Essential connectedness and the rigidity problem for Gaussian symmetrization

We provide a geometric characterization of rigidity of equality cases in Ehrhard's symmetrization inequality for Gaussian perimeter. This condition is formulated in terms of a new measure-theoretic notion of connectedness for Borel sets, inspired by Federer's definition of indecomposable current.Comment: 38 page

Geotropic tracers in turbulent flows: a proxy for fluid acceleration

We investigate the statistics of orientation of small, neutrally buoyant, spherical tracers whose center of mass is displaced from the geometrical center. If appropriate-sized particles are considered, a linear relation can be derived between the horizontal components of the orientation vector and the same components of acceleration. Direct numerical simulations are carried out, showing that such relation can be used to reconstruct the statistics of acceleration fluctuations up to the order of the gravitational acceleration. Based on such results, we suggest a novel method for the local experimental measurement of accelerations in turbulent flows.Comment: 14 pages, 6 figure

energy retrofit of historic buildings in the mediterranean area the case of the palaeontology museum of naples

Abstract This paper aims to identify some optimal system solutions for the energy refurbishment of a specific historic building, through energy simulations in dynamic conditions performed with a suitable software. The analysis is carried out by the evaluation of energy requirements of the building, in terms of both primary and electric energy. The hypotheses of intervention regard only the air conditioning system components and take into account the existing architectural constraints. The case study refers to the Palaeontology Museum of Naples (Southern Italy), whose rooms are currently in a historic building located in the ancient centre of the city

The Ferroelectric-Ferroelastic Debate about Metal Halide Perovskites

Metal halide perovskites (MHPs) are solution-processed materials with exceptional photoconversion efficiencies that have brought a paradigm shift in photovoltaics. The nature of the peculiar optoelectronic properties underlying such astounding performance is still controversial. The existence of ferroelectricity in MHPs and its alleged impact on photovoltaic activity have fueled an intense debate, in which unanimous consensus is still far from being reached. Here we critically review recent experimental and theoretical results with a two-fold objective: we argue that the occurrence of ferroelectric domains is incompatible with the A-site cation dynamics in MHPs and propose an alternative interpretation of the experiments based on the concept of ferroelasticity. We further underline that ferroic behavior in MHPs would not be relevant at room temperature or higher for the physics of photogenerated charge carriers, since it would be overshadowed by competing effects like polaron formation and ion migration

A fully Eulerian solver for the simulation of multiphase flows with solid bodies: application to surface gravity waves

In this paper a fully Eulerian solver for the study of multiphase flows for simulating the propagation of surface gravity waves over submerged bodies is presented. We solve the incompressible Navier-Stokes equations coupled with the volume of fluid technique for the modeling of the liquid phases with the interface, an immersed body method for the solid bodies and an iterative strong-coupling procedure for the fluid-structure interaction. The flow incompressibility is enforced via the solution of a Poisson equation which, owing to the density jump across the interfaces of the liquid phases, has to resort to the splitting procedure of Dodd & Ferrante [12]. The solver is validated through comparisons against classical test cases for fluid-structure interaction like migration of particles in pressure-driven channel, multiphase flows, water exit of a cylinder and a good agreement is found for all tests. Furthermore, we show the application of the solver to the case of a surface gravity wave propagating over a submerged reversed pendulum and verify that the solver can reproduce the energy exchange between the wave and the pendulum. Finally the three-dimensional spilling breaking of a wave induced by a submerged sphere is considered

Dynamical moments reveal a topological quantum transition in a photonic quantum walk

Many phenomena in solid-state physics can be understood in terms of their topological properties. Recently, controlled protocols of quantum walks are proving to be effective simulators of such phenomena. Here we report the realization of a photonic quantum walk showing both the trivial and the non-trivial topologies associated with chiral symmetry in one-dimensional periodic systems, as in the Su-Schrieffer-Heeger model of polyacetylene. We find that the probability distribution moments of the walker position after many steps behave differently in the two topological phases and can be used as direct indicators of the quantum transition: while varying a control parameter, these moments exhibit a slope discontinuity at the transition point, and remain constant in the non-trivial phase. Extending this approach to higher dimensions, different topological classes, and other typologies of quantum phases may offer new general instruments for investigating quantum transitions in such complex systems