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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 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

10-th order of accuracy for numerical solution of 3-D elasticity equations for heterogeneous materials on unfitted Cartesian meshes

We have developed the Optimal Local Truncation Error Method (OLTEM) with 10-th order of accuracy on unfitted Cartesian meshes for a system of 3-D elasticity equations with smooth irregular interfaces. 5 x 5 x 5 = 125-point stencils (similar to those for quadratic finite elements) for elastic heterogeneous materials are used for OLTEM. There are no unknowns at the interface points between different materials; the structure of the global discrete equations is the same for homogeneous and heterogeneous materials. The calculation of unknown stencil coefficients is based on the minimization of the local truncation error of the stencil equations and yields the optimal 10-th order of accuracy for OLTEM on unfitted Cartesian meshes, i.e., the increase by 7 orders in accuracy compared to quadratic finite elements on conformal meshes. A new post-processing procedure provides the 9-th order of accuracy for stresses in the 3-D case. Similar to basic computations it uses OLTEM with the 125-point stencils, the interface conditions and the elasticity equations. It was shown that the use of the elasticity equations for post-processing improves the accuracy of 0.1% stresses by 6 orders compared to post-processing without the use of PDEs. At an accuracy of for stresses, OLTEM with the new post-processing procedure reduces the number of degrees of freedom by 360 - 8000 times compared to quadratic finite elements with similar stencils. OLTEM with the 125-point stencils yields even more accurate results than high-order finite elements with much wider stencils. OLTEM provides accurate numerical results for compressible and nearly incompressible materials.

elasticity equations↗
DOE OSTI2023

Solution and sensitivity analysis of nonlinear equations using a hypercomplex-variable Newton-Raphson method

Here, the classical Newton-Raphson (NR) method for solving nonlinear equations is enhanced in two ways through the use of hypercomplex variables and algebra. In particular, i) the Jacobian is computed in a highly accurate and automated way, and ii) the derivative of the solution to the nonlinear equations is computed with respect to any parameter contained within the system of equations. These advances provide two significant enhancements in that it is straightforward to provide an accurate Jacobian and to construct a reduced order model (ROM) of arbitrary order with respect to any parameter of the system. The ROM can then be used to approximate the solution for other parameter values without requiring additional solutions of the nonlinear equations. Several case studies are presented including 1D and 2D academic examples with fully functioning Python code provided. Additionally, a case of study of the catenary of an elastic cable subject to its own weight and a vertical point load. Derivatives up to 10th order were computed with respect to material, loading, and geometrical parameters. The derivatives were used to generate reduced order models of the cable deformation and reaction forces at its ends with respect to multiple input parameters. Results show that from a single hypercomplex evaluation of the cable under a single vertical point load, it is possible to generate an accurate reduced order model capable of predicting the cable deformation with 1.5 times the load in the opposite direction and with 3.5 times the load in the same direction without resolving the system of equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

The development of natural gas and hydrogen pipeline capital cost estimating equations

Natural gas pipeline cost data collected by the Oil and Gas Journal (O&GJ) for interstate pipelines constructed from 1980 through 2017 were used to develop capital cost estimating equations that are a function of pipeline diameter, length, and U.S. region. Equations were developed for material, labor, miscellaneous, and right-of-way costs, the four cost components in the O&GJ data, for six different regions of the United States (U.S.). Each equation is a function of pipeline diameter and length. Adjustment mechanisms were then developed for converting the natural gas pipeline equations into equations for estimating the costs of hydrogen pipelines. These adjustments were based in part on an analysis completed by the National Institute for Standards and Technology (NIST). Here the results of this work were used to update cost models in the Hydrogen Delivery Scenario Analysis Model (HDSAM), developed by Argonne National Laboratory for the U.S. Department of Energy’s Hydrogen Program. Our analysis shows a wide range of pipeline cost across different U.S. regions, especially with respect to labor and right-of-way costs. The developed cost formulas for hydrogen pipelines are both important and timely as hydrogen is being considered as a zero-carbon energy carrier with the potential to decarbonize all energy sectors, and the cost of hydrogen transportation is essential for techno-economic analysis of its potential use in these sectors.

03 NATURAL GAS↗
DOE OSTI2023

Learning effective stochastic differential equations from microscopic simulations: Linking stochastic numerics to deep learning

We identify effective stochastic differential equations (SDEs) for coarse observables of fine-grained particle- or agent-based simulations; these SDEs then provide useful coarse surrogate models of the fine scale dynamics. We approximate the drift and diffusivity functions in these effective SDEs through neural networks, which can be thought of as effective stochastic ResNets. The loss function is inspired by, and embodies, the structure of established stochastic numerical integrators (here, Euler–Maruyama and Milstein); our approximations can thus benefit from backward error analysis of these underlying numerical schemes. They also lend themselves naturally to “physics-informed” gray-box identification when approximate coarse models, such as mean field equations, are available. Existing numerical integration schemes for Langevin-type equations and for stochastic partial differential equations can also be used for training; we demonstrate this on a stochastically forced oscillator and the stochastic wave equation. Our approach does not require long trajectories, works on scattered snapshot data, and is designed to naturally handle different time steps per snapshot. We consider both the case where the coarse collective observables are known in advance, as well as the case where they must be found in a data-driven manner.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A flexible gyro-fluid system of equations

Gyro-fluid equations are velocity space moments of the gyrokinetic equations. Special gyro-Landau-fluid closures have been developed that include the damping due to kinetic resonances by fitting to the collisionless local plasma response functions. This damping allows for accurate linear eigenmodes to be computed with a relatively low number of velocity space moments compared to the number of velocity quadrature points in gyrokinetic codes. However, none of the published gyro-Landau-fluid closure schemes considers the Onsager symmetries of the resulting quasi-linear fluxes as a constraint. Onsager symmetry guarantees that the matrix of diffusivities is positive definite, an important property for the numerical stability of a transport solver. A two-parameter real closure for improving the accuracy of low-resolution gyro-fluid equations, which preserves the Onsager symmetry and allows higher velocity space moments, is presented in this paper. The new linear gyro-fluid system (GFS) is used to extend the TGLF quasi-linear transport model so that it can compute the energy and momentum fluxes due to parallel magnetic fluctuations, completing the transport matrix. The GFS equations do not use a bounce average approximation. The GFS equations are fully electromagnetic with general flux surface magnetic geometry, pitch angle scattering for electron collisions, and subsonic equilibrium toroidal rotation. Using GFS eigenmodes in the quasi-linear TGLF model will be shown to yield a more accurate match to fluxes computed by CGYRO turbulence simulations. In conclusion, prospects for future applications of a quasi-linear theory to new plasma transport regimes and magnetic confinement devices in addition to tokamaks are opened by the flexibility of the GFS eigensolver.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Hot and dense matter equation of state probability distributions for astrophysical simulations

We add an ensemble of nuclei to the equation of state for homogeneous nucleonic matter to generate a new set of models suitable for astrophysical simulations of core-collapse supernovae and neutron star mergers. We implement empirical constraints from (i) nuclear mass measurements, (ii) proton-proton scattering phase shifts, and (iii) neutron star observations. Our model is also guided by microscopic many-body theory calculations based on realistic nuclear forces, including the zero-temperature neutron matter equation of state from quantum Monte Carlo simulations and thermal contributions to the free energy from finite-temperature many-body perturbation theory. We ensure that the parameters of our model can be varied while preserving thermodynamic consistency and the connection to experimental or observational data, thus providing a probability distribution of the astrophysical hot and dense matter equation of state. Furthermore, we compare our results with those obtained from other available equations of state. While our probability distributions indeed represent a large number of possible equations of state, we cannot yet claim to have fully explored all of the uncertainties, especially with regard to the structure of nuclei in the hot and dense medium.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Direct solution of Minkowski-space Bethe-Salpeter equation in the massive Wick-Cutkosky model

Here in order to solve the Bethe-Salpeter equation (BSE) in the Minkowski space, we first introduce the Nakanishi integral representations of the Bethe-Salpeter amplitude and the Bethe-Salpeter wave function. We then derive the explicit integral equations for the corresponding spectral functions from the BSE for states of two scalar particles bound by a scalar-particle exchange interaction, where the propagators of constituents are allowed to be fully dressed. These integral equations are subsequently solved numerically in the variation of the Wick-Cutkosky model with massive exchange particles, where an algorithm of adaptive mash grid is proposed. The equations and algorithm we develop here serve as the foundation of Minkowski-space formulation of BSE for bound states of fermions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Logarithmic forms and differential equations for Feynman integrals

We describe in detail how a d log representation of Feynman integrals leads to simple differential equations. We derive these differential equations directly in loop momentum or embedding space making use of a localization trick and generalized unitarity. For the examples we study, the alphabet of the differential equation is related to special points in kinematic space, described by certain cut equations which encode the geometry of the Feynman integral. At one loop, we reproduce the motivic formulae described by Goncharov [1] that reappeared in the context of Feynman integrals in [2–4]. The d log representation allows us to generalize the differential equations to higher loops and motivates the study of certain mixed-dimension integrals.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

A novel conditional formulation of the Vlasov–Ampère equations: a conservative, positivity, asymptotic and Gauss law preserving scheme

We propose a novel reformulation of the Vlasov–Ampère equations for plasmas that reveals discrete symmetries that enables simultaneous conservation of mass, momentum and energy; preservation of Gauss’s law; positivity of the distribution function; and consistency with quasi-neutral asymptotics. The approach employs variable and coordinate transformations to yield a coupled system comprising a modified Vlasov equation and associated moment–field equations. The modified Vlasov equation advances a conditional distribution function that excludes mass, momentum and energy densities, which are instead evolved through moment equations enforcing the relevant symmetries, conservation laws and involution constraints. This reformulation aligns naturally with a recent slow-manifold reduction technique, which separates fast electron time scales and simplifies the treatment of the quasi-neutral limit within the reduced moment–field subsystem. Using this framework, we develop a numerical method for the reduced 1D1V subsystem that, for the first time in the literature, satisfies all key physical constraints while maintaining a quasi-neutral asymptotic behaviour. The advantages of the method are demonstrated on canonical electrostatic test problems, including the multiscale ion acoustic shock wave.

1D1V↗
DOE OSTI2020

A measurement of the equation of state of carbon envelopes of white dwarfs

White dwarfs represent the final state of evolution for most stars. Certain classes of white dwarfs pulsate, leading to observable brightness variations, and analysis of these variations with theoretical stellar models probes their internal structure. Modelling of these pulsating stars provides stringent tests of white dwarf models and a detailed picture of the outcome of the late stages of stellar evolution. However, the high-energy-density states that exist in white dwarfs are extremely difficult to reach and to measure in the laboratory, so theoretical predictions are largely untested at these conditions. In this paper we report measurements of the relationship between pressure and density along the principal shock Hugoniot (equations describing the state of the sample material before and after the passage of the shock derived from conservation laws) of hydrocarbon to within five per cent. The observed maximum compressibility is consistent with theoretical models that include detailed electronic structure. This is relevant for the equation of state of matter at pressures ranging from 100 million to 450 million atmospheres, where the understanding of white dwarf physics is sensitive to the equation of state and where models differ considerably. The measurements test these equation-of-state relations that are used in the modelling of white dwarfs and inertial confinement fusion experiments, and we predict an increase in compressibility due to ionization of the inner-core orbitals of carbon. We also find that a detailed treatment of the electronic structure and the electron degeneracy pressure is required to capture the measured shape of the pressure–density evolution for hydrocarbon before peak compression. Our results illuminate the equation of state of the white dwarf envelope (the region surrounding the stellar core that contains partially ionized and partially degenerate non-ideal plasmas), which is a weak link in the constitutive physics informing the structure and evolution of white dwarf stars.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Characterization of the high-pressure and high-temperature phase diagram and equation of state of chromium

The high-pressure and high-temperature phase diagram of chromium has been investigated both experimentally (in situ), using a laser-heated diamond-anvil cell technique coupled with synchrotron powder X-ray diffraction, and theoretically, using ab initio density-functional theory simulations. In the pressure–temperature range covered experimentally (up to 90 GPa and 4500 K, respectively) only the solid body-centred-cubic and liquid phases of chromium have been observed. Experiments and computer calculations give melting curves in agreement with each other that can both be described by the Simon–Glatzel equation $T_{m}(P) = 2136K (1 + P/25.9)^{0.41}$ In addition, a quasi-hydrostatic equation of state at ambient temperature has been experimentally characterized up to 131 GPa and compared with the present simulations. Both methods give very similar third-order Birch–Murnaghan equations of state with bulk moduli of 182–185 GPa and respective pressure derivatives of 4.74–5.15. According to the present calculations, the obtained melting curve and equation of state are valid up to at least 815 GPa, at which pressure the melting temperature is 9310 K. Finally, from the obtained results, it was possible to determine a thermal equation of state of chromium valid up to 65 GPa and 2100 K.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Tree tensor network hierarchical equations of motion based on time-dependent variational principle for efficient open quantum dynamics in structured thermal environments

In this work, we introduce an efficient method, TTN-HEOM, for exactly calculating the open quantum dynamics for driven quantum systems interacting with highly structured bosonic baths by combining the tree tensor network (TTN) decomposition scheme with the bexcitonic generalization of the numerically exact hierarchical equations of motion (HEOM). The method yields a series of quantum master equations for all core tensors in the TTN that efficiently and accurately capture the open quantum dynamics for non-Markovian environments to all orders in the system–bath interaction. These master equations are constructed based on the time-dependent Dirac–Frenkel variational principle, which isolates the optimal dynamics for the core tensors given the TTN ansatz. The dynamics converges to the HEOM when increasing the rank of the core tensors, a limit in which the TTN ansatz becomes exact. We introduce TENSO, tensor equations for non-Markovian structured open systems, as a general-purpose Python code to propagate the TTN-HEOM dynamics. We implement three general propagators for the coupled master equations: two fixed-rank methods that require a constant memory footprint during the dynamics and one adaptive-rank method with a variable memory footprint controlled by the target level of computational error. We exemplify the utility of these methods by simulating a two-level system coupled to a structured bath containing one Drude–Lorentz component and eight Brownian oscillators, which is beyond what can presently be computed using the standard HEOM. Our results show that the TTN-HEOM is capable of simulating both dephasing and relaxation dynamics of driven quantum systems interacting with structured baths, even those of chemical complexity, with an affordable computational cost.

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

Generalized fractional approach to solving partial differential equations with arbitrary dispersion relations

The dynamics of physical systems are typically modeled by partial differential equations (PDEs). Because of the complexity in physical systems, PDE models rely on approximations or limiting cases. To model the full complexity of physical systems, it is necessary to use multiscale approaches where appropriate models are used at each level. Alternatively, complexity can be directly tackled by fractional integrodifferential equations that must be derived for each system. Here, we argue that complexity can be restored in PDEs by describing them from a fractional calculus perspective. Rather than deriving a fractional integrodifferential equation, we reinterpret the dispersion relation of the system by use of the Riesz definition, which contains the required information relating the energy and momentum space of the system and thus fully describes their dynamics. The approach is demonstrated by two examples: the Landau–Lifshitz equation in a 1D ferromagnetic chain and a modified KdV equation supporting surface gravity waves or Euler dispersion. The presented approach is applicable to fluids, soft matter, and solid-state matter and can be readily generalized to higher dimensions and more complex systems. While numerical calculations are needed to determine the fractional operator, the approach is analytical and can be utilized to determine analytical solutions and investigate nonlinear problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Quantum algorithm for the linear Vlasov equation with collisions

The Vlasov equation is a nonlinear partial differential equation that provides a first-principles description of the dynamics of plasmas. Its linear limit is routinely used in plasma physics to investigate plasma oscillations and stability. In this paper, we present a quantum algorithm that simulates the linearized Vlasov equation with and without collisions, in the one-dimensional electrostatic limit. Rather than solving this equation in its native spatial and velocity phase space, we adopt an efficient representation in the dual space yielded by a Fourier-Hermite expansion. For a given simulation time, the Fourier-Hermite representation is exponentially more compact, thus yielding a classical algorithm that can match the performance of a previously proposed quantum algorithm for this problem. Further, this representation results in a system of linear ordinary differential equations (ODEs) which can be solved with well-developed quantum algorithms: a Hamiltonian simulation in the collisionless case, and quantum ODE solvers in the collisional case. In particular, we demonstrate that a quadratic speedup in system size is attainable.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Phase transition phenomenology with nonparametric representations of the neutron star equation of state

Astrophysical observations of neutron stars probe the structure of dense nuclear matter and have the potential to reveal phase transitions at high densities. Most recent analyses are based on parametrized models of the equation of state with a finite number of parameters and occasionally include extra parameters intended to capture phase-transition phenomenology. However, such models restrict the types of behavior allowed and may not match the true equation of state. We introduce a complementary approach that extracts phase transitions directly from the equation of state without relying on, and thus being restricted by, an underlying parametrization. We then constrain the presence of phase transitions in neutron stars with astrophysical data. Current pulsar mass, tidal deformability, and mass-radius measurements disfavor only the strongest of possible phase transitions (latent energy per particle ≳ 100 MeV). Weaker phase transitions are consistent with observations. Here we further investigate the prospects for measuring phase transitions with future gravitational-wave observations and find that catalogs of O (100) events will (at best) yield Bayes factors of ~ 10 : 1 in favor of phase transitions even when the true equation of state contains very strong phase transitions. Our results reinforce the idea that neutron star observations will primarily constrain trends in macroscopic properties rather than detailed microscopic behavior. Fine-tuned equation of state models will likely remain unconstrained in the near future.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Revisiting the gluon density from the Balitsky-Kovchegov equation with kinematical constraints and large 𝑥 terms

We perform analysis of the small 𝑥 nonlinear evolution equation formulated in momentum space supplemented by higher order terms. The equation is defined in the wide range of transverse momentum and longitudinal momentum fractions extending previous studies performed in Kutak and Kwiecinski [Screening effects in the ultrahigh-energy neutrino interactions, Eur. Phys. J. C 29, 521 (2003).] and in Kutak and Stasto [Unintegrated gluon distribution from modified BK equation, Eur. Phys. J. C 41, 343 (2005).]. The linear part of the equation is motivated by the renormalization group improved small 𝑥 approach, which accounts for resummation of higher orders, and includes collinear splitting functions and kinematical constraints. The solution to the equation is then used to perform the fit to deep inelastic scattering reduced cross section data.

Perturbative QCD↗
DOE OSTI2026

Fokker-Planck Equation Governing the Distribution of Walkers in Auxiliary-Field Quantum Monte Carlo

Auxiliary-field quantum Monte Carlo (AFQMC) is typically formulated as an open-ended random walk in an overcomplete space of Slater determinants, implemented through a Langevin equation. However, the explicit form of the underlying Fokker-Planck equation governing the walker population distribution has remained unknown. Here, in this Letter, we derive the Fokker-Planck equation for AFQMC and propose a novel numerical scheme to solve it. The solution of the Fokker-Planck equation reveals the wave function actually sampled by the AFQMC algorithm. Interestingly, we find that even when the exact ground state is used as a guiding wave function in constrained path AFQMC, contrary to the common assumption, the wave function sampled by AFQMC is not exact. Beyond clarifying several fundamental aspects of AFQMC, the availability of a Fokker-Planck equation formulation opens new avenues for systematically improving its accuracy, which we outline in this Letter.

Monte Carlo methods↗
DOE OSTI2020

Evaluation of the 2018 Version of the Integrated Surveillance Program Database Pressure Equation

The Integrated Surveillance Program (ISP) Database Pressure Equation was developed to determine with reasonable certainty the total maximum pressure of hydrogen and other gases in packaged 3013 containers stored at Savannah River Site (SRS) in support of the destructive evaluation (DE) process. The pressure equation in the Department of Energy (DOE) 3013 Standard, “Standard for Stabilization, Packaging and Storage of Plutonium- Bearing Materials” (DOE-STD-3013-2004) used a bounding assumption that all the water is decomposed to form hydrogen. However, the results of Los Alamos National Laboratory (LANL) shelf-life experiments showed that hydrogen is consumed, and that the maximum pressures would not approach the design pressure of the 3013 container. Therefore, the ISP Database Pressure Equation was revised in 2008 to include terms for the generation of helium and hydrogen as a function of time, as well as the consumption of water and destruction of hydrogen based on shelf-life results. The 2008 ISP Database Pressure Equation provided a more reasonable estimate of the total maximum pressure in packaged 3013 containers than the pressure equation in versions of the 3013 Standard issued prior to 2018.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗