Global Existence of Weak Solutions to the Compressible Primitive Equations of Atmospheric Dynamics with Degenerate Viscosities

We show the existence of global weak solutions to the three-dimensional compressible primitive equations of atmospheric dynamics with degenerate viscosities. In analogy with the case of the compressible Navier-Stokes equations, the weak solutions satisfy the basic energy inequality, the Bresh-Desjardins entropy inequality and the Mellet-Vasseur estimate. These estimates play an important role in establishing the compactness of the vertical velocity of the approximating solutions, and therefore are essential to recover the vertical velocity in the weak solutions

A Theoretical Framework for Modeling Asymmetric, Nonpositive Definite and Nonuniform Distance Functions on Rn

In this paper, we give theoretical foundations for modeling distance functions on the usual Euclidean space Rn, wheredistance may refer to physical kilometers, liters of fuel consumed, time spent in traveling, or transportation cost. In ourapproach, a distance function d is derived from a function F0 called the fundamental function of d. Our distancefunctions, unlike metrics, can be asymmetric and non-positive definite, and unlike the Lp norms, they can be nonuniform.We illustrate our theoretical framework by modeling an asymmetric and non-uniform distance function on R2which can take negative values

Tackling the muon identification in water Cherenkov detectors problem for the future Southern Wide-field Gamma-ray Observatory by means of Machine Learning

We would like to thank to A. Bueno for all the support and useful discussions during the development of this work. The authors thank also for the financial support by OE - Portugal, FCT, I. P., under project PTDC/FIS-PAR/29158/2017. R. C. is grateful for the financial support by OE-Portugal, FCT, I. P., under DL57 /2016/cP1330/cT0002. A. G. is grateful for the financial support by the projects MINECO FPA2017-85197-P and PID2019-104676GB-C32. B.S.G. is grateful for the financial support by grant LIP/BI - 14/2020, under project IC&DT, POCI-01-0145-FEDER-029158.This paper presents several approaches to deal with the problem of identifying muons in a water Cherenkov detector with a reduced water volume and 4 PMTs. Different perspectives of information representation are used, and new features are engineered using the specific domain knowledge. As results show, these new features, in combination with the convolutional layers, are able to achieve a good performance avoiding overfitting and being able to generalise properly for the test set. The results also prove that the combination of state-of-the-art machine learning analysis techniques and water Cherenkov detectors with low water depth can be used to efficiently identify muons, which may lead to huge investment savings due to the reduction of the amount of water needed at high altitudes. This achievement can be used in further research to be able to discriminate between gamma and hadron-induced showers using muons as discriminant.OE - Portugal, FCT, I. P. PTDC/FIS-PAR/29158/2017 DL57 /2016/cP1330/cT0002Spanish Government FPA2017-85197-P PID2019-104676GB-C32 LIP/BI - 14/2020 POCI-01-0145-FEDER-02915

Statistical convergence in strong topology of probabilistic normed spaces

Following the concept of statistical convergence, we define and study statistical analog concepts of convergence and Cauchy's sequence on a probabilistic normed space that is endowed with a strong topology. Some important properties of statistical convergence have been extended in this new setting

Is There Convergence Across Countries? A Spatial Approach

We analyze convergence across countries over the last half century as a result of globalizing forces. Drawing on theories of modernization, dependency, the world-system, political trade blocs, and the world-society, we consider economic, demographic, knowledge, financial, and political dimensions of convergence. Using a new methodology, we calculate the minimum volume ellipsoid encompassing different groupings of countries, finding that during the 1960–2009 period, countries have not evolved significantly closer or similar to one another, although groups of countries based on their core-periphery status or membership in trade blocs exhibit increasing internal convergence and divergence between one another

Control strategies for Energy Recovery Ventilators in the South of Europe for residential nZEB. Quantitative analysis of the air conditioning demand

Mechanical ventilation systems are essential for ensuring the indoor quality of air in nZEB (nearly Zero Energy Buildings) with a high level of airtightness. In cold countries, it has already been demonstrated that Heat Recovery Ventilators (HRV) recovering the sensible energy from air ventilation are needed to achieve the energy demand goals for nZEB set by Passivhaus. In tropical areas with hot temperatures and high relative humidity in the ambient air, the necessity of recovering latent and sensible energy with Energy Recovery Ventilators (ERV) has also been demonstrated. However, in warm climates with medium relative humidity levels, for example in cities located on the Mediterranean coast, the evaluation of the effectiveness of an EVR for residential buildings has to be analyzed and optimized. This article establishes the effectiveness of several control strategies for ventilation air systems including ERV with the aim of optimizing the air conditioning energy demand of dwellings located in several cities in the South of Europe. Possible control strategies have been analyzed to minimize the undesirable operation of ERVs which could otherwise increase the air conditioning energy demand for winter and summer seasons. The impact of the latent effectiveness and the effect of free-cooling on the air conditioning energy demand is also studied

Millimeter polarisation of the protoplanetary nebula OH 231.8+4.2: A follow-up study with CARMA

In order to investigate the characteristics and influence of the magnetic field in evolved stars, we performed a follow-up investigation of our previous submillimeter analysis of the proto-planetary nebula (PPN) OH 231.8+4.2 (Sabin et al. 2014), this time at 1.3mm with the CARMA facility in polarisation mode for the purpose of a multi-scale analysis. OH 231.8+4.2 was observed at ~2.5" resolution and we detected polarised emission above the 3-sigma threshold (with a mean polarisation fraction of 3.5 %). The polarisation map indicates an overall organised magnetic field within the nebula. The main finding in this paper is the presence of a structure mostly compatible with an ordered toroidal component that is aligned with the PPN's dark lane. We also present some alternative magnetic field configuration to explain the structure observed. These data complete our previous SMA submillimeter data for a better investigation and understanding of the magnetic field structure in OH 231.8+4.2.Comment: 7 pages, 5 figures, 2 tables. Accepted for publication in MNRA