First locking of the Virgo central area interferometer with suspension hierarchical control

Operation of the central portion of Virgo as a simple 6 m Michelson interferometer has given the first demonstration of the possibility to control an interferometer suspended from Virgo full scale multistage seismic attenuators using information derived from the interferometer locking signal. A special role in the control is played by the first stage of these suspensions, an inverted pendulum: besides its seismic preisolation action, this stage has positioning dynamics of several mm, and it allows to exert a very low frequency control at the upper level of the suspension using the interferometer fringe signal. The application of this feedback to the top-stage of the suspension allows corrections of drifts, such as tidal ones, at a stage of the suspension where a large dynamic range in displacements is available, without introducing noise at the level of the mirror, resulting in a significant reduction of the lock keeping force applied directly on the mirror at the lowest stage of the attenuator.     

The impact of parameter lumping and geometric simplification in modelling runoff and erosion in the shrublands of southeast Arizona

There have been many studies of hydrologic processes and scale. However, some researchers have found that predictions from hydrologic models may not be improved by attempting to incorporate the understanding of these processes into hydrologic models. This paper quantifies the effect of simplifying watershed geometry and averaging the parameter values on simulations generated using the KINEROS2 model. Furthermore, it examines how these changes in model input effect model output. The model was applied on a small semiarid rangeland watershed in which runoff is generated by the infiltration excess mechanism. The study concludes that averaging input parameter values has little effect on runoff volume and peak in simulating runoff. However, geometric simplification does have an effect on runoff peak and volume, but it is not statistically significant. In contrast, both averaging input parameter values and geometric simplification have an effect on model‐predicted sediment yield. Copyright © 2005 John Wiley & Sons, Ltd.     

Eccentricities of Planets in Binary Systems

The most puzzling property of the extrasolar planets discovered by recent radial velocity surveys is their high orbital eccentricities, which are very difficult to explain within our current theoretical paradigm for planet formation. Current data reveal that at least 25% of these planets, including some with particularly high eccentricities, are orbiting a component of a binary star system. The presence of a distant companion can cause significant secular perturbations in the orbit of a planet. At high relative inclinations, large-amplitude, periodic eccentricity perturbations can occur. These are known as “Kozai cycles” and their amplitude is purely dependent on the relative orbital inclination. Assuming that every planet host star also has a (possibly unseen, e.g., substellar) distant companion, with reasonable distributions of orbital parameters and masses, we determine the resulting eccentricity distribution of planets and compare it to observations? We find that perturbations from a binary companion always appear to produce an excess of planets with both very high (?0.6) and very low (e ? 0.1) eccentricities. The paucity of near-circular orbits in the observed sample implies that at least one additional mechanism must be increasing eccentricities. On the other hand, the overproduction of very high eccentricities observed in our models could be combined with plausible circularization mechanisms (e.g., friction from residual gas) to create more planets with intermediate eccentricities (e? 0.1–0.6).     

Hamiltonian Dynamics of a Gyrostat in the N-Body Problem: Relative Equilibria

We consider the non-canonical Hamiltonian dynamics of a gyrostat in Newtonian interaction with n spherical rigid bodies. Using the symmetries of the system we carry out two reductions. Then, working in the reduced problem, we obtain the equations of motion, a Casimir function of the system and the equations that determine the relative equilibria. Global conditions for existence of relative equilibria are given. Besides, we give the variational characterization of these equilibria and three invariant manifolds of the problem; being calculated the equations of motion in these manifolds, which are described by means of a canonical Hamiltonian system. We give some Eulerian and Lagrangian equilibria for the four body problem with a gyrostat. Finally, certain classical problems of Celestial Mechanics are generalized.     

A Three Body Solution for the DI Her System

The DI Herculis system has been extensively studied over the past few decades because its observed rate of apsidal advance is less than a quarter of that which is expected from its physical and orbital properties. Work by Khaliullin et al. (1991) proposed that this slow rate of apsidal advance is a result of the presence of a third (stellar mass) body orbiting the system, however, observations by Guinan et al. (1994) severely restrict the orbital properties of such a solution. We show that a planetary mass object in a highly inclined orbit relative to the binary is capable of producing the observed apsidal motion, while remaining within the bounds of the most recent set of observations. A wide range of stable solutions are possible.     

Stability and Geometry of Third-Order Resonances in four-Dimensional Symplectic Mappings

We analyze four-dimensional symplectic mappings in the neighbourhood of an elliptic fixed point whose eigenvalues are close to satisfy a third-order resonance. Using the perturbative tools of resonant normal forms, the geometry of the orbits and the existence of elliptic or hyperbolic one-dimensional tori (fixed lines) is worked out. This allows one to give an analytical estimate of the stability domain when the resonance is unstable. A comparison with numerical results for the four-dimensional Hénon mapping is given. This revised version was published online in July 2006 with corrections to the Cover Date.