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In this work we study an inhomogeneous two-phase obstacle-type problem associated to the $s$-fractional $p$-Laplacian. Besides the existence and uniqueness of solutions, we study the convergence of the solutions when $s\to 1$ to the classical problem. We also study the continuous dependence with respect to the level-set function $v$, yielding an existence result for a two-phase obstacle-type problem with an implicit level-set function., Comment: 21 pages

The recent discoveries of Neptune-sized ultra-short period planets (USPs) challenge existing planet formation theories. It is unclear whether these residents of the Hot Neptune Desert have similar origins to smaller, rocky USPs, or if this discrete population is evidence of a different formation pathway altogether. We report the discovery of TOI-3261b, an ultra-hot Neptune with an orbital period $P$ = 0.88 days. The host star is a $V = 13.2$ magnitude, slightly super-solar metallicity ([Fe/H] $\simeq$ 0.15), inactive K1.5 main sequence star at $d = 300$ pc. Using data from the Transiting Exoplanet Survey Satellite and the Las Cumbres Observatory Global Telescope, we find that TOI-3261b has a radius of $3.82_{-0.35}^{+0.42}$ $R_{\oplus}$. Moreover, radial velocities from ESPRESSO and HARPS reveal a mass of $30.3_{-2.4}^{+2.2}$ $M_{\oplus}$, more than twice the median mass of Neptune-sized planets on longer orbits. We investigate multiple mechanisms of mass loss that can reproduce the current-day properties of TOI-3261b, simulating the evolution of the planet via tidal stripping and photoevaporation. Thermal evolution models suggest that TOI-3261b should retain an envelope potentially enriched with volatiles constituting $\sim$5% of its total mass. This is the second highest envelope mass fraction among ultra-hot Neptunes discovered to date, making TOI-3261b an ideal candidate for atmospheric follow-up observations., Comment: 20 pages, 11 figures, accepted to AJ

The conservation of stone-based cultural heritage sites is a critical concern for preserving cultural and historical landmarks. With the advent of Large Multimodal Models, as GPT-4omni (OpenAI), Claude 3 Opus (Anthropic) and Gemini 1.5 Pro (Google), it is becoming increasingly important to define the operational capabilities of these models. In this work, we systematically evaluate the abilities of the main foundational multimodal models to recognise and classify anomalies and deterioration patterns of the stone elements that are useful in the practice of conservation and restoration of world heritage. After defining a taxonomy of the main stone deterioration patterns and anomalies, we asked the foundational models to identify a curated selection of 354 highly representative images of stone-built heritage, offering them a careful selection of labels to choose from. The result, which varies depending on the type of pattern, allowed us to identify the strengths and weaknesses of these models in the field of heritage conservation and restoration., Comment: 10 pages, 5 figures, submitted to Journal of Cultural Heritage

We consider the one and the two obstacles problems for the nonlocal nonlinear anisotropic $g$-Laplacian $\mathcal{L}_g^s$, with $0

We show that the solutions to the nonlocal obstacle problems for the nonlocal $-\Delta_p^s$ operator, when the fractional parameter $s\to\sigma$ for $0<\sigma\leq1$, converge to the solution of the corresponding obstacle problem for $-\Delta_p^\sigma$, being $\sigma=1$ the classical obstacle problem for the local $p$-Laplacian. We discuss the weak stability of the quasi-characteristic functions of coincidence sets of the solution with the obstacle, which is a strong convergence of their characteristic functions when $s\nearrow 1$ under a nondegeneracy condition. This stability can be shown also in terms of the convergence of the free boundaries, as well as of the coincidence sets, in Hausdorff distance when $s\nearrow 1$, under non-degeneracy local assumptions on the external force and a local topological property of the coincidence set of the limit classical obstacle problem for the local $p$-Laplacian, essentially when the limit coincidence set is the closure of its interior.

Within high-performance computing (HPC), solving large sparse linear systems efficiently remains paramount, with iterative methods being the predominant choice. However, the performance of these methods is tightly coupled to the aptness of the chosen preconditioner. The multifaceted nature of sparse matrices makes the universal prescription of preconditioners elusive. Notably, the key attribute of sparsity is not precisely captured by scalar metrics such as bandwidth or matrix dimensions. Advancing prior methodologies, this research introduces matrix sparsity depiction via RGB images. Utilizing a convolutional neural network (CNN), the task of preconditioner selection turns into a multi-class classification problem. Extensive tests on 126 SuiteSparse matrices emphasize the enhanced prowess of the CNN model, noting a 32% boost in accuracy and a 25% reduction in computational slowdown., Comment: 23 pages, 8 figures, 9 tables

We consider weak solutions for the obstacle-type viscoelastic ($\nu>0$) and very weak solutions for the obstacle inviscid ($\nu=0$) Dirichlet problems for the heterogeneous and anisotropic wave equation in a fractional framework based on the Riesz fractional gradient $D^s$ ($0

We report the discovery of two exoplanets orbiting around HD 212729 (TOI\,1052, TIC 317060587), a $T_{\rm eff}=6146$K star with V=9.51 observed by TESS in Sectors 1 and 13. One exoplanet, TOI-1052b, is Neptune-mass and transits the star, and an additional planet TOI-1052c is observed in radial velocities but not seen to transit. We confirm the planetary nature of TOI-1052b using precise radial velocity observations from HARPS and determined its parameters in a joint RV and photometry analysis. TOI-1052b has a radius of $2.87^{+0.29}_{-0.24}$ R$_{\oplus}$, a mass of $16.9\pm 1.7$ M$_{\oplus}$, and an orbital period of 9.14 days. TOI-1052c does not show any transits in the TESS data, and has a minimum mass of $34.3^{+4.1}_{-3.7}$ M$_{\oplus}$ and an orbital period of 35.8 days, placing it just interior to the 4:1 mean motion resonance. Both planets are best fit by relatively high but only marginally significant eccentricities of $0.18^{+0.09}_{-0.07}$ for planet b and $0.24^{+0.09}_{-0.08}$ for planet c. We perform a dynamical analysis and internal structure model of the planets as well as deriving stellar parameters and chemical abundances. The mean density of TOI-1052b is $3.9^{+1.7}_{-1.3}$ g cm$^{-3}$ consistent with an internal structure similar to Neptune. A nearby star is observed in Gaia DR3 with the same distance and proper motion as TOI-1052, at a sky projected separation of ~1500AU, making this a potential wide binary star system., Comment: Accepted to MNRAS. 11 pages

We present the discovery of an exoplanet transiting TOI-908 (TIC-350153977) using data from TESS sectors 1, 12, 13, 27, 28 and 39. TOI-908 is a T = 10.7 mag G-dwarf ($T_{eff}$ = 5626 $\pm$ 61 K) solar-like star with a mass of 0.950 $\pm$ 0.010 $M_{\odot}$ and a radius of 1.028 $\pm$ 0.030 $R_{\odot}$. The planet, TOI-908 b, is a 3.18 $\pm$ 0.16 $R_{\oplus}$ planet in a 3.18 day orbit. Radial velocity measurements from HARPS reveal TOI-908 b has a mass of approximately 16.1 $\pm$ 4.1 $M_{\oplus}$ , resulting in a bulk planetary density of 2.7+0.2-0.4 g cm-3. TOI-908 b lies in a sparsely-populated region of parameter space known as the Neptune desert. The planet likely began its life as a sub-Saturn planet before it experienced significant photoevaporation due to X-rays and extreme ultraviolet radiation from its host star, and is likely to continue evaporating, losing a significant fraction of its residual envelope mass., Comment: 17 pages, 17 figures

We prove the existence of generalised solutions of the Monge-Kantorovich equations with fractional $s$-gradient constraint, $0

Reservoir simulations for petroleum fields and seismic imaging are known as the most demanding workloads for high-performance computing (HPC) in the oil and gas (O&G) industry. The optimization of the simulator numerical parameters plays a vital role as it could save considerable computational efforts. State-of-the-art optimization techniques are based on running numerous simulations, specific for that purpose, to find good parameter candidates. However, using such an approach is highly costly in terms of time and computing resources. This work presents TunaOil, a new methodology to enhance the search for optimal numerical parameters of reservoir flow simulations using a performance model. In the O&G industry, it is common to use ensembles of models in different workflows to reduce the uncertainty associated with forecasting O&G production. We leverage the runs of those ensembles in such workflows to extract information from each simulation and optimize the numerical parameters in their subsequent runs. To validate the methodology, we implemented it in a history matching (HM) process that uses a Kalman filter algorithm to adjust an ensemble of reservoir models to match the observed data from the real field. We mine past execution logs from many simulations with different numerical configurations and build a machine learning model based on extracted features from the data. These features include properties of the reservoir models themselves, such as the number of active cells, to statistics of the simulation's behavior, such as the number of iterations of the linear solver. A sampling technique is used to query the oracle to find the numerical parameters that can reduce the elapsed time without significantly impacting the quality of the results. Our experiments show that the predictions can improve the overall HM workflow runtime on average by 31%., Comment: 21 pages, 9 figures. Preprint submitted to Journal of Computational Science

Consider the quasilinear diffusion problem \[\begin{cases}\mathbf{u}'+\Pi(t,x,\mathbf{u},\Sigma \mathbf{u})\mathbb{A}\mathbf{u}=\mathbf{f}(t,x,\mathbf{u},\Sigma \mathbf{u})&\text{ in }]0,T[\times\Omega,\\\mathbf{u}=\mathbf{0}&\text{ in }]0,T[\times\Omega^c,\\\mathbf{u}(0,\cdot)=\mathbf{u}_0(\cdot)&\text{ in }\Omega\end{cases}\] for an open set $\Omega\subset\mathbb{R}^n$, $\mathbf{u}_0\in \mathbf{H}^s_0(\Omega):=[H^s_0(\Omega)]^m$ and any $T\in]0,\infty[$, where $\Sigma \mathbf{u}\in \mathbb{R}^q$ for $0

In this work, we consider the fractional Stefan-type problem in a Lipschitz bounded domain $\Omega\subset\mathbb{R}^d$ with time-dependent Dirichlet boundary condition for the temperature $\vartheta=\vartheta(x,t)$, $\vartheta=g$ on $\Omega^c\times]0,T[$, and initial condition $\eta_0$ for the enthalpy $\eta=\eta(x,t)$, given in $\Omega\times]0,T[$ by \[\frac{\partial \eta}{\partial t} +\mathcal{L}_A^s \vartheta= f\quad\text{ with }\eta\in \beta(\vartheta),\] where $\mathcal{L}_A^s$ is an anisotropic fractional operator defined in the distributional sense by \[\langle\mathcal{L}_A^su,v\rangle=\int_{\mathbb{R}^d}AD^su\cdot D^sv\,dx,\] $\beta$ is a maximal monotone graph, $A(x)$ is a symmetric, strictly elliptic and uniformly bounded matrix, and $D^s$ is the distributional Riesz fractional gradient for $0

The Jordan--Moore--Gibson--Thompson (JMGT) equation is a well-established and recently widely studied model for nonlinear acoustics (NLA). It is a third-order (in time) semilinear Partial Differential Equation (PDE) model with the distinctive feature of predicting the propagation of ultrasound waves at \textit{finite} speed due to heat phenomenon know as \textit{second sound} which leads to the hyperbolic character of heat propagation. In this paper, we consider the problem of stabilizability of the linear (known as) MGT--equation. We consider a special geometry that is suitable for studying the problem of controlling (from the boundary) the acoustic pressure involved in medical treatments like lithotripsy, thermotherapy, sonochemistry, or any other procedures using High Intensity Focused Ultrasound (HIFU).