Aubry sets for weakly coupled systems of Hamilton--Jacobi equations

We introduce a notion of Aubry set for weakly coupled systems of Hamilton--Jacobi equations on the torus and characterize it as the region where the obstruction to the existence of globally strict critical subsolutions concentrates. As in the case of a single equation, we prove the existence of critical subsolutions which are strict and smooth outside the Aubry set. This allows us to derive in a simple way a comparison result among critical sub and supersolutions with respect to their boundary data on the Aubry set, showing in particular that the latter is a uniqueness set for the critical system. We also highlight some rigidity phenomena taking place on the Aubry set.Comment: 35 pages v.2 the introduction has been rewritten and shortened. Some proofs simplified. Corrections and references added. Corollary 5.3 added stating antisymmetry of the Ma\~n\'e matrix on points of the Aubry set. Section 6 contains a new example

On the Large Time Behavior of Solutions of Hamilton-Jacobi Equations Associated with Nonlinear Boundary Conditions

In this article, we study the large time behavior of solutions of first-order Hamilton-Jacobi Equations, set in a bounded domain with nonlinear Neumann boundary conditions, including the case of dynamical boundary conditions. We establish general convergence results for viscosity solutions of these Cauchy-Neumann problems by using two fairly different methods : the first one relies only on partial differential equations methods, which provides results even when the Hamiltonians are not convex, and the second one is an optimal control/dynamical system approach, named the "weak KAM approach" which requires the convexity of Hamiltonians and gives formulas for asymptotic solutions based on Aubry-Mather sets

Solar neutrino detection in a large volume double-phase liquid argon experiment

Precision measurements of solar neutrinos emitted by specific nuclear reaction chains in the Sun are of great interest for developing an improved understanding of star formation and evolution. Given the expected neutrino fluxes and known detection reactions, such measurements require detectors capable of collecting neutrino-electron scattering data in exposures on the order of 1 ktonne yr, with good energy resolution and extremely low background. Two-phase liquid argon time projection chambers (LAr TPCs) are under development for direct Dark Matter WIMP searches, which possess very large sensitive mass, high scintillation light yield, good energy resolution, and good spatial resolution in all three cartesian directions. While enabling Dark Matter searches with sensitivity extending to the "neutrino floor" (given by the rate of nuclear recoil events from solar neutrino coherent scattering), such detectors could also enable precision measurements of solar neutrino fluxes using the neutrino-electron elastic scattering events. Modeling results are presented for the cosmogenic and radiogenic backgrounds affecting solar neutrino detection in a 300 tonne (100 tonne fiducial) LAr TPC operating at LNGS depth (3,800 meters of water equivalent). The results show that such a detector could measure the CNO neutrino rate with ~15% precision, and significantly improve the precision of the 7Be and pep neutrino rates compared to the currently available results from the Borexino organic liquid scintillator detector.Comment: 21 pages, 7 figures, 6 table

New experimental limits on the Pauli forbidden transitions in 12^{12}C nuclei obtained with 485 days Borexino data

The Pauli exclusion principle (PEP) has been tested for nucleons ($n,p$) in $^{12}C$ with the Borexino detector.The approach consists of a search for $\gamma$, $n$, $p$ and $\beta^\pm$ emitted in a non-Paulian transition of 1$P_{3/2}$- shell nucleons to the filled 1$S_{1/2}$ shell in nuclei. Due to the extremely low background and the large mass (278 t) of the Borexino detector, the following most stringent up-to-date experimental bounds on PEP violating transitions of nucleons have been established: $\tau({^{12}\rm{C}}\to{^{12}\widetilde{\rm{C}}}+\gamma) \geq 5.0\cdot10^{31}$ y, $\tau({^{12}\rm{C}}\to{^{11}\widetilde{\rm{B}}}+ p) \geq 8.9\cdot10^{29}$ y, $\tau({^{12}\rm{C}}\to{^{11}\widetilde{\rm{C}}}+ n) \geq 3.4 \cdot 10^{30}$ y, $\tau({^{12}\rm{C}}\to{^{12}\widetilde{\rm{N}}}+ e^- + \widetilde{\nu_e}) \geq 3.1\cdot 10^{30}$ y and $\tau({^{12}\rm{C}}\to{^{12}\widetilde{\rm{B}}}+ e^+ + \nu_e) \geq 2.1 \cdot 10^{30}$ y, all at 90% C.L. The corresponding upper limits on the relative strengths for the searched non-Paulian electromagnetic, strong and weak transitions have been estimated: $\delta^2_{\gamma} \leq 2.2\cdot10^{-57}$, $\delta^2_{N} \leq 4.1\cdot10^{-60}$ and $\delta^2_{\beta} \leq 2.1\cdot10^{-35}$.Comment: 9 pages, 6 figure

Northern winter climate change: assessment of uncertainty in CMIP5 projections related to stratosphere-troposphere coupling

Journal ArticlePublished versionFuture changes in the stratospheric circulation could have an important impact on northern winter tropospheric climate change, given that sea level pressure (SLP) responds not only to tropospheric circulation variations but also to vertically coherent variations in troposphere-stratosphere circulation. Here we assess northern winter stratospheric change and its potential to influence surface climate change in the Coupled Model Intercomparison Project-Phase 5 (CMIP5) multimodel ensemble. In the stratosphere at high latitudes, an easterly change in zonally averaged zonal wind is found for the majority of the CMIP5 models, under the Representative Concentration Pathway 8.5 scenario. Comparable results are also found in the 1% CO2 increase per year projections, indicating that the stratospheric easterly change is common feature in future climate projections. This stratospheric wind change, however, shows a signi fi cant spread among the models. By using linear regression, we quantify the impact of tropical upper troposphere warming, polar amplification, and the stratospheric wind change on SLP. We find that the intermodel spread in stratospheric wind change contributes substantially to the intermodel spread in Arctic SLP change. The role of the stratosphere in determining part of the spread in SLP change is supported by the fact that the SLP change lags the stratospheric zonally averaged wind change. Taken together, these findings provide further support for the importance of simulating the coupling between the stratosphere and the troposphere, to narrow the uncertainty in the future projection of tropospheric circulation changes

New limits on heavy sterile neutrino mixing in 8B{^{8}\rm{B}}-decay obtained with the Borexino detector

If heavy neutrinos with mass $m_{\nu_{H}}\geq$2$m_e$ are produced in the Sun via the decay ${^8\rm{B}} \rightarrow {^8\rm{Be}} + e^+ + \nu_H$ in a side branch of pp-chain, they would undergo the observable decay into an electron, a positron and a light neutrino $\nu_{H}\rightarrow\nu_{L}+e^++e^-$. In the present work Borexino data are used to set a bound on the existence of such decays. We constrain the mixing of a heavy neutrino with mass 1.5 MeV $\leq m_{\nu_{H}} \le$ 14 MeV to be $|U_{eH}|^2\leq (10^{-3}-4\times10^{-6})$ respectively. These are tighter limits on the mixing parameters than obtained in previous experiments at nuclear reactors and accelerators.Comment: 7 pages, 6 figure

Solar neutrino with Borexino: results and perspectives

Borexino is a unique detector able to perform measurement of solar neutrinos fluxes in the energy region around 1 MeV or below due to its low level of radioactive background. It was constructed at the LNGS underground laboratory with a goal of solar $^{7}$Be neutrino flux measurement with 5\% precision. The goal has been successfully achieved marking the end of the first stage of the experiment. A number of other important measurements of solar neutrino fluxes have been performed during the first stage. Recently the collaboration conducted successful liquid scintillator repurification campaign aiming to reduce main contaminants in the sub-MeV energy range. With the new levels of radiopurity Borexino can improve existing and challenge a number of new measurements including: improvement of the results on the Solar and terrestrial neutrino fluxes measurements; measurement of pp and CNO solar neutrino fluxes; search for non-standard interactions of neutrino; study of the neutrino oscillations on the short baseline with an artificial neutrino source (search for sterile neutrino) in context of SOX project.Comment: 15 pages, 4 figure

Muon and Cosmogenic Neutron Detection in Borexino

Borexino, a liquid scintillator detector at LNGS, is designed for the detection of neutrinos and antineutrinos from the Sun, supernovae, nuclear reactors, and the Earth. The feeble nature of these signals requires a strong suppression of backgrounds below a few MeV. Very low intrinsic radiogenic contamination of all detector components needs to be accompanied by the efficient identification of muons and of muon-induced backgrounds. Muons produce unstable nuclei by spallation processes along their trajectory through the detector whose decays can mimic the expected signals; for isotopes with half-lives longer than a few seconds, the dead time induced by a muon-related veto becomes unacceptably long, unless its application can be restricted to a sub-volume along the muon track. Consequently, not only the identification of muons with very high efficiency but also a precise reconstruction of their tracks is of primary importance for the physics program of the experiment. The Borexino inner detector is surrounded by an outer water-Cherenkov detector that plays a fundamental role in accomplishing this task. The detector design principles and their implementation are described. The strategies adopted to identify muons are reviewed and their efficiency is evaluated. The overall muon veto efficiency is found to be 99.992% or better. Ad-hoc track reconstruction algorithms developed are presented. Their performance is tested against muon events of known direction such as those from the CNGS neutrino beam, test tracks available from a dedicated External Muon Tracker and cosmic muons whose angular distribution reflects the local overburden profile. The achieved angular resolution is 3-5 deg and the lateral resolution is 35-50 cm, depending on the impact parameter of the crossing muon. The methods implemented to efficiently tag cosmogenic neutrons are also presented.Comment: 42 pages. 32 figures on 37 files. Uses JINST.cls. 1 auxiliary file (defines.tex) with TEX macros. submitted to Journal of Instrumentatio

The Main Results of the Borexino Experiment

The main physical results on the registration of solar neutrinos and the search for rare processes obtained by the Borexino collaboration to date are presented.Comment: 8 pages, 8 figgures, To be published as Proceedings of the Third Annual Large Hadron Collider Physics Conference, St. Petersburg, Russia, 201