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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.

In this paper, we present a new computational framework using coupled and decoupled approximations for a Cahn-Hilliard-Navier-Stokes model with variable densities and degenerate mobility. In this sense, the coupled approximation is shown to conserve the mass of the fluid, preserve the point-wise bounds of the density and decrease an energy functional. In contrast, the decoupled scheme is presented as a more computationally efficient alternative but the discrete energy-decreasing property can not be assured. Both schemes are based on a finite element approximation for the Navier-Stokes fluid flow with discontinuous pressure and an upwind discontinuous Galerkin scheme for the Cahn-Hilliard part. Finally, several numerical experiments contrasting both approaches are conducted. In particular, results for a convergence test, a simple qualitative comparison and some well-known benchmark problems are shown., Comment: 32 pages, 11 figures, 2 tables

In this work, we present a modification of the phase-field tumor growth model given in [26] that leads to bounded, more physically meaningful, volume fraction variables. In addition, we develop an upwind discontinuous Galerkin (DG) scheme preserving the mass conservation, pointwise bounds and energy stability of the continuous model. Finally, some computational tests in accordance with the theoretical results are introduced. In the first test, we compare our DG scheme with the finite element (FE) scheme related to the same time approximation. The DG scheme shows a well-behavior even for strong cross-diffusion effects in contrast with FE where numerical spurious oscillations appear. Moreover, the second test exhibits the behavior of the tumor-growth model under different choices of parameters and also of mobility and proliferation functions., Comment: 32 pages, 15 figures

We consider a bilinear optimal control problem associated to the following chemotaxis-consumption model in a bounded domain $\Omega \subset \mathbb{R}^3$ during a time interval $(0,T)$: $$\partial_t u - \Delta u = - \nabla \cdot (u \nabla v), \quad \partial_t v - \Delta v = - u^s v + f v 1_{\Omega_c},$$ with $s \geq 1$, endowed with isolated boundary conditions and initial conditions for $(u,v)$, $u$ being the cell density, $v$ the chemical concentration and $f$ the bilinear control acting in a subdomain $\Omega_c \subset \Omega$. The existence of weak solutions $(u,v)$ to this model given $f \in L^q((0,T) \times \Omega)$, for some $q > 5/2$, has been proved in [F. Guill\'en-Gonz\'alez and A. L. Corr\^ea Vianna Filho, Optimal Control Related to Weak Solutions of a Chemotaxis-Consumption Model, arXiv:2211.14612, 2022]. In this paper, we study a related optimal control problem in the strong solution setting. First, imposing the regularity criterion $u ^s \in L^q((0,T) \times \Omega)$ ($q > 5/2$) for a given weak solution, we prove existence and uniqueness of global-in-time strong solutions. Then, the existence of a global optimal solution can be deduced. Finally, using a Lagrange multipliers theorem, we establish first order optimality conditions for any local optimal solution, proving existence, uniqueness and regularity of the associated Lagrange multipliers.

The interaction of supercritical turbulent flows with granular sediment beds is challenging to study both experimentally and numerically; this challenging task has hampered the advances in understanding antidunes, the most characteristic bedform of supercritical flows. This article presents the first numerical attempt to simulate upstream-migrating antidunes with geometrically resolved particles and a liquid-gas interface. Our simulations provide data at a resolution higher than laboratory experiments, and they can therefore provide new insights into the mechanisms of antidune migration and contribute to a deeper understanding of the underlying physics. To manage the simulations' computational costs and physical complexity, we employ the cumulant lattice Boltzmann method in conjunction with a discrete element method for particle interactions, as well as a volume of fluid scheme to track the deformable free surface of the fluid. By reproducing two flow configurations of previous experiments (Pascal et al., Earth Surf. Proc. Land., vol. 46(9), 2021, 1750-1765), we demonstrate that our approach is robust and accurately predicts the antidunes' amplitude, wavelength, and celerity. Furthermore, the simulated wall-shear stress, a key parameter governing sediment transport, is in excellent agreement with the experimental measurements. The highly resolved data of fluid and particle motion from our simulation approach open new perspectives for detailed studies of morphodynamics in shallow supercritical flows.

Two new numerical schemes to approximate the Cahn-Hilliard equation with degenerate mobility (between stable values 0 and 1) are presented, by using two different non-centered approximation of the mobility. We prove that both schemes are energy stable and preserve the maximum principle approximately, i.e. the amount of the solution being outside of the interval [0,1] goes to zero in terms of a truncation parameter. Additionally, we present several numerical results in order to show the accuracy and the well behavior of the proposed schemes, comparing both schemes and the corresponding centered scheme.

The Nab experiment at Oak Ridge National Laboratory, USA, aims to measure the beta-antineutrino angular correlation following neutron $\beta$ decay to an anticipated precision of approximately 0.1\%. The proton momentum is reconstructed through proton time-of-flight measurements, and potential systematic biases in the timing reconstruction due to detector effects must be controlled at the nanosecond level. We present a thorough and detailed semiconductor and quasiparticle transport simulation effort to provide precise pulse shapes, and report on relevant systematic effects and potential measurement schemes.

In the present work we investigate an optimal control problem related to the following chemotaxis-consumption model in a bounded domain $\Omega\subset \mathbb{R}^3$: $$\partial_t u - \Delta u = - \nabla \cdot (u \nabla v), \quad \partial_t v - \Delta v = - u^s v + f \,v\, 1_{\Omega_c},$$ with $s \geq 1$, endowed with isolated boundary conditions and initial conditions for $(u,v)$, being $u$ the cell density, $v$ the chemical concentration and $f$ the control acting in the $v$-equation through the bilinear term $f \,v\, 1_{\Omega_c}$, in a subdomain $\Omega_c \subset \Omega$. We address the existence of optimal control restricted to a weak solution setting, where, in particular, uniqueness of state $(u,v)$ given a control $f$ is not clear. Then by considering weak solutions satisfying an adequate energy inequality, we prove the existence of optimal control subject to uniformly bounded controls. Finally, we discuss the relation between the considered control problem and two other related ones, where the existence of optimal solution can not be proved.

Understanding defect-phonon interactions in solid-state devices is crucial for improving our current knowledge of quantum platforms. In this work, we develop first-principles calculations for a defect composed of two spin-$1/2$ particles that interact with phonon modes in a one-dimensional lattice. We follow a bottom-up approach that begins with a dipolar magnetic interaction to ultimately derive the spectral density function and time-local master equation that describes the open dynamics of the defect. We provide theoretical and numerical analysis for the non-Markovian features of the defect-phonon dynamics induced by a pure dephasing channel acting on the Bell basis. Finally, we analyze two measures of non-Markovianity based on the canonical rates and Coherence, shedding more light on the role of the spectral density function and temperature; and envisioning experimental realizations., Comment: 25 pages, 6 figures

This article is devoted to the mathematical modeling of migration of neuroblasts, precursor cells of neurons, along the pathway they usually follow before maturing. This pathway is determined mainly by chemotaxis and the heterogeneous mobility of neuroblasts in different regions of the brain. In numerical simulations, the application of novel discontinuous Galerkin methods allows to maintain the properties of the continuous model such as the maximum principle. We present some successful computer tests including parameter adjust to fit real data from rodent brains.

The well-suited discretization of the Keller-Segel equations for chemotaxis has become a very challenging problem due to the convective nature inherent to them. This paper aims to introduce a new upwind, mass-conservative, positive and energy-dissipative discontinuous Galerkin scheme for the Keller-Segel model. This approach is based on the gradient-flow structure of the equations. In addition, we show some numerical experiments in accordance with the aforementioned properties of the discretization. The numerical results obtained emphasize the really good behaviour of the approximation in the case of chemotactic collapse, where very steep gradients appear., Comment: 27 pages, 21 figures, 4 tables