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At least 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Filling the black hole mass gap: Avoiding pair instability in massive stars through addition of nonnuclear energy

In standard stellar evolution, stars with masses ranging from approximately 150 to 240M ⊙ are expected to evolve to a pair instability supernova with no black hole (BH) remnant. This evolutionary behavior leads to a predicted gap in the black hole mass function from approximately 50 to 140M ⊙ . Yet the LIGO and Virgo Collaborations recently discovered black holes of masses 66M ⊙ and 85M ⊙ in the gravitational wave event GW190521. Here, we propose a new method to populate the BH mass gap. If an energy source is added throughout the star in addition to nuclear fusion, it is possible for the altered evolution to avoid the complete destruction of a pair instability supernova, and instead a BH remnant is left behind. An example of an extra energy source is dark matter annihilation within the star, but our results hold more generally. We show this phenomenon by exploring the effect of adding an energy source independent of temperature and density to a 180M ⊙ star, using the MESA one-dimensional stellar evolution software. If ~50% of the star’s energy is due to this new source, the star is capable of avoiding the pair instability entirely and evolving towards a core-collapse supernova and ultimately a BH remnant with mass ~ 120M ⊙ .

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Generalized moving least squares vs. radial basis function finite difference methods for approximating surface derivatives

Approximating differential operators defined on two-dimensional surfaces is an important problem that arises in many areas of science and engineering. Over the past ten years, localized meshfree methods based on generalized moving least squares (GMLS) and radial basis function finite differences (RBF-FD) have been shown to be effective for this task as they can give high orders of accuracy at low computational cost, and they can be applied to surfaces defined only by point clouds. However, there have yet to be any studies that perform a direct comparison of these methods for approximating surface differential operators (SDOs). The first purpose of this work is to fill that gap. For this comparison, we focus on an RBF-FD method based on polyharmonic spline kernels and polynomials (PHS+Poly) since they are most closely related to the GMLS method. Additionally, we use a relatively new technique for approximating SDOs with RBF-FD called the tangent plane method since it is simpler than previous techniques and natural to use with PHS+Poly RBF-FD. Further, the second purpose of this work is to relate the tangent plane formulation of SDOs to the local coordinate formulation used in GMLS and to show that they are equivalent when the tangent space to the surface is known exactly. The final purpose is to use ideas from the GMLS SDO formulation to derive a new RBF-FD method for approximating the tangent space for a point cloud surface when it is unknown. For the numerical comparisons of the methods, we examine their convergence rates for approximating the surface gradient, divergence, and Laplacian as the point clouds are refined for various parameter choices. We also compare their efficiency in terms of accuracy per computational cost, both when including and excluding setup costs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Calibration of photoelastic modulator based dichrometers: maintaining constant phase across the spectrum

Photoelastic modulators can alter the polarization state of a beam of ultraviolet, visible or infrared photons by means of periodic stress-induced differences in the refractive index of a transparent material that forms the optical element of the device and is isotropic in the absence of stress. Furthermore, they have found widespread application in instruments that characterize or alter the polarization state of a beam in fields as diverse as astronomy, structural biology, materials science and ultraviolet lithography for the manufacture of nano-scale integrated circuits. Measurement of circular dichroism, the differential absorption of left- and right circularly polarized light, and of strain-induced birefringence of optical components are major applications. Instruments using synchrotron radiation and photoelastic modulators with CaF 2 optical elements have extended circular dichroism measurements down to wavelengths of about 130 nm in the vacuum ultraviolet. Maintaining a constant phase shift between two orthogonal polarization states across a spectrum requires that the amplitude of the modulated stress be changed as a function of wavelength. For commercially available photoelastic modulators, the voltage that controls the amplitude of modulation required to produce a specified phase shift, which is a surrogate for the stress modulation amplitude, has been shown to be an approximately linear function of wavelength in the spectral region where the optical element is transparent. But, extrapolations of such straight lines cross zero voltage at a non-zero wavelength, not at zero-wavelength. For modulators with calcium fluoride and fused silica optical elements, the zero-crossing wavelength is always in the spectral region where the optical element of the modulator strongly absorbs the incident radiation, and at a wavelength less than the longest-wavelength apparent resonance deduced from experimental values of the refractive index fit to the Sellmeier equation. Using a model that relates the refractive indices of a stressed optical element to the refractive index of its unstressed state, an expression for the modulator control voltage was derived that closely fits the experimental data. Our result provides a theoretical rational for the apparently linear constant-phase programming voltage, and thus provides theoretical backing for the calibration procedure frequently used for these modulators. Lastly there are other factors that can influence the calibration of a photoelastic modulator, including temperature and atmospheric pressure, are discussed briefly.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2016

Tight-binding approximations to time-dependent density functional theory — A fast approach for the calculation of electronically excited states

We propose a new method of calculating electronically excited states that combines a density functional theory based ground state calculation with a linear response treatment that employs approximations used in the time-dependent density functional based tight binding (TD-DFTB) approach. The new method termed time-dependent density functional theory TD-DFT+TB does not rely on the DFTB parametrization and is therefore applicable to systems involving all combinations of elements. We show that the new method yields UV/Vis absorption spectra that are in excellent agreement with computationally much more expensive TD-DFT calculations. Errors in vertical excitation energies are reduced by a factor of two compared to TD-DFTB.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Weighted nodal domain averages of eigenstates for quantum Monte Carlo and beyond

In this report we study the nodal properties of many-body eigenstates of stationary Schrödinger equation that affect the accuracy of real-space quantum Monte Carlo calculations. In particular, we introduce weighted nodal domain averages that provide a new probe of nodal surfaces beyond the usual expectations. Particular choices for the weight function reveal, for example, that the difference between two arbitrary fermionic eigenvalues is given by the nodal hypersurface integrals normalized by overlaps with the bosonic ground state of the given Hamiltonian. Noninteracting and fully interacting Be atom with corresponding almost exact and approximate wave functions are used to illustrate several aspects of these concepts. Variational formulations that employ different weights are proposed for prospective improvement of nodes in variational and fixed-node diffusion Monte Carlo calculations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

On the minimum number of radiation field parameters to specify gas cooling and heating functions

Fast and accurate approximations of gas cooling and heating functions are needed for hydrodynamic galaxy simulations. We use machine learning to analyze atomic gas cooling and heating functions in the presence of a generalized incident local radiation field computed by Cloudy. We characterize the radiation field through binned radiation field intensities instead of the photoionization rates used in our previous work. We find a set of 6 energy bins whose intensities exhibit relatively low correlation. We use these bins as features to train machine learning models to predict Cloudy cooling and heating functions at fixed metallicity. We compare the relative SHapley Additive exPlanation (SHAP) value importance of the features. From the SHAP analysis, we identify a feature subset of 3 energy bins (0.5-1, 1-4, and 13-16Ry) with the largest importance and train additional models on this subset. We compare the mean squared errors and distribution of errors on both the entire training data table and a randomly selected 20% test set withheld from model training. The machine learning models trained with 3 and 6 bins, as well as 3 and 4 photoionization rates, have comparable accuracy everywhere, with errors ≳10 times smaller than for the interpolation table of Gnedin and Hollon (2012). We conclude that 3 energy bins (or 3 analogous photoionization rates: molecular hydrogen photodissociation, neutral hydrogen HI, and fully ionized carbon CVI) are sufficient to characterize the dependence of the gas cooling and heating functions on our assumed incident radiation field model.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

On the minimum number of radiation field parameters to specify gas cooling and heating functions

Fast and accurate approximations of gas cooling and heating functions are needed for hydrodynamic galaxy simulations. We use machine learning to analyze atomic gas cooling and heating functions computed by Cloudy in the presence of a generalized incident local radiation field. We characterize the radiation field through binned radiation field intensities instead of the photoionization rates used in our previous work. We find a set of 6 energy bins whose intensities exhibit relatively low correlation. We use these bins as features to train machine learning models to predict Cloudy cooling and heating functions at fixed metallicity. We compare the relative SHapley Additive exPlanation (SHAP) value importance of the features. From the SHAP analysis, we identify a feature subset of 3 energy bins ($0.5-1, 1-4$, and $13-16 \, \mathrm{Ry}$) with the largest importance and train additional models on this subset. We compare the mean squared errors and distribution of errors on both the entire training data table and a randomly selected 20% test set withheld from model training. The machine learning models trained with 3 and 6 bins, as well as 3 and 4 photoionization rates, have comparable accuracy everywhere, with errors $\gtrsim 10$ times smaller than for the interpolation table of Gnedin and Hollon (2012). We conclude that 3 energy bins (or 3 analogous photoionization rates: molecular hydrogen photodissociation, neutral hydrogen HI, and fully ionized carbon CVI) are sufficient to characterize the dependence of the gas cooling and heating functions on our assumed incident radiation field model.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Accurate frozen core approximation for all-electron density-functional theory

We implement and benchmark the frozen core approximation, a technique commonly adopted in electronic structure theory to reduce the computational cost by means of mathematically fixing the chemically inactive core electron states. The accuracy and efficiency of this approach are well controlled by a single parameter, the number of frozen orbitals. Explicit corrections for the frozen core orbitals and the unfrozen valence orbitals are introduced, safeguarding against seemingly minor numerical deviations from the assumed orthonormality conditions of the basis functions. A speedup of over twofold can be achieved for the diagonalization step in all-electron density-functional theory simulations containing heavy elements, without any accuracy degradation in terms of the electron density, total energy, and atomic forces. This is demonstrated in a benchmark study covering 103 materials across the Periodic Table and a large-scale simulation of CsPbBr3 with 2560 atoms. Our study provides a rigorous benchmark of the precision of the frozen core approximation (sub-meV per atom for frozen core orbitals below −200 eV) for a wide range of test cases and for chemical elements ranging from Li to Po. The algorithms discussed here are implemented in the open-source Electronic Structure Infrastructure software package.

Yu, Victor Wen-zhe↗
DOE OSTI2023

Imposing correct jellium response is key to predict the density response by orbital-free DFT

Orbital-free density functional theory constitutes a computationally highly effective tool for modeling electronic structures of systems ranging from room-temperature materials to warm dense matter. Its accuracy critically depends on the employed kinetic energy (KE) density functional, which has to be supplied as an external input. In this work we consider several nonlocal and Laplacian-level KE functionals and use an external harmonic perturbation to compute the static density response at T = 0 K in the linear and beyond-linear response regimes. We test for the satisfaction of exact conditions in the limit of uniform densities and for how approximate KE functionals reproduce the density response of realistic materials (e.g., Al and Si) against the Kohn-Sham DFT reference, which employs the exact KE. The results illustrate that several functionals violate exact conditions in the uniform electron gas (UEG) limit. We find a strong correlation between the accuracy of the KE functionals in the UEG limit and in the strongly inhomogeneous case. This empirically demonstrates the importance of imposing the limit of UEG response for uniform densities and validates the use of the Lindhard function in the formulation of kernels for nonlocal functionals. This conclusion is substantiated by additional calculations for bulk aluminum (Al) with a face-centered cubic (fcc) lattice and silicon (Si) with an fcc lattice, body-centered cubic (bcc) lattice, and semiconducting crystal diamond state. The analysis of fcc Al, and fcc as well as bcc Si data follows closely the conclusions drawn for the UEG, allowing us to extend our conclusions to realistic systems that are subject to density inhomogeneities induced by ions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Noise effects on Padé approximants and conformal maps

Here, we analyze the properties of Padé and conformal map approximants for functions with branch points, in the situation where the expansion coefficients are only known with finite precision or are subject to noise. We prove that there is a universal scaling relation between the strength of the noise and the expansion order at which Padé or the conformal map breaks down. We illustrate this behavior with some physically relevant model test functions and with two non-trivial physical examples where the relevant Riemann surface has complicated structure.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Kohn-Sham Density Functional Theory with Complex, Spin-Restricted Orbitals: Accessing a New Class of Densities without the Symmetry Dilemma

Here, we show that using complex, spin-restricted orbitals in Kohn-Sham (KS) density functional theory allows one to access a new class of densities that is not accessible by either spin-restricted (RKS) or spin-unrestricted (UKS) orbitals. We further show that the real part of a complex RKS (CRKS) density matrix can be nonidempotent when the imaginary part of the density matrix is not zero. Using CRKS orbitals shows significant improvements in the triplet-singlet gaps of a benchmark set, called TS12, for well-established, widely used density functionals. Moreover, it was shown that RKS and UKS yield qualitatively wrong charge densities and spin densities, respectively, leading to worse energetics. We demonstrate that representative modern density functionals show surprisingly no improvement even with a qualitatively more accurate density from CRKS orbitals. To this end, our work not only provides a way to escape the symmetry dilemma whenever there exists a CRKS solution, but also suggests a new route to design better approximate density functionals.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2021

Stability Functions in the Stable Surface Layer Derived from the Mellor–Yamada–Nakanishi–Niino (MYNN) Scheme

It is desirable that a surface layer scheme in an atmospheric numerical model is consistent with an atmospheric boundary layer scheme incorporated in the same model. In this study, stability functions based on Monin–Obukhov similarity theory for momentum and heat, φ m and φ h , in the stable surface layer are derived from the Mellor–Yamada–Nakanishi–Niino (MYNN) scheme. The resulting stability functions are approximated by φ m = 1 + 4.8z/L and φ h = 0.74 + 6.0z/L, which can be analytically integrated with respect to height z to obtain momentum and heat fluxes, where L is the Obukhov length. The fluxes thus, obtained are compared with those acquired from stability functions in four previous studies: they are nearly the same as those from two of them, and show better agreement with observational data of the Surface Heat Budget of the Arctic Ocean experiment (SHEBA) over sea ice than those from the other two studies. Detailed comparisons of the results of the MYNN scheme with the SHEBA data suggest that significant variations of the fluxes observed during “winter” when the ice was covered with dry snow may have been caused by those of the surface roughness around the observational site. The stability functions obtained from the MYNN scheme predict that the bulk and flux Richardson numbers approach critical values of 0.26 and 0.21, respectively, in the limit of z/L → ∞. These critical values result from the Kolmogorov hypothesis applied to the turbulent dissipation in the MYNN scheme and are considered to correspond to a transition from Kolmogorov to non-Kolmogorov turbulence.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

Automated Mapping of a Plane Curvilinear Contour by a Smooth Set of Arcs in Rotary and Deep Extrusion

The use of smooth continuous approximating curves consisting of arcs of circles to solve production problems is considered. A relatively simple and efficient recurrent algorithm is developed for use with Kompas-3D, MS Excel, and other software. The algorithm is based on the property of the bisector of a triangle. An analytical form of the approximating curve is determined. A real-time graphic interactive interface in Kompas-3D software is derived. Some irregular mapping situations are described. Practical results are outlined.

42 ENGINEERING↗
DOE OSTI2021

A MIMO AAA Agorithm for Frequency Dependent Line Modeling

Modeling of power distribution system components that are valid for a wide range of frequencies are crucial for highly accurate modeling of electromagnetic transient (EMT) events. This has recently become of interest due to the improvements needed for the resilient operation of distribution systems. Vector fitting (VF) is a very popular and commonly used algorithm for wide band representations of power system components in EMT simulations. In this research, we present a new multi-input rational approximation algorithm (MIAAA) and illustrate its advantages with respect to VF using examples of approximations of admittance matrices discussed in the literature. We show that MIAAA not only outperforms VF in terms of achieving better accuracy using lesser number of poles, but also has no numerical issues achieving convergence. In contrast to VF, MIAAA is not sensitive to the location of input sample points and it does not require good estimates for the location of the desired approximation poles. The novelty of this research work is the use of recent mathematical results to solve existing challenges in distribution system modeling and to develop rational approximations for power system models that intend to be optimal in terms of accuracy and performance.

AAA algorithm↗
DOE OSTI2021

A fast particle-mesh simulation of non-linear cosmological structure formation with massive neutrinos

Quasi-N-body simulations, such as FastPM, provide a fast way to simulate cosmological structure formation, but have yet to adequately include the effects of massive neutrinos. In this work, we present a method to include neutrino particles in FastPM, enabling computation of the CDM and total matter power spectra to percent-level accuracy in the non-linear regime. The CDM-neutrino cross-power can also be computed at a sufficient accuracy to constrain cosmological observables. To avoid the shot noise that typically plagues neutrino particle simulations, we employ a quasi-random algorithm to sample the relevant Fermi-Dirac distribution when setting the initial neutrino thermal velocities. We additionally develop an effective distribution function to describe a set of non-degenerate neutrinos as a single particle to speed up non-degenerate simulations. The simulation is accurate for the full range of physical interest, M ν ≲ 0.6eV, and applicable to redshifts z ≲ 2. Such accuracy can be achieved by initializing particles with the two-fluid approximation transfer functions (using the REPS package). Convergence can be reached in ~ 25 steps, with a starting redshift of z=99. Probing progressively smaller scales only requires an increase in the number of CDM particles being simulated, while the number of neutrino particles can remain fixed at a value less than or similar to the number of CDM particles. In turn, the percentage increase in runtime-per-step due to neutrino particles is between ~ 5-20% for runs with 1024 3 CDM particles, and decreases as the number of CDM particles is increased. The code has been made publicly available, providing an invaluable resource to produce fast predictions for cosmological surveys and studying reconstruction.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Predicting Mössbauer Parameters of Nonheme Diiron Complexes with Density Functional Theory

Mössbauer spectroscopy provides significant insights into the electronic structure and environment of the metal centers. In this work, we investigate the electronic structures of a set of nonheme diiron complexes by evaluating two key parameters pertaining to Mössbauer spectroscopy, namely, the isomer shift (δ) and quadrupole splitting (|ΔE Q |), using different levels of density functional theory (DFT). The diiron systems investigated here span diverse oxidation states, bridging motifs, and spin coupling patterns, which present a challenging case for theoretical predictions. We demonstrate that the combination of B97-D3/def2-TZVP is an efficient approach in modeling both the δ and |ΔEQ| values with high accuracy for the representative nonheme diiron complexes. We also show that δ is accurately predicted irrespective of the choice of approximate density functional while the |ΔE Q | is sensitive to the level of theory employed. Further investigation shows that the present methodology assessed using synthetic nonheme diiron complexes could be extended to nonheme diiron enzyme active sites, featuring both ferromagnetic and antiferromagnetic coupling between the iron centers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Electronic and optical properties of titanium nitride bulk and surfaces from first principles calculations

Prediction of the frequency-dependent dielectric function of thin films poses computational challenges, and at the same time experimental characterization by spectroscopic ellipsometry remains difficult to interpret because of changes in stoichiometry and surface morphology, temperature, thickness of the film, or substrate. In this work, we report calculations for titanium nitride (TiN), a promising material for plasmonic applications because of less loss and other practical advantages compared to noble metals. We investigated structural, electronic, and optical properties of stoichiometric bulk TiN, as well as of the TiN(100), TiN(110), and TiN(111) outermost surfaces. Density functional theory (DFT) and many-body GW methods (Green's (G) function-based approximation with screened Coulomb interaction (W)) were used, ranging from G{sub 0}W{sub 0}, GW{sub 0} to partially self-consistent sc-GW{sub 0}, as well as the GW-BSE (Bethe-Salpeter equation) and time-dependent DFT (TDDFT) methods for prediction of the optical properties. Structural parameters and the band structure for bulk TiN were shown to be consistent with previous work. Calculated dielectric functions, plasma frequencies, reflectivity, and the electron energy loss spectrum demonstrated consistency with experiment at the GW{sub 0}-BSE level. Deviations from experimental data are expected due to varying experimental conditions. Comparison of our results to spectroscopic ellipsometry data for realistic nanostructures has shown that although TDDFT may provide a computationally feasible level of theory in evaluation of the dielectric function, application is subject to validation with GW-BSE calculations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

NENCI-2021. I. A large benchmark database of non-equilibrium non-covalent interactions emphasizing close intermolecular contacts

In this work, we present NENCI-2021, a benchmark database of ~8000 Non-Equilibirum Non-Covalent Interaction energies for a large and diverse selection of intermolecular complexes of biological and chemical relevance. To meet the growing demand for large and high-quality quantum mechanical data in the chemical sciences, NENCI-2021 starts with the 101 molecular dimers in the widely used S66 and S101 databases and extends the scope of these works by (i) including 40 cation–π and anion–π complexes, a fundamentally important class of non-covalent interactions that are found throughout nature and pose a substantial challenge to theory, and (ii) systematically sampling all 141 intermolecular potential energy surfaces (PESs) by simultaneously varying the intermolecular distance and intermolecular angle in each dimer. Designed with an emphasis on close contacts, the complexes in NENCI-2021 were generated by sampling seven intermolecular distances along each PES (ranging from 0.7× to 1.1× the equilibrium separation) and nine intermolecular angles per distance (five for each ion–π complex), yielding an extensive database of 7763 benchmark intermolecular interaction energies (E int ) obtained at the coupled-cluster with singles, doubles, and perturbative triples/complete basis set [CCSD(T)/CBS] level of theory. The E int values in NENCI-2021 span a total of 225.3 kcal/mol, ranging from -38.5 to +186.8 kcal/mol, with a mean (median) E int value of -1.06 kcal/mol (-2.39 kcal/mol). In addition, a wide range of intermolecular atom-pair distances are also present in NENCI-2021, where close intermolecular contacts involving atoms that are located within the so-called van der Waals envelope are prevalent—these interactions, in particular, pose an enormous challenge for molecular modeling and are observed in many important chemical and biological systems. A detailed symmetry-adapted perturbation theory (SAPT)- based energy decomposition analysis also confirms the diverse and comprehensive nature of the intermolecular binding motifs present in NENCI-2021, which now includes a significant number of primarily induction-bound dimers (e.g., cation–π complexes). NENCI-2021 thus spans all regions of the SAPT ternary diagram, thereby warranting a new four-category classification scheme that includes complexes primarily bound by electrostatics (3499), induction (700), dispersion (1372), or mixtures thereof (2192). A critical error analysis performed on a representative set of intermolecular complexes in NENCI-2021 demonstrates that the E int values provided herein have an average error of ±0.1 kcal/mol, even for complexes with strongly repulsive E int values, and maximum errors of ±0.2–0.3 kcal/mol (i.e., ~±1.0 kJ/mol) for the most challenging cases. For these reasons, we expect that NENCI-2021 will play an important role in the testing, training, and development of next-generation classical and polarizable force fields, density functional theory approximations, wavefunction theory methods, and machine learning based intra- and inter-molecular potentials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗