Dissipative continuous Euler flows

We show the existence of continuous periodic solutions of the 3D incompressible Euler equations which dissipate the total kinetic energy

Rectifiability and upper Minkowski bounds for singularities of harmonic Q-valued maps

In this article we prove that the singular set of Dirichlet-minimizing Q-valued functions is countably .m2/-rectifiable and we give upper bounds for the .m2/-dimensional Minkowski content of the set of singular points with multiplicity Q

Regularity of higher codimension area minimizing integral currents

This lecture notes are an expanded version of the course given at the ERC-School on Geometric Measure Theory and Real Analysis, held in Pisa, September 30th - October 30th 2013. The lectures aim to explain the main steps of a new proof of the partial regularity of area minimizing integer rectifiable currents in higher codimension, due originally to F. Almgren, which is contained in a series of papers in collaboration with C. De Lellis (University of Zurich).Comment: This text will appear in "Geometric Measure Theory and Real Analysis", pp. 131--192, Proceedings of the ERC school in Pisa (2013), L. Ambrosio Ed., Edizioni SNS (CRM Series

SBV regularity for Hamilton-Jacobi equations in Rn\mathbb R^n

In this paper we study the regularity of viscosity solutions to the following Hamilton-Jacobi equations $$\partial_t u + H(D_{x} u)=0 \qquad \textrm{in} \Omega\subset \mathbb R\times \mathbb R^{n} .$$ In particular, under the assumption that the Hamiltonian $H\in C^2(\mathbb R^n)$ is uniformly convex, we prove that $D_{x}u$ and $\partial_t u$ belong to the class $SBV_{loc}(\Omega)$.Comment: 15 page

Young Measures Generated by Ideal Incompressible Fluid Flows

In their seminal paper "Oscillations and concentrations in weak solutions of the incompressible fluid equations", R. DiPerna and A. Majda introduced the notion of measure-valued solution for the incompressible Euler equations in order to capture complex phenomena present in limits of approximate solutions, such as persistence of oscillation and development of concentrations. Furthermore, they gave several explicit examples exhibiting such phenomena. In this paper we show that any measure-valued solution can be generated by a sequence of exact weak solutions. In particular this gives rise to a very large, arguably too large, set of weak solutions of the incompressible Euler equations.Comment: 35 pages. Final revised version. To appear in Arch. Ration. Mech. Ana

Weak solutions to problems involving inviscid fluids

We consider an abstract functional-differential equation derived from the pressure-less Euler system with variable coefficients that includes several systems of partial differential equations arising in the fluid mechanics. Using the method of convex integration we show the existence of infinitely many weak solutions for prescribed initial data and kinetic energy

High-resolution tracking in a GEM-Emulsion detector

SHiP (Search for Hidden Particles) is a beam dump experiment proposed at the CERN SPS aiming at the observation of long lived particles very weakly coupled with ordinary matter mostly produced in the decay of charmed hadrons. The beam dump facility of SHiP is also a copious factory of neutrinos of all three kinds and therefore a dedicated neutrino detector is foreseen in the SHiP apparatus. The neutrino detector exploits the Emulsion Cloud Chamber technique with a modular structure, alternating walls of target units and planes of electronic detectors providing the time stamp to the event. GEM detectors are one of the possible choices for this task. This paper reports the results of the first exposure to a muon beam at CERN of a new hybrid chamber, obtained by coupling a GEM chamber and an emulsion detector. Thanks to the micrometric accuracy of the emulsion detector, the position resolution of the GEM chamber as a function of the particle inclination was evaluated in two configurations, with and without the magnetic fiel

Low energy high angular resolution neutral atom detection by means of micro-shuttering techniques: the BepiColombo SERENA/ELENA sensor

The neutral sensor ELENA (Emitted Low-Energy Neutral Atoms) for the ESA cornerstone BepiColombo mission to Mercury (in the SERENA instrument package) is a new kind of low energetic neutral atoms instrument, mostly devoted to sputtering emission from planetary surfaces, from E ~20 eV up to E~5 keV, within 1-D (2x76 deg). ELENA is a Time-of-Flight (TOF) system, based on oscillating shutter (operated at frequencies up to a 100 kHz) and mechanical gratings: the incoming neutral particles directly impinge upon the entrance with a definite timing (START) and arrive to a STOP detector after a flight path. After a brief dissertation on the achievable scientific objectives, this paper describes the instrument, with the new design techniques approached for the neutral particles identification and the nano-techniques used for designing and manufacturing the nano-structure shuttering core of the ELENA sensor. The expected count-rates, based on the Hermean environment features, are shortly presented and discussed. Such design technologies could be fruitfully exported to different applications for planetary exploration.Comment: 11 page

Space Weathering on Near-Earth Objects investigated by neutral-particle detection

The ion-sputtering (IS) process is active in many planetary environments in the Solar System where plasma precipitates directly on the surface (for instance, Mercury, Moon, Europa). In particular, solar-wind sputtering is one of the most important agents for the surface erosion of a Near-Earth Object (NEO), acting together with other surface release processes, such as Photon Stimulated Desorption (PSD), Thermal Desorption (TD) and Micrometeoroid Impact Vaporization (MIV). The energy distribution of the IS-released neutrals peaks at a few eVs and extends up to hundreds of eVs. Since all other release processes produce particles of lower energies, the presence of neutral atoms in the energy range above 10 eV and below a few keVs (Sputtered High-Energy Atoms - SHEA) identifies the IS process. SHEA easily escape from the NEO, due to NEO's extremely weak gravity. Detection and analysis of SHEA will give important information on surface-loss processes as well as on surface elemental composition. The investigation of the active release processes, as a function of the external conditions and the NEO surface properties, is crucial for obtaining a clear view of the body's present loss rate as well as for getting clues on its evolution, which depends significantly on space weather. In this work, an attempt to analyze the processes that take place on the surface of these small airless bodies, as a result of their exposure to the space environment, has been realized. For this reason a new space weathering model (Space Weathering on NEO - SPAWN), is presented. Moreover, an instrument concept of a neutral-particle analyzer specifically designed for the measurement of neutral density and the detection of SHEA from a NEO is proposedComment: 36 page