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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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Example on how to (intelligently) augment the nuclear-data pipeline with machine learning [Slides]

The presentation discusses how machine learning has helped the Los Alamos National Laboratory (LANL) nuclear-data pipeline. It also discusses the strengths of machine learning as it finds trends in large amounts of data where human brains are overwhelmed and that this information may be crucial to improve our nuclear data. It does stress, however, that machine learning is no "silver bullet" and that it is critical to feed it expert knowledge and use physics intuition to interpret the results. The presentation discusses the need to develop infrastructure and tools to provide data in an easily readable and unambiguously interpretable format (e.g., EXFOR format), to develop experimental data and theory to solve physics questions, and that statisticians and nuclear-data experts must be brought together to correctly interpret the results. The presentation concludes by stating that machine learning is a great tool and that LANL needs to use the algorithms along with developing physics data, tools and infrastructure.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Multirate Exponential Rosenbrock Methods

In this paper we propose a novel class of methods for high-order accurate integration of multirate systems of ordinary differential equation initial-value problems. The proposed methods construct multirate schemes by approximating the action of matrix φ functions within explicit exponential Rosenbrock (ExpRB) methods, thereby called multirate ExpRB (MERB) methods. They consist of the solution to a sequence of modified “fast” initial-value problems, which may themselves be approximated through subcycling any desired initial-value problem solver. In addition to proving how to construct MERB methods from certain classes of ExpRB methods, we provide rigorous convergence analysis of these methods and derive efficient MERB schemes of orders 2 through 6 (the highest-order infinitesimal multirate methods to date). Lastly, we then present numerical simulations to confirm these theoretical convergence rates and to compare the efficiency of MERB methods against other recently introduced high-order multirate methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Parametric Modeling and Economic Analysis of a 2MW th 3-Stream sCO 2 Heat Exchanger

Here, this paper presents the design and cost optimization of a novel 2MW th 3-stream sCO2 plate-fin heat exchanger. This heat exchanger design is unique in that it uses reduced metal oxide particle-to-sCO2 heat exchanger for cost-effective energy storage applications. The design uses low velocity, laminar air as the re-oxidizing reactant to transfer the heat of the re-oxidizing reaction to a sCO2 power loop. The design of the heat exchanger is based on a 2-D, 3-fluid plate/fin heat transfer model. The model parameterizes the size, shape, and number of passages of the heat exchanger to calculate the temperature profile, pressure drop, and fluid velocities of all three fluids. Global heat exchanger parameters such as the effectiveness and total heat transferred to the sCO2 are then calculated for overall performance. Due to the value and increased use of sCO2 heat exchangers in power cycles, a cost model of the system based on the unique high temperature/high pressure operating conditions was created using quotes from reference projects and market analysis. These quoted air-to-sCO2 heat exchangers are then processed using multiple weighting factors pertinent to heat exchanger design, including heat exchanger type, maximum temperature, differential pressures, fluids, duty, and more. These factors are then used in an exponential function in order to generate a parameterized cost curve. The design and cost of the heat exchanger are then optimized using the SMPSO genetic algorithm in Python. The optimization objectives for the system are to maximize the overall system effectiveness, including an air recuperator for preheating, and to minimize unit costs. Additional constraints are added to the system for the sCO2 and air pressure drops, air velocity to reduce particle entrainment, and the length and volume of the heat exchanger.

Cost Model↗
DOE OSTI2023

X-ray Diffraction of Water in Polyvinylpyrrolidone

PVP is a hydrophilic polymer commonly used as an excipient in pharmaceutical formulations. Here we have performed time-resolved high-energy X-ray scattering experiments on pellets of PVP at different humidity conditions for 1-2 days. A two-phase exponential decay in water sorption is found with a peak in the differential pair distribution function at 2.85 Å, which is attributed to the average (hydrogen bonded) carbonyl oxygen-water oxygen distance. Additional scattering measurements on powders with fixed compositions ranging from 2 to 12.3 wt % H 2 O were modeled with Empirical Potential Structure Refinement (EPSR). Further, the models reveal approximately linear relations between the carbonyl oxygen-water oxygen coordination number (nO C - O W ) and the water oxygen-water oxygen coordination number (nO W - O W ) versus water content in PVP. A stronger preference for water-water hydrogen bonding over carbonyl-water bonding is found. At all the concentrations studied the majority of water molecules were found to be randomly isolated, but a wide distribution of coordination environments of water molecules is found within the PVP polymer strands at the highest concentrations. Overall, the EPSR models indicate a continuous evolution in structure versus water content with nO W - O W =1 occurring at similar to 12 wt % H 2 O, i.e., the composition where, on average, each watermolecule is surrounded by one other water molecule.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Measurement of the central exclusive production of charged particle pairs in proton-proton collisions at $\sqrt{s}$ = 200 GeV with the STAR detector at RHIC

We report on the measurement of the Central Exclusive Production of charged particle pairs h+h- (h = π, K, p) with the STAR detector at RHIC in proton-proton collisions at $\sqrt{s}$ = 200 GeV. The charged particle pairs produced in the reaction pp → p' + h + h - + p' are reconstructed from the tracks in the central detector and identified using the specific energy loss and the time of flight method, while the forward-scattered protons are measured in the Roman Pot system. Exclusivity of the event is guaranteed by requiring the transverse momentum balance of all four final-state particles. Differential cross sections are measured as functions of observables related to the central hadronic final state and to the forward-scattered protons. They are measured in a fiducial region corresponding to the acceptance of the STAR detector and determined by the central particles’ transverse momenta and pseudorapidities as well as by the forward-scattered protons’ momenta. This fiducial region roughly corresponds to the square of the four-momentum transfers at the proton vertices in the range 0.04 GeV 2 < -t 1 , -t 2 < 0.2 GeV 2 , invariant masses of the charged particle pairs up to a few GeV and pseudorapidities of the centrally-produced hadrons in the range |η| < 0.7. The measured cross sections are compared to phenomenological predictions based on the Double Pomeron Exchange (DPE) model. Structures observed in the mass spectra of π + π - and K + K - pairs are consistent with the DPE model, while angular distributions of pions suggest a dominant spin-0 contribution to π + π - production. For π + π - production, the fiducial cross section is extrapolated to the Lorentz-invariant region, which allows decomposition of the invariant mass spectrum into continuum and resonant contributions. The extrapolated cross section is well described by the continuum production and at least three resonances, the f 0 (980), f 2 (1270) and f 0 (1500), with a possible small contribution from the f 0 (1370). Fits to the extrapolated differential cross section as a function of t 1 and t 2 enable extraction of the exponential slope parameters in several bins of the invariant mass of π + π - pairs. These parameters are sensitive to the size of the interaction region.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Partitioned exponential methods for coupled multiphysics systems

Multiphysics problems involving two or more coupled physical phenomena are ubiquitous in science and engineering. This work develops a new partitioned exponential approach for the time integration of multiphysics problems. After a possible semi-discretization in space, the class of problems under consideration is modeled by a system of ordinary differential equations where the right-hand side is a summation of two component functions, each corresponding to a given set of physical processes. The partitioned-exponential methods proposed herein evolve each component of the system via an exponential integrator, and information between partitions is exchanged via coupling terms. Here, the traditional approach to constructing exponential methods, based on the variation-of-constants formula, is not directly applicable to partitioned systems. Rather, our approach to developing new partitioned-exponential families is based on a general-structure additive formulation of the schemes. Two method formulations are considered, one based on a linear-nonlinear splitting of the right hand component functions, and another based on approximate Jacobians. The paper develops classical (non-stiff) order conditions theory for partitioned exponential schemes based on particular families of T-trees and B-series theory. Several practical methods of third order are constructed that extend the Rosenbrock-type and EPIRK families of exponential integrators. Several implementation optimizations specific to the application of these methods to reaction-diffusion systems are also discussed. Numerical experiments reveal that the new partitioned-exponential methods can perform better than traditional unpartitioned exponential methods on some problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Uplift and Seismicity Driven by Magmatic Inflation at Sierra Negra Volcano, Galápagos Islands

Abstract Although episodes of surface uplift and elevated seismicity precede many volcanic eruptions, their temporal evolution is often complex, and apparently in contradiction to simple trends predicted by mechanical deformation models. Here, we use continuous global positioning system and seismic data recorded at Sierra Negra volcano, Galápagos Islands, to show how the edifice responded to stress changes driven by magma accumulation in a shallow sill. The rate of uplift varied during the 13 years and 6.5 m of inflation before the 2018 eruption. The number of earthquakes per unit of uplift increased exponentially with total uplift as the differential stress increased. Accordingly, the temporal seismicity rate varied in time as a function of both the total uplift and the uplift rate. The Gutenberg‐Richter b ‐value decreased as a function of total uplift. In the final six months before the eruption, a sequence of large ( M > 4) earthquakes regulated the state of stress on the fault, each being followed by 2–3 days of postseismic quiescence, and retarding the increase in seismicity rate. These earthquakes did not affect the overall uplift rate. Subsidence of 8.5 m accompanied the 2‐month eruption. On resumption of uplift, the number of earthquakes per unit of uplift was very low, and the b ‐value high, reflecting the relaxed stress state of the fault system. These observations show that crustal deformation becomes increasingly brittle at higher stress states, and supports theoretical models based on elastic‐brittle mechanics. They suggest that joint interpretation of deformation and seismicity is key for forecasting future eruptions in similar volcanic settings.

Bell, Andrew Forbes↗
DOE OSTI2024

Spectral scheme for atomic structure calculations in density functional theory

In this study, we present a spectral scheme for atomic structure calculations in pseudopotential Kohn-Sham density functional theory. In particular, after applying an exponential transformation of the radial coordinates, we employ global polynomial interpolation on a Chebyshev grid, with derivative operators approximated using the Chebyshev differentiation matrix, and integrations using Clenshaw-Curtis quadrature. We demonstrate the accuracy and efficiency of the scheme through spin-polarized and unpolarized calculations for representative atoms, while considering local, semilocal, and hybrid exchange-correlation functionals. In particular, we find that $\mathcal{O}$(200) grid points are sufficient to achieve an accuracy of 1 microhartree in the eigenvalues for optimized norm conserving Vanderbilt pseudopotentials spanning the periodic table from atomic number Ζ = 1 to 83.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2025

Fermi Velocity Dependent Critical Current in Ballistic Bilayer Graphene Josephson Junctions

We perform transport measurements on proximitized, ballistic, bilayer graphene Josephson junctions (BGJJs) in the intermediate-to-long junction regime (L > ξ). We measure the device’s differential resistance as a function of bias current and gate voltage for a range of different temperatures. The extracted critical current IC follows an exponential trend with temperature: exp(−k B T/δE). Here δE = ħν F /2πL: an expected trend for intermediate-to-long junctions. From δE, we determine the Fermi velocity of the bilayer graphene, which is found to increase with gate voltage. Simultaneously, we show the carrier density dependence of δE, which is attributed to the quadratic dispersion of bilayer graphene. This is in contrast to single layer graphene Josephson junctions, where δE and the Fermi velocity are independent of the carrier density. The carrier density dependence in BGJJs allows for additional tuning parameters in graphene-based Josephson junction devices.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Real-time spin systems from lattice field theory

We construct a lattice field theory method for computing the real-time dynamics of spin systems in a thermal bath. This is done by building on previous work of Takano with Schwinger-Keldysh and functional differentiation techniques. We derive a Schwinger-Keldysh path integral for generic spin Hamiltonians, then demonstrate the method on a simple system. Our path integral has a sign problem, which generally requires exponential run time in the system size, but requires only linear storage. The latter may place this method at an advantage over exact diagonalization, which is exponential in both. Our path integral is amenable to contour deformations, a technique for reducing sign problems.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker–Planck Equations

The Fokker-Planck (FP) equation is a foundational partial differential equation (PDE) in stochastic processes involving Brownian motions. However, the curse of dimensionality (CoD) poses a formidable challenge when dealing with high-dimensional FP equations. Although Monte Carlo simulation and (vanilla) Physics-Informed Neural Networks (PINNs) have shown the potential to tackle CoD, both methods exhibit significant numerical errors in high dimensions when dealing with the probability density function (PDF) associated with Brownian motion. The point-wise PDF values tend to decrease exponentially as dimensionality increases, surpassing the precision of numerical simulations and resulting in substantial errors. In addition, due to its massive sampling, Monte Carlo fails to offer fast sampling. Modeling the logarithm likelihood (LL) via vanilla PINNs transforms the FP equation into a notoriously difficult Hamilton-Jacobi-Bellman (HJB) equation, which is impractical for PINN learning, whose error grows rapidly with dimension. To this end, we propose a novel approach utilizing a score-based solver to fit the score function in stochastic differential equations (SDEs). The score function, defined as the gradient of the LL, plays a fundamental role in inferring LL and PDF and enables fast SDE sampling, offering an effective means to overcome the CoD. Three fitting methods, Score Matching (SM), Sliced Score Matching (SSM), and Score-PINN, are introduced, each contributing unique advantages in computational complexity, accuracy, and generality. The proposed score-based SDE solver operates in two stages: first, employing score matching or Score-PINN to acquire the score function; and second, solving the LL via an ordinary differential equation (ODE) using the obtained score function. Comparative evaluations across these methods showcase varying trade-offs. The proposed methodology is evaluated across diverse SDEs, including anisotropic Ornstein-Uhlenbeck processes, geometric Brownian motion, and Brownian motion with varying eigenspace. We also test various distributions, including Gaussian, Log-normal, Laplace, and Cauchy distributions. The numerical results demonstrate the score-based SDE solver’s stability, speed, and performance across different experimental settings, solidifying its potential as a solution to CoD for high-dimensional FP equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Gauges, loops, and polynomials for partition functions of graphical models

Graphical models represent multivariate and generally not normalized probability distributions. Computing the normalization factor, called the partition function, is the main inference challenge relevant to multiple statistical and optimization applications. The problem is #P-hard that is of an exponential complexity with respect to the number of variables. Here, aimed at approximating the partition function, we consider multi-graph models where binary variables and multivariable factors are associated with edges and nodes, respectively, of an undirected multi-graph. We suggest a new methodology for analysis and computations that combines the Gauge function technique from Chertkov and Chernyak with the technique developed in Anari and Oveis Gharan 2017 arXiv:1702.02937; Gurvits 2011 arXiv:1106.2844; Straszak and Vishnoi 2017 55th Annual Allerton Conf. on Communication, Control, and Computing, based on the recent progress in the field of real stable polynomials. We show that the Gauge function, representing a single-out term in a finite sum expression for the partition function which achieves extremum at the so-called belief-propagation gauge, has a natural polynomial representation in terms of gauges/variables associated with edges of the multi-graph. Moreover, Gauge function can be used to recover the partition function through a sequence of transformations allowing appealing algebraic and graphical interpretations. Algebraically, one step in the sequence consists of the application of a differential operator over gauges associated with an edge. Graphically, the sequence is interpreted as a repetitive elimination/contraction of edges resulting in multi-graph models on decreasing in size (number of edges) graphs with the same partition function as in the original multi-graph model. Even though the complexity of computing factors in the sequence of the derived multi-graph models and respective Gauge functions grow exponentially with the number of eliminated edges, polynomials associated with the new factors remain bi-stable if the original factors have this property. Moreover, we show that BP estimations in the sequence do not decrease, each low-bounding the partition function.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Hadamard products and BPS networks

We study examples of fourth-order Picard-Fuchs operators that are Hadamard products of two second-order Picard-Fuchs operators. Each second-order Picard-Fuchs operator is associated with a family of elliptic curves, and the Hadamard product computes period integrals on the fibred product of the two elliptic surfaces. We construct 3-cycles on this geometry as the union of 2-cycles in the fibre over contours on the base. We then use the special Lagrangian condition to constrain the contours on the base. This leads to a construction that is reminiscent of spectral networks and exponential networks that have previously appeared in string theory literature.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

ORMATEX

The Oak Ridge Matrix Exponential (ORMATEX) software library contains methods to compute the matrix exponential and the action of the matrix exponential on a vector. Additionally, this package contains the related methods for the phi-functions which commonly appear in a wide class of exponential time integration methods. Krylov methods are provided to evaluate the matrix exponential-vector and phi-vector products for cases where the matrix is large and sparse. Utilizing these methods, ORMATEX implements performant exponential integrators for large systems of coupled ordinary differential equations (ODEs). The exponential time integration routines in ORMATEX are particularly suitable to large, stiff systems of equations. These routines may be utilized as a competitive alternative to classical implicit and explicit time integration schemes for certain classes of differential equations where the problem stiffness can be predominately explained by the linear terms.

Gurecky, William [Oak Ridge National Laboratory (O↗
DOE OSTI2024

Separable physics-informed DeepONet: Breaking the curse of dimensionality in physics-informed machine learning

The deep operator network (DeepONet) has shown remarkable potential in solving partial differential equations (PDEs) by mapping between infinite-dimensional function spaces using labeled datasets. However, in scenarios lacking labeled data, the physics-informed DeepONet (PI-DeepONet) approach, which utilizes the residual loss of the governing PDE to optimize the network parameters, faces significant computational challenges, particularly due to the curse of dimensionality. This limitation has hindered its application to high-dimensional problems, making even standard 3D spatial with 1D temporal problems computationally prohibitive. Additionally, the computational requirement increases exponentially with the discretization density of the domain. Here, to address these challenges and enhance scalability for high-dimensional PDEs, we introduce the Separable physics-informed DeepONet (Sep-PI-DeepONet). This framework employs a factorization technique, utilizing sub-networks for individual one-dimensional coordinates, thereby reducing the number of forward passes and the size of the Jacobian matrix required for gradient computations. By incorporating forward-mode automatic differentiation (AD), we further optimize computational efficiency, achieving linear scaling of computational cost with discretization density and dimensionality, making our approach highly suitable for high-dimensional PDEs. We demonstrate the effectiveness of Sep-PI-DeepONet through three benchmark PDE models: the viscous Burgers’ equation, Biot’s consolidation theory, and a parameterized heat equation. Our framework maintains accuracy comparable to the conventional PI-DeepONet while reducing training time by two orders of magnitude. Notably, for the heat equation solved as a 4D problem, the conventional PI-DeepONet was computationally infeasible (estimated 289.35 h), while the Sep-PI-DeepONet completed training in just 2.5 h. These results underscore the potential of Sep-PI-DeepONet in efficiently solving complex, high-dimensional PDEs, marking a significant advancement in physics-informed machine learning.

Neural operator↗
DOE OSTI2020

Parameter space mapping of the Princeton magnetorotational instability experiment

Extensive simulations of the Princeton Magnetorotational Instability (MRI) Experiment with the Spectral/Finite Element code for Maxwell and Navier-Stokes Equations (SFEMaNS) have been performed to map the MRI-unstable region as a function of inner cylinder angular velocity and applied vertical magnetic field. The angular velocities of the outer cylinder and the end-cap rings follow the inner cylinder in fixed ratios optimized for MRI. Here, we first confirm the exponential growth of the MRI linear phase using idealized conducting vertical boundaries (end caps) rotating differentially with a Taylor-Couette profile. Subsequently, we run a multitude of simulations to scan the experimental parameter space and find that the normalized volume-averaged mean-square radial magnetic field, our main instability indicator, rises significantly where MRI is expected. At various locations, the local radial components of fluid velocity and generated magnetic field are well correlated with the volume-averaged indicator. Based on this correlation, a diagnostic system that will measure the radial magnetic field at several locations on the inner cylinder is proposed as the main comparison between simulation and experiment. A detailed analysis of poloidal mode structures in the SFEMaNS code indicates that MRI, rather than Ekman circulation or Rayleigh instability, dominates the fluid behavior in the region where MRI is expected.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Sparse Cholesky factorization for solving nonlinear PDEs via Gaussian processes

In recent years, there has been widespread adoption of machine learning-based approaches to automate the solving of partial differential equations (PDEs). Among these approaches, Gaussian processes (GPs) and kernel methods have garnered considerable interest due to their flexibility, robust theoretical guarantees, and close ties to traditional methods. They can transform the solving of general nonlinear PDEs into solving quadratic optimization problems with nonlinear, PDE-induced constraints. However, the complexity bottleneck lies in computing with dense kernel matrices obtained from pointwise evaluations of the covariance kernel, and its partial derivatives, a result of the PDE constraint and for which fast algorithms are scarce. The primary goal of this paper is to provide a near-linear complexity algorithm for working with such kernel matrices. We present a sparse Cholesky factorization algorithm for these matrices based on the near-sparsity of the Cholesky factor under a novel ordering of pointwise and derivative measurements. The near-sparsity is rigorously justified by directly connecting the factor to GP regression and exponential decay of basis functions in numerical homogenization. We then employ the Vecchia approximation of GPs, which is optimal in the Kullback-Leibler divergence, to compute the approximate factor. This enables us to compute ϵ-approximate inverse Cholesky factors of the kernel matrices with complexity O(N log d (N/ϵ)) in space and O(N log 2d (N/ϵ)) in time. We integrate sparse Cholesky factorizations into optimization algorithms to obtain fast solvers of the nonlinear PDE. We numerically illustrate our algorithm’s near-linear space/time complexity for a broad class of nonlinear PDEs such as the nonlinear elliptic, Burgers, and Monge-Ampère equations. In summary, we provide a fast, scalable, and accurate method for solving general PDEs with GPs and kernel methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

The Spiral Galaxies Flat Rotational Velocity Curve Explained by the Constant Group Velocity of a Nonlinear Density Wave

The rotation velocity curves of stars in galaxies, the motions of pairs of galaxies, and the behavior of galaxies in clusters and super-clusters all indicate that there is a lack of mass on different scales in the universe. In this paper, we derive the expression for rotational velocity using the nonlinear density wave theory considering only stellar components and we show that such theory can support the observed flat rotational velocity curve due to the main property of the soliton wave, which is a constant group velocity of the wave. The surface mass density (SMD) function, used to derive gravitational potential gradient and rotational velocity, is not assumed but rather derived as a solution of the nonlinear Srödinger equation, on the contrary to the widely used, in the literature, exponential disk approximation. Three parameters relevant to the curve shape are the intensities of equilibrium SMD, the amplitude of the wave, and total angular velocity or differential rotation, equivalently. Since the shape of the rotational velocity is highly sensitive to the mentioned parameters, this theory eventually provides a method for a very accurate estimation of galaxy mass and angular velocity as well.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗