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The interior of a neutron star is a unique astrophysical laboratory for studying matter at extreme densities and pressures beyond what is replicable in terrestrial experiments. While there is no direct way to simulate the interior of these stars, one promising avenue to learning more about the equation of state (EOS) of such matter is through X‐rays emitted from the star's surface. The current state‐of‐the‐art method for inference of EOS from a star's X‐ray spectra uses piece‐wise, simulation‐based likelihoods that rely on theoretical assumptions complicated by systematic uncertainties. To reduce the dimensionality of the problem, this method infers macroscopic properties of the star (mass and radius) from emitted X‐ray spectra, and from those quantities infers the EOS. This work approaches the same problem using machine learning techniques, demonstrating a series of enhancements to the current state‐of‐the‐art by realistic uncertainty quantification and reducing the need for theoretical assumptions. We also demonstrate novel inference of the EOS directly from high‐dimensional simulated X‐ray spectra from neutron stars that negate the need for a piece‐wise approach. This inference allows for a natural propagation of uncertainties from the X‐ray spectra by conditioning the discussed networks on realistic sources of uncertainty for each star. [ABSTRACT FROM AUTHOR]

Molecular dynamics (MD) simulations are used in biochemistry, physics, and other fields to study the motions, thermodynamic properties, and the interactions between molecules. Computational limitations and the complexity of these problems, however, create the need for approximations to the standard MD methods and for uncertainty quantification and reliability assessment of those approximations. In this paper, we exploit the intrinsic two-scale nature ofMDto construct a class of large-scale dynamics approximations. The reliability of these methods is evaluated here by measuring the differences between full, classical MD simulations and those based on these large-scale approximations. Molecular dynamics evolutions are non-linear and chaotic, so the complete details of molecular evolutions cannot be accurately predicted even using full, classical MD simulations. This paper provides numerical results that demonstrate the existence of computationally efficient large-scale MD approximations which accurately model certain large-scale properties of the molecules: the energy, the linear and angular momenta, and other macroscopic features of molecular motions. [ABSTRACT FROM AUTHOR]

Scalar, vector and tensor harmonics on the three-sphere were introduced originally to facilitate the study of various problems in gravitational physics. These harmonics are defined as eigenfunctions of the covariant Laplace operator which satisfy certain divergence and trace identities, and ortho-normality conditions. This paper provides a summary of these properties, along with a new notation that simplifies and clarifies some of the key expressions. Practical methods are described for accurately and efficiently computing these harmonics numerically, and test results are given that illustrate how well the analytical identities are satisfied by the harmonics computed numerically in this way. [ABSTRACT FROM AUTHOR]

A simple method is proposed for improving the accuracy of WKB eigenvalues by using the WKB eigenfunctions as trial functions in a variational-principle expression for the eigenvalues. The first-order eigenvalues obtained from this estimate are shown to differ from the exact values by terms of order ε6 (where ε is an appropriately defined small parameter that specifies the accuracy of the WKB approximation). For comparison, the fifth-order WKB eigenvalues also differ from the exact values by terms of order ε6. Higher-order variational eigenvalues are also defined, and the third-order estimate is shown to differ from the exact by terms of order ε10. The accuracy of these variational and WKB estimates are illustrated with a numerical example. [ABSTRACT FROM AUTHOR]

In this paper the uniqueness of the static solutions of Einstein’s equation that represent isolated uniform-density perfect-fluid stellar models is demonstrated: any static asymptotically flat space-time containing only a uniform-density perfect fluid confined to a spatially compact world tube is necessarily spherically symmetric. This result generalizes to relativistic uniform-density models the well known Newtonian theorem of Carleman and Lichtenstein. [ABSTRACT FROM AUTHOR]

Two senses in which the perturbation equations of general relativity can be misleading are explored. (i) Under certain circumstances there exist solutions of the perturbation equations that appear to be gauge, in that the metric perturbation is the symmetrized derivative of a vector field, but which nonetheless are not true gauge. (ii) Under certain circumstances there exist solutions of the perturbation equations that cannot, even locally, be extended to higher order in perturbation theory. The latter is a local version of the well-known phenomenon of "linearization instability. [ABSTRACT FROM AUTHOR]