Dissipative continuous Euler flows

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

Lack of uniqueness for weak solutions of the incompressible porous media equation

In this work we consider weak solutions of the incompressible 2-D porous media equation. By using the approach of De Lellis-Sz\'ekelyhidi we prove non-uniqueness for solutions in $L^\infty$ in space and time.Comment: 23 pages, 2 fugure

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

On admissibility criteria for weak solutions of the Euler equations

We consider solutions to the Cauchy problem for the incompressible Euler equations satisfying several additional requirements, like the global and local energy inequalities. Using some techniques introduced in an earlier paper we show that, for some bounded compactly supported initial data, none of these admissibility criteria singles out a unique weak solution. As a byproduct we show bounded initial data for which admissible solutions to the p-system of isentropic gas dynamics in Eulerian coordinates are not unique in more than one space dimension.Comment: 33 pages, 1 figure; v2: 35 pages, corrected typos, clarified proof

Search for spontaneous muon emission from lead nuclei

We describe a possible search for muonic radioactivity from lead nuclei using the base elements ("bricks" composed by lead and nuclear emulsion sheets) of the long-baseline OPERA neutrino experiment. We present the results of a Monte Carlo simulation concerning the expected event topologies and estimates of the background events. Using few bricks, we could reach a good sensitivity level.Comment: 12 pages, 4 figure

The geometry of a vorticity model equation

We provide rigorous evidence of the fact that the modified Constantin-Lax-Majda equation modeling vortex and quasi-geostrophic dynamics describes the geodesic flow on the subgroup of orientation-preserving diffeomorphisms fixing one point, with respect to right-invariant metric induced by the homogeneous Sobolev norm $H^{1/2}$ and show the local existence of the geodesics in the extended group of diffeomorphisms of Sobolev class $H^{k}$ with $k\ge 2$.Comment: 24 page

Procedure for short-lived particle detection in the OPERA experiment and its application to charm decays

The OPERA experiment, designed to perform the first observation of $\nu_\mu \rightarrow \nu_\tau$ oscillations in appearance mode through the detection of the $\tau$ leptons produced in $\nu_\tau$ charged current interactions, has collected data from 2008 to 2012. In the present paper, the procedure developed to detect $\tau$ particle decays, occurring over distances of the order of 1 mm from the neutrino interaction point, is described in detail. The results of its application to the search for charmed hadrons are then presented as a validation of the methods for $\nu_\tau$ appearance detection

Observation of nu_tau appearance in the CNGS beam with the OPERA experiment

The OPERA experiment is searching for nu_mu -> nu_tau oscillations in appearance mode i.e. via the direct detection of tau leptons in nu_tau charged current interactions. The evidence of nu_mu -> nu_tau appearance has been previously reported with three nu_tau candidate events using a sub-sample of data from the 2008-2012 runs. We report here a fourth nu_tau candidate event, with the tau decaying into a hadron, found after adding the 2012 run events without any muon in the final state to the data sample. Given the number of analysed events and the low background, nu_mu -> nu_tau oscillations are established with a significance of 4.2sigma.Comment: Submitted to Progress of Theoretical and Experimental Physics (PTEP

Determination of the muon charge sign with the dipolar spectrometers of the OPERA experiment

The OPERA long-baseline neutrino-oscillation experiment has observed the direct appearance of $\nu_\tau$ in the CNGS $\nu_\mu$ beam. Two large muon magnetic spectrometers are used to identify muons produced in the $\tau$ leptonic decay and in $\nu_\mu^{CC}$ interactions by measuring their charge and momentum. Besides the kinematic analysis of the $\tau$ decays, background resulting from the decay of charmed particles produced in $\nu_\mu^{CC}$ interactions is reduced by efficiently identifying the muon track. A new method for the charge sign determination has been applied, via a weighted angular matching of the straight track-segments reconstructed in the different parts of the dipole magnets. Results obtained for Monte Carlo and real data are presented. Comparison with a method where no matching is used shows a significant reduction of up to 40\% of the fraction of wrongly determined charges.Comment: 10 pages. Improvements in the tex

First events from the CNGS neutrino beam detected in the OPERA experiment

The OPERA neutrino detector at the underground Gran Sasso Laboratory (LNGS) was designed to perform the first detection of neutrino oscillations in appearance mode, through the study of nu_mu to nu_tau oscillations. The apparatus consists of a lead/emulsion-film target complemented by electronic detectors. It is placed in the high-energy, long-baseline CERN to LNGS beam (CNGS) 730 km away from the neutrino source. In August 2006 a first run with CNGS neutrinos was successfully conducted. A first sample of neutrino events was collected, statistically consistent with the integrated beam intensity. After a brief description of the beam and of the various sub-detectors, we report on the achievement of this milestone, presenting the first data and some analysis results.Comment: Submitted to the New Journal of Physic