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Results for “differential transformation”

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 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

A perturbation method and some applications

For differential equations with one fast variable, a perturbation method is introduced that transforms a solution valid over only a short time interval to a new solution composed of averaged variables plus a periodic function of the averaged variables. The averaged variables are governed by a set of differential equations where the fast variable has been removed and thus can be numerically integrated quickly or solved directly. This method is applied to a perturbed harmonic oscillator with a cubic perturbation, van der Pol's equation, coorbital motion in the restricted three-body problem, and to nearly circular motion of a particle near one of the primaries in the restricted three-body problem.

Konopliv, Alex↗
NASA NTRS1980

Heat storage in alloy transformations

Heats of transformation of eutectic alloys were measured for many binary and ternary systems by differential scanning calorimetry and thermal analysis. Only the relatively cheap and plentiful elements Mg, Al, Si, P, Ca, Cu, Zn were considered. A method for measuring volume change during transformation was developed using x-ray absorption in a confined sample. Thermal expansion coefficients of both solid and liquid states of aluminum and of its eutectics with copper and with silicon also were determined. Preliminary evaluation of containment materials lead to the selection of silicon carbide as the initial material for study. Possible applications of alloy PCMs for heat storage in conventional and solar central power stations, small solar receivers and industrial furnace operations are under consideration.

Birchenall, C. E.↗
DOE OSTI2025

Joint Modeling of Quasar Variability and Accretion Disk Reprocessing Using Latent Stochastic Differential Equations

Quasars are bright active galactic nuclei powered by the accretion of matter around supermassive black holes at the center of galaxies. Their stochastic brightness variability depends on the physical properties of the accretion disk and black hole. The upcoming Rubin Observatory Legacy Survey of Space and Time (LSST) is expected to observe tens of millions of quasars, so there is a need for efficient techniques like machine learning that can handle the large volume of data. Quasar variability is believed to be driven by an X-ray corona, which is reprocessed by the accretion disk and emitted as UV/optical variability. We are the first to introduce an auto-differentiable simulation of the accretion disk and reprocessing. We use the simulation as a direct component of our neural network to jointly model the driving variability and reprocessing, trained with supervised learning on simulated LSST-like 10 yr quasar light curves. We encode the light curves using a transformer encoder, and the driving variability is reconstructed using latent stochastic differential equations, a physically motivated generative deep learning method that can model continuous-time stochastic dynamics. By embedding the physical processes of the driving signal and reprocessing into our network, we achieve a model that is more robust and interpretable. We demonstrate that our model outperforms a Gaussian process regression baseline and can infer accretion disk parameters and time delays between wave bands, even for out-of-distribution driving signals. Our approach provides a powerful framework that can be adapted to solve other inverse problems in multivariate time series.

Fagin, Joshua [City Univ. of New York (CUNY), NY (↗
DOE OSTI2020

Influence of plasticizers on thermal and mechanical properties of biocomposite filaments made from lignin and polylactic acid for 3D printing

Polylactic acid (PLA) and organosolv lignin were mixed at different ratios and extruded to obtain PLA-lignin composite filaments. PLA was replaced with lignin up to 20 wt%. Two plasticizers (polyethylene glycol (PEG) 2000 and struktol TR451) were added in varying concentrations to enhance the properties of PLA_L20 (20% lignin in PLA) composite filaments. Furthermore, the effect of lignin in PLA, and PEG, and struktol in PLA_L20 composites was investigated via tensile test, differential scanning calorimetry, thermogravimetric analysis, scanning electron microscopy, Fourier transform infrared spectroscopy of the filaments, and dynamic mechanical analysis of 3D printed samples. A 2 wt% PEG was able to enhance both tensile stress and elongation at maximum load of PLA_L20 composite by 19% and 35%, respectively, whereas struktol TR451 was able to improve elongation at maximum load by 24%.

3D printing↗
DOE OSTI2024

Connecting radiation-driven changes in structural, thermal, and mechanical properties in several medical device polymers

Stemming from security threats and shortages in supply, a recent push has emerged to develop alternatives to radioisotope Cobalt-60 gamma radiation for sterilization of polymeric medical products, including electron beam (e-beam) and X-ray machine-based sources. However, before large-scale implementation, the effects of these non-isotope-based methods must be thoroughly investigated from several perspectives, involving their potential detrimental effects on the structural, thermal, and mechanical properties of polymers in medical devices. This paper investigates such effects in commonly used medical device polymers, including polypropylene homopolymer (PPH), polyolefin elastomer (POE), low-density polyethylene (LDPE), acrylonitrile butadiene styrene (ABS), and chlorobutyl rubber (CIIR). To connect radiation-driven changes in polymer structural and thermal properties and corresponding changes in mechanical properties, several characterization techniques were utilized, including gel permeation chromatography (GPC), Fourier transform infrared spectroscopy (FTIR), dynamic mechanical analysis (DMA) and differential scanning calorimetry (DSC). We found that the tensile strength of X-ray irradiated PPH, as well as X-ray, e-beam, and gamma irradiated CIIR decreases due to chain scission, which is corroborated by GPC and DMA. The GPC results of LDPE suggest chain scission, but interestingly without a corresponding decline in tensile strength. By comparison, POE and ABS appear to undergo further crosslinking with increasing irradiation dose, which generally strengthens them. Importantly, in the vast majority of the cases, there were small to no changes in properties upon changing radiation technologies (at a given dose), i.e., no radiation source dependence. However, in a few specific cases, radiation method dependencies did arise, for instance, in terms of the molecular weight of PPH being significantly increased upon X-ray irradiation, while the melting temperature, glass transition temperature, and elongation at break reduced compared to gamma. Overall, this study provides valuable insight into radiation-driven chemical and structural changes in polymers that produce changes in physical and functional properties.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Limits of Detection for EXAFS Characterization of Heterogeneous Single-Atom Catalysts

Single-atom catalysts (SACs), consisting of individual metal atoms dispersed on a support, attract attention due to their unique reactivity, efficient use of precious metals, and precise chemical tunability. Characterization of the metal species is crucial to substantiate structure–function relationships. Authors often use—and referees often require—X-ray absorption spectroscopy (XAS) data to prove the absence of clustered metal (or metal oxide) structures after pre-treatment and under in situ or operando conditions. However, there has been no critical assessment of the limitations of XAS in substantiating such conclusive statements, which is particularly important given the potential outsized influence of minority catalyst structures in dictating catalytic activity. Here, in this article, we quantitatively assess the detection limits of XAS to identify metal (or metal oxide) clusters in samples containing predominantly single atoms by modeling the extended X-ray absorption fine structure (EXAFS) of mixtures of structures. We identified that a significant fraction of clusters can coexist with SAC active sites (e.g., ~10% metallic Pt or ~40% oxidized Pt clusters in Pt/CeO 2 SACs), while eluding detection via EXAFS with any statistical significance. To generalize these conclusions, a descriptor-based screening of bulk metal oxides using a continuous Cauchy wavelet transform was proposed that suggests certain materials for which differentiating atomically dispersed metal species and metal oxide clusters would be infeasible by EXAFS (e.g., ReO x ). Based on this analysis, we suggest best practices for the study of SACs using EXAFS and provide recommendations to ensure that conclusions do not outpace the evidence used to support them. In this rapidly expanding research area, rigorous characterization will lead to greater understanding of the behavior of SACs and ultimately improved catalytic materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Differentiable vertex fitting for jet flavor tagging

This work explores the use of differentiable programming to integrate domain knowledge, in the form of domain specific software, into neural networks to develop scientific machine learning systems. We propose a differentiable vertex fitting algorithm that estimates the crossing point of multiple curves. In the high energy physics setting, these curves are defined by particle equations of motion and the crossing point represents the origin of particle production. This differentiable vertex fitting algorithm can be seamlessly integrated into neural networks, and we show its utility and efficacy in the high energy physics application of the classification of jets, i.e., collimated streams of particles in particle detectors whose originating parent particle we aim to classify. We demonstrate how differentiable vertex fitting can be integrated into larger transformer-based models for jet flavor tagging and show improvements in heavy flavor jet classification when compared to baseline models. Published by the American Physical Society 2024

Smith, Rachel E. C. (ORCID:0000000335851262)↗
DOE OSTI2026

Energy–Performance Trade-offs in Privacy-Preserving Federated Learning on SmartNIC-Enabled HPC Systems

Federated learning (FL) is increasingly deployed on accelerator-rich high-performance computing (HPC) systems, yet the system-level energy cost of privacy-aware FL remains poorly understood, particularly across heterogeneous networking and server-placement options. We present a measurement-driven study of energy–performance trade-offs for FL on GH200-class nodes across three deployment configurations: CPU-Ethernet, CPU-InfiniBand (RDMA-capable), and a DPU-hosted FL server over InfiniBand using a BlueField-3 SmartNIC/DPU. Using NVIDIA FLARE (NVFLARE), we align node-level power telemetry with per-round timing extracted from NVFLARE logs to quantify time-to-solution (TTS), energy-to-solution (ETS), energy-delay product (EDP), and synchronization behavior for three transformer models (ALBERT, DistilBERT, BERT), trained with and without differential privacy (DP). We find that interconnect choice is the dominant driver of runtime and energy: host-managed InfiniBand consistently reduces communication overhead versus Ethernet, yielding lower TTS/ETS/EDP. In contrast, in our NVFLARE deployment, placing the FL server on the DPU does not consistently match CPU-InfiniBand performance and can be slower—especially for larger models—highlighting that server placement alone is not sufficient to guarantee end-to-end gains. Finally, under our fixed-round protocol, DP increases per-round cost and runtime variance; ETS increases largely in proportion to TTS because average node power remains relatively stable across configurations.

Kotevska, Olivera [ORNL] (ORCID:0000000316772243)↗
DOE OSTI2026

WFSUITE: A PYTHON SOFTWARE SUITE FOR X-RAY WAVEFRONT SENDING AND AT-WAVELENGTH METROLOGY

SF-26-025 WFSuite is a graphical and command-line toolkit for coded-mask-based X-ray wavefront sensing and phase reconstruction at synchrotron beamlines. It integrates analysis tools for both relative and absolute speckle-based measurements. In the relative metrology module, WFSuite implements Wavelet-transform-based X-ray Speckle Tracking (WXST) and Wavelet-transform-based Speckle Vector Tracking (WSVT) methods to retrieve differential phase and wavefront distortions by comparing speckle patterns recorded with and without the test sample. In the absolute phase module, WFSuite uses coded-mask speckle patterns and replaces the measured reference with a numerically simulated one, enablingsingle-shot wavefront reconstruction using either WXST or a neural-network-based method (SPINNet).

Rebuffi, Luca [Argonne National Laboratory (ANL), ↗
NASA NTRS1969

Dynamic characteristics of a variable-mass flexible missile: Dynamics of a two-stage variable-mass flexible rocket

The dynamic characteristics of two-stage slender elastic body were investigated. The first stage, containing a solid-fuel rocket, possesses variable mass while the second stage, envisioned as a flexible case, contains packaged instruments of constant mass. The mathematical formulation was in terms of vector equations of motion transformed by a variational principle into sets of scalar differential equations in terms of generalized coordinates. Solutions to the complete equations were obtained numerically by means of finite difference techniques. The problem has been programmed in the FORTRAN 4 language and solved on an IBM 360/50 computer. Results for limited cases are presented showing the nature of the solutions.

Meirovitch, L.↗
NASA NTRS1976

Implicit finite-difference procedures for the computation of vortex wakes

Implicit finite-difference procedures for the primitive form of the incompressible Navier-Stokes and the compressible Euler equations are used to compute vortex wake flows. The partial differential equations in strong conservation-law form are transformed to cluster grid points in regions with large changes in vorticity. In addition to clustering, fourth-order accurate, spatial difference operators are used to help resolve the flow-field gradients. The use of implicit time-differencing permits large time steps to be taken since temporal variations are typically small. Computational efficiency is achieved by approximate factorization. Both two-dimensional and preliminary three-dimensional calculations are described and qualitatively compared with existing experimental data.

Steger, J. L.↗
NASA NTRS1977

Transient wave propagation in composite plates due to impact

Stress-wave propagation in a composite plate due to an impact has been examined using anisotropic elasticity theory. The plate is modelled as a number of identical anisotropic layers whose elastic moduli are given. Mindlin's (1959) approximate theory of plates is then applied to each layer to obtain a set of difference-differential equations of motion by using the interlaminar stresses and displacements as explicit variables. Dispersion relationships for harmonic waves are found when traction-free boundary conditions are applied to both surfaces of the plate. The difference-differential equations are reduced to difference equations via integral transforms. With given impact boundary conditions these equations are solved for an arbitrary number of layers in the plate, and the transient propagation of a stress wave is calculated by means of a fast Fourier transform algorithm.

Sung Kim, B.↗
NASA NTRS1980

Steady, Oscillatory, and Unsteady Subsonic and Supersonic Aerodynamics, production version (SOUSSA-P 1.1). Volume 1: Theoretical manual

Recent developments of the Green's function method and the computer program SOUSSA (Steady, Oscillatory, and Unsteady Subsonic and Supersonic Aerodynamics) are reviewed and summarized. Applying the Green's function method to the fully unsteady (transient) potential equation yields an integro-differential-delay equation. With spatial discretization by the finite-element method, this equation is approximated by a set of differential-delay equations in time. Time solution by Laplace transform yields a matrix relating the velocity potential to the normal wash. Premultiplying and postmultiplying by the matrices relating generalized forces to the potential and the normal wash to the generalized coordinates one obtains the matrix of the generalized aerodynamic forces. The frequency and mode-shape dependence of this matrix makes the program SOUSSA useful for multiple frequency and repeated mode-shape evaluations.

Morino, L.↗
NASA NTRS1980

Numerical grid generation techniques

The state of the art in topology and flow geometry is presented. Solution techniques for partial differential equations are reviewed and included developments in coordinate transformations, conformal mapping, and invariant imbeddings. Applications of these techniques in fluid mechanics, flow geometry, boundary value problems, and fluidics are presented.

Source record↗
NASA NTRS1984

On the use of parametric differentiation to predict weak shock waves

The method of parametric differentiation is shown to be an effective means to transform both the time-linearized and the fully nonlinear transonic small disturbance potential flow equations to a linear system of equations. The globally linearized equations are then solved in phase space by finite difference methods and integral equation methods. The predicted birth, growth, and motion of weak shock waves in two-dimensional transonic flows are compared with existing theory and experiment.

Harris, W. L.↗
NASA NTRS1988

Analytical solutions of a class of multidimensional Fokker-Planck equations

Analytical representations of the solutions of Kolmogorov's forward (i.e., Fokker-Planck) and backward partial differential equations are obtained by employing Girsanov's (1960) transformation. The equations considered are restricted to those with the drift vector being the gradient of a function and the diffusion matrix being nonsingular and dependent upon time only.

Zhang, Weijian↗