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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 487 records · Page 27
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Virtual element approximations of the time-fractional nonlinear convection-diffusion equation on polygonal meshes

We extend the Virtual Element Method to a two-dimensional unsteady nonlinear convection-diffusion equation characterized by a fractional-order derivative with respect to the time variable. Our methodology is based on three fundamental technical components: a fractional version of the Grunwald-Letnikov approximation, discrete maximal regularity, and the regularity theory associated with non-linearity. We prove the method's well-posedness, i.e., the approximate solution's existence and uniqueness to the time-fractional convection-diffusion equation with a Lipschitz nonlinear source term. The fully discrete scheme inherently maintains stability and consistency by leveraging the discrete maximal regularity and the energy projection operator. The convergence in the L 2 -norm and H 1 -norm to various mesh configurations is validated by numerical results, underlining the practical effectiveness of the proposed method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Equation-Free Coarse Control of Distributed Parameter Systems via Local Neural Operators

The control of high-dimensional distributed parameter systems (DPS) remains a challenge when explicit coarse-grained equations are unavailable. Classical equation-free (EF) approaches rely on fine-scale simulators treated as black-box timesteppers. However, repeated simulations for steady-state computation, linearization, and control design are often computationally prohibitive, or the microscopic timestepper may not even be available, leaving us with data as the only resource. We propose a data-driven alternative that uses local neural operators, trained on spatiotemporal microscopic/mesoscopic data, to obtain efficient short-time solution operators. These surrogates are employed within Krylov subspace methods to compute coarse steady and unsteady-states, while also providing Jacobian information in a matrix-free manner. Krylov-Arnoldi iterations then approximate the dominant eigenspectrum, yielding reduced models that capture the open-loop slow dynamics without explicit Jacobian assembly. Both discrete-time Linear Quadratic Regulator (dLQR) and pole-placement (PP) controllers are based on this reduced system and lifted back to the full nonlinear dynamics, thereby closing the feedback loop.

93B52, 93C20, 47N70, 65J15, 65M32, 68T07, 68T20, 6↗
DOE OSTI2022

Embedding a Critical Point in a Hadron to Quark–Gluon Crossover Equation of State

It is shown how to embed a critical point in a smooth background equation of state so as to yield the critical exponents and critical amplitude ratios expected of a transition in the same universality class as the liquid–gas phase transition and the 3D Ising model. There are only two independent critical exponents; the relations α + 2β + $\gamma$ = 2 and β(δ - 1) = $\gamma$ arise automatically, as does a new relation between the two critical amplitudes. The resulting equation of state has parameters which may be inferred by hydrodynamic modeling of heavy-ion collisions in the Beam Energy Scan II at the Relativistic Heavy Ion Collider.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Qubit Lattice Algorithms Based on the Schrödinger-Dirac Representation of Maxwell Equations and Their Extensions

It is well known that Maxwell equations can be expressed in a unitary Schrodinger-Dirac representation for homogeneous media. However, difficulties arise when considering inhomogeneous media. A Dyson map points to a unitary field qubit basis, but the standard qubit lattice algorithm of interleaved unitary collision-stream operators must be augmented by some sparse non-unitary potential operators that recover the derivatives on the refractive indices. Here, the effect of the steepness of these derivatives on two-dimensional scattering is examined with simulations showing quite complex wavefronts emitted due to transmissions/reflections within the dielectric objects. Maxwell equations are extended to handle dissipation using Kraus operators. Then, our theoretical algorithms are extended to these open quantum systems. A quantum circuit diagram is presented as well as estimates on the required number of quantum gates for implementation on a quantum computer.

2D electromagnetic scattering↗
DOE OSTI2020

ULYSSES: Universal LeptogeneSiS Equation Solver

ULYSSES is a python package that calculates the baryon asymmetry produced from leptogenesis in the context of a type-I seesaw mechanism. The code solves the semi-classical Boltzmann equations for points in the model parameter space as specified by the user. We provide a selection of predefined Boltzmann equations as well as a plugin mechanism for externally provided models of leptogenesis. Furthermore, the ULYSSES code provides tools for multi-dimensional parameter space exploration. The emphasis of the code is on user flexibility and rapid evaluation. It is publicly available at https://github.com/earlyuniverse/ulysses

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Battery models, systems, and methods using robust fail-safe iteration free approach for solving differential algebraic equations

Battery models using robust fail-safe iteration free approach for solving Differential Algebraic Equations, and associated systems and methods are disclosed. In one embodiment, a method includes generating a model of the rechargeable battery; determining one or more initial conditions for one or more algebraic variables of the model using a solver; holding differential variables of the model static by a switch function while determining the one or more initial conditions; applying the initial conditions to the model by the switch function; and determining one or more parameters for the rechargeable battery by solving the algebraic and differential equations.

25 ENERGY STORAGE↗
DOE OSTI2021

Generalization Equations for Machine Learners Based on Physical and Abstract Laws

The physical and abstract laws derived from the first principles have been recently exploited to customize and sharpen machine learning (ML) methods and also derive their generalization equations. These laws often encapsulate knowledge that complements datasets and ML models. We present a generic framework that uses these laws to provide ML codes that are transferable across multiple areas, including data transport infrastructures and thermal hydraulics analytics of nuclear reactors. By anchoring on datasets from these areas and the statistical generalization theory, we present a rigorous approach to co-develop ML solutions and the generalization equations that characterize them, by exploiting the structure and constraints from the laws. We present illustrative examples using practical problems from existing literature on the performance characterization of data transport infrastructures, and the sensor error and power level estimation in nuclear reactor systems using sensor measurements of primary and secondary coolant systems, respectively.

Rao, Nageswara↗
DOE OSTI2023

Qubit Lattice Algorithms based on the Schrodinger-Dirac representation of Maxwell Equations and their Extensions

It is well known that Maxwell equations can be expressed in a unitary Schrodinger-Dirac representation for homogeneous media. However, difficulties arise when considering inhomoge- neous media. A Dyson map points to a unitary field qubit basis, but the standard qubit lattice algorithm of interleaved unitary collision-stream operators must be augmented by some sparse non-unitary potential operators that recover the derivatives on the refractive indices. The effect of the steepness of these derivatives on two dimensional scattering is examined with simulations showing quite complex wavefronts emitted due to transmissions/reflections within the dielectric objects. Maxwell equations are extended to handle dissipation using Kraus operators. Then, our theoretical algorithms are extended to these open quantum systems. A quantum circuit diagram is presented as well as estimates on the required number of quantum gates for implementation on a quantum computer.

Vahala, George↗
DOE OSTI2024

Learning the boundary-to-domain mapping using Lifting Product Fourier Neural Operators for partial differential equations

Neural operators such as the Fourier Neural Operator (FNO) have been shown to provide resolution-independent deep learning models that can learn mappings between function spaces. For example, an initial condition can be mapped to the solution of a partial differential equation (PDE) at a future time-step using a neural operator. Despite the popularity of neural operators, their use to predict solution functions over a domain given only data over the boundary (such as a spatially varying Dirichlet boundary condition) remains unexplored. In this paper, we refer to such problems as boundary-to-domain problems; they have a wide range of applications in areas such as fluid mechanics, solid mechanics, heat transfer etc. We present a novel FNO-based architecture, named Lifting Product FNO (or LP-FNO) which can map arbitrary boundary functions defined on the lower-dimensional boundary to a solution in the entire domain. Specifically, two FNOs defined on the lower-dimensional boundary are lifted into the higher dimensional domain using our proposed lifting product layer. We demonstrate the efficacy and resolution independence of the proposed LP-FNO for the 2D Poisson equation.

Kashi, Aditya↗
DOE OSTI2021

Second-order invariant domain preserving approximation of the compressible Navier–Stokes equations

Here, we present a fully discrete approximation technique for the compressible Navier–Stokes equations that is second-order accurate in time and space, semi-implicit, and guaranteed to be invariant domain preserving. The restriction on the time step is the standard hyperbolic CFL condition, i.e. τ ≲ O ( h ) / V where V is some reference velocity scale and h the typical meshsize.

42 ENGINEERING↗
DOE OSTI2023

Dense nuclear matter equation of state from heavy-ion collisions

The nuclear equation of state (EOS) is at the center of numerous theoretical and experimental efforts in nuclear physics. With advances in microscopic theories for nuclear interactions, the availability of experiments probing nuclear matter under conditions not reached before, endeavors to develop sophisticated and reliable transport simulations to interpret these experiments, and the advent of multi-messenger astronomy, the next decade will bring new opportunities for determining the nuclear matter EOS, elucidating its dependence on density, temperature, and isospin asymmetry. Among controlled terrestrial experiments, collisions of heavy nuclei at intermediate beam energies (from a few tens of MeV/nucleon to about 25 GeV/nucleon in the fixed-target frame) probe the widest ranges of baryon density and temperature, enabling studies of nuclear matter from a few tenths to about 5 times the nuclear saturation density and for temperatures from a few to well above a hundred MeV, respectively. Collisions of neutron-rich isotopes further bring the opportunity to probe effects due to the isospin asymmetry. However, capitalizing on the enormous scientific effort aimed at uncovering the dense nuclear matter EOS, both at RHIC and at FRIB as well as at other international facilities, depends on the continued development of state-of-the-art hadronic transport simulations. Furthermore, this white paper highlights the essential role that heavy-ion collision experiments and hadronic transport simulations play in understanding strong interactions in dense nuclear matter, with an emphasis on how these efforts can be used together with microscopic approaches and neutron star studies to uncover the nuclear EOS.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Enabling New Flexibility in the SUNDIALS Suite of Nonlinear and Differential/Algebraic Equation Solvers

In recent years, the SUite of Nonlinear and DIfferential/ALgebraic equation Solvers (SUNDIALS) has been redesigned to better enable the use of application-specific and third-party algebraic solvers and data structures. Throughout this work, we have adhered to specific guiding principles that minimized the impact to current users while providing maximum flexibility for later evolution of solvers and data structures. The redesign was done through the addition of new linear and nonlinear solvers classes, enhancements to the vector class, and the creation of modern Fortran interfaces. The vast majority of this work has been performed “behind-the-scenes,” with minimal changes to the user interface and no reduction in solver capabilities or performance. These changes allow SUNDIALS users to more easily utilize external solver libraries and create highly customized solvers, enabling greater flexibility on extreme-scale, heterogeneous computational architectures.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

The W4 method: A new multi-dimensional root-finding scheme for nonlinear systems of equations

We propose a new class of method for solving nonlinear systems of equations, which, among other things, has four nice features: (i) it is inspired by the mathematical property of damped oscillators, (ii) it can be regarded as a simple extension to the Newton-Raphson (NR) method, (iii) it has the same local convergence as the NR method does, (iv) it has a significantly wider convergence region or the global convergence than that of the NR method. In this article, we present the evidence of these properties, applying our new method to some examples and comparing it with the NR method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Approximation rates of DeepONets for learning operators arising from advection–diffusion equations

Here we present the analysis of approximation rates of operator learning in Chen and Chen (1995) and Lu et al. (2021), where continuous operators are approximated by a sum of products of branch and trunk networks. In this work, we consider the rates of learning solution operators from both linear and nonlinear advection–diffusion equations with or without reaction. We find that the approximation rates depend on the architecture of branch networks as well as the smoothness of inputs and outputs of solution operators.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

High-pressure high-temperature synthesis and thermal equation of state of high-entropy transition metal boride

High-entropy transition metal boride (Hf 0.2 Ti 0.2 Zr 0.2 Ta 0.2 Mo 0.2 )B 2 sample was synthesized under high-pressure and high-temperature starting from ball-milled oxide precursors (HfO 2 , TiO 2 , ZrO 2 , Ta 2 O 5 , MoO 3 ) mixed with graphite and boron-carbide. Experiments were conducted in a large-volume Paris Edinburgh press combined with an in-situ Energy Dispersive X-ray Diffraction. The hexagonal AlB 2 phase with an ambient pressure volume V 0 = 27.93 ± 0.03 Å 3 was synthesized at a pressure of 0.9 GPa and temperatures above 1373K. High-pressure high-temperature studies on the synthesized high-entropy transition metal boride sample were performed to 7.6 GPa and 1873 K. The thermal equation of state fitted to the experimental data resulted in an ambient pressure bulk-modulus K 0 = 344 ± 39 GPa, dK/dT = –0.108 ± 0.027 GPa/K, and a temperature dependent volumetric thermal expansion coefficient α = α 0 + α 1 T + α 2 T –2 . The thermal stability combined with a high bulk-modulus establishes this high-entropy transition metal boride as an ultrahard high-temperature ceramic material.

36 MATERIALS SCIENCE↗
DOE OSTI2024

The development of thermodynamically consistent and physics-informed equation-of-state model through machine learning

Ab initio molecular dynamics (AIMD) simulations have become an important tool used in the construction of equations of state (EOS) tables for warm dense matter. Due to computational costs, only a limited number of system state conditions can be simulated, and the remaining EOS surface must be interpolated for use in radiation-hydrodynamic simulations of experiments. In this work, we develop a thermodynamically consistent EOS model that utilizes a physics-informed machine learning approach to implicitly learn the underlying Helmholtz free-energy from AIMD generated energies and pressures. The model, referred to as PIML-EOS, was trained and tested on warm dense polystyrene producing a fit within a 1% relative error for both energy and pressure and is shown to satisfy both the Maxwell and Gibbs–Duhem relations. In addition, we provide a path toward obtaining thermodynamic quantities, such as the total entropy and chemical potential (containing both ionic and electronic contributions), which are not available from current AIMD simulations.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Shock equation of state experiments in MgO up to 1.5 TPa and the effects of optical depth on temperature determination

Laser-driven shock compression enables an experimental study of phase transitions at unprecedented pressures and temperatures. One example is the shock Hugoniot of magnesium oxide (MgO), which crosses the B1–B2-liquid triple point at 400–600 GPa, 10 000–13 000 K (0.86–1.12 eV). MgO is a major component within the mantles of terrestrial planets and has long been a focus of high-pressure research. Here, we combine time-resolved velocimetry and pyrometry measurements with a decaying shock platform to obtain pressure–temperature data on MgO from 300 to 1500 GPa and 9000 to 50 000 K. Pressure–temperature–density Hugoniot data are reported at 1500 GPa. These data represent the near-instantaneous response of an MgO [100] single crystal to shock compression. We report on a prominent temperature anomaly between 400 and 460 GPa, in general agreement with previous shock studies, and draw comparison with equation-of-state models. We provide a detailed analysis of the decaying shock compression platform, including a treatment of a pressure-dependent optical depth near the shock front. We show that if the optical depth of the shocked material is larger than 1 μm, treating the shock front as an optically thick gray body will lead to a noticeable overestimation of the shock temperature.

36 MATERIALS SCIENCE↗
DOE OSTI2025

An implementation of a high-order generalized finite difference method for solving the time-harmonic cold plasma wave equation in toroidal geometry

A high-order physics-informed meshless finite difference numerical technique is introduced for solving the time-harmonic cold plasma wave equation in toroidal geometries, presenting a novel application of the generalized finite difference (GFD) method to plasma wave simulations. The algorithm employs an irregular distribution of computational points, with local point density informed by the shortest wavelength derived from the cold plasma dispersion relation. Numerical stability and robustness are addressed using regularization techniques. The algorithm, implemented for two spatial dimensions, solves for the wave electric field and is demonstrated to achieve convergence rates of $\mathcal{O}$($\mathcal{h}$ $\mathcal{P}$ )⁠. Verification tests reproduce plane wave solutions, and example simulations of ion cyclotron resonance heating and electron cyclotron resonance heating demonstrate its capability, approaching realistic tokamak plasma scenarios. This work contributes to laying a foundation for the GFD method to be used in more sophisticated, optimized, and physically realistic full-wave simulations in time-harmonic plasma wave research.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗