Abstract: The aim of this paper is to construct accelerated, stationary and axisymmetric exact solutions of the Einstein theory with self interacting scalar fields in (A)dS4. To warm up, the backreaction of the (non)-minimally coupled scalar field is solved, the scalar field equations are integrated and all the potentials compatible with the metric ansatz and Einstein gravity are found. With these results at hand the non-linear sigma model is tackled. The scalar field Lagrangian is generic; neither the coupling to the curvature, neither the metric in the scalar manifold nor the potential, are fixed ab initio. The unique assumption in the analysis is the metric ansatz: it has the form of the most general Petrov type D vacuum solution of general relativity; it is a a cohomogeneity two Weyl rescaling of the Carter metric and therefore it has the typical Plebanski-Demianski form with two arbitrary functions of one variable and one arbitrary function of two variables. It is shown, by an straightforward manipulation of the field equations, that the metric is completely integrable without necessity of specifiying anything in the scalar Lagrangian. This results is that the backreaction of the scalar fields, within this class of metrics, is universal. The metric functions generically show an explicit dependence on a dynamical exponent that allows to smoothly connect this new family of solutions with the actual Plebanski-Demianski spacetime. The remaining field equations imply that the scalar fields follow geodesics in the scalar manifold with an affine parameter given by a non-linear function of the spacetime coordinates and define the on-shell form of the potential plus a functional equation that it has to satisfy. To further find the exact form of the potential the simplest case associated to a flat scalar manifold is taken. The most general potential compatible with the Einstein theory and the metric ansatz is constructed in this case and it is shown that it has less symmetry than the maximal compact subgroup of the coset construction. Finally, the most general family of (A) dS4 static hairy black holes is explicitly constructed and its properties are outlined.

Abstract: We consider physics-informed neural networks (PINNs) (Raissiet al., 2019) for forward physical problems. In order to find optimal PINNs configuration, we introduce a hyper-parameter optimization (HPO) procedure via Gaussian processes-based Bayesian optimization. We apply the HPO to Helmholtz equation for bounded domains and conduct a thorough study, focusing on: (i) performance, (ii) the collocation points density r and (iii) the frequency kappa, confirming the applicability and necessity of the method. Numerical experiments are performed in two and three dimensions, including comparison to finite element methods.

Abstract: We review recent works on the dynamics of circumbinary accretion, including time variability, angular momentum transfer between the disk and the binary, and the secular evolution of accreting binaries. These dynamics impact stellar binary formation/evolution, circumbinary planet formation/migration, and the evolution of (super)massive black hole binaries. We discuss the dynamics and evolution of inclined/warped circumbinary disks and connect with observations of protoplanetary disks. A special kind of circumbinary accretion involves binaries embedded in big disks, which may contribute to the mergers of stellar-mass black holes in AGN disks. Highlights include the following:
Circumbinary accretion is highly variable, being modulated at P-b (the binary period) or similar to 5P(b), depending on the binary eccentricity e(b) and mass ratio q(b).
The inner region of the circumbinary disk can develop coherent eccentric structure, which may modulate the accretion and affect the physical processes (e.g., planet migration) taking place in the disk.
Over long timescales, circumbinary accretion steers binaries toward equal masses, and it does not always lead to binary orbital decay. The secular orbital evolution depends on the binary parameters (e(b) and q(b)) and on the thermodynamic properties of the accreting gas.
A misaligned disk around a low-eccentricity binary tends to evolve toward coplanarity due to viscous dissipation. But when e(b) is significant, the disk can evolve toward “polar alignment,” with the disk plane perpendicular to the binary plane.

Abstract: The collective behavior of thermally active structures offers clues on the emergent degrees of freedom and the physical mechanisms that determine the low-energy state of a variety of systems. Here, the thermally active dynamics of magnetic dipoles at square plaquettes is modeled in terms of Brownian oscillators in contact with a heat bath. Solution of the Langevin equation for a set of interacting x-y dipoles allows the identification of the timescales and correlation length that reveal how interactions, temperature, damping, and inertia may determine the frequency modes of edge and bulk magnetic mesospins in artificial dipolar systems.

Abstract: We provide numerical solutions based on the path integral representation of stochastic processes for non-gradient drift Langevin forces in the presence of noise, to follow the temporal evolution of the probability density function and to compute exit times even for arbitrary noise. We compare the results with theoretical calculations, obtaining excellent agreement in the weak noise limit. This article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 2)'.

Abstract: Determination of soil volumetric water content theta in forest ecosystems is particularly challenging due to deep rooting systems and unknown soil vertical and spatial heterogeneity. This research aims to test two undisturbed methods, electrical resistivity tomography (ERT) and HYDRUS 2D/3D, for 2D theta determination in a thorny forest ecosystem. The experiment consisted of infiltrating 10 L of water lasting 60 min. During infiltration, ERT measured apparent resistivity by time-lapse measurements, and theta was measured with an FDR probe (EnviroSCAN) at 33, 63, 83, 97, and 163 cm depth close to the infiltration site. At the end of infiltration, a soil pit was dug, and 100 measurements of theta were performed with a TDR in a 10 x 10 cm regular grid. Archie law transformed soil resistivity (ERT) into theta using manual calibration, verified by an independent dataset. The 2D theta profile obtained by ERT was qualitatively compared with the HYDRUS 2D/3D one. HYDRUS 2D/3D was parametrized with calibrated parameters obtained with HYDRUS 1D using 106 days of theta obtained with EnviroSCAN. The results of HYDRUS 1D calibration and verification were satisfactory, with RMSE and Nash-Sutcliffe coefficients ranging from 0.021 to 0.034 cm(3 )cm(-3) and 0.11 to 0.77, respectively. The forward HYDRUS 2D/3D theta simulation disagrees with EnviroSCAN data for 33 cm depth. However, it follows the trend with near to zero variation of water content at 63 cm depth. Water content determination by ERT was satisfactory with RMSE for calibration and verification of 0.017 and 0.021 cm(3) cm(-3). HYDRUS 2D/3D and ERT comparisons were not equal, with a shallower wetting front by ERT and a deeper one for HYDRUS. Still, both wetting fronts agree with the wetting depth estimated by EnviroSCAN. We conclude that both methods are an alternative for theta determination in heterogeneous and deep soils of forest ecosystems.