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

Weak KAM aspects of convex Hamilton-Jacobi equations with Neumann type boundary conditions

We establish the stability under the formations of infimum and of convex combinations of subsolutions of convex Hamilton-Jacobi equations, some comparison and existence results for convex and coercive Hamilton-Jacobi equations with the Neumann type boundary condition as well as existence results for the Skorokhod problem. We define the Aubry-Mather set associated with the Neumann type boundary problem and establish some properties of the Aubry-Mather set including the existence results for the ``calibrated'' extremals for the corresponding action functional (or variational problem).Comment: 39 pages, 1 figur

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

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

Euro-Atlantic weather regimes in the PRIMAVERA coupled climate simulations: impact of resolution and mean state biases on model performance

Recently, much attention has been devoted to better understand the internal modes of variability of the climate system. This is particularly important in mid-latitude regions like the North-Atlantic, which is characterized by a large natural variability and is intrinsically difficult to predict. A suitable framework for studying the modes of variability of the atmospheric circulation is to look for recurrent patterns, commonly referred to as Weather Regimes. Each regime is characterized by a specific large-scale atmospheric circulation pattern, thus influencing regional weather and extremes over Europe. The focus of the present paper is the study of the Euro-Atlantic wintertime Weather Regimes in the climate models participating to the PRIMAVERA project. We analyse here the set of coupled historical simulations (hist-1950), which have been performed both at standard and increased resolution, following the HighresMIP protocol. The models’ performance in reproducing the observed Weather Regimes is assessed in terms of different metrics, focussing on systematic biases and on the impact of resolution. We also analyse the connection of the Weather Regimes with the Jet Stream latitude and blocking frequency over the North-Atlantic sector. We find that—for most models—the regime patterns are better represented in the higher resolution version, for all regimes but the NAO-. On the other side, no clear impact of resolution is seen on the regime frequency of occurrence and persistence. Also, for most models, the regimes tend to be more tightly clustered in the increased resolution simulations, more closely resembling the observed ones. However, the horizontal resolution is not the only factor determining the model performance, and we find some evidence that biases in the SSTs and mean geopotential field might also play a role

Atmospheric response to cold wintertime Tibetan Plateau conditions over eastern Asia in climate models

Central Asian orography (namely the Tibetan and Mongolian plateaux) sets important features of the winter climate over eastern Asia and the Pacific. By deflecting the mid-latitude jet polewards it contributes to the formation of the Siberian high and, on the lee side, to the advection of dry cold continental air over the eastern Asian coast and the Pacific Ocean, where atmospheric instability and cyclogenesis thrive. While the mechanic forcing by the orography is assessed in a number of modelling studies, it is still not clear how near-surface temperature over the two most prominent orographic barriers of the central Asian continent – the Tibetan and Mongolian plateaux – influences the winter climate. The problem is particularly relevant in view of a well-known cold bias in state-of-the-art climate models in proximity to the Tibetan Plateau, likely related to the modelling of land processes and land–atmosphere interaction over complex orography. Here we take advantage of the large spread in near-surface temperature over the central Asian plateaux within the Coupled Model Intercomparison Project Phase 6 (CMIP6) to study how colder-than-average Asian plateau temperatures impact the atmospheric circulation. Based on composites of the CMIP6 models' climatologies showing the coldest Tibetan Plateau conditions, we find that such negative temperature anomalies appear to amplify the atmospheric response to orography, with an intensification of the eastern Asian winter monsoon and of the equatorward flank of the Pacific jet. The results of the CMIP6 composite analysis are supported by experiments run with an intermediate-complexity atmospheric model, forced by a similar pattern of cold surface temperatures over the central Asian plateaux. Within this setting, the relative influence of the Tibetan and the Mongolian Plateau surface conditions is analysed. Based on the results reported in this work we project that advances in the modelling of the land energy budget over the elevated regions of central Asia could improve the simulation of the climate in the Asian–Pacific sector climate, together with the reliability of climate projections and the performance of shorter-term forecasts.</p

Existence theorems in the geometrically non-linear 6-parametric theory of elastic plates

In this paper we show the existence of global minimizers for the geometrically exact, non-linear equations of elastic plates, in the framework of the general 6-parametric shell theory. A characteristic feature of this model for shells is the appearance of two independent kinematic fields: the translation vector field and the rotation tensor field (representing in total 6 independent scalar kinematic variables). For isotropic plates, we prove the existence theorem by applying the direct methods of the calculus of variations. Then, we generalize our existence result to the case of anisotropic plates. We also present a detailed comparison with a previously established Cosserat plate model.Comment: 19 pages, 1 figur