Charged anisotropic matter with linear or nonlinear equation of state

Ivanov pointed out substantial analytical difficulties associated with self-gravitating, static, isotropic fluid spheres when pressure explicitly depends on matter density. Simplification achieved with the introduction of electric charge were noticed as well. We deal with self-gravitating, charged, anisotropic fluids and get even more flexibility in solving the Einstein-Maxwell equations. In order to discuss analytical solutions we extend Krori and Barua's method to include pressure anisotropy and linear or non-linear equations of state. The field equations are reduced to a system of three algebraic equations for the anisotropic pressures as well as matter and electrostatic energy densities. Attention is paid to compact sources characterized by positive matter density and positive radial pressure. Arising solutions satisfy the energy conditions of general relativity. Spheres with vanishing net charge contain fluid elements with unbounded proper charge density located at the fluid-vacuum interface. Notably the electric force acting on these fluid elements is finite, although the acting electric field is zero. Net charges can be huge ($10^{19}\,C$) and maximum electric field intensities are very large ($10^{23}-10^{24}\,statvolt/cm$) even in the case of zero net charge. Inward-directed fluid forces caused by pressure anisotropy may allow equilibrium configurations with larger net charges and electric field intensities than those found in studies of charged isotropic fluids. Links of these results with charged strange quark stars as well as models of dark matter including massive charged particles are highlighted. The van der Waals equation of state leading to matter densities constrained by cubic polynomial equations is briefly considered. The fundamental question of stability is left open.Comment: 22 Latex pages, 17 figures, Inclusion of new paragraph at the end of Conclusion & some of the old captions of the Figures are replaced with new caption

The Cauchy-Schlomilch transformation

The Cauchy-Schl\"omilch transformation states that for a function $f$ and $a, \, b > 0$, the integral of $f(x^{2})$ and $af((ax-bx^{-1})^{2}$ over the interval $[0, \infty)$ are the same. This elementary result is used to evaluate many non-elementary definite integrals, most of which cannot be obtained by symbolic packages. Applications to probability distributions is also given

Superconductivity and charge carrier localization in ultrathin La1.85Sr0.15CuO4/La2CuO4\mathbf{{La_{1.85}Sr_{0.15}CuO_4}/{La_2CuO_4}} bilayers

$\mathrm{La_{1.85}Sr_{0.15}CuO_4}$/$\mathrm{La_2CuO_4}$ (LSCO15/LCO) bilayers with a precisely controlled thickness of N unit cells (UCs) of the former and M UCs of the latter ([LSCO15\_N/LCO\_M]) were grown on (001)-oriented {\slao} (SLAO) substrates with pulsed laser deposition (PLD). X-ray diffraction and reciprocal space map (RSM) studies confirmed the epitaxial growth of the bilayers and showed that a [LSCO15\_2/LCO\_2] bilayer is fully strained, whereas a [LSCO15\_2/LCO\_7] bilayer is already partially relaxed. The \textit{in situ} monitoring of the growth with reflection high energy electron diffraction (RHEED) revealed that the gas environment during deposition has a surprisingly strong effect on the growth mode and thus on the amount of disorder in the first UC of LSCO15 (or the first two monolayers of LSCO15 containing one $\mathrm{CuO_2}$ plane each). For samples grown in pure $\mathrm{N_2O}$ gas (growth type-B), the first LSCO15 UC next to the SLAO substrate is strongly disordered. This disorder is strongly reduced if the growth is performed in a mixture of $\mathrm{N_2O}$ and $\mathrm{O_2}$ gas (growth type-A). Electric transport measurements confirmed that the first UC of LSCO15 next to the SLAO substrate is highly resistive and shows no sign of superconductivity for growth type-B, whereas it is superconducting for growth type-A. Furthermore, we found, rather surprisingly, that the conductivity of the LSCO15 UC next to the LCO capping layer strongly depends on the thickness of the latter. A LCO capping layer with 7~UCs leads to a strong localization of the charge carriers in the adjacent LSCO15 UC and suppresses superconductivity. The magneto-transport data suggest a similarity with the case of weakly hole doped LSCO single crystals that are in a so-called {"{cluster-spin-glass state}"

Correlation entropy of synaptic input-output dynamics

The responses of synapses in the neocortex show highly stochastic and nonlinear behavior. The microscopic dynamics underlying this behavior, and its computational consequences during natural patterns of synaptic input, are not explained by conventional macroscopic models of deterministic ensemble mean dynamics. Here, we introduce the correlation entropy of the synaptic input-output map as a measure of synaptic reliability which explicitly includes the microscopic dynamics. Applying this to experimental data, we find that cortical synapses show a low-dimensional chaos driven by the natural input pattern.Comment: 7 pages, 6 Figures (7 figure files

Literature review and discussion on collaborative decision making approaches in industry 4.0

Nowadays, companies are faced with an increasingly higher level of competition while trying to adapt to the exigencies imposed by the Industry 4.0, regarding its usually referred dimensions and pillars, among which one that although is not so often referred is also expressing an increasing visibility and importance, related to collaboration, and more specifically to collaborative decision making and co-working. Thus, in this paper an analysis is carried out regarding the evolution of publications that have been put available over the last decade about collaborative decision making approaches, varying from approaches based on mathematical models up to the application of artificial intelligence and other kind of approaches. Moreover, a discussion about the relation between collaborative decision making, concurrent engineering and Industry 4.0 dimensions is also done.This work has been supported by FCT -Fundacao para a Ciencia e Tecnologia within the R&D Units Project Scope: UIDB/00319/2020

Differences in coastal and oceanic SST trends north of Yucatan Peninsula

The coastal area north of Yucatan has experienced a cooling SST trend from 1982 to 2015 during the upwelling season (May–September) that contrasts with the warming observed at the adjacent ocean area. Different drivers were analyzed to identify the possible causes of that unusual coastal cooling. Changes in coastal upwelling and in sea-atmosphere heat fluxes are not consistent with the observed coastal cooling. The eastward shift of the Yucatan Current observed over the last decades is hypothesized as the most probable cause of coastal cooling. This shift enhances the vertical transport of cold deeper water to the continental shelf from where it is pumped to the surface by upwelling favorable westerly winds.publishe