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Understanding the properties of Au$_{10}$ clusters entails identifying the lowest energy structure at cold and warm temperatures. While functional materials operate at finite temperatures, energy computations using density functional theory are typically performed at zero temperature, resulting in unexplored properties. Our study undertook an exploration of the potential and free energy surface of the neutral Au$_{10}$ nanocluster at finite temperatures by employing a genetic algorithm combined with density functional theory and nanothermodynamics. We computed the thermal population and infrared Boltzmann spectrum at a finite temperature, aligning the results with validated experimental data. The Zero-Order Regular Approximation (ZORA) gave consideration to relativistic effects, and dispersion was incorporated using Grimme's dispersion D3BJ with Becke-Johnson damping. Moreover, nanothermodynamics was utilized to account for temperature contributions. The computed thermal population strongly supports the dominance of the 2D elongated hexagon configuration within a temperature range of 50 to 800 K. Importantly, at a temperature of 100 K, the calculated IR Boltzmann spectrum aligns with the experimental IR spectrum. Lastly, the chemical bonding analysis on the lowest energy structure indicates a closed-shell Au-Au interaction with a weak or partially covalent character., Comment: 5 figures

To establish a self-sustained human presence in space and to explore deeper into the solar system, extensive research has been conducted on In-Situ Resource Utilization (ISRU) systems. Past studies have proposed and researched many technologies to produce oxygen from regolith, such as carbothermal reduction and water extraction from icy regolith, to utilize it for astronauts' life support and as the propellant of space systems. However, determining the most promising technology remains challenging due to uncertainties in the lunar environment and processing methods. To better understand the lunar environment and ISRU operations, it is crucial to gather more information. Motivated by this need for information gathering, this paper proposes a new ISRU plant architecture integrating carbothermal reduction of dry regolith and water extraction from icy regolith. Two different hybrid plant architectures integrating both technologies (1) in parallel and (2) in series are examined. The former involves mining and processing in both a Permanently Shadowed Region (PSR) and a peak of eternal light in parallel, while the latter solely mines in a PSR. In this series hybrid architecture, the dry regolith tailings from water extraction are further processed by carbothermal reduction. This paper conducts a comparative analysis of the landed mass and required power of each plant architecture utilizing subsystem-level models. Furthermore, based on uncertain parameters such as resource content in regolith, the potential performance range of each plant was discovered through Monte Carlo simulations. The result indicates the benefit of the series hybrid architecture in terms of regolith excavation rate, while its mass cost seems the highest among the studied architectures., Comment: 26 pages, 21 figures, 7 tables, under review by Acta Astronautica

In this work we present two new numerical schemes to approximate the Navier-Stokes-Cahn-Hilliard system with degenerate mobility using finite differences in time and finite elements in space. The proposed schemes are conservative, energy-stable and preserve the maximum principle approximately (the amount of the phase variable being outside of the interval [0,1] goes to zero in terms of a truncation parameter). Additionally, we present several numerical results to illustrate the accuracy and the well behavior of the proposed schemes, as well as a comparison with the behavior of the Navier-Stokes-Cahn-Hilliard model with constant mobility.

Conversions between neutrons $n$ and Dark Matter candidate sterile neutrons $n'$ have been proposed as a mechanism for Baryon Number $\mathcal{B}$ violation. In the case that there is a small mass difference $\Delta{m}$ between the $n$ and the $n'$ states, oscillations can be induced by compensating for $\Delta{m}$ with a magnetic field. A search for such neutron oscillations was performed at the Spallation Neutron Source by looking for anomalous neutron transmission through a strongly absorbing cadmium wafer inside of a $6.6$~T magnet. The approach described here saw no regenerated neutrons above background, which provides an improved limit for neutron - sterile neutrons transformations for a range of $\Delta{m}$ between $0.1$~neV and $1000$~neV., Comment: 18 pages, 15 figures

In the present review we focus on the chemotaxis-consumption model $\partial_t u - \Delta u = - \nabla \cdot (u \nabla v)$ and $\partial_t v - \Delta v = - u^s v$ in $(0,T) \times \Omega$, for any fixed $s \geq 1$, endowed with isolated boundary conditions and nonnegative initial conditions, where $(u,v)$ model cell density and chemical signal concentration. Our objective is to present an overview of the related literature and latest results on the aforementioned model concerning the following three distinct research lines we have obtained in [12,24-26]: the mathematical analysis, the numerical analysis and the related optimal control theory with a bilinear control acting on the chemical equation.

The main purpose of this work is the modelling of large single populations of cells under different interactions among themselves, in balance with natural random diffusion. We focus on cell-cell adhesion mechanisms for one single population confined in isolated domains. Our most relevant contribution is the proposal of a mathematical model, that includes a nonlocal saturation coefficient multiplying an appropriate nonlocal drift term, that can even induce repulsion effects from saturated areas.