Daily Papers

We study the Cauchy problem for the one-dimensional isothermal compressible Navier--Stokes system with the van der Waals equation of state, and analyze the well-posedness and asymptotic stability of steady-state phase-transition solutions at subcritical temperatures. Working in Lagrangian coordinates, we use variational techniques to construct piecewise smooth steady-state solutions corresponding to two-phase equilibrium states under finite-mass perturbations. Introducing artificial-viscosity regularization, we first establish existence of the global minimizer of the regularized variational problem, unique within each fixed symmetry class; passing to the vanishing artificial-viscosity limit then yields a physically admissible steady-state solution with two phase interfaces. For initial perturbations that are small with respect to energy, piecewise-gradient, total-variation, and integral norms but may exhibit large pointwise jumps across phase boundaries, we derive uniform a priori bounds for weak solutions near the two-phase equilibrium profile. We further prove that these global weak solutions converge to the steady-state two-phase equilibrium in L^infty(R) as ttoinfty, thereby characterizing their large-time asymptotic behavior. Physically, finite mass perturbations break the uniqueness of the uniform steady state and generate infinitely many piecewise constant two-phase equilibria satisfying the Maxwell equal-area rule. Artificial viscosity acts as a selection principle that singles out the physically relevant two-interface steady-state configuration, and this two-phase equilibrium is asymptotically stable under small integral perturbations that allow large-amplitude discontinuities at phase interfaces.

Molecular clouds exhibit complex, multi-scale dynamics driven by the interplay of turbulence, self-gravity, and gas pressure. Modelling these systems with conventional grid-based methods becomes increasingly expensive as spatial resolution and dimensionality increase. Physics-Informed Neural Networks (PINNs) offer a mesh-free alternative by incorporating the governing equations directly into the training objective, but their ability to model realistic turbulent self-gravitating flows remains largely unexplored. We apply PINNs to isothermal molecular clouds initialized with astrophysically motivated turbulent velocity fields, considering subsonic and supersonic evolution in two and three dimensions. We benchmark the predicted density and velocity fields against the finite-volume code Athena++. PINNs accurately recover the global evolution of the flow over multiple free-fall times across turbulent realizations, Mach numbers, and dimensionalities. Their training cost also exhibits weak dependence on spatial resolution, increasing by less than 25% from 128^3 to 1024^3 in our experiments. These results demonstrate that PINNs can model substantially more realistic self-gravitating turbulent flows than previously explored and provide a promising complementary framework for studying these systems.

Macroscopic entropy production σ^{(tot)} in the general nonlinear isothermal chemical reaction system with mass action kinetics is decomposed into a free energy dissipation and a house-keeping heat: σ^{(tot)}=σ^{(fd)}+σ^{(hk)}; σ^{(fd)}=-rd A/rd t, where A is a generalized free energy function. This yields a novel nonequilibrium free energy balance equation rd A/rd t=-σ^{(tot)}+σ^{(hk)}, which is on a par with celebrated entropy balance equation rd S/rd t=σ^{(tot)}+η^{(ex)} where η^{(ex)} is the rate of entropy exchange with the environment.For kinetic systems with complex balance, σ^{(fd)} and σ^{(hk)} are the macroscopic limits of stochastic free energy dissipation and house-keeping heat, which are both nonnegative, in the Delbrück-Gillespie description of the stochastic chemical kinetics.Therefore, we show that a full kinetic and thermodynamic theory of chemical reaction systems that transcends mesoscopic and macroscopic levels emerges.

In this work, we introduce a novel approach for predicting thermodynamic properties of binary mixtures, which we call the similarity-based method (SBM). The method is based on quantifying the pairwise similarity of components, which we achieve by comparing quantum-chemical descriptors of the components, namely σ-profiles. The basic idea behind the approach is that mixtures with similar pairs of components will have similar thermodynamic properties. The SBM is trained on a matrix that contains some data for a given property for different binary mixtures; the missing entries are then predicted by the SBM. As an example, we consider the prediction of isothermal activity coefficients at infinite dilution (γ^infty_{ij}) and show that the SBM outperforms the well-established physical methods modified UNIFAC (Dortmund) and COSMO-SAC-dsp. In this case, the matrix is only sparsely occupied, and it is shown that the SBM works also if only a limited number of data for similar mixtures is available. The SBM idea can be transferred to any mixture property and is a powerful tool for generating essential data for many applications.

Machine learning is now used in many areas of astrophysics, from detecting exoplanets in Kepler transit signals to removing telescope systematics. Recent work demonstrated the potential of using machine learning algorithms for atmospheric retrieval by implementing a random forest to perform retrievals in seconds that are consistent with the traditional, computationally-expensive nested-sampling retrieval method. We expand upon their approach by presenting a new machine learning model, plan-net, based on an ensemble of Bayesian neural networks that yields more accurate inferences than the random forest for the same data set of synthetic transmission spectra. We demonstrate that an ensemble provides greater accuracy and more robust uncertainties than a single model. In addition to being the first to use Bayesian neural networks for atmospheric retrieval, we also introduce a new loss function for Bayesian neural networks that learns correlations between the model outputs. Importantly, we show that designing machine learning models to explicitly incorporate domain-specific knowledge both improves performance and provides additional insight by inferring the covariance of the retrieved atmospheric parameters. We apply plan-net to the Hubble Space Telescope Wide Field Camera 3 transmission spectrum for WASP-12b and retrieve an isothermal temperature and water abundance consistent with the literature. We highlight that our method is flexible and can be expanded to higher-resolution spectra and a larger number of atmospheric parameters.

The presence of thermal gradients in alloys often leads to non-uniformity in concentration profiles, which can induce the thermomigration of microstructural features such as precipitates. To investigate such microstructural changes, we present a phase-field model that incorporates coupling between concentration and thermal gradients. First, we simulated the evolution of non-uniform concentration profiles in the single-phase regions of Fe-C and Fe-N alloy systems due to imposed thermal gradients. To validate our model with the classical experiments performed by Darken and Oriani, we studied the evolution of spatially varying concentration profiles where thermal gradients encompass single-phase and two-phase regions. We developed a parameterized thermodynamic description of the two-phase region of a binary alloy to systematically study the effect of interactions between chemically-driven and thermal gradient-driven diffusion of solute on the evolution of precipitates. Our simulations show how thermal gradient, precipitate size, and interparticle distance influence the migration and associated morphological changes of precipitates. The composition profiles and migration rates obtained from single-particle simulations show an exact match with our analytical model. We use twoparticle simulations to show conditions under which thermomigration induces the growth of the smaller particle and shrinkage of the larger one in contrast to the isothermal Ostwald ripening behavior. Our multiparticle simulations show similar behavior during coarsening. Moreover, in the presence of a thermal gradient, there is a shift in the center of mass of the precipitates towards the high-temperature region. Thus, our study offers new insights into the phenomena of microstructure evolution in the presence of thermal gradient.

We present the first high-precision model for the group-scale strong lensing system CASSOWARY 19 (CSWA19), utilising images from the Hubble Space Telescope (HST). Sixteen member galaxies identified via the red-sequence method, and the main halo, all modelled as the dual Pseudo Isothermal Elliptical profile (dPIE), are incorporated into a parametric lens model alongside an external shear field. To model the system, we adopt the PyAutoLens software package, employing a progressive search chain strategy for realizing the transition of source model from multiple S\'ersic profiles to a brightness-adaptive pixelization, which uses 1000 pixels in the source plane to reconstruct the background source corresponding to 177,144 image pixels in the image plane. Our results indicate that the total mass within the Einstein radius is M_{theta_E} approx 1.41times10^{13}M_{odot} and the average slope of the total mass density rho (r)propto r^{-gamma} is gamma=1.33 within the effective radius. This slope is shallower than those measured in galaxies and groups but is closer to those of galaxy clusters. In addition, our approach successfully resolves the two merging galaxies in the background source and yields a total magnification of mu=103.18^{+0.23}_{-0.19}, which is significantly higher than the outcomes from previous studies of CSWA19. In summary, our research demonstrates the effectiveness of the brightness-adaptive pixelization source reconstruction technique for modelling group-scale strong lensing systems. It can serve as a technical reference for future investigations into pixel-level modelling of the group- and cluster-scale strong lensing systems.

A scuba diver holding constant depth balances on an unstable equilibrium: the gas carried in the suit and buoyancy compensator compresses with depth, so the buoyant force falls as the diver sinks and rises as the diver ascends. We represent the diver as a proportional-derivative controller that regulates this compressible-buoyancy saddle after a finite reaction delay, and we derive the governing delay differential equation from the vertical force balance and the isothermal gas law, reducing it to a damping ratio, two control gains, and a dimensionless delay. The characteristic spectrum, obtained by pseudospectral collocation of the semigroup generator and checked against a direct Newton solution of the characteristic equation, locates the Hopf boundary that separates stable hovering from sustained porpoising; for the baseline diver the critical reaction delay is 3.36 s and the onset period is 28.8 s. The bifurcation is supercritical, and because the saturating force is the quadratic hydrodynamic drag, the limit-cycle amplitude grows in proportion to the delay excess rather than as its square root. The safe-operating envelope shows that runaway ascent is triggered by saturation of the compensator, not by loss of linear stability, so a stable and an unstable diver can share the same escape threshold. As onset is approached, the lag-one autocorrelation and variance rise while the fitted recovery rate falls and matches the spectral abscissa, giving an eigenvalue-exact early warning of the transition.