Multi-Layer Hydrostatic Equilibrium of Planets and Synchronous Moons: Theory and Application to Ceres and to Solar System Moons

The hydrostatic equilibrium of multi-layer bodies lacks a satisfactory theoretical treatment despite its wide range of applicability. Here we show that by using the exact analytical potential of homogeneous ellipsoids we can obtain recursive analytical solutions and an exact numerical method for the hydrostatic equilibrium shape problem of multi-layer planets and synchronous moons. The recursive solutions rely on the series expansion of the potential in terms of the polar and equatorial shape eccentricities, while the numerical method uses the exact potential expression. These solutions can be used to infer the interior structure of planets and synchronous moons from the observed shape, rotation, and gravity. When applied to dwarf planet Ceres, we show that it is most likely a differentiated body with an icy crust of equatorial thickness 30-90 km and a rocky core of density 2.4-3.1 g/cm$^3$. For synchronous moons, we show that the $J_2/C_{22} \simeq 10/3$ and the $(b-c)/(a-c) \simeq 1/4$ ratios have significant corrections of order $\Omega^2/(\pi G \rho)$, with important implications on how their gravitational coefficients are determined from flyby radio science data and on how we assess their hydrostatic equilibrium state.Comment: 12 pages, 6 figures, in press in Ap

Full-wave electromagnetic modes and hybridization in nanoparticle dimers

The plasmon hybridization theory is based on a quasi-electrostatic approximation of the Maxwell's equations. It does not take into account magnetic interactions, retardation effects, and radiation losses. Magnetic interactions play a dominant role in the scattering from dielectric nanoparticles. The retardation effects play a fundamental role in the coupling of the modes with the incident radiation and in determining their radiative strength; their exclusion may lead to erroneous predictions of the excited modes and of the scattered power spectra. Radiation losses may lead to a significant broadening of the scattering resonances. We propose a hybridization theory for non-hermitian composite systems based on the full-Maxwell equations that, overcoming all the limitations of the plasmon hybridization theory, unlocks the description of dielectric dimers. As an example, we decompose the scattered field from silicon and silver dimers, under different excitation conditions and gap-sizes, in terms of dimer modes, pinpointing the hybridizing isolated-sphere modes behind them.Comment: Supplemental material available upon reques

Full-wave electromagnetic modes and hybridization in nanoparticle dimers

The plasmon hybridization theory is based on a quasi-electrostatic approximation of the Maxwell’s equations. It does not take into account magnetic interactions, retardation effects, and radiation losses. Magnetic interactions play a dominant role in the scattering from dielectric nanoparticles. The retardation effects play a fundamental role in the coupling of the modes with the incident radiation and in determining their radiative strength; their exclusion may lead to erroneous predictions of the excited modes and of the scattered power spectra. Radiation losses may lead to a significant broadening of the scattering resonances. We propose a hybridization theory for non-Hermitian composite systems based on the full-Maxwell equations that, overcoming all the limitations of the plasmon hybridization theory, unlocks the description of dielectric dimers. As an example, we decompose the scattered field from silicon and silver dimers, under different excitation conditions and gap-sizes, in terms of dimer modes, pinpointing the hybridizing isolated-sphere modes behind them

Community in the urban debate: new research trends to support future planning agendas

The community concept has maintained a constant and growing interest in urban studies and many related fields. The analysis of the policy boundaries and related issues on community action practices are nowadays important to understand various political interests concerning these territorial phenomena. The aim of this contribution is to propose a new interpretation able to clarify how a better definition of this concept can play a role in shaping future planning agenda

Energia come community asset e orizzonte di sviluppo per le imprese di comunità

Le nuove tecnologie per le produzioni distribuite di energia stanno raggiungendo un livello di maturità che lascia presagire un diffuso sviluppo di iniziative dal basso nella costituzione di “sistemi energetici locali”. Queste formule hanno un ruolo cruciale per la ridiscussione dell'intero sistema infrastrutturale e del mercato dell'energia. Se questo tema è ampiamente discusso dal punto di vista tecnologico e ingegneristico, il dibattito sulle caratteristiche delle organizzazioni che dovranno guidare le iniziative locali è appena iniziato. L'obiettivo del paper è di verificare a che punto è il dibattito nella diffusione dei sistemi energetici locali, gli approcci sperimentati e quale possibile ruolo per le imprese di comunità. Il key-issue evidenziato è rappresentato dagli aspetti normativi e regolatori relativi al “grande” mercato energetico. Un “ecosistema normativo” basato su operatori, produzioni e reti “centralizzate”che poco si presta alle particolari esigenze delle iniziative locali. L'analisi intende aprire un nuovo orizzonte di diffusione delle “Imprese di Comunità Energetiche”, concludendo con una riflessione sul ruolo nel dibattito generale sul tema e nello sviluppo di città e territori policentrici

Figure-Figure Interaction Between Bodies Having Arbitrary Shapes and Mass Distributions: A Power Series Expansion Approach

We derive an expression for the mutual gravitational force and torque of two bodies having arbitrary shapes and mass distributions, as an expansion in power series of their products of inertia and of the relative coordinates of their centres of mass. The absolute convergence of all the power series developed is rigorously demonstrated. The absence of transcendental functions makes this formalism suitable for fast numerical applications. The products of inertia used here are directly related to the spherical harmonics coefficients, and we provide a detailed analysis of this relationship.Comment: 13 pages, accepted by Celestial Mechanics and Dynamical Astronom