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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 559 records · Page 31
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Linearized frequency domain Landau-Lifshitz-Gilbert equation formulation

We present a general finite element linearized Landau-Lifshitz-Gilbert equation (LLGE) solver for magnetic systems under weak time-harmonic excitation field. The linearized LLGE is obtained by assuming a small deviation around the equilibrium state of the magnetic system. Inserting such expansion into LLGE and keeping only first order terms gives the linearized LLGE, which gives a frequency domain solution for the complex magnetization amplitudes under an external time-harmonic applied field of a given frequency. We solve the linear system with an iterative solver using generalized minimal residual method. We construct a preconditioner matrix to effectively solve the linear system. The validity, effectiveness, speed, and scalability of the linear solver are demonstrated via numerical examples.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Sparse adaptive basis set methods for solution of the time dependent Schrodinger equation

Scalable numerical solutions to the time dependent Schrodinger equation remain an outstanding goal in theoretical chemistry. Here we present a method which utilises recent breakthroughs in signal processing to consistently adapt a dictionary of basis functions to the dynamics of the system. Further, we show that for two low-dimensional model problems the size of the basis set does not grow quickly with time and appears only weakly dependent on dimensionality. The generality of this finding remains to be seen. The method primarily uses energies and gradients of the potential, opening the possibility for its use in on-the-fly ab initio quantum wavepacket dynamics.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2022

Introduction of the Adding and Doubling Method for Solving Bateman Equations for Nuclear Fuel Depletion

This paper introduces and evaluates the Adding and Doubling Method (ADM) for solving the Bateman equations for depletion systems with varying numbers of nuclides and compares it to the Chebyshev Rational Approximation Method (CRAM), both implemented in the reactor physics analysis application Griffin. ADM, when applied to the Crank-Nicolson Finite Difference method, can produce results comparable in accuracy and precision to CRAM with comparable run times for systems with 35 or 297 nuclides. For systems with more than 300 nuclides, the matrix-matrix operations required by ADM are significantly more costly than the matrix-vector operations required by CRAM, making CRAM the more efficient method for systems with large numbers of nuclides. ADM is an accurate method that maintains other advantages over CRAM in that it does not depend on pre-generated coefficients or require complex number operations. ADM also manages to outperform CRAM by a factor of more than 250 in terms of run time for depletion systems that require multiple Bateman solves while the depletion matrix and time step size remain constant over all depletion intervals.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

A physics-constrained neural ordinary differential equations approach for robust learning of stiff chemical kinetics

The high computational cost associated with solving for detailed chemistry poses a significant challenge for predictive computational fluid dynamics (CFD) simulations of turbulent reacting flows. While deep learning techniques have been explored to develop faster surrogate models, they often fail to integrate reliably with CFD solvers. This instability arises because traditional deep learning approaches optimize for training error without ensuring compatibility with ordinary differential equation (ODE) solvers, resulting in accumulation of errors over time. Recently, neuralODE (NODE) based approaches have been shown to be a promising technique to emulate and accelerate detailed chemistry computations. Here, in the present work, we extend this NODE framework for stiff chemical kinetics by incorporating mass conservation constraints directly into the loss function during training. This ensures that the total mass as well as the individual elemental species masses are conserved in an a-posteriori manner. Proof-of-concept studies are performed with the novel physics-constrained NODE (PC-NODE) approach for homogeneous autoignition of hydrogen-air mixture over a range of composition and thermodynamic conditions. It is demonstrated that the PC-NODE framework not only improves the physical consistency of the resulting data-driven model with respect to mass conservation criteria, but also improves training efficiency. PC-NODE is shown to achieve 2–100× speedup relative to the hydrogen-air detailed chemical mechanism depending on the type of the ODE solver (implicit or explicit) used during autoregressive inference tests. Lastly, a-posteriori studies are performed wherein the trained PC-NODE model is coupled with a CFD solver. It is shown that higher accuracy is achieved with PC-NODE relative to the purely data-driven NODE approach. Moreover, PC-NODE also exhibits robustness and generalizability to unseen initial conditions from within (interpolative capability) as well as outside (extrapolative capability) the training regime.

computational combustion↗
DOE OSTI2020

The Dirac equation as a model of topological insulators

The Dirac equation with a spatially dependent mass can be used as a simple, exactly soluble, continuum model of a three-dimensional Topological Insulator. For a bulk system, the sign of the mass determines the parity at the only time-reversal point ( k _ = 0 ) and, thus, leads to the designation of the bulk as being topologically trivial or non-trivial. Since the mass changes sign at the interface between a topologically trivial and non-trivial materials, topological surface states appear on that boundary. We present that electron scattering experiments may provide an alternate probe of the topological character of the surface states. For infinitely thick slabs, the states on the opposite sides of the slab decouple. The spatial decoupling results in the surface states become gapless, non-degenerate and, due to the Rashba spin–orbit coupling generated by the loss of inversion symmetry, exhibit spin-momentum locking. We review several characteristic properties of the topological surface states which are dependent on the topological quantum numbers and show that, using this model, they can be calculated exactly using simple approaches.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Theoretical and numerical studies of inverse source problem for the linear parabolic equation with sparse boundary measurements

We consider the inverse source problem in the parabolic equation, where the unknown source possesses the semi-discrete formulation. Theoretically, we prove that the flux data from any nonempty open subset of the boundary can uniquely determine the semi-discrete source. This means the observed area can be extremely small, and that is the reason we call it sparse boundary data. For the numerical reconstruction, we formulate the problem from the Bayesian sequential prediction perspective and conduct the numerical examples which estimate the space-time-dependent source state by state. To better demonstrate the method’s performance, we solve two common multiscale problems from two models with a long source sequence. The numerical results illustrate that the inversion is accurate and efficient.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Atomic forces from Dirac-Kohn-Sham equations: Implementation in flexible (APW+lo/LAPW)+LO basis set

The atomic forces formulation based on the Dirac-Kohn-Sham equation and the flexible (APW+lo/LAPW)+LO basis set is presented here. The formulation was implemented in the code FlapwMBPT and allows a user to easily switch between different basis functions of the augmentation type (APW or LAPW) and between different kind of local orbitals. Similar to the work (Phys.Rev.B 91 (2015) 035105), the implementation takes into account small discontinuities of the wave functions, density, and potential at the muffin-tin sphere boundaries. Applications to the materials with strong relativistic effects, such as $\alpha$-Uranium, PuCoGa$_{5}$, and FePt, demonstrate robustness of the method. The comparison of the calculated forces with the ones obtained by numerical differentiation of free energy shows close agreement with deviations about 0.1% or less.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Tabulated equations of state from models informed by chiral effective field theory

Abstract We construct four equation of state (EoS) tables, tabulated over a range of temperatures, densities, and charge fractions, relevant for neutron star applications such as simulations of neutron star mergers. The EoS are computed from a relativistic mean-field theory constrained by the pure neutron matter EoS from chiral effective field theory, inferred properties of isospin-symmetric nuclear matter, and astrophysical observations of neutron star structure. To model nuclear matter at low densities, we attach an EoS that models inhomogeneous nuclear matter at arbitrary temperatures and charge fractions. The four EoS tables we develop are available from the CompOSE EoS repository https://compose.obspm.fr/eos/297 and gitlab.com/ahaber/qmc-rmf-tables .

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Stability of trapped solutions of a nonlinear Schrödinger equation with a nonlocal nonlinear self-interaction potential

This work focuses on the study of the stability of trapped soliton-like solutions of a (1 + 1)-dimensional nonlinear Schrödinger equation (NLSE) in a nonlocal, nonlinear, self-interaction potential of the form [|Ψ(x,t)| 2 +|Ψ(-x,t)| 2 ] κ where κ is an arbitrary nonlinearity parameter. Although the system with κ = 1 (i.e. fully integrable case) was first reported by Yang (2018 Phys. Rev. E 98 042202), here in the present work, we extend this model to the one in which κ is arbitrary. This allows us to compare the stability properties of the now trapped solutions to previously found solutions of the more usual NLSE with κ ≠ 1 which are moving soliton solutions. We show that there is a simple, one-component, nonlocal Lagrangian and corresponding action governing the dynamics of the system. Using a collective coordinate method derived from the action as well as assuming the validity of Derrick's theorem, we find that these trapped solutions are stable for 0 < κ < 2 and unstable when κ > 2. At the critical value of κ, i.e. κ = 2, the solution can either collapse or blowup linearly in time when q 0 = 0, where q 0 is the center of the initial density ρ(x, t = 0) = ψ*ψ of the solution. For q 0 ≠ 0 the displaced solution collapses. When κ > 2 initial small displacements from the origin also lead to collapse of the wave function. This phenomenon is not seen in the usual NLSE.

collective coordinates↗
DOE OSTI2021

AT2017gfo: Bayesian inference and model selection of multicomponent kilonovae and constraints on the neutron star equation of state

The joint detection of the gravitational wave GW170817, of the short γ-ray burst GRB170817A and of the kilonova AT2017gfo, generated by the the binary neutron star (NS) merger observed on 2017 August 17, is a milestone in multimessenger astronomy and provides new constraints on the NS equation of state. We perform Bayesian inference and model selection on AT2017gfo using semi-analytical, multicomponents models that also account for non-spherical ejecta. Observational data favour anisotropic geometries to spherically symmetric profiles, with a log-Bayes’ factor of ~104, and favour multicomponent models against single-component ones. The best-fitting model is an anisotropic three-component composed of dynamical ejecta plus neutrino and viscous winds. Using the dynamical ejecta parameters inferred from the best-fitting model and numerical–relativity relations connecting the ejecta properties to the binary properties, we constrain the binary mass ratio to q < 1.54 and the reduced tidal parameter to $120\lt \tilde{\Lambda }\lt 1110$. Finally, we combine the predictions from AT2017gfo with those from GW170817, constraining the radius of a NS of 1.4 M ⊙ to 12.2 ± 0.5 km (1σ level). This prediction could be further strengthened by improving kilonova models with numerical-relativity information.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Microscopic constraints for the equation of state and structure of neutron stars: A Bayesian model mixing framework

Bayesian model mixing (BMM) is a statistical technique that can combine constraints from different regions of an input space in a principled way. Here we extend our BMM framework for the equation of state (EOS) of strongly interacting matter from symmetric nuclear matter to asymmetric matter, specifically focusing on zero-temperature, charge-neutral, 𝛽-equilibrated matter. We use Gaussian processes (GPs) to infer constraints on the neutron-star matter EOS at intermediate densities from two different microscopic theories: chiral effective-field theory (𝜒⁢EFT) at baryon densities around nuclear saturation, 𝑛 𝐵 ∼ 𝑛 0 , and perturbative QCD at asymptotically high baryon densities, 𝑛 𝐵 ⩾ 20⁢𝑛 0 . The uncertainties of the 𝜒⁢EFT and pQCD EOSs are obtained using the BUQEYE truncation error model. We demonstrate the flexibility of our framework through the use of two categories of GP kernels: conventional stationary kernels and a nonstationary changepoint kernel. We use the latter to explore potential constraints on the dense matter EOS by including exogenous data representing theory predictions and heavy-ion collision measurements at densities ⩾ 2⁢𝑛 0 . We also use our EOSs to obtain neutron-star mass-radius relations and their uncertainties. Finally, our framework, whose implementation will be available through a GitHub repository, provides a prior distribution for the EOS that can be used in large-scale neutron-star inference frameworks.

Bayesian methods↗
DOE OSTI2025

Unified nonparametric equation-of-state inference from the neutron-star crust to perturbative-QCD densities

Perturbative quantum chromodynamics (pQCD), while valid only at densities exceeding those found in the cores of neutron stars, could provide constraints on the dense-matter equation of state (EOS). Here, in this work, we examine the impact of pQCD information on the inference of the EOS using a nonparametric framework based on Gaussian processes (GPs). We examine the application of pQCD constraints through a ``pQCD likelihood,'' and verify the findings of previous works; namely, a softening of the EOS at the central densities of the most massive neutron stars and a reduction in the maximum neutron-star mass. Although the pQCD likelihood can be easily integrated into existing EOS inference frameworks, this approach requires an arbitrary selection of the density at which the constraints are applied. The EOS behavior is also treated differently on either side of the chosen density. To mitigate these issues, we extend the EOS model to higher densities, thereby constructing a ``unified'' description of the EOS from the neutron-star crust to densities relevant for pQCD. In this approach the pQCD constraints effectively become part of the prior. Since the EOS is unconstrained by any calculation or data between the densities applicable to neutron stars and pQCD, we argue for maximum modeling flexibility in that regime. We compare the unified EOS with the traditional pQCD likelihood, and although we confirm the EOS softening, we do not see a reduction in the maximum neutron-star mass or any impact on macroscopic observables. Though residual model dependence cannot be ruled out, we find that pQCD suggests the speed of sound in the densest neutron-star cores has already started decreasing toward the asymptotic limit; we find that the speed of sound squared at the center of the most massive neutron star has an upper bound of $\sim 0.5$ at the 90% level.

equations of state of nuclear matter↗
DOE OSTI2022

Quantum time dynamics employing the Yang-Baxter equation for circuit compression

Quantum time dynamics (QTD) is considered a promising problem for quantum supremacy on near-term quantum computers. However, QTD quantum circuits grow with increasing time simulations. This study focuses on simulating the time dynamics of one-dimensional (1D) integrable spin chains with nearest-neighbor interactions. We have proved the existence of a reflection symmetry in the quantum circuit employed for simulating the time evolution of certain classes of 1D Heisenberg model Hamiltonians by virtue of the quantum Yang-Baxter equation, and how this symmetry can be exploited to compress and produce a shallow quantum circuit. With this compression scheme, the depth of the quantum circuit becomes independent of step size and only depends on the number of spins. We show that the depth of the compressed circuit is rigorously a linear function of the system size for the studied Heisenberg model Hamiltonians in the present work. As a consequence, the number of CNOT gates in the compressed circuit only scales quadratically with the system size, which allows for the simulations of time dynamics of very large 1D spin chains. We derive the compressed circuit representations for different special cases of the Heisenberg Hamiltonian. We compare and demonstrate the effectiveness of this approach by performing simulations on quantum computers.

1-dimensional spin chains↗
DOE OSTI2021

Multiphase tin equation of state using density functional theory

In this work, we perform density functional theory (DFT) calculations of five solid phases and the liquid phase of tin. The calculations include cold curves of the five solid phases, phonon calculations in the quasiharmonic approximation over a range of volumes for each solid phase, and DFT-based molecular dynamics (DFT-MD) simulations of the liquid phase, including those of the melt curve using the Z method. Using the DFT results, we construct a tabular multiphase sesame equation of state for tin, referred to as sesame 2162. Comparisons to experimental data are made and show a high level of agreement in isobaric data, isothermal data, shock data, and phase boundary measurements, including measurements of the melt curve. The 2162 EOS will be useful for hydrodynamics simulations and has been designed with an eye toward hydrodynamics simulations that incorporate materials strength models and allow for modeling of the kinetics of phase transitions.

3-dimensional systems↗
DOE OSTI2022

Argon equation of state data to 1 TPa: Shock compression experiments and simulations

Argon is the most abundant noble gas on Earth and its noble, atomic fluid nature makes it an excellent candidate for comparison of experiment and theory at extreme conditions. For this study, we performed a combined computational and experimental study on shock compressed cryogenic liquid argon. Using Sandia's Z machine, we shock compressed liquid argon to 600 GPa and reshock states up to 950 GPa. Laser shock experiments at the Omega Laser facility extend the principal Hugoniot to 1000 GPa and provided temperature data along the principal Hugoniot. The plate impact experiments and laser shock experiments used well-characterized impedance matching standards and demonstrate consistent results between the two platforms over a common range. Density functional theory based molecular dynamics simulations provided additional data on the Hugoniot to 600 GPa. The combined experimental data and simulation results provide constraints on the development of new equation of state models at extreme conditions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Toward an accurate equation of state and B1-B2 phase boundary for magnesium oxide up to terapascal pressures and electron-volt temperatures

By applying auxiliary-field quantum Monte Carlo, we calculate the equation of state (EOS) and B1-B2 phase transition of magnesium oxide (MgO) up to 1 TPa. Here, the results agree with available experimental data at low pressures and are used to benchmark the performance of various exchange-correlation functionals in density functional theory calculations. We determine PBEsol is an optimal choice for the exchange-correlation functional and perform extensive phonon and quantum molecular-dynamics calculations to obtain the thermal EOS. Our results provide a preliminary reference for the EOS and B1-B2 phase boundary of MgO from zero up to 10,500 K.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Fluid-phase helium: Shock-compression experiments, quantum molecular dynamics simulations, and development of an equation of state

Helium (He) plays a critical role in numerous areas ranging from the study of celestial objects like brown dwarfs and gas giants to modern-day technologies like nuclear energy and rocket propulsion. For many of these applications, it is essential to have a reliable equation of state (EOS) for He that yields an accurate representation of its thermodynamic behavior. To help constrain and develop such EOS models, we have performed a series of shock-compression experiments on cryogenic liquid He to pressures exceeding 100 GPa using a magnetically accelerated flyer plate on Sandia National Laboratories' Z-machine. We have also performed quantum molecular dynamics simulations that are consistent with our shock measurements. None of the previously available EOSs agree with our experimental and simulation results, motivating the development of a fluid-phase He EOS that we present in this study. Here, we show that our EOS yields good agreement with published data that span temperatures and pressures encountered across a diverse array of applications.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Reexamining the relation between the binding energy of finite nuclei and the equation of state of infinite nuclear matter

The energy density is calculated in coordinate space for 12 C, 40 Ca, 48 Ca, and 208 Pb using a dispersive optical model constrained by all relevant data including the corresponding energy of the ground state. The energy density of 8 Be is also calculated using the Green’s function Monte-Carlo method employing the Argonne/Urbana two and three-body interactions. The nuclear interior minimally contributes to the total binding energy due to the 4πr 2 phase space factor. Thus, the volume contribution to the energy in the interior is not well constrained. The dispersive-optical-model energy densities are in good agreement with ab initio self-consistent Green’s function calculations of infinite nuclear matter restricted to treat only short-range and tensor correlations. These results call into question the degree to which the equation of state for nuclear matter is constrained by the empirical mass formula. In particular, the results in this work indicate that saturated nuclear matter does not require the canonical value of 16 MeV binding per particle but only about 13-14 MeV when the interior of 208 Pb is considered.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗