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We analyze a diffuse interface model that describes the dynamics of incompressible two-phase flows influenced by interactions with a soluble chemical substance, encompassing the chemotaxis effect, mass transport, and reactions. In the resulting coupled evolutionary system, the macroscopic fluid velocity field $\boldsymbol{v}$ satisfies a Navier--Stokes system driven by a capillary force, the phase field variable $\varphi$ is governed by a convective Cahn--Hilliard equation incorporating a mass source and a singular potential (e.g., the Flory--Huggins type), and the chemical concentration $\sigma$ obeys an advection-reaction-diffusion equation with logistic degradation, exhibiting a cross-diffusion structure akin to the Keller--Segel model for chemotaxis. Under general structural assumptions, we establish the existence of global weak solutions to the initial boundary value problem within a bounded smooth domain $\Omega\subset \mathbb{R}^d$, $d=2,3$. The proof hinges on a novel semi-Galerkin scheme for a suitably regularized system, featuring a non-standard approximation of the singular potential. Moreover, with more restrictive assumptions on coefficients and data, we establish regularity properties and uniqueness of global weak solutions in the two-dimensional case. Our analysis contributes to a further understanding of phase separation processes under the interplay of fluid dynamics and chemotaxis, in particular, the influence of cross diffusion and logistic degradation.

We study the Cahn-Hilliard equation with non-degenerate concentration-dependent mobility and logarithmic potential in two dimensions. We show that any weak solution is unique, exhibits propagation of uniform-in-time regularity, and stabilizes towards an equilibrium state of the Ginzburg-Landau free energy for large times. These results improve the state of the art dating back to a work by Barrett and Blowey. Our analysis relies on the combination of enhanced energy estimates, elliptic regularity theory and tools in critical Sobolev spaces.

Managing the growing data from renewable energy production plants for effective decision-making often involves leveraging Ontology-based Data Access (OBDA), a well-established approach that facilitates querying diverse data through a shared vocabulary, presented in the form of an ontology. Our work addresses one of the common problems in this context, deriving from feeding complex class hierarchies defined by such ontologies from fragmented and imbalanced (w.r.t. class labels) data sources. We introduce an innovative framework that enhances existing OBDA systems. This framework incorporates a dynamic class management approach to address hierarchical classification, leveraging machine learning. The primary objectives are to enhance system performance, extract richer insights from underrepresented data, and automate data classification beyond the typical capabilities of basic deductive reasoning at the ontological level. We experimentally validate our methodology via real-world, industrial case studies from the renewable energy sector, demonstrating the practical applicability and effectiveness of the proposed solution., Comment: Paper accepted for pubblication to the 32nd Symposium on Advanced Database Systems (SEBD) 2024: https://ceur-ws.org/Vol-3741/paper28.pdf

Superfluidity describes the ability of quantum matter to flow without friction. Due to its fundamental role in many transport phenomena, it is crucial to understand the robustness of superfluid properties to external perturbations. Here, we theoretically study the effects of speckle disorder on the propagation of sound waves in a two-dimensional Bose-Einstein condensate at zero temperature. We numerically solve the Gross-Pitaevskii equation in the presence of disorder and employ a superfluid hydrodynamic approach to elucidate the role of the compressibility and superfluid fraction on the propagation of sound. A key result is that disorder reduces the superfluid fraction and hence the speed of sound; it also introduces damping and mode coupling. In the limit of weak disorder, the predictions for the speed of sound and its damping rate are well reproduced by a quadratic perturbation theory. The hydrodynamic description is valid over a wide range of parameters, while discrepancies become evident if the disorder becomes too strong, the effect being more significant for disorder applied in only one spatial direction. Our predictions are well within the reach of state-of-the-art cold-atom experiments and carry over to more general disorder potentials., Comment: 18 pages, 9 figures

The survival probability for a periodic non-autonomous Ornstein-Uhlenbeck process is calculated analytically using two different methods. The first uses an asymptotic approach. We treat the associated Kolmogorov Backward Equation with an absorbing boundary by dividing the domain into an interior region, centered around the origin, and a "boundary layer" near the absorbing boundary. In each region we determine the leading-order analytical solutions, and construct a uniformly valid solution over the entire domain using asymptotic matching. In the second method we examine the integral relationship between the probability density function and the mean first passage time probability density function. These allow us to determine approximate analytical forms for the exit rate. The validity of the solutions derived from both methods is assessed numerically, and we find the asymptotic method to be superior., Comment: 22 pages, 6 figures

We discuss numerical aspects of instantons in two- and three-dimensional $\phi^4$ theories with an internal $O(N)$ symmetry group, the so-called $N$-vector model. Combining asymptotic transseries expansions for large argument with convergence acceleration techniques, we obtain high-precision values for certain integrals of the instanton that naturally occur in loop corrections around instanton configurations. Knowledge of these numerical properties are necessary in order to evaluate corrections to the large-order factorial growth of perturbation theory in $\phi^4$ theories. The results contribute to the understanding of the mathematical structures underlying the instanton configurations., Comment: 11 pages; RevTeX

We investigate the formation of quantum droplets at finite temperature in attractive Bose mixtures subject to a strong transverse harmonic confinement. By means of exact path-integral Monte Carlo methods we determine the equilibrium density of the gas and the liquid as well as the pressure vs. volume dependence along isothermal curves. Results for the equation of state and for the gas-liquid coexistence region in quasi-2D configurations are compared with calculations in strictly two dimensions, finding excellent agreement. Within the pure 2D model we explore the relevance of the quantum scale anomaly and we determine the critical interaction strength for the occurrence of the first-order gas to liquid transition. Furthermore, we find that the superfluid response develops suddenly, following the density jump from the gas to the liquid state., Comment: v1: 6 pages, 4 figures; v2: minor improvements, matches published version

The recursive Neville algorithm allows one to calculate interpolating functions recursively. Upon a judicious choice of the abscissas used for the interpolation (and extrapolation), this algorithm leads to a method for convergence acceleration. For example, one can use the Neville algorithm in order to successively eliminate inverse powers of the upper limit of the summation from the partial sums of a given, slowly convergent input series. Here, we show that, for a particular choice of the abscissas used for the extrapolation, one can replace the recursive Neville scheme by a simple one-step transformation, while also obtaining access to subleading terms for the transformed series after convergence acceleration. The matrix-based, unified formulas allow one to estimate the rate of convergence of the partial sums of the input series to their limit. In particular, Bethe logarithms for hydrogen are calculated to 100 decimal digits. Generalizations of the method to series whose remainder terms can be expanded in terms of inverse factorial series, or series with half-integer powers, are also discussed., Comment: 17 pages; RevTeX

We introduce an approach for analyzing the responses of dynamical systems to external perturbations that combines score-based generative modeling with the Generalized Fluctuation-Dissipation Theorem (GFDT). The methodology enables accurate estimation of system responses, including those with non-Gaussian statistics. We numerically validate our approach using time-series data from three different stochastic partial differential equations of increasing complexity: an Ornstein-Uhlenbeck process with spatially correlated noise, a modified stochastic Allen-Cahn equation, and the 2D Navier-Stokes equations. We demonstrate the improved accuracy of the methodology over conventional methods and discuss its potential as a versatile tool for predicting the statistical behavior of complex dynamical systems., Comment: In press. Includes supplementary material in the file supp_material.pdf

The paper presents a comprehensive performance evaluation of some heuristic search algorithms in the context of autonomous systems and robotics. The objective of the study is to evaluate and compare the performance of different search algorithms in different problem settings on the pathfinding domain. Experiments give us insight into the behavior of the evaluated heuristic search algorithms, over the variation of different parameters: domain size, obstacle density, and distance between the start and the goal states. Results are then used to design a selection algorithm that, on the basis of problem characteristics, suggests the best search algorithm to use., Comment: In Proceedings AREA 2023, arXiv:2310.00333

Making autonomous agents effective in real-life applications requires the ability to decide at run-time and a high degree of adaptability to unpredictable and uncontrollable events. Reacting to events is still a fundamental ability for an agent, but it has to be boosted up with proactive behaviors that allow the agent to explore alternatives and decide at run-time for optimal solutions. This calls for a continuous planning as part of the deliberation process that makes an agent able to reconsider plans on the base of temporal constraints and changes of the environment. Online planning literature offers several approaches used to select the next action on the base of a partial exploration of the solution space. In this paper, we propose a BDI continuous temporal planning framework, where interleave planning and execution loop is used to integrate online planning with the BDI control-loop. The framework has been implemented with the ROS2 robotic framework and planning algorithms offered by JavaFF.

Leveraging recent work on data-driven methods for constructing a finite state space Markov process from dynamical systems, we address two problems for obtaining further reduced statistical representations. The first problem is to extract the most salient reduced-order dynamics for a given timescale by using a modified clustering algorithm from network theory. The second problem is to provide an alternative construction for the infinitesimal generator of a Markov process that respects statistical features over a large range of timescales. We demonstrate the methodology on three low-dimensional dynamical systems with stochastic and chaotic dynamics. We then apply the method to two high-dimensional dynamical systems, the Kuramoto-Sivashinky equations and data sampled from fluid-flow experiments via Particle-Image Velocimetry. We show that the methodology presented herein provides a robust reduced-order statistical representation of the underlying system.

We study the thermodynamic behavior of attractive binary Bose mixtures using exact path-integral Monte-Carlo methods. Our focus is on the regime of interspecies interactions where the ground state is in a self-bound liquid phase, stabilized by beyond mean-field effects. We calculate the isothermal curves in the pressure vs density plane for different values of the attraction strength and establish the extent of the coexistence region between liquid and vapor using the Maxwell construction. Notably, within the coexistence region, Bose-Einstein condensation occurs in a discontinuous way as the density jumps from the normal gas to the superfluid liquid phase. Furthermore, we determine the critical point where the line of first-order transition ends and investigate the behavior of the density discontinuity in its vicinity. We also point out that the density discontinuity at the transition could be observed in experiments of mixtures in traps., Comment: v1: 6 pages, 5 figures. Supplemental material: 4 pages, 2 figures. Data available on zenodo.org; v2: minor improvements, matches PRL published version

In this note, we consider the nonlocal Cahn-Hilliard equation with constant mobility and singular potential in three dimensional bounded and smooth domains. Given any global solution (whose existence and uniqueness are already known), we prove the so-called {\it instantaneous} and {\it uniform} separation property: any global solution with initial finite energy is globally confined (in the $L^\infty$ metric) in the interval $[-1+\delta,1-\delta]$ on the time interval $[\tau,\infty)$ for any $\tau>0$, where $\delta$ only depends on the norms of the initial datum, $\tau$ and the parameters of the system. We then exploit such result to improve the regularity of the global attractor for the dynamical system associated to the problem.

The Double Asteroid Redirection Test (DART) spacecraft successfully performed the first test of a kinetic impactor for asteroid deflection by impacting Dimorphos, the secondary of near-Earth binary asteroid (65803) Didymos, and changing the orbital period of Dimorphos. A change in orbital period of approximately 7 minutes was expected if the incident momentum from the DART spacecraft was directly transferred to the asteroid target in a perfectly inelastic collision, but studies of the probable impact conditions and asteroid properties indicated that a considerable momentum enhancement ($\beta$) was possible. In the years prior to impact, we used lightcurve observations to accurately determine the pre-impact orbit parameters of Dimorphos with respect to Didymos. Here we report the change in the orbital period of Dimorphos as a result of the DART kinetic impact to be -33.0 +/- 1.0 (3$\sigma$) minutes. Using new Earth-based lightcurve and radar observations, two independent approaches determined identical values for the change in the orbital period. This large orbit period change suggests that ejecta contributed a significant amount of momentum to the asteroid beyond what the DART spacecraft carried., Comment: Accepted by Nature

We study repulsive two-component Bose mixtures with equal populations and confined in a finite-size box through path-integral Monte Carlo simulations. For different values of the $s$-wave scattering length of the interspecies potential, we calculate the local population imbalance in a region of fixed volume inside the box at different temperatures. We find two different behaviors: for phase-separated states at $T=0$, thermal effects induce a diffusion process which reduces the local imbalance whereas, for miscible states at $T=0$, a maximum in the local population imbalance appears at a certain temperature, below the critical one. We show that this intriguing behavior is strongly related to the bunching effect associated with the Bose-Einstein statistics of the particles in the mixture and to an unexpected behavior of the cross pair distribution function not reported before., Comment: 7 pages, 7 figures

We study a diffuse interface model describing the complex rheology and the interfacial dynamics during phase separation in a polar liquid-crystalline emulsion. More precisely, the physical systems comprises a two-phase mixture consisting in a polar liquid crystal immersed in a Newtonian fluid. Such composite material is a paradigmatic example of complex fluids arising in Soft Matter which exhibits multiscale interplay. Beyond the Ginzburg-Landau and Frank elastic energies for the concentration and the polarization, the free energy of the system is characterized by a quadratic anchoring term which tunes the orientation of the polarization at the interface. This leads to several quasi-linear nonlinear couplings in the resulting system describing the macroscopic dynamics. In this work, we establish the first mathematical results concerning the global dynamics of two-phase complex fluids with interfacial anchoring mechanism. First, we determine a set of sufficient conditions on the parameters of the system and the initial conditions which guarantee the existence of global weak solutions in two and three dimensions. Secondly, we show that weak solutions are unique and globally regular in the two dimensional case. Finally, we complement our analysis with some numerical simulations to display polarization and interfacial anchoring., Comment: 52 pages, 5 figures

We investigate the nonlocal version of the Abels-Garcke-Gr\"{u}n (AGG) system, which describes the motion of a mixture of two viscous incompressible fluids. This consists of the incompressible Navier-Stokes-Cahn-Hilliard system characterized by concentration-dependent density and viscosity, and an additional flux term due to interface diffusion. In particular, the Cahn-Hilliard dynamics of the concentration (phase-field) is governed by the aggregation/diffusion competition of the nonlocal Helmholtz free energy with singular (logarithmic) potential and constant mobility. We first prove the existence of global strong solutions in general two-dimensional bounded domains and their uniqueness when the initial datum is strictly separated from the pure phases. The key points are a novel well-posedness result of strong solutions to the nonlocal convective Cahn-Hilliard equation with singular potential and constant mobility under minimal integral assumption on the incompressible velocity field, and a new two-dimensional interpolation estimate for the $L^4(\Omega)$ control of the pressure in the stationary Stokes problem. Secondly, we show that any weak solution, whose existence was already known, is globally defined, enjoys the propagation of regularity and converges towards an equilibrium (i.e., a stationary solution) as $t\rightarrow \infty$. Furthermore, we demonstrate the uniqueness of strong solutions and their continuous dependence with respect to general (not necessarily separated) initial data in the case of matched densities and unmatched viscosities (i.e., the nonlocal model H with variable viscosity, singular potential and constant mobility). Finally, we provide a stability estimate between the strong solutions to the nonlocal AGG model and the nonlocal Model H in terms of the difference of densities.

We investigate the magnetic behavior of finite-temperature repulsive two-component Bose mixtures by means of exact path-integral Monte-Carlo simulations. Novel algorithms are implemented for the free energy and the chemical potential of the two components. Results on the magnetic susceptibility suggest that the conditions for phase separation are not modified from the zero temperature case. This contradicts previous predictions based on approximate theories. We also determine the temperature dependence of the chemical potential and the contact parameters for experimentally relevant balanced mixtures., Comment: v2: 19 pages, 10 figures, matches published version; v1: 6 pages, 5 figures plus supplemental material of 8 pages, 5 figures)

We analyze and model the stochastic behavior of paleoclimate time series and assess the implications for the coupling of climate variables during the Pleistocene glacial cycles. We examine 800 kyr of carbon dioxide, methane, nitrous oxide, and temperature proxy data from the EPICA Dome-C ice core, which are characterized by 100~kyr glacial cycles overlain by fluctuations across a wide range of time scales. We quantify this behavior through multifractal time-weighted detrended fluctuation analysis, which distinguishes near red-noise and white-noise behavior below and above the 100~kyr glacial cycle respectively in all records. This allows us to model each time series as a one-dimensional periodic non-autonomous stochastic dynamical system, and assess the stability of physical processes and the fidelity of model-simulated time series. We extend this approach to a four-variable model with linear coupling terms, which we interpret in terms of the interrelationships between the time series. Methane and nitrous oxide are found to have significant destabilizing influences, while carbon dioxide and temperature have smaller stabilizing influences. We draw conclusions about causal relationships in glacial transitions and the climate processes that may have facilitated these couplings, and highlight opportunities to further develop stochastic modeling approaches., Comment: 14 pages, 6 figures

We study an initial-boundary value problem for the incompressible Navier-Stokes-Cahn-Hilliard system with non-constant density proposed by Abels, Garcke and Gr\"{u}n in 2012. This model arises in the diffuse interface theory for binary mixtures of viscous incompressible fluids. This system is a generalization of the well-known model H in the case of fluids with unmatched densities. In three dimensions, we prove that any global weak solution (for which uniqueness is not known) exhibits a propagation of regularity in time and stabilizes towards an equilibrium state as $t \rightarrow \infty$. More precisely, the concentration function $\phi$ is a strong solution of the Cahn-Hilliard equation for (arbitrary) positive times, whereas the velocity field $\mathbf{u}$ becomes a strong solution of the momentum equation for large times. Our analysis hinges upon the following key points: a novel global regularity result (with explicit bounds) for the Cahn-Hilliard equation with divergence-free velocity belonging only to $L^2(0,\infty; \mathbf{H}^1_{0,\sigma}(\Omega))$, the energy dissipation of the system, the separation property for large times, a weak-strong uniqueness type result, and the Lojasiewicz-Simon inequality. Additionally, in two dimensions, we show the existence and uniqueness of global strong solutions for the full system. Finally, we discuss the existence of global weak solutions for the case of the double obstacle potential., Comment: 41 pages

We derive a novel thermodynamically consistent Navier--Stokes--Cahn--Hilliard system with dynamic boundary conditions. This model describes the motion of viscous incompressible binary fluids with different densities. In contrast to previous models in the literature, our new model allows for surface diffusion, a variable contact angle between the diffuse interface and the boundary, and mass transfer between bulk and surface. In particular, this transfer of material is subject to a mass conservation law including both a bulk and a surface contribution. The derivation is carried out by means of local energy dissipation laws and the Lagrange multiplier approach. Next, in the case of fluids with matched densities, we show the existence of global weak solutions in two and three dimensions as well as the uniqueness of weak solutions in two dimensions., Comment: This version contains some minor modifications compared to the journal version

We present a coordinated campaign of observations to monitor the brightness of the James Webb Space Telescope (JWST) as it travels toward the second Earth-Sun Lagrange point and unfolds using the network ofUnistellar digital telescopes. Those observations collected by citizen astronomers across the world allowed us to detect specific phases such as the separation from the booster, glare due to a change of orientation after a maneuver, the unfurling of the sunshield, and deployment of the primary mirror. After deployment of the sunshield on January 6 2022, the 6-h lightcurve has a significant amplitude and shows small variations due to the artificial rotation of the space telescope during commissionning. These variations could be due to the deployment of the primary mirror or some changes in orientation of the space telescope. This work illustrates the power of a worldwide array of small telescopes, operated by citizen astronomers, to conduct large scientific campaigns over a long timeframe. In the future, our network and others will continue to monitor JWST to detect potential degradations to the space environment by comparing the evolution of the lightcurve., Comment: 15 pages, 13 figures and 2 tables, SPIE Ground-based and Airborne Telescopes IX, AS22 SPIE Astronomical Telescopes + Instrumentation, 12182-144