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Tidal Deformation and Dissipation Processes in Icy Worlds.

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Faculty of Mathematics and Physics, Department of Geophysics, Charles University, V Holesšovičkách 2, Praha, Praha 8 180 00 Czech Republic.

Tidal interactions play a key role in the dynamics and evolution of icy worlds. The intense tectonic activity of Europa and the eruption activity on Enceladus are clear examples of the manifestation of tidal deformation and associated dissipation. While tidal heating has long been recognized as a major driver in the activity of these icy worlds, the mechanism controlling how tidal forces deform the different internal layers and produce heat by tidal friction still remains poorly constrained.

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This study focuses on the analysis of a unique composition between two well-established models, known as the Logistic-Gauss map. The investigation cohesively transitions to an exploration of parameter space, essential for unraveling the complexity of dissipative mappings and understanding the intricate relationships between periodic structures and chaotic regions. By manipulating control parameters, our approach reveals intriguing patterns, with findings enriched by extreme orbits, trajectories that connect local maximum and minimum values of one-dimensional maps.

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Recently, we investigated a number of so-called σ- and τ-functionals based on the adiabatic-connection fluctuation-dissipation theorem (ACFDT); particularly, extensions of the random phase approximation (RPA) with inclusion of an exchange kernel in the form of an antisymmetrized Hartree kernel. One of these functionals, based upon the approximate exchange kernel (AXK) of Bates and Furche, leads to a nonlinear contribution of the spline function used within σ-functionals, which we previously avoided through the introduction of a simplified "top-down" approach in which the σ-functional modification is inserted a posteriori following the analytic coupling strength integration within the framework of the ACFDT and which was shown to provide excellent performance for the GMTKN55 database when using hybrid PBE0 reference orbitals. In this work, we examine the analytic "bottom-up" approach in which the spline function is inserted a priori, i.

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