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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Guiding center equations for the magnetic dipole

Since the discovery of Van Allen radiation belts in the 1960s, observations of energetic ions trapped in the Earth's dipole magnetic field have illustrated the remarkable confinement properties of this configuration. As such, it has been used for confining a hot plasma for nuclear fusion studies, starting from the pioneering work of Bo Lehnert and Akira Hasegawa, in the Levitated Dipole Experiment (LDX) at MIT until 2011 and in the RT-1 experiment at the University of Tokyo. More recently, the dipole has been subject to a renewed interest for fusion studies by a couple of startups and for smaller applications as a cold plasma source. While the equilibrium and magneto-hydrodynamic stability of the dipole have been investigated quite in detail, neoclassical properties of the dipole are comparatively much less known: the dipole is more known in geophysics than in fusion science. For this reason, in this paper, we propose a set of Hamiltonian, guiding-center equations to describe the motion of electrons and ions in a magnetic dipole configuration. We also developed a code, and we show the main features of particle motion, benchmarking our results with the analytical solutions for the bounce and precession motion, which are well documented in the literature. We also draw some general conclusions for the neoclassical transport in usual toroidal confinement schemes, such as the tokamak and the stellarator, pointing out the unique advantages of the dipole in confining energetic particles.

Hamiltonian mechanics↗
DOE OSTI2022

The rapid destruction of toroidal magnetic surfaces

The operation of ITER will require reliable simulations in order to avoid major damage to the device from disruptions. Disruptions are the sudden breakup of magnetic surfaces across the plasma volume—a fast magnetic reconnection. This reconnection can be caused by the growth of perturbations outside of the plasma core causing an ideal perturbation to the core. This causes an increasing ratio of the maximum to the minimum separation, Δmax/Δmin, between neighboring magnetic surfaces. Magnetic reconnection becomes a dominant process when magnetic field lines can quickly interchange connections over a spatial scale ar. This occurs when Δmax/Δmin≳ar/Δd, where Δd is the scale over which non-ideal effects make magnetic field lines indistinguishable. Traditional reconnection theory is fundamentally different. It is a study of the steady-state cancelation of oppositely directed magnetic field components across a thin layer. During more than sixty years, mathematical implications of Faraday's law have been derived that clarify and constrain the physics of fast magnetic reconnection. These are reviewed because they are not commonly known but are needed to understand and to place in context how an ideal magnetic evolution can cause reconnection to quickly become a dominant process no matter how small Δd/ar may be.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Parameterization of cloud transmittance for expeditious assessment and forecasting of all-sky DNI

Radiative transfer models require vast computing resources to solve cloud transmittance and reflectance from the radiative transfer equation. As a result, models offering precise simulation in operations often acquire individual cloud transmittance or reflectance from a lookup table precomputed for practicable scenarios. To further expedite the computation of global horizontal irradiance and to reduce the storage requirements, the Fast All-sky Radiation Model for Solar applications (FARMS) parameterized the lookup table using elementary functions with specified coefficients. This study extends FARMS direct normal irradiance (DNI) computation by utilizing hyperbolic tangent functions and various polynomial functions to parameterize the cloud transmittance for scattered solar radiation in the circumsolar region. The parameterization is implemented in FARMS with DNI (FARMS-DNI) and accounts for the circumsolar radiation when assessing or forecasting DNI. The evaluation, with long-term observations at the National Renewable Energy Laboratory's, Solar Radiation Research Laboratory, and the Atmospheric Radiation Measurement, Southern Great Plains, Central Facility, shows that the parameterized DNIs are virtually identical with those computed by coupling FARMS-DNI to a lookup table of cloud transmittance. This parameterization has diverse applications in radiative transfer models and numerical weather prediction models used to assess or forecast direct solar radiation.

14 SOLAR ENERGY↗
DOE OSTI2023

Adjustments to the law of the wall above an Amazon forest explained by a spectral link

Modification to the law of the wall represented by a dimensionless correction function ϕ RSL (z/h) is derived using atmospheric turbulence measurements collected at two sites in the Amazon in near-neutral stratification, where z is the distance from the forest floor and h is the mean canopy height. The sites are the Amazon Tall Tower Observatory for z/h∈ [1,2.3] and the Green Ocean Amazon (GoAmazon) site for z/h∈ [1,1.4]. Here, a link between the vertical velocity spectrum E ww (k) (k is the longitudinal wavenumber) and ϕ RSL is then established using a co-spectral budget (CSB) model interpreted by the moving-equilibrium hypothesis. The key finding is that ϕ RSL is determined by the ratio of two turbulent viscosities and is given as ν t,BL /ν t,RSL, where ν t,RSL = (1/A)∫$^{∞}_{0}$ τ(k)E ww (k)dk, ν t,BL = k v (z−d)u * , τ(k) is a scale-dependent decorrelation time scale between velocity components, A = C R /(1−C I ) = 4.5 is predicted from the Rotta constant C R = 1.8, and the isotropization of production constant C I = 3/5 given by rapid distortion theory, k v is the von Kármán constant, u * is the friction velocity at the canopy top, and d is the zero-plane displacement. Because the transfer of energy across scales is conserved in E ww (k) and is determined by the turbulent kinetic energy dissipation rate (ε), the CSB model also predicts that ϕ RSL scales with L BL /L d , where L BL is the length scale of attached eddies to z = d, and L d = u$_{*}^{3}$/ε is a macro-scale dissipation length.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Constraining chaos: Enforcing dynamical invariants in the training of reservoir computers

Drawing on ergodic theory, we introduce a novel training method for machine learning based forecasting methods for chaotic dynamical systems. The training enforces dynamical invariants—such as the Lyapunov exponent spectrum and the fractal dimension—in the systems of interest, enabling longer and more stable forecasts when operating with limited data. The technique is demonstrated in detail using reservoir computing, a specific kind of recurrent neural network. Finally, results are given for the Lorenz 1996 chaotic dynamical system and a spectral quasi-geostrophic model of the atmosphere, both typical test cases for numerical weather prediction.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

From PINNs to PIKANs: recent advances in physics-informed machine learning

Physics-Informed Neural Networks (PINNs) have emerged as a key tool in Scientific Machine Learning since their introduction in 2017, enabling the efficient solution of ordinary and partial differential equations using sparse measurements. Over the past few years, significant advancements have been made in the training and optimization of PINNs, covering aspects such as network architectures, adaptive refinement, domain decomposition, and the use of adaptive weights and activation functions. A notable recent development is the Physics-Informed Kolmogorov-Arnold Networks (PIKANS), which leverage a representation model originally proposed by Kolmogorov in 1957, offering a promising alternative to traditional PINNs. In this review, we provide a comprehensive overview of the latest advancements in PINNs, focusing on improvements in network design, feature expansion, optimization techniques, uncertainty quantification, and theoretical insights. We also survey key applications across a range of fields, including biomedicine, fluid and solid mechanics, geophysics, dynamical systems, heat transfer, chemical engineering, and beyond. Lastly, we review computational frameworks and software tools developed by both academia and industry to support PINN research and applications.

Kolmogorov-Arnold networks↗
DOE OSTI2021

Turbulence theories and statistical closure approaches

When discussing research in physics and in science more generally, it is common to ascribe equal importance to the three components of the scientific trinity: theoretical, experimental, and computational studies. This review will explore the future of modern turbulence theory by tracing its history, which began in earnest with Kolmogorov’s 1941 analysis of turbulence cascade and inertial range [A.N. Kolmogorov, Dokl. Akad. Nauk SSSR, 30, 299, (1941); 32, 19, (1941)]. The 80th Anniversary of Kolmogorov’s landmark study is a welcome opportunity to survey the achievements and evaluate the future of the theoretical approach of turbulence research. Over the years, turbulence theories have been critically important in laying the foundation of our understanding of the nature of turbulent flows. In particular, the Direct Interaction Approximation (DIA) [R.H. Kraichnan, J. Fluid Mech., 5, 497 (1959)] and its subsequent development, known as the statistical closure approach, can be identified as perhaps the most profound single advancement. The remarkable success of the statistical closure has furnished a platform to study such essential concepts as the energy transfer process and interacting scales, and the roles of the straining and sweeping motions. More recently, the quasi-Lagrangian formulation of V. L’vov & I. Procaccia and Kraichnan’s solvable passive scalar model provided powerful ways to explore another fundamental aspect of turbulent flows, the phenomena of intermittency, and the associated anomalous scaling exponents. In the meantime, the theory of fluid equilibria has been developed to describe the large-scale structures that can emerge from turbulent cascades of two-dimensional and geophysical flows at a later time. And yet, despite all these successes, analytical treatments suffer from mathematical complexities. As a result, the utility of theoretical approaches has been limited to relatively idealized flows. On the other hand, in recent decades, computational abilities and experimental facilities have reached an unprecedented scale. Looking beyond the horizon, the imminent deployment of exascale supercomputers will generate complete datasets of the entire flow field of key benchmark flows, allowing researchers to extract additional measurements concerning fully developed, complex turbulent flow fields far beyond those available from the statistical closure theories. Some other developments that could potentially influence the future course of turbulence theories include the advancement of machine learning, artificial intelligence, and data science; likely disruptions arising from the advent of quantum computation; and the increasingly prominent role of turbulence research in providing more accurate climate scientific data. Finally, turbulence theorists can leverage these developments by asking the right questions and developing advanced, sophisticated frameworks that will be able to predict and correlate vast amounts of data from the other two components of the trinity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

An adjoint-based optimization method for jointly inverting heterogeneous material properties and fault slip from earthquake surface deformation data

SUMMARY Analysis of tectonic and earthquake-cycle associated deformation of the crust can provide valuable insights into the underlying deformation processes including fault slip. How those processes are expressed at the surface depends on the lateral and depth variations of rock properties. The effect of such variations is often tested by forward models based on a priori geological or geophysical information. Here, we first develop a novel technique based on an open-source finite-element computational framework to invert geodetic constraints directly for heterogeneous media properties. We focus on the elastic, coseismic problem and seek to constrain variations in shear modulus and Poisson’s ratio, proxies for the effects of lithology and/or temperature and porous flow, respectively. The corresponding nonlinear inversion is implemented using adjoint-based optimization that efficiently reduces the cost function that includes the misfit between the calculated and observed displacements and a penalty term. We then extend our theoretical and numerical framework to simultaneously infer both heterogeneous Earth’s structure and fault slip from surface deformation. Based on a range of 2-D synthetic cases, we find that both model parameters can be satisfactorily estimated for the megathrust setting-inspired test problems considered. Within limits, this is the case even in the presence of noise and if the fault geometry is not perfectly known. Our method lays the foundation for a future reassessment of the information contained in increasingly data-rich settings, for example, geodetic GNSS constraints for large earthquakes such as the 2011 Tohoku-oki M9 event, or distributed deformation along plate boundaries as constrained from InSAR.

Geochemistry & Geophysics↗
DOE OSTI2022

Dynamic mode decomposition with core sketch

With the increase in collected data volumes, either from experimental measurements or high fidelity simulations, there is an ever-growing need to develop computationally efficient tools to process, analyze, and interpret these datasets. Modal analysis techniques have gained great interest due to their ability to identify patterns in the data and extract valuable information about the system being considered. Dynamic mode decomposition (DMD) relies on elements of the Koopman approximation theory to compute a set of modes, each associated with a fixed oscillation frequency and a decay/growth rate. Extracting these details from large datasets can be computationally expensive due to the need to implement singular value decomposition of the input data matrix. Sketching algorithms have become popular in numerical linear algebra where statistical theoretic approaches are utilized to reduce the cost of major operations. A sketch of a matrix is another matrix, which is significantly smaller, but still sufficiently approximates the original system. We put forth an efficient DMD framework, SketchyDMD, based on a core sketching algorithm that captures information about the range and corange (their mutual relationship) of input data. The proposed sketching-based framework can accelerate various portions of the DMD routines, compared to classical methods that operate directly on the raw input data. We conduct numerical experiments using the spherical shallow water equations as a prototypical model in the context of geophysical flows. In conclusion, we show that the proposed SketchyDMD is superior to existing randomized DMD methods that are based on capturing only the range of the input data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

A Fast Solver for the Fractional Helmholtz Equation

The purpose of this paper is to study a Helmholtz problem with a spectral fractional Laplacian, instead of the standard Laplacian. Recently, it has been established that such a fractional Helmholtz problem better captures the underlying behavior in Geophysical Electromagnetics. In this work, we establish the well-posedness and regularity of this problem. We introduce a hybrid spectral-finite element approach to discretize it and show well-posedness of the discrete system. In addition, we derive a priori discretization error estimates. Finally, we introduce an efficient solver that scales aswell as the best possible solver for the classical integer-order Helmholtz equation. We conclude withseveral illustrative examples that confirm our theoretical findings.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Using Deep Learning to Derive Shear-Wave Velocity Models from Surface-Wave Dispersion Data

We present a new algorithm for derivations of 1D shear-wave velocity models from surface-wave dispersion data using convolutional neural networks (CNNs). The technique is applied for continental China and the plate boundary region in southern California. Different CNNs are designed for these two regions and are trained using theoretical Rayleigh-wave phase and group velocity images computed from reference 1D VS models. The methodology is tested with 3260 phase–group images for continental China and 4160 phase–group images for southern California. The conversions of these images to velocity profiles take ~23 s for continental China and ~30 s for southern California on a personal laptop with the NVIDIA GeForce GTX 1060 core and a memory of 6 GB. The results obtained by the CNNs show high correlation with previous studies using conventional methods. The effectiveness of the CNN technique makes this fast method an important alternative for deriving shear-wave velocity models from large datasets of surface-wave dispersion data.

Geochemistry & Geophysics↗
DOE OSTI2021

Multichannel Analysis of Surface Waves Accelerated (MASWAccelerated): Software for efficient surface wave inversion using MPI and GPUs

Multichannel Analysis of Surface Waves (MASW) is a technique frequently used in geotechnical engineering and engineering geophysics to infer 1D layered models of seismic shear wave velocities in the top tens to hundreds of meters of the subsurface. We aim to accelerate MASW calculations by capitalizing on modern computer hardware available in the workstations of most engineers: multiple cores and graphics processing units (GPUs). We propose new parallel and GPU accelerated algorithms for computing 1D MASW inversion, and provide software implementations in C using Message Passing Interface (MPI) and CUDA. These algorithms take advantage of sparsity that arises in the problem, and the work balance between processes considers typical data trends. We compare our methods to an existing open source Matlab MASW tool. Our serial C implementation achieves a 2x speedup over the Matlab software, and we continue to see improvements by parallelizing the problem with MPI. Here we see nearly perfect strong and weak scaling for uniform data, and improve strong scaling for realistic data by repartitioning the problem to process mapping. By utilizing GPUs available on most modern workstations, we observe an additional 1.3x speedup over the serial C implementation on the first use of the method. We typically repeatedly evaluate theoretical dispersion curves as part of an optimization procedure, and on the GPU the kernel can be cached for faster reuse on later runs. We observe a 3.2x speedup on the cached GPU runs compared to the serial C runs. This work is the first open-source parallel or GPU-accelerated software tool for MASW imaging, and should enable geotechnical engineers to fully utilize all computer hardware at their disposal.

58 GEOSCIENCES↗
DOE OSTI2025

Investigating the Relationship Between Bolide Entry Angle and Apparent Direction of Infrasound Signal Arrivals

Infrasound sensing offers critical capabilities for detecting and geolocating bolide events globally. However, the observed back azimuths, directions from which infrasound signals arrive at stations, often differ from the theoretical expectations based on the bolide’s peak brightness location. For objects with shallow entry angles, which traverse longer atmospheric paths, acoustic energy may be emitted from multiple points along the trajectory, leading to substantial variability in back azimuth residuals. This study investigates how the entry angle of energetic bolides affects the back azimuth deviations, independent of extrinsic factors such as atmospheric propagation, station noise, and signal processing methodologies. A theoretical framework, the Bolide Infrasound Back-Azimuth EXplorer Model (BIBEX-M), was developed to compute predicted back azimuths solely from geometric considerations. The model quantifies how these residuals vary as a function of source-to-receiver distance, revealing that bolides entering at shallow angles, e.g., 10°, can produce average residuals of 20°, with deviations reaching up to 46° at distances below 1000 km, and remaining significant even at 5000 km (up to 8°). In contrast, bolides with steeper entry angles, e.g., > 60°, show smaller deviations, typically under 5° at 1000 km and diminishing to less than ~1° beyond 5000 km. These findings attest to the need for careful interpretation when evaluating signal detections and estimating bolide locations. This work is not only pertinent to bolides but also to other high-energy, extended-duration atmospheric phenomena such as space debris and reentry events, where similar geometric considerations can influence infrasound arrival directions.

Acoustics↗
DOE OSTI2022

Combining different 3-D global and regional seismic wave propagation solvers towards box tomography in the deep Earth

SUMMARY In previous publications, we presented a general framework, which we called ‘box tomography’, that allows the coupling of any two different numerical seismic wave propagation solvers, respectively outside and inside a target region, or ‘box’. The goal of such hybrid wavefield computations is to reduce the cost of computations in the context of full-waveform inversion for structure within the target region, when sources and/or receivers are located at large distances from the box. Previously, we had demonstrated this approach with sources and receivers outside the target region in a 2-D acoustic spherical earth model, and demonstrated and applied this methodology in the 3-D spherical elastic Earth in a continental scale inversion in which all stations were inside the target region. Here we extend the implementation of the approach to the case of a 3-D global elastic earth model in the case where both sources and stations are outside the box. We couple a global 3-D solver, SPECFEM3D_GLOBE, for the computation of the wavefield and Green’s functions in a reference 3-D model, with a regional 3-D solver, RegSEM, for the computation of the wavefield within the box, by means of time-reversal mirrors. We briefly review key theoretical aspects, showing in particular how only the displacement is needed to be stored at the boundary of the box. We provide details of the practical implementation, including the geometrical design of the mirrors, how we deal with different sizes of meshes in the two solvers, and how we address memory-saving through the use of B-spline compression of the recorded wavefield on the mirror. The proposed approach is numerically efficient but also versatile, since adapting it to other solvers is straightforward and does not require any changes in the solver codes themselves, as long as the displacement can be recovered at any point in time and space. We present benchmarks of the hybrid computations against direct computations of the wavefield between a source and an array of stations in a realistic geometry centred in the Yellowstone region, with and without a hypothetical plume within the ‘box’, and with a 1-D or a 3-D background model, down to a period of 20 s. The ultimate goal of this development is for applications in the context of imaging of remote target regions in the deep mantle, such as, for example, Ultra Low Velocity Zones.

Geochemistry & Geophysics↗
DOE OSTI2020

Integration of Soft Data Into Geostatistical Simulation of Categorical Variables

Uncertain or indirect “soft” data, such as geologic interpretation, driller’s logs, geophysical logs or imaging, offer potential constraints or “soft conditioning” to stochastic models of discrete categorical subsurface variables in hydrogeology such as hydrofacies. Previous bivariate geostatistical simulation algorithms have not fully addressed the impact of data uncertainty in formulation of the (co) kriging equations and the objective function in simulated annealing (or quenching). This paper introduces the geostatistical simulation code tsim-s, which accounts for categorical data uncertainty through a data “hardness” parameter. In generating geostatistical realizations with tsim-s, the uncertainty inherent to soft conditioning is factored into both 1) the data declustering and spatial correlation functions in cokriging and 2) the acceptance probability for change of category in simulated quenching. The degree or sensitivity to which soft data conditions a realization as a function of hardness can be quantified by mapping category probabilities derived from multiple realizations. In addition to point or borehole data, arrays of data (e.g., as derived from a depth-dependency function, probability map, or “prior realization”) can be used as soft conditioning. The tsim-s algorithm provides a theoretically sound and general framework for integrating datasets of variable location, resolution, and uncertainty into geostatistical simulation of categorical variables. A practical example shows how tsim-s is capable of generating a large-scale three-dimensional simulation including curvilinear features.

54 ENVIRONMENTAL SCIENCES↗