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We model compact objects of known stellar mass and radius made of isotropic matter within Einstein’s gravity. The interior solution describing hydrostatic equilibrium we are using throughout the manuscript corresponds to the Tolman IV exact analytic solution obtained a long time ago. The three free parameters of the solutions are determined by imposing the matching conditions for objects of known stellar mass and radius. Finally, using well established criteria, it is shown that, contrary to the Kohler Chao solution, the Tolman IV solution is compatible with all requirements for well-behaved and realistic solutions, except for the relativistic adiabatic index that diverges at the surface of stars. The divergence of the index Γ may be resolved, including a thin crust assuming a polytropic equation of state, which is precisely the case seen in studies of neutron stars. To the best of our knowledge, we model here for the first time the recently discovered massive pulsar PSR J0740+6620 and the strangely light HESS compact object via the Tolman IV solution. The present work may be of interest to model builders as well as a useful reference for future research.

In this paper, we aim to explore novel machine learning (ML) techniques to facilitate and accelerate the construction of universal equation-Of-State (EOS) models with a high accuracy while ensuring important thermodynamic consistency. When applying ML to fit a universal EOS model, there are two key requirements: (1) a high prediction accuracy to ensure precise estimation of relevant physics properties and (2) physical interpretability to support important physics-related downstream applications. We first identify a set of fundamental challenges from the accuracy perspective, including an extremely wide range of input/output space and highly sparse training data. We demonstrate that while a neural network (NN) model may fit the EOS data well, the black-box nature makes it difficult to provide physically interpretable results, leading to weak accountability of prediction results outside the training range and lack of guarantee to meet important thermodynamic consistency constraints. To this end, we propose a principled deep regression model that can be trained following a meta-learning style to predict the desired quantities with a high accuracy using scarce training data. We further introduce a uniquely designed kernel-based regularizer for accurate uncertainty quantification. An ensemble technique is leveraged to battle model overfitting with improved prediction stability. Auto-differentiation is conducted to verify that necessary thermodynamic consistency conditions are maintained. Our evaluation results show an excellent fit of the EOS table and the predicted values are ready to use for important physics-related tasks.

The superdense hexagonal phosphides BP and AlP, whose structures are formed by distorted tetrahedra and characterized by quartz-derived (qtz) topology, were predicted from crystal chemistry and first principles as potential high-pressure phases. From full geometry structure relaxations and ground state energy calculations based on quantum density functional theory (DFT), qtz BP and AlP were found to be less cohesive than the corresponding cubic zinc-blende (zb) phases with diamond-like (dia) topology, but were confirmed to be mechanically (elastic constants) and dynamically (phonons) stable. From the energy–volume equations of state, qtz phases were found to be energetically favorable at small volumes (high pressures), with zb-to-qtz transition pressures of 144 GPa for BP and 28 GPa for AlP. According to the electronic band structures and the site projected density of states, both phosphides exhibit larger band gaps of the zinc-blende phases compared to the qtz phases; the smaller values for the latter result from the smaller volumes per formula unit, leading to increased covalence.

The last decade has seen a continued development of better experimental techniques to measure equation-of-state (EOS) for various materials. These improvements of both static and shock-compression approaches have increased the accuracy of the EOS and challenged the complimentary theoretical modeling. The conventional modeling of EOS, at least at pressure and temperature conditions that are not too extreme, is founded on density-functional theory (DFT). Naturally, there is an increased interest in the accuracy of DFT as the measurements are becoming more refined and there is a particular interest in the robustness and validity of DFT at conditions where experimental data are not available. Here, we consider a broad and large set of 64 elemental solids from low atomic number Z up to the very high Z actinide metals. The intent is to compare DFT with experimental zero-temperature isotherms up to 1 Mbar (100 GPa) and draw conclusions regarding the theoretical (DFT) error and quantify a reasonable and defensible approach to define the theoretical uncertainty. We find that in all 64 cases the DFT error at high pressure is smaller than or equal to the DFT error at lower pressures which thus provides an upper bound to the error at high compression.

As experimental measurements of thermodynamic properties have improved in accuracy, to five or six figures, over the decades, cubic equations that are widely used for modern thermodynamic fluid property data banks require ever-increasing numbers of terms with more fitted parameters. Functional forms with continuity for Gibbs density surface ρ(p,T) which accommodate a critical-point singularity are fundamentally inappropriate in the vicinity of the critical temperature (Tc) and pressure (pc) and in the supercritical density mid-range between gas- and liquid-like states. A mesophase, confined within percolation transition loci that bound the gas- and liquid-state by third-order discontinuities in derivatives of the Gibbs energy, has been identified. There is no critical-point singularity at Tc on Gibbs density surface and no continuity of gas and liquid. When appropriate functional forms are used for each state separately, we find that the mesophase pressure functions are linear. The negative and positive deviations, for both gas and liquid states, on either side of the mesophase, are accurately represented by three or four-term virial expansions. All gaseous states require only known virial coefficients, and physical constants belonging to the fluid, i.e., Boyle temperature (TB), critical temperature (Tc), critical pressure (pc) and coexisting densities of gas (ρcG) and liquid (ρcL) along the critical isotherm. A notable finding for simple fluids is that for all gaseous states below TB, the contribution of the fourth virial term is negligible within experimental uncertainty. Use may be made of a symmetry between gas and liquid states in the state function rigidity (dp/dρ)T to specify lower-order liquid-state coefficients. Preliminary results for selected isotherms and isochores are presented for the exemplary fluids, CO2, argon, water and SF6, with focus on the supercritical mesophase and critical region.