Alberto Escapa

Indirect effect of the triaxiality in the Hamiltonian theory for the rigid Earth nutations

In this investigation we determine a new contribution to the nutation series due to an indirect eect of the triaxiality of the rigid Earth. We undertake this work in the context of the Hamiltonian theory for the rigid Earth, developed by Kinoshita (1977) and recently updated by Souchay et al. (1999). To do this, we express the potential energy in terms of the action{angle variables for the triaxial Earth. Then, we work out analytical formulae for the new contributions, showing that their numerical values are within the truncation level adopted by REN{2000 (Souchay et al. 1999), which was xed to 0:1 as.

Canonical approach to the free nutations of a three‐layer Earth model

The Hamiltonian formalism is applied to a three layer Earth model composed of a rigid mantle, a fluid outer core and a rigid inner core, with no dissipation of frictional or electromagnetic origin. Analytical expressions for the free nutations are derived in a set of nonsingular canonical variables that allow a much simpler mathematical treatment, They are checked versus numerical solutions and compared with previous results by Mathews et al. [1991a] and Getino and Ferrandiz [1996, 1998a] with complete agreement up to the first order in the ellipticities.

GENERAL THEORY OF THE ROTATION OF THE NON-RIGID EARTH AT THE SECOND ORDER. I. THE RIGID MODEL IN ANDOYER VARIABLES

This paper is the first part of an investigation where we will present an analytical general theory of the rotation of the non-rigid Earth at the second order, which considers the effects of the interaction of the rotation of the Earth with itself, also named as the spin-spin coupling. Here, and as a necessary step in the development of that theory, we derive complete, explicit, analytical formulae of the rigid Earth rotation that account for the second-order rotation-rotation interaction. These expressions are not provided in this form by any current rigid Earth model. Working within the Hamiltonian framework established by Kinoshita, we study the second-order effects arising from the interaction of the main term in the Earth geopotential expansion with itself, and with the complementary term arising when referring the rotational motion to the moving ecliptic. To this aim, we apply a canonical perturbation method to solve analytically the canonical equations at the second order, determining the expressions that provide the nutation-precession, the polar motion, and the length of day. In the case of the motion of the equatorial plane, nutation-precession, we compare our general approach with the particular study for this motion developed by Souchay et al., showing the existence of new terms whose numerical values are within the truncation level of 0.1 μas adopted by those authors. These terms emerge as a consequence of not assuming in this work the same restrictive simplifications taken by Souchay et al. The importance of these additional contributions is that, as the analytical formulae show, they depend on the Earth model considered, in such a way that the fluid core resonance could amplify them significatively when extending this theory to the non-rigid Earth models.

FREE TRANSLATIONAL OSCILLATIONS OF ICY BODIES WITH A SUBSURFACE OCEAN USING A VARIATIONAL APPROACH

We analyze the influence of the interior structure of an icy body with an internal ocean on the relative translational motions of its solid constituents. We consider an isolated body differentiated into three homogeneous layers with spherical symmetry: an external ice-I layer, a subsurface ammonia‐water ocean, and a rocky inner core. This composition represents icy bodies such as Europa, Titania, Oberon, and Triton, as well as Pluto, Eris, Sedna, and 2004 DW. We construct the equations of motion by assuming that the solid constituents are rigid and that the ocean is an ideal fluid, the internal motion being characterized by the relative translations of the solids and the induced flow in the fluid. Then we determine the dynamics of the icy body using the methods of analytical mechanics, that is, we compute the kinetic energy and the gravitational potential energy, and obtain the Lagrangian function. The resulting solution of the Lagrange equations shows that the solid layers perform translational oscillations of different amplitudes with respect to the barycenter of the body. We derive the dependence of the frequency of the free oscillations of the system on the characteristics of each layer, expressing the period of the oscillations as a function of the densities and masses of the ocean and the rocky inner core, and the mass of the icy body. We apply these results to previously developed subsurface models and obtain numerical values for the period and the ratio between the amplitudes of the translational oscillations of the solid components. The features obtained are quite different from the cases of Earth and Mercury. Our analytical formulas satisfactorily explain the source of these differences. When models of the same icy body, compatible with the existence of an internal ocean, differ in the thickness of the ice-I layer, their associated periods experience a relative variation of at least 10%. In particular, the different models for Titania and Oberon exhibit a larger variation of about 37% and 30%. This indicates an absolute difference of the order of three and two hours, respectively. This suggests that the free period of the internal oscillations might provide a new procedure to constrain the internal structure of icy bodies with a subsurface ocean.

New measures for open-domain question answering evaluation within a time constraint

Previous works on evaluating the performance of Question Answering (QA) systems are focused on the evaluation of the precision. In this paper, we developed a mathematic procedure in order to explore new evaluation measures in QA systems considering the answer time. Also, we carried out an exercise for the evaluation of QA systems within a time constraint in the CLEF-2006 campaign, using the proposed measures. The main conclusion is that the evaluation of QA systems in realtime can be a new scenario for the evaluation of QA systems.

Evaluation of Open-Domain Question Answering Systems within a Time Constraint

Previous works on evaluating the performance of Question Answering (QA) systems are focused in the evaluation of the precision. Nevertheless, the importance of the answer time never has been evaluated. This paper studies the problem of the evaluation in QA systems, focusing on the way in which the time can be considered. Specifically, we carried out an exercise for the evaluation of QA systems within a time constraint in the CLEF-2006 campaign, proposing new measures which combine the precision with the answer time. Also, the performance achieved by each participant system and statistical analysis of the results is given. The main conclusion is that the evaluation of QA systems in realtime can be a more realistic scenario than the traditional used for the main evaluations forums in QA.

Consistency Problems in the Improvement of the IAU Precession–Nutation Theories: Effects of the Dynamical Ellipticity Differences

The complexity of the modeling of the rotational motion of the Earth in space has produced that no single theory has been adopted to describe it in full. Hence, it is customary using at least a theory for precession and another one for nutation. The classic approach proceeds by deriving some of the fundamental parameters from the precession theory, like, e.g., the dynamical ellipticity

Dynamical adjustments in IAU 2000A nutation series arising from IAU 2006 precession

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