many of these planets follow eccentric orbits and are believed to host dense atmospheres, we expect the equilibrium rotation to differ from the synchronous motion. Here we provide a general description of the allowed final equilibrium rotation states of these planets, and apply this to already discovered cases in which the mass is lower than twelve Earth-masses. At low obliquity and moderate eccentricity, it is shown that there are at most four distinct equilibrium possibilities, one of which can be retrograde. Because most presently known "Earth-like" planets present eccentric orbits, their equilibrium rotation is unlikely to be synchronous.Comment: 4 pages, 2 figures. accepted for publication in Astronomy and Astrophysics. to be published in Astronomy and Astrophysic

Nash Equilibria in the Response Strategy of Correlated Games

In nature and society problems arise when different interests are difficult to reconcile, which are modeled in game theory. While most applications assume uncorrelated games, a more detailed modeling is necessary to consider the correlations that influence the decisions of the players. The current theory for correlated games, however, enforces the players to obey the instructions from a third party or "correlation device" to reach equilibrium, but this cannot be achieved for all initial correlations. We extend here the existing framework of correlated games and find that there are other interesting and previously unknown Nash equilibria that make use of correlations to obtain the best payoff. This is achieved by allowing the players the freedom to follow or not to follow the suggestions of the correlation device. By assigning independent probabilities to follow every possible suggestion, the players engage in a response game that turns out to have a rich structure of Nash equilibria that goes beyond the correlated equilibrium and mixed-strategy solutions. We determine the Nash equilibria for all possible correlated Snowdrift games, which we find to be describable by Ising Models in thermal equilibrium. We believe that our approach paves the way to a study of correlations in games that uncovers the existence of interesting underlying interaction mechanisms, without compromising the independence of the players

Stellar wobble caused by a nearby binary system: eccentric and inclined orbits

Most extrasolar planets currently known were discovered by means of an indirect method that measures the stellar wobble caused by the planet. We previously studied a triple system composed of a star and a nearby binary on circular coplanar orbits. We showed that although the effect of the binary on the star can be differentiated from the stellar wobble caused by a planet, because of observational limitations the two effects may often remain indistinguishable. Here, we develop a model that applies to eccentric and inclined orbits. We show that the binary's effect is more likely to be mistaken by planet(s) in the case of coplanar motion observed equator-on. Moreover, when the orbits are eccentric, the magnitude of the binary's effect may be larger than in the circular case. Additionally, an eccentric binary can mimic two planets with orbital periods in the ratio 2/1. However, when the star's orbit around the binary's center of mass has a high eccentricity and a reasonably well-constrained period, it should be easier to distinguish the binary's effect from a planet.Comment: 10 pages, 9 figures, 2 table

Spin-orbit resonances and rotation of coorbital bodies in quasi-circular orbits

The rotation of asymmetric bodies in eccentric Keplerian orbits can be chaotic when there is some overlap of spin-orbit resonances. Here we show that the rotation of two coorbital bodies (two planets orbiting a star or two satellites of a planet) can also be chaotic even for quasi-circular orbits around the central body. When dissipation is present, the rotation period of a body on a nearly circular orbit is believed to always end synchronous with the orbital period. Here we demonstrate that for coorbital bodies in quasi-circular orbits, stable non-synchronous rotation is possible for a wide range of mass ratios and body shapes. We further show that the rotation becomes chaotic when the natural rotational libration frequency, due to the axial asymmetry, is of the same order of magnitude as the orbital libration frequency

Resource design in constrained networks for network lifetime increase

As constrained "things" become increasingly integrated with the Internet and accessible for interactive communication, energy efficient ways to collect, aggregate, and share data over such constrained networks are needed. In this paper, we propose the use of constrained RESTful environments interfaces to build resource collections having a network lifetime increase in mind. More specifically, based on existing atomic resources, collections are created/designed to become available as new resources, which can be observed. Such resource design should not only match client's interests, but also increase network lifetime as much as possible. For this to happen, energy consumption should be balanced/fair among nodes so that node depletion is delayed. When compared with previous approaches, results show that energy efficiency and network lifetime can be increased while reducing control/registration messages, which are used to set up or change observations