Distribution of Gaussian Process Arc Lengths

We present the first treatment of the arc length of the Gaussian Process (GP) with more than a single output dimension. GPs are commonly used for tasks such as trajectory modelling, where path length is a crucial quantity of interest. Previously, only paths in one dimension have been considered, with no theoretical consideration of higher dimensional problems. We fill the gap in the existing literature by deriving the moments of the arc length for a stationary GP with multiple output dimensions. A new method is used to derive the mean of a one-dimensional GP over a finite interval, by considering the distribution of the arc length integrand. This technique is used to derive an approximate distribution over the arc length of a vector valued GP in $\mathbb{R}^n$ by moment matching the distribution. Numerical simulations confirm our theoretical derivations.Comment: 10 pages, 4 figures, Accepted to The 20th International Conference on Artificial Intelligence and Statistics (AISTATS

Bulk and surface energetics of lithium hydride crystal: benchmarks from quantum Monte Carlo and quantum chemistry

We show how accurate benchmark values of the surface formation energy of crystalline lithium hydride can be computed by the complementary techniques of quantum Monte Carlo (QMC) and wavefunction-based molecular quantum chemistry. To demonstrate the high accuracy of the QMC techniques, we present a detailed study of the energetics of the bulk LiH crystal, using both pseudopotential and all-electron approaches. We show that the equilibrium lattice parameter agrees with experiment to within 0.03 %, which is around the experimental uncertainty, and the cohesive energy agrees to within around 10 meV per formula unit. QMC in periodic slab geometry is used to compute the formation energy of the LiH (001) surface, and we show that the value can be accurately converged with respect to slab thickness and other technical parameters. The quantum chemistry calculations build on the recently developed hierarchical scheme for computing the correlation energy of a crystal to high precision. We show that the hierarchical scheme allows the accurate calculation of the surface formation energy, and we present results that are well converged with respect to basis set and with respect to the level of correlation treatment. The QMC and hierarchical results for the surface formation energy agree to within about 1 %.Comment: 16 pages, 4 figure

Double layer in ionic liquids: Overscreening vs. crowding

We develop a simple Landau-Ginzburg-type continuum theory of solvent-free ionic liquids and use it to predict the structure of the electrical double layer. The model captures overscreening from short-range correlations, dominant at small voltages, and steric constraints of finite ion sizes, which prevail at large voltages. Increasing the voltage gradually suppresses overscreening in favor of the crowding of counterions in a condensed inner layer near the electrode. The predicted ion profiles and capacitance-voltage relations are consistent with recent computer simulations and experiments on room-temperature ionic liquids, using a correlation length of order the ion size.Comment: 4 pages + supplementary informatio

The habitability of a stagnant-lid Earth

Plate tectonics is a fundamental component for the habitability of the Earth. Yet whether it is a recurrent feature of terrestrial bodies orbiting other stars or unique to the Earth is unknown. The stagnant lid may rather be the most common tectonic expression on such bodies. To understand whether a stagnant-lid planet can be habitable, i.e. host liquid water at its surface, we model the thermal evolution of the mantle, volcanic outgassing of H$_2$O and CO$_2$, and resulting climate of an Earth-like planet lacking plate tectonics. We used a 1D model of parameterized convection to simulate the evolution of melt generation and the build-up of an atmosphere of H$_2$O and CO$_2$ over 4.5 Gyr. We then employed a 1D radiative-convective atmosphere model to calculate the global mean atmospheric temperature and the boundaries of the habitable zone (HZ). The evolution of the interior is characterized by the initial production of a large amount of partial melt accompanied by a rapid outgassing of H$_2$O and CO$_2$. At 1 au, the obtained temperatures generally allow for liquid water on the surface nearly over the entire evolution. While the outer edge of the HZ is mostly influenced by the amount of outgassed CO$_2$, the inner edge presents a more complex behaviour that is dependent on the partial pressures of both gases. At 1 au, the stagnant-lid planet considered would be regarded as habitable. The width of the HZ at the end of the evolution, albeit influenced by the amount of outgassed CO$_2$, can vary in a non-monotonic way depending on the extent of the outgassed H$_2$O reservoir. Our results suggest that stagnant-lid planets can be habitable over geological timescales and that joint modelling of interior evolution, volcanic outgassing, and accompanying climate is necessary to robustly characterize planetary habitability

Simple model of the static exchange-correlation kernel of a uniform electron gas with long-range electron-electron interaction

A simple approximate expression in real and reciprocal spaces is given for the static exchange-correlation kernel of a uniform electron gas interacting with the long-range part only of the Coulomb interaction. This expression interpolates between the exact asymptotic behaviors of this kernel at small and large wave vectors which in turn requires, among other thing, information from the momentum distribution of the uniform electron gas with the same interaction that have been calculated in the G0W0 approximation. This exchange-correlation kernel as well as its complement analogue associated to the short-range part of the Coulomb interaction are more local than the Coulombic exchange-correlation kernel and constitute potential ingredients in approximations for recent adiabatic connection fluctuation-dissipation and/or density functional theory approaches of the electronic correlation problem based on a separate treatment of long-range and short-range interaction effects.Comment: 14 pages, 14 figures, to be published in Phys. Rev.

Hubble Tarantula Treasury Project: Unraveling Tarantula's Web. II. Optical and Near Infrared Star Formation History of the Starburst Cluster NGC 2070 in 30 Doradus

We present a study of the recent star formation of 30 Doradus in the Large Magellanic Cloud (LMC) using the panchromatic imaging survey Hubble Tarantula Treasury Project (HTTP). In this paper we focus on the stars within 20 pc of the center of the massive ionizing cluster of 30 Doradus, NGC 2070. We recovered the star formation history by comparing deep optical and NIR color-magnitude diagrams (CMDs) with state-of-the-art synthetic CMDs generated with the latest PARSEC models, which include all stellar phases from pre-main sequence to post- main sequence. For the first time in this region we are able to measure the star formation using intermediate and low mass stars simultaneously. Our results suggest that NGC2070 experienced a prolonged activity. In particular, we find that the star formation in the region: i) exceeded the average LMC rate ~ 20 Myr ago; ii) accelerated dramatically ~ 7 Myr ago; and iii) reached a peak value 1-3 Myr ago. We did not find significant deviations from a Kroupa initial mass function down to 0.5 Msun. The average internal reddening E(B-V) is found to be between 0.3 and 0.4 mag.Comment: Submitted to Ap

Carbon and nitrogen abundances of individual stars in the Sculptor dwarf spheroidal galaxy

We present [C/Fe] and [N/Fe] abundance ratios and CH({\lambda}4300) and S({\lambda}3883) index measurements for 94 red giant branch (RGB) stars in the Sculptor dwarf spheroidal galaxy from VLT/VIMOS MOS observations at a resolving power R= 1150 at 4020 {\AA}. This is the first time that [N/Fe] abundances are derived for a large number of stars in a dwarf spheroidal. We found a trend for the [C/Fe] abundance to decrease with increasing luminosity on the RGB across the whole metallicity range, a phenomenon observed in both field and globular cluster giants, which can be interpreted in the framework of evolutionary mixing of partially processed CNO material. Both our measurements of [C/Fe] and [N/Fe] are in good agreement with the theoretical predictions for stars at similar luminosity and metallicity. We detected a dispersion in the carbon abundance at a given [Fe/H], which cannot be ascribed to measurement uncertainties alone. We interpret this observational evidence as the result of the contribution of different nucleosynthesis sources over time to a not well-mixed interstellar medium. We report the discovery of two new carbon-enhanced, metal-poor stars. These are likely the result of pollution from material enriched by asymptotic giant branch stars, as indicated by our estimates of [Ba/Fe]> +1. We also attempted a search for dissolved globular clusters in the field of the galaxy by looking for the distinctive C-N pattern of second population globular clusters stars in a previously detected, very metal-poor, chemodynamical substructure. We do not detect chemical anomalies among this group of stars. However, small number statistics and limited spatial coverage do not allow us to exclude the hypotheses that this substructure forms part of a tidally shredded globular cluster.Comment: 18 pages, 14 figures, 3 tables. Accepted to A&

The Star Formation History of IZw18

The star formation history in IZw18 has been inferred from HST/WFPC2 archival data. This is done by comparing the derived V, B-V and V, V-I color-magnitude diagrams and luminosity functions with synthetic ones, based on various sets of stellar evolutionary tracks. At a distance of 10 Mpc, the stars resolved in the field of IZw18 allow for a lookback time up to 1 Gyr. We find that the main body is not experiencing its first episode of star formation. Instead, it has been forming stars over the last 0.5-1 Gyr, at a rate of ~ 1-2 * 10**(-2) Msol per year per kpc**2. A more intense activity of 6-16 * 10**(-2) Msol per year per kpc**2 has taken place between 15 and 20 Myr ago. For the secondary body, the lookback time is 0.2 Gyr at most and the uncertainty is much higher, due to the shallower diagrams and the small number of resolved stars. The derived range of star formation rate is 3-10 * 10**(-3) Msol per year per kpc**2. The IMF providing the best fit to the observed stellar populations in the main body has a slope 1.5, much flatter than in any similar galaxy analyzed with the same method. In the secondary body, it is peaked at 2.2, closer to Salpeter's slope (2.35).Comment: 70 pages including 18 figures, to be published in The Astronomical Journa