Abstract: We present a spectral Galerkin numerical scheme for solving Helmholtz and Laplace prob- lems with Dirichlet boundary conditions on a finite collection of open arcs in two-dimensional space. A boundary integral method is employed, giving rise to a first kind Fredholm equation whose variational form is discretized using weighted Chebyshev polynomials. Well-posedness of the discrete problems is established as well as algebraic or even exponential convergence rates depending on the regularities of both arcs and excitations. Our numerical experiments show the robustness of the method with respect to number of arcs and large wavenumber range. Moreover, we present a suitable compression algorithm that further accelerates computational times.

Abstract: We report the discovery of two transiting Neptunes by the HATSouth survey. The planet HATS-37Ab has a mass of 0.099 +/- 0.042 MJ (31.5.+/-.13.4M(circle dot)) and a radius of 0.606 +/- 0.016 R-J, and is on a P = 4.3315 day orbit around a V = 12.266 +/- 0.030 mag, 0.843(-0.012)(+0.017)M(circle dot) star with a radius of 0.877(-0.012)(+0.019) R-circle dot We also present evidence that the star HATS-37A has an unresolved stellar companion HATS-37B, with a photometrically estimated mass of 0.654 +/- 0.033.M-circle dot The planet HATS-38b has a mass of 0.074. 0.011MJ (23.5 +/- 3.5M(circle dot)) and a radius of 0.614 +/- 0.017 R-J, and is on a P = 4.3750 day orbit around a V = 12.411 +/- 0.030 mag, 0.890(-0.012)(+0.016) M-circle dot star with a radius of 1.105 +/- 0.016.R-circle dot Both systems appear to be old, with isochrone-based ages of 11.46(-1.45)(+0.79) Gyr, and 11.89 +/- 0.60 Gyr, respectively. Both HATS-37Ab and HATS-38b lie in the Neptune desert and are thus examples of a population with a low occurrence rate. They are also among the lowest-mass planets found from ground-based wide-field surveys to date.

Abstract: The nature of the fluctuations of the dissipation rate in fluid turbulence is still under debate. One reason may be that the observed fluctuations are strong events of dissipation, which reveal the trace of spatiotemporal singularities of the Euler equations, which are the zero viscosity limit of ordinary incompressible fluids. Viscosity regularizes these hypothetical singularities, resulting in a chaotic fluctuating state in which the strong events appear randomly in space and time, making the energy dissipation highly fluctuating. Yet, to date, it is not known if smooth initial conditions of the Euler equations with finite energy do or do not blow up in finite time. We overcome this central difficulty by providing a scenario for singularity-mediated turbulence based on the self-focusing nonlinear Schrodinger equation. It avoids the intrinsic difficulty of Euler equations since it is well known that solutions of this NLS equation with smooth initial conditions do blow up in finite time. When adding viscosity, the model shows (i) that dissipation takes place near the singularities only, (ii) that such intense events are random in space and time, (iii) that the mean dissipation rate is almost constant as the viscosity varies, and (iv) the observation of an Obukhov-Kolmogorov spectrum with a power-law dependence together with an intermittent behavior using structure function correlations, in close correspondence with the one measured in fluid turbulence.

Abstract: The White Dwarf Binary Pathways Survey aims at increasing the number of known detached A, F, G, and K main-sequence stars in close orbits with white dwarf companions (WD+AFGK binaries) to refine our understanding about compact binary evolution and the nature of Supernova Ia progenitors. These close WD+AFGK binary stars are expected to form through common envelope evolution, in which tidal forces tend to circularize the orbit. However, some of the identified WD+AFGK binary candidates show eccentric orbits, indicating that these systems are either formed through a different mechanism or perhaps they are not close WD+AFGK binaries. We observed one of these eccentric WD+AFGK binaries with SPHERE and find that the system TYC 7218-934-1 is in fact a triple system where the WD is a distant companion. The inner binary likely consists of the G-type star plus an unseen low-mass companion in an eccentric orbit. Based on this finding, we estimate the fraction of triple systems that could contaminate the WD+AFGK sample. We find that less than 15 per cent of our targets with orbital periods shorter than 100 d might be hierarchical triples.

Abstract: We report the period, eccentricity, and mass determination for the Transiting Exoplanet Survey Satellite (TESS) single-transit event candidate TOI-222, which displayed a single 3000 ppm transit in the TESS 2-min cadence data from Sector 2. We determine the orbital period via radial velocity measurements (P = 33.9 d), which allowed for ground-based photometric detection of two subsequent transits. Our data show that the companion to TOI-222 is a low-mass star, with a radius of 0.18(-0.10)(+0.39) R-circle dot and a mass of 0.23 +/- 0.01 M-circle dot. This discovery showcases the ability to efficiently discover long-period systems from TESS single-transit events using a combination of radial velocity monitoring coupled with high-precision ground-based photometry.

Abstract: We present a study of ultracompact dwarf (UCD) galaxies in the Virgo cluster based mainly on imaging from the Next Generation Virgo Cluster Survey (NGVS). Using similar to 100 deg(2) of u*giz imaging, we have identified more than 600 candidate UCDs, from the core of Virgo out to its virial radius. Candidates have been selected through a combination of magnitudes, ellipticities, colors, surface brightnesses, half-light radii, and, when available, radial velocities. Candidates were also visually validated from deep NGVS images. Subsamples of varying completeness and purity have been defined to explore the properties of UCDs and compare to those of globular clusters and the nuclei of dwarf galaxies with the aim of delineating the nature and origins of UCDs. From a surface density map, we find the UCDs to be mostly concentrated within Virgo's main subclusters, around its brightest galaxies. We identify several subsamples of UCDs-i.e., the brightest, largest, and those with the most pronounced and/or asymmetric envelopes-that could hold clues to the origin of UCDs and possible evolutionary links with dwarf nuclei. We find some evidence for such a connection from the existence of diffuse envelopes around some UCDs and comparisons of radial distributions of UCDs and nucleated galaxies within the cluster.

Abstract: Context. The transiting exoplanetary system WASP-174 was reported to be composed by a main-sequence F star (V = 11.8 mag) and a giant planet, WASP-174b (orbital period P-orb = 4.23 days). However only an upper limit was placed on the planet mass (<1.3 M-Jup), and a highly uncertain planetary radius (0.7-1.7 R-Jup) was determined.Aims. We aim to better characterise both the star and the planet and precisely measure their orbital and physical parameters.Methods. In order to constrain the mass of the planet, we obtained new measurements of the radial velocity of the star and joined them with those from the discovery paper. Photometric data from the HATSouth survey and new multi-band, high-quality (precision reached up to 0.37 mmag) photometric follow-up observations of transit events were acquired and analysed for getting accurate photometric parameters. We fit the model to all the observations, including data from the TESS space telescope, in two different modes: incorporating the stellar isochrones into the fit, and using an empirical method to get the stellar parameters. The two modes resulted to be consistent with each other to within 2<sigma>.Results. We confirm the grazing nature of the WASP-174b transits with a confidence level greater than 5 sigma, which is also corroborated by simultaneously observing the transit through four optical bands and noting how the transit depth changes due to the limb-darkening effect. We estimate that approximate to 76% of the disk of the planet actually eclipses the parent star at mid-transit of its transit events. We find that WASP-174b is a highly-inflated hot giant planet with a mass of M-p = 0.330 +/- 0.091 M-Jup and a radius of R-p = 1.435 +/- 0.050 R-Jup, and is therefore a good target for transmission-spectroscopy observations. With a density of rho (p) = 0.135 +/- 0.042 g cm(-3), it is amongst the lowest-density planets ever discovered with precisely measured mass and radius.

Abstract: We present a new optical (400-950 nm) transmission spectrum of the hot Jupiter WASP-31b (M = 0.48 M-J; R = 1.54 R-J; P = 3.41 days), obtained by combining four transit observations. These transits were observed with IMACS on the Magellan Baade Telescope at Las Campanas Observatory as part of the ACCESS project. We investigate the presence of clouds/hazes in the upper atmosphere of this planet, as well as the contribution of stellar activity on the observed features. In addition, we search for absorption features of the alkali elements Na i and K i, with particular focus on K i, for which there have been two previously published disagreeing results. Observations with Hubble Space Telescope (HST)/STIS detected K i, whereas ground-based low- and high-resolution observations did not. We use equilibrium and nonequilibrium chemistry retrievals to explore the planetary and stellar parameter space of the system with our optical data combined with existing near-IR observations. Our best-fit model is that with a scattering slope consistent with a Rayleigh slope (alpha = 5(-3.1)(+2.9)), high-altitude clouds at a log cloud top pressure of -3.6(-2.1)(+2.7) bars, and possible muted H2O features. We find that our observations support other ground-based claims of no K I. Clouds are likely why signals like H2O are extremely muted and Na or K cannot be detected. We then juxtapose our Magellan/IMACS transmission spectrum with existing VLT/FORS2, HST/WFC3, HST/STIS, and Spitzer observations to further constrain the optical-to-infrared atmospheric features of the planet. We find that a steeper scattering slope (alpha = 8.3 +/- 1.5) is anchored by STIS wavelengths blueward of 400 nm and only the original STIS observations show significant potassium signal.

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 report the discovery of TOI 694 b and TIC 220568520 b, two low-mass stellar companions in eccentric orbits around metal-rich Sun-like stars, first detected by the Transiting Exoplanet Survey Satellite (TESS). TOI 694 b has an orbital period of 48.05131 +/- 0.00019 days and eccentricity of 0.51946 +/- 0.00081, and we derive a mass of 89.0 +/- 5.3 M-Jup (0.0849 +/- 0.0051 M-circle dot) and radius of 1.111 +/- 0.017 R-Jup (0.1142 +/- 0.0017 R-circle dot). TIC 220568520 b has an orbital period of 18.55769 +/- 0.00039 days and eccentricity of 0.0964 +/- 0.0032, and we derive a mass of 107.2 +/- 5.2 M-Jup (0.1023 +/- 0.0050 M-circle dot) and radius of 1.248 +/- 0.018 R-Jup (0.1282 +/- 0.0019 R-circle dot). Both binary companions lie close to and above the hydrogen-burning mass threshold that separates brown dwarfs and the lowest-mass stars, with TOI 694 b being 2s above the canonical mass threshold of 0.075 M-circle dot. The relatively long periods of the systems mean that the magnetic fields of the low-mass companions are not expected to inhibit convection and inflate the radius, which according to one leading theory is common in similar objects residing in short-period tidally synchronized binary systems. Indeed we do not find radius inflation for these two objects when compared to theoretical isochrones. These two new objects add to the short but growing list of low-mass stars with well-measured masses and radii, and highlight the potential of the TESS mission for detecting such rare objects orbiting bright stars.