We construct topological defects generating non-abelian T-duality for isometry groups acting without isotropy. We find that these defects are given by line bundles on the correspondence space with curvature which can be considered as a non-abelian generalization of the curvature of the Poincarè bundle. We show that the defect equations of motion encode the non-abelian T-duality transformation. The Fourier-Mukai transform of the Ramond-Ramond fields generated by the gauge invariant flux of these defects is studied. We show that it provides elegant and compact way of computation of the transformation of the Ramond-Ramond fields under the non-abelian T-duality.
The main purpose of this work is to present a time-domain implementation of the Andrade rheology, instead of the traditional expansion in terms of a Fourier series of the tidal potential. This approach can be used in any fully three dimensional numerical simulation of the dynamics of a system of many deformable bodies. In particular, it allows large eccentricities, large mutual inclinations, and it is not limited to quasi-periodic perturbations. It can take into account an extended class of perturbations, such as chaotic motions, transient events, and resonant librations.The results are presented by means of a concrete application: the analysis of the libration of Enceladus. This is done by means of both analytic formulas in the frequency domain and direct numerical simulations. We do not a priori assume that Enceladus has a triaxial shape, the eventual triaxiality is a consequence of the satellite motion and its rheology. As a result we obtain an analytic formula for the amplitude of libration that incorporates a new correction due to the rheology.Our results provide an estimation of the amplitude of libration of the core of Enceladus as 0.6% of that of the shell. They also reproduce the observed 10 GW of tidal heat generated by Enceladus with a value of 0.17 × 10 14 Pa·s for the global effective viscosity under both Maxwell and Andrade rheology.
In this work, we investigate whether a multilayered planet can be approximated as a homogeneous planet, and in particular how well the dissipation rate of a multilayered planet can be reproduced with a homogeneous rheology. We study the case of a stratified body with an icy crust that, according to recent studies, displays a double peak feature in the tidal response that cannot be reproduced with a homogeneous planet with an Andrade rheology. We revisit the problem with a slightly more complex rheology for the homogeneous body, the Sundberg–Cooper rheology, which naturally has a double peak feature, and apply the model to the TRAPPIST-1e planet. Our results compare very well with the results obtained when employing a multilayered model, showing that it is possible to approximate the behavior of a multilayer icy planet with a homogeneous planet using the Sundberg–Cooper rheology. This highlights the fact that we do not need the complexity of the multilayer planet model in order to estimate the tidal dissipation of an icy planet.
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