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The analyses of interior penalty discontinuous Galerkin methods of any order k for solving elliptic and parabolic problems with Dirac line sources are presented. For the steady state case, we prove convergence of the method by deriving a priori error estimates in the L2 norm and in weighted energy norms. In addition, we prove almost optimal local error estimates in the energy norm for any approximation order. Further, almost optimal local error estimates in the L2 norm are obtained for the case of piecewise linear approximations whereas suboptimal error bounds in the L2 norm are shown for any polynomial degree. For the time-dependent case, convergence of semi-discrete and of backward Euler fully discrete scheme is established by proving error estimates in L2 in time and in space. Numerical results for the elliptic problem are added to support the theoretical results.

The sulfur abundance is poorly known in most environments. Yet, deriving the sulfur abundance is key to understanding the evolution of the chemistry from molecular clouds to planetary atmospheres. We present observations of H$_2$S 110-101 at 168.763 GHz toward the Herbig Ae star AB Aur. We aim to study the abundance of sulfuretted species toward AB Aur and to constrain how different species and phases contribute to the sulfur budget. We present new NOrthern Extended Millimeter Array (NOEMA) interferometric observations of the continuum and H$_2$S 110-101 line at 168.763 GHz toward AB Aur. We derived radial and azimuthal profiles and used them to compare the geometrical distribution of different species in the disk. Assuming local thermodynamical equilibrium (LTE), we derived column density and abundance maps for H$_2$S, and we further used Nautilus to produce a more detailed model of the chemical abundances at different heights over the mid-plane at a distance of r=200 au. We have resolved H$_2$S emission in the AB Aur protoplanetary disk. The emission comes from a ring extending from 0.67 (109 au) to 1.69 (275 au). Under simple assumptions, we derived an abundance of (3.1$\pm$0.8)$\times$10$\rm ^{-10}$ with respect to H nuclei, which we compare with Nautilus models to deepen our understanding of the sulfur chemistry in protoplanetary disks. Chemical models indicate that H$-2$S is an important sulfur carrier in the solid and gas phase. We also find an important transition at a height of 12 au, where the sulfur budget moves from being dominated by ice species to being dominated by gas species. Studying sulfuretted species in detail in the different phases of the interstellar medium is key to solving the issue., Comment: 11 pages, 14 figures, 4 tables

In analogy with the study of Pollicott-Ruelle resonances on negatively curved manifolds, we define anisotropic Sobolev spaces that are well-adapted to the analysis of the geodesic vector field associated with any translation invariant Finsler metric on the torus $\mathbb{T}^d$. Among several applications of this functional point of view, we study properties of geodesics that are orthogonal to two convex subsets of $\mathbb{T}^d$ (i.e. projection of the boundaries of strictly convex bodies of $\mathbb{R}^d$). Associated with the set of lengths of such orthogeodesics, we define a geometric Epstein function and prove its meromorphic continuation. We compute its residues in terms of intrinsic volumes of the convex sets. We also prove Poisson-type summation formulae relating the set of lengths of orthogeodesics and the spectrum of magnetic Laplacians.

Using the spin properties of nitrogen-vacancy (NV) centers in levitated diamond, we characterize the absorption of single nanodiamonds. We first calibrate the thermometry response of the NV centers embedded in our nanodiamonds. Then, using this calibration, we estimate the absorption cross-section of single levitated nanodiamonds. We show that this absorption is extrinsic and dominated by volumic effects. Our work opens the way to diamond materials optimization for levitation quantum experiments. It also demonstrates optical levitation as a unique platform to characterize material thermal properties at the nanoparticle level.

Stellar ages are key to improving our understanding of different astrophysical phenomena. However, many techniques to estimate stellar ages are highly model-dependent. The lithium depletion boundary (LDB), based on the presence or absence of lithium in low-mass stars, can be used to derive ages in stellar associations of between 20 and 500~Ma. The purpose of this work is to revise former LDB ages in stellar associations in a consistent way, taking advantage of the homogeneous \textit{Gaia} parallaxes as well as bolometric luminosity estimations that do not rely on monochromatic bolometric corrections. We studied nine open clusters and three moving groups characterised by a previous determination of the LDB age. We gathered all the available information from our data and the literature: membership, distances, photometric data, reddening, metallicity, and surface gravity. We re-assigned membership and calculated bolometric luminosities and effective temperatures using distances derived from Gaia DR2 and multi-wavelength photometry for individual objects around the former LDB. We located the LDB using a homogeneous method for all the stellar associations. Finally, we estimated the age by comparing it with different evolutionary models. We located the LDB for the twelve stellar associations and derived their ages using several theoretical evolutionary models. We compared the LDB ages among them, along with data obtained with other techniques, such as isochrone fitting, ultimately finding some discrepancies among the various approaches. Finally, we remark that the 32 Ori MG is likely to be composed of at least two populations of different ages., Comment: 78 pages, accepted by A&A

In the context of the IRAM 30m Large Program GEMS, we present a study of thioformaldehyde in several starless cores located in star-forming filaments of Taurus, Perseus, and Orion. We investigate the influence of the environmental conditions on the abundances of these molecules in the cores, and the effect of time evolution. We have modelled the observed lines of H2CS, HDCS, and D2CS using the radiative transfer code RADEX. We have also used the chemical code Nautilus to model the evolution of these species depending on the characteristics of the starless cores. We derive column densities and abundances for all the cores. We also derive deuterium fractionation ratios, Dfrac, to determine and compare the evolutionary stage between different parts of each star-forming region. Our results indicate that the north region of the B213 filament in Taurus is more evolved than the south, while the north-eastern part of Perseus presents an earlier evolutionary stage than the south-western zone. Model results also show that Dfrac decreases with the cosmic-ray ionisation rate, while it increases with density and with the degree of sulphur depletion. In particular, we only reproduce the observations when the initial sulphur abundance in the starless cores is at least one order of magnitude lower than the solar elemental sulphur abundance. The progressive increase in HDCS/H2CS and D2CS/H2CS with time makes these ratios powerful tools for deriving the chemical evolutionary stage of starless cores. However, they cannot be used to derive the temperature of these regions, since both ratios present a similar evolution at two different temperature ranges (7-11 K and 15-19 K). Regarding chemistry, (deuterated) thioformaldehyde is mainly formed through gas-phase reactions (double-replacement and neutral-neutral displacement reactions), while surface chemistry plays an important role as a destruction mechanism., Comment: 31 pages, 26 figures

Peer sampling is a first-class abstraction used in distributed systems for overlay management and information dissemination. The goal of peer sampling is to continuously build and refresh a partial and local view of the full membership of a dynamic, large-scale distributed system. Malicious nodes under the control of an adversary may aim at being over-represented in the views of correct nodes, increasing their impact on the proper operation of protocols built over peer sampling. State-of-the-art Byzantine resilient peer sampling protocols reduce this bias as long as Byzantines are not overly present. This paper studies the benefits brought to the resilience of peer sampling services when considering that a small portion of trusted nodes can run code whose authenticity and integrity can be assessed within a trusted execution environment, and specifically Intel's software guard extensions technology (SGX). We present RAPTEE, a protocol that builds and leverages trusted gossip-based communications to hamper an adversary's ability to increase its system-wide representation in the views of all nodes. We apply RAPTEE to BRAHMS, the most resilient peer sampling protocol to date. Experiments with 10,000 nodes show that with only 1% of SGX-capable devices, RAPTEE can reduce the proportion of Byzantine IDs in the view of honest nodes by up to 17% when the system contains 10% of Byzantine nodes. In addition, the security guarantees of RAPTEE hold even in the presence of a powerful attacker attempting to identify trusted nodes and injecting view-poisoned trusted nodes.

The pyramids of the Giza plateau have fascinated visitors since ancient times and are the last of the Seven Wonders of the ancient world still standing. It has been half a century since Luiz Alvarez and his team used cosmic-ray muon imaging to look for hidden chambers in Khafres Pyramid. Advances in instrumentation for High-Energy Physics (HEP) allowed a new survey, ScanPyramids, to make important new discoveries at the Great Pyramid (Khufu) utilizing the same basic technique that the Alvarez team used, but now with modern instrumentation. The Exploring the Great Pyramid Mission plans to field a very-large muon telescope system that will be transformational with respect to the field of cosmic-ray muon imaging. We plan to field a telescope system that has upwards of 100 times the sensitivity of the equipment that has recently been used at the Great Pyramid, will image muons from nearly all angles and will, for the first time, produce a true tomographic image of such a large structure.

We present experiments on large air cavities spanning a wide range of sizes relative to the Hinze scale $d_\mathrm{H}$, the scale at which turbulent stresses are balanced by surface tension, disintegrating in turbulence. For cavities with initial sizes $d_0$ much larger than $d_\mathrm{H}$ (probing up to $d_0 / d_\mathrm{H} = 8.3$), the size distribution of bubbles smaller than $d_\mathrm{H}$ follows $N(d) \propto d^{-3/2}$, with $d$ the bubble diameter. The capillary instability of ligaments involved in the deformation of the large bubbles is shown visually to be responsible for the creation of the small ones. Turning to dynamical, three-dimensional measurements of individual break-up events, we describe the break-up child size distribution and the number of child bubbles formed as a function of $d_0 / d_\mathrm{H}$. Then, to model the evolution of a population of bubbles produced by turbulent bubble break-up, we propose a population balance framework in which break-up involves two physical processes: an inertial deformation to the parent bubble that sets the size of large child bubbles, and a capillary instability that sets the size of small child bubbles. A Monte Carlo approach is used to construct the child size distribution, with simulated stochastic break-ups constrained by our experimental measurements and the understanding of the role of capillarity in small bubble production. This approach reproduces the experimental time evolution of the bubble size distribution during the disintegration of large air cavities in turbulence.

Clusters of similar or dissimilar objects are encountered in many fields. Frequently used approaches treat the central object of each cluster as latent. Yet, often objects of one or more types cluster around objects of another type. Such arrangements are common in biomedical images of cells, in which nearby cell types likely interact. Quantifying spatial relationships may elucidate biological mechanisms. Parent-offspring statistical frameworks can be usefully applied even when central objects (parents) differ from peripheral ones (offspring). We propose the novel multivariate cluster point process (MCPP) to quantify multi-object (e.g., multi-cellular) arrangements. Unlike commonly used approaches, the MCPP exploits locations of the central parent object in clusters. It accounts for possibly multilayered, multivariate clustering. The model formulation requires specification of which object types function as cluster centers and which reside peripherally. If such information is unknown, the relative roles of object types may be explored by comparing fit of different models via the deviance information criterion (DIC). In simulated data, we compared DIC of a series of models; the MCPP correctly identified simulated relationships. It also produced more accurate and precise parameter estimates than the classical univariate Neyman-Scott process model. We also used the MCPP to quantify proposed configurations and explore new ones in human dental plaque biofilm image data. MCPP models quantified simultaneous clustering of Streptococcus and Porphyromonas around Corynebacterium and of Pasteurellaceae around Streptococcus and successfully captured hypothesized structures for all taxa. Further exploration suggested the presence of clustering between Fusobacterium and Leptotrichia, a previously unreported relationship.

We formulate a numerical method for solving the two-phase flow poroelasticity equations. The scheme employs the interior penalty discontinuous Galerkin method and a sequential time-stepping method. The unknowns are the phase pressures and the displacement. Existence of the solution is proved. Three-dimensional numerical results show the accuracy and robustness of the proposed method.

The Brownian motion of a particle hotter than its environment is an iconic out-of-equilibrium system. Its study provides valuable insights into nanoscale thermal effects. Notably, it supplies an excellent diagnosis of thermal effects in optically levitated particles, a promising platform for force sensing and quantum physics tests. Thus, understanding the relevant parameters in this effect is critical. In this context, we test the role of particles' shape and material, using optically levitated nanodiamonds hosting NV centers to measure the particles' internal temperature and center-of-mass dynamics. We present a model to assess the nanodiamond internal temperature from its dynamics, adaptable to other particles. We also demonstrate that other mechanisms affect the nanodiamond dynamics and its stability in the trap. Finally, our work, by showing levitating nanodiamonds as an excellent tool for studying nano-thermal effects, opens prospects for increasing the trapping stability of optically levitated particles., Comment: 14 pages with supporting information

The bubble size distribution below a breaking wave is of paramount interest when quantifying mass exchanges between the atmosphere and oceans. Mass fluxes at the interface are driven by bubbles that are small compared to the Hinze scale $d_h$, the critical size below which bubbles are stable, even though individually these are negligible in volume. Combining experimental and numerical approaches, we report a power law scaling 3/2 of the diameter of small bubble size distribution, for sufficiently large separation of scales between the injection size and the Hinze scale. From an analysis of individual bubble break-up events, we show that break-ups generating small bubbles are driven by capillary effects, and that their break-up time scales with the diameter to the 3/2, which physically explains the sub-Hinze scaling observed.

The pressure correction scheme is combined with interior penalty discontinuous Galerkin method to solve the time-dependent Navier-Stokes equations. Optimal error estimates are derived for the velocity in the L$^2$ norm in time and in space. Error bounds for the discrete time derivative of the velocity and for the pressure are also established.

We present a renormalization procedure of the Dirichlet Lagrangian for maps from surfaces with or without boundary into $S^1$ and whose finite energy critical points are the $S^1-$harmonic maps with isolated singularities. We give some applications of this renormalization scheme in two different frameworks. The first application has to do with the renormalization of the Willmore energy for Lagrangian singular immersions into K\"ahler-Einstein Surfaces while the second application is dealing with frame energies for surfaces immersions into Euclidian spaces.

Speech emotion conversion is the task of modifying the perceived emotion of a speech utterance while preserving the lexical content and speaker identity. In this study, we cast the problem of emotion conversion as a spoken language translation task. We use a decomposition of the speech signal into discrete learned representations, consisting of phonetic-content units, prosodic features, speaker, and emotion. First, we modify the speech content by translating the phonetic-content units to a target emotion, and then predict the prosodic features based on these units. Finally, the speech waveform is generated by feeding the predicted representations into a neural vocoder. Such a paradigm allows us to go beyond spectral and parametric changes of the signal, and model non-verbal vocalizations, such as laughter insertion, yawning removal, etc. We demonstrate objectively and subjectively that the proposed method is vastly superior to current approaches and even beats text-based systems in terms of perceived emotion and audio quality. We rigorously evaluate all components of such a complex system and conclude with an extensive model analysis and ablation study to better emphasize the architectural choices, strengths and weaknesses of the proposed method. Samples are available under the following link: https://speechbot.github.io/emotion., Comment: Paper was published at EMNLP 2022

Popular ASR benchmarks such as Librispeech and Switchboard are limited in the diversity of settings and speakers they represent. We introduce a set of benchmarks matching real-life conditions, aimed at spotting possible biases and weaknesses in models. We have found out that even though recent models do not seem to exhibit a gender bias, they usually show important performance discrepancies by accent, and even more important ones depending on the socio-economic status of the speakers. Finally, all tested models show a strong performance drop when tested on conversational speech, and in this precise context even a language model trained on a dataset as big as Common Crawl does not seem to have significant positive effect which reiterates the importance of developing conversational language models, Comment: Submitted to ICASSP 2022

This paper presents and analyzes a discontinuous Galerkin method for the incompressible three-phase flow problem in porous media. We use a first order time extrapolation which allows us to solve the equations implicitly and sequentially. We show that the discrete problem is well-posed, and obtain a priori error estimates. Our numerical results validate the theoretical results, i.e. the algorithm converges with first order.

Context. Sulfur is used as a tracer of the evolution from interstellar clouds to stellar systems. However, most of the expected sulfur in molecular clouds remains undetected. Sulfur disappears from the gas phase in two steps. One first depletion occurs during the translucent phase, reducing the gas phase sulfur by 7-40 times, while the following freeze-out step occurs in molecular clouds, reducing it by another order of magnitude. This long-standing dilemma awaits an explanation. Aims. The aim of this study is to understand under which form the missing sulfur is hiding in molecular clouds. Depletion onto dust grains is considered. Methods. Experimental simulations mimicking H2S ice UV-photoprocessing in molecular clouds were conducted. The ice was monitored using infrared spectroscopy and the desorbing molecules were measured by quadrupole mass spectrometry. Theoretical Monte Carlo simulations were performed for interpretation of the experimental results and extrapolation to astrophysical conditions. Results. H2S2 formation was observed during irradiation at 8 K. Molecules H2Sx with x > 2 were also identified and found to desorb during warm-up, along with S2 to S4 species. Larger Sx molecules up to S8 are refractory at room temperature and remained on the substrate forming a residue. Monte Carlo simulations were able to reproduce the molecules desorbing during warming up, and found that residues are chains or sulfur consisting of 6-7 atoms. Conclusions. We propose that S+ in translucent clouds contributes notoriously to S depletion in denser regions by forming long S-chains on dust in few times 10^4 years. We suggest that the S2 to S4 molecules observed in comets are not produced by fragmentation of these large chains. Instead, they probably come either from UV-photoprocessing of H2S-bearing ice produced in molecular clouds or from short S chains formed during the translucent cloud phase, Comment: Accepted to A&A

Debris discs represent the last stages of planet formation and as such are expected to be depleted of primordial gas. Nonetheless, in the last few years the presence of cold gas has been reported in $\sim$ 20 debris discs from far-IR to (sub-)mm observations and hot gas has been observed in the optical spectra of debris discs for decades. While the origin of this gas is still uncertain, most evidences point towards a secondary origin, as a result of collisions and evaporation of small bodies in the disc. In this paper, we present ALMA observations aimed at the detection of CO gas in a sample of 8 debris discs with optical gas detections. We report the detection of CO ($^{12}$CO and $^{13}$CO) gas in HD 36546, the brightest and youngest disc in our sample, and provide upper limits to the presence of gas in the remaining seven discs., Comment: 8 pages, 6 figures, 2 tables. Accepted for publication in MNRAS

A discontinuous Galerkin pressure correction numerical method for solving the incompressible Navier-Stokes equations is formulated and analyzed. We prove unconditional stability of the propose scheme. Convergence of the discrete velocity is established by deriving a priori error estimates. Numerical results verify the convergence rates.

Speech pre-training has primarily demonstrated efficacy on classification tasks, while its capability of generating novel speech, similar to how GPT-2 can generate coherent paragraphs, has barely been explored. Generative Spoken Language Modeling (GSLM) \cite{Lakhotia2021} is the only prior work addressing the generative aspects of speech pre-training, which replaces text with discovered phone-like units for language modeling and shows the ability to generate meaningful novel sentences. Unfortunately, despite eliminating the need of text, the units used in GSLM discard most of the prosodic information. Hence, GSLM fails to leverage prosody for better comprehension, and does not generate expressive speech. In this work, we present a prosody-aware generative spoken language model (pGSLM). It is composed of a multi-stream transformer language model (MS-TLM) of speech, represented as discovered unit and prosodic feature streams, and an adapted HiFi-GAN model converting MS-TLM outputs to waveforms. We devise a series of metrics for prosody modeling and generation, and re-use metrics from GSLM for content modeling. Experimental results show that the pGSLM can utilize prosody to improve both prosody and content modeling, and also generate natural, meaningful, and coherent speech given a spoken prompt. Audio samples can be found at https://speechbot.github.io/pgslm. Codes and models are available at https://github.com/pytorch/fairseq/tree/main/examples/textless_nlp/pgslm., Comment: ACL 2022

We describe the long time behavior of small non-smooth solutions to the nonlinear Klein-Gordon equations on the sphere S^2. More precisely, we prove that the low harmonic energies (also called super-actions) are almost preserved for times of order $\epsilon$^--r , where r >> 1 is an arbitrarily large number and $\epsilon$ << 1 is the norm of the initial datum in the energy space H^1 x L^2. Roughly speaking, it means that, in order to exchange energy, modes have to oscillate at the same frequency. The proof relies on new multilinear estimates on Hamiltonian vector fields to put the system in Birkhoff normal form. They are derived from new probabilistic bounds on products of Laplace eigenfunctions that we obtain using Levy's concentration inequality.

In the present paper, we establish the uniqueness of tangent maps for general weakly holomorphic and locally approximable maps from an arbitrary almost complex manifold into projective algebraic varieties. As a byproduct of the approach and the techniques developed we also obtain the unique tangent cone property for a special class of non-rectifiable positive pseudo-holomorphic cycles. This approach gives also a new proof of the main result by C. Bellettini on the uniqueness of tangent cones for positive integral $(p,p)$-cycles in arbitrary almost complex manifolds., Comment: 52 pages

We consider the Dirac Operator acting on the Clifford Algebra ${C\ell}_{m}$. We show that under critical assumptions on the potential and the spinor field the equation is subject to an integrability by compensation phenomenon and has a sub-critical behaviour below some positive energy threshold (i.e. $\epsilon-$regularity theorem). This extends in 4 space dimensions as well as in 3 dimensions a similar result obtained previously by the two first authors in 2 D in \cite{DLR1}.

We prove an almost monotonicity formula for H-minimal Legendrian Surfaces (also called {\it contact stationary legendrian immersions}) in the Heisenberg Group ${\mathbb H}^2$ . From this formula we deduce a Bernstein-Liouville type theorem for H-minimal Legendrian Surfaces. This last result happens to be in particular a central ingredient in the analysis part of the proof of the Willmore conjecture given by the author in arXiv:2007.05467

We propose PET scanners using low atomic number media that undergo a persistent local change of state along the paths of the Compton recoil electrons. Measurement of the individual scattering locations and angles, deposited energies, and recoil electron directions allows using the kinematical constraints of the 2-body Compton scattering process to perform a statistical time-ordering of the scatterings, with a high probability of precisely identifying where the gamma first interacted in the detector. In these cases the Line-of-Response is measured with high resolution, determined by the underlying physics processes and not the detector segmentation. There are multiple such media that act through different mechanisms. As an example in which the change of state is quantum-mechanical through a change in molecular configuration, rather than thermodynamic, as in a bubble chamber, we present simulations of a two-state photoswitchable organic dye, a `Switchillator', that is activated to a fluorescent-capable state by the ionization of the recoil electrons. The activated state is persistent, and can be optically excited multiple times to image individual activated molecules. Energy resolution is provided by counting the activated molecules. Location along the LOR is implemented by large-area time-of-flight MCP-PMT photodetectors with single photon time resolution in the tens of ps and sub-mm spatial resolution. Simulations indicate a large reduction of dose.

We present high angular resolution 1.1mm continuum and spectroscopic ALMA observations of the well-known massive proto-cluster Mon R 2 IRS 3.The continuum image at 1.1mm shows two components, IRS 3 A and IRS 3 B, that are separated by $\sim$0.65$"$. We estimate that IRS 3 A is responsible of $\sim$80 % of the continuum flux, being the most massive component. We explore the chemistry of IRS 3 A based on the spectroscopic observations. In particular, we have detected intense lines of S-bearing species such as SO, SO$_2$, H$_2$CS and OCS, and of the Complex Organic Molecules (COMs) methyl formate (CH$_3$OCHO) and dimethyl ether (CH$_3$OCH$_3$). The integrated intensity maps of most species show a compact clump centered on IRS 3 A, except the emission of the COMs that is more intense towards the near-IR nebula located to the south of IRS 3 A, and HC$_3$N whose emission peak is located $\sim$0.5$"$ NE from IRS 3 A. The kinematical study suggests that the molecular emission is mainly coming from a rotating ring and/or an unresolved disk. Additional components are traced by the ro-vibrational HCN $\nu_2$=1 3$\rightarrow$2 line which is probing the inner disk/jet region, and the weak lines of CH$_3$OCHO, more likely arising from the walls of the cavity excavated by the molecular outflow. Based on SO$_2$ we derive a gas kinetic temperature of T$_k$$\sim$ 170 K towards the IRS 3 A. The most abundant S-bearing species is SO$_2$ with an abundance of $\sim$ 1.3$\times$10$^{-7}$, and $\chi$(SO/SO$_2$) $\sim$ 0.29. Assuming the solar abundance, SO$_2$ accounts for $\sim$1 % of the sulphur budget., Comment: 12 pages, 8 figures, accepted for publication in MNRAS

We propose Shard Scheduler, a system for object placement and migration in account-based sharded blockchains. Our system calculates optimal placement and decides of object migrations across shards and supports complex multi-account transactions caused by smart contracts. Placement and migration decisions made by Shard Scheduler are fully deterministic, verifiable, and can be made part of the consensus protocol. Shard Scheduler reduces the number of costly cross-shard transactions, ensures balanced load distribution and maximizes the number of processed transactions for the blockchain as a whole. It leverages a novel incentive model motivating miners to maximize the global throughput of the entire blockchain rather than the throughput of a specific shard. Shard Scheduler reduces the number of costly cross-shard transactions by half in our simulations, ensuring equal load and increasing the throughput 3 fold when using 60 shards. We also implement and evaluate Shard Scheduler on Chainspace, more than doubling its throughput and reducing user-perceived latency by 70% when using 10 shards.

The chemical and physical evolution of starless and pre-stellar cores are of paramount importance to understanding the process of star formation. The Taurus Molecular Cloud cores TMC 1-C and TMC 1-CP share similar initial conditions and provide an excellent opportunity to understand the evolution of the pre-stellar core phase. We investigated the evolutionary stage of starless cores based on observations towards the prototypical dark cores TMC 1-C and TMC 1-CP, mapping them in the CS $3\rightarrow 2$, C$^{34}$S $3\rightarrow 2$, $^{13}$CS $2\rightarrow 1$, DCN $1\rightarrow 0$, DCN $2\rightarrow 1$, DNC $1\rightarrow 0$, DNC $2\rightarrow 1$, DN$^{13}$C $1\rightarrow 0$, DN$^{13}$C $2\rightarrow 1$, N$_2$H$^+$ $1\rightarrow 0$, and N$_2$D$^+$ $1\rightarrow 0$ transitions. We performed a multi-transitional study of CS and its isotopologs, DCN, and DNC lines to characterize the physical and chemical properties of these cores. We studied their chemistry using the state-of-the-art gas-grain chemical code Nautilus and pseudo time-dependent models to determine their evolutionary stage. Observational diagnostics seem to indicate that TMC 1-C is in a later evolutionary stage than TMC 1-CP, with a chemical age $\sim$1 Myr. TMC 1-C shows signs of being an evolved core at the onset of star formation, while TMC 1-CP appears to be in an earlier evolutionary stage due to a more recent formation or, alternatively, a collapse slowed down by a magnetic support., Comment: 26 pages, 10 figures

Variable red- and blue-shifted absorption features observed in the Ca ii K line towards the A-type shell star $\phi$ Leo have been suggested by us in a previous work to be likely due to solid, comet-like bodies in the circumstellar (CS) environment. Our aim is to expand our observational study of this object to other characteristic spectral lines of A-type photospheres as well as to lines arising in their CS shells. We have obtained more than 500 high-resolution optical spectra collected at different telescopes from December 2015 to January 2019. We have analysed some photospheric lines, in particular Ca i 4226 \AA ~and Mg ii 4481 \AA, as well as the circumstellar shell lines Ca ii H\&K, Ca ii IR triplet, Fe ii, Ti ii, and the Balmer lines H$\alpha$ and H$\beta$. Our observational study reveals that $\phi$ Leo is a variable $\delta$ Scuti star whose spectra show remarkable dumps and bumps superimposed on the photospheric line profiles, which vary their strength and sharpness, propagate from blue- to more red-shifted radial velocities and persisting during a few hours, likely produced by non-radial pulsations. At the same time, all shell lines present an emission at $\sim$3 km/s centered at the core of the CS features, and two variable absorption minima at both sides of the emission. The variations observed in the Ca ii H\&K, Fe ii and Ti ii lines occur at any time scale from minutes to days and observing run, but without any clear correlation or recognizable temporal pattern among the different lines. In the case of H$\alpha$ the CS contribution is also variable in just one of the observing runs. We suggest that $\phi$ Leo is a rapidly rotating $\delta$ Scuti star surrounded by a variable, (nearly) edge-on CS disk possibly re-supplied by the $\delta$ Scuti pulsations., Comment: Accepted in Astronomy&Astrophysics. 15 pages, 15 figures. C1 table available on CDS

In this era of spatially resolved observations of planet forming disks with ALMA and large ground-based telescopes such as the VLT, Keck and Subaru, we still lack statistically relevant information on the quantity and composition of the material that is building the planets, such as the total disk gas mass, the ice content of dust, and the state of water in planetesimals. SPICA is an infrared space mission concept developed jointly by JAXA and ESA to address these questions. The key unique capabilities of SPICA that enable this research are (1) the wide spectral coverage 10-220 micron, (2) the high line detection sensitivity of (1-2) 10-19 W m-2 with R~2000-5000 in the far-IR (SAFARI) and 10-20 W m-2 with R~29000 in the mid-IR (SMI, spectrally resolving line profiles), (3) the high far-IR continuum sensitivity of 0.45 mJy (SAFARI), and (4) the observing efficiency for point source surveys. This paper details how mid- to far-IR infrared spectra will be unique in measuring the gas masses and water/ice content of disks and how these quantities evolve during the planet forming period. These observations will clarify the crucial transition when disks exhaust their primordial gas and further planet formation requires secondary gas produced from planetesimals. The high spectral resolution mid-IR is also unique for determining the location of the snowline dividing the rocky and icy mass reservoirs within the disk and how the divide evolves during the build-up of planetary systems. Infrared spectroscopy (mid- to far-IR) of key solid state bands is crucial for assessing whether extensive radial mixing, which is part of our Solar System history, is a general process occurring in most planetary systems and whether extrasolar planetesimals are similar to our Solar System comets/asteroids. ... (abbreviated), Comment: accepted for publication in PASA

This paper proposes a fully implicit numerical scheme for immiscible incompressible two-phase flow in porous media taking into account gravity, capillary effects, and heterogeneity. The objective is to develop a fully implicit stable discontinuous Galerkin (DG) solver for this system that is accurate, bound-preserving, and locally mass conservative. To achieve this, we augment our DG formulation with post-processing flux and slope limiters. The proposed framework is applied to several benchmark problems and the discrete solutions are shown to be accurate, to satisfy the maximum principle and local mass conservation., Comment: 33 pages, 27 figures

Context. Studying gas chemistry in protoplanetary disks is key to understanding the process of planet formation. Sulfur chemistry in particular is poorly understood in interstellar environments, and the location of the main reservoirs remains unknown. Protoplanetary disks in Taurus are ideal targets for studying the evolution of the composition of planet forming systems. Aims. We aim to elucidate the chemical origin of sulfur-bearing molecular emission in protoplanetary disks, with a special focus on H$_2$S emission, and to identify candidate species that could become the main molecular sulfur reservoirs in protoplanetary systems. Methods. We used IRAM 30m observations of nine gas-rich young stellar objects (YSOs) in Taurus to perform a survey of sulfur-bearing and oxygen-bearing molecular species. In this paper we present our results for the CS 3-2 ($\nu_0$ = 146.969 GHz), H$_2$CO 2$_{11}$-1$_{10}$ ($\nu_0$ = 150.498 GHz), and H$_2$S 1$_{10}$-1$_{01}$ ($\nu_0$ = 168,763 GHz) emission lines. Results. We detected H$_2$S emission in four sources out of the nine observed, significantly increasing the number of detections toward YSOs. We also detected H$_2$CO and CS in six out of the nine. We identify a tentative correlation between H$_2$S 1$_{10}$-1$_{01}$ and H$_2$CO 2$_{11}$-1$_{10}$ as well as a tentative correlation between H$_2$S 1$_{10}$-1$_{01}$ and H$_2$O 8$_{18}$-7$_{07}$. By assuming local thermodynamical equilibrium, we computed column densities for the sources in the sample, with N(o-H$_2$S) values ranging between $2.6\times10^{12}$ cm$^{-2}$ and $1.5\times10^{13}$ cm$^{-2}$., Comment: 13 pages, 6 figures, 6 tables