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Results for “Integral transforms”

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 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

On the apparent velocity of integrated sunlight. 2: 1983-1992 and comparisons with magnetograms

We report additional results in our program to monitor the wavelength stability of lines in the 2.3 micrometer spectrum of integrated sunlight. We use the McMath Fourier transform spectrometer (FTS) of the National Solar Observatory to monitor 16 delta V = 2 lines of (12)C(16)O, as well as five atomic lines. Wavenumber calibration is achieved using a low-pressure N2O absorption cell and checked against terrestrial atmospheric lines. Imperfect optical integration of the solar disk remains the principal source of error, but this error has been reduced by improved FTS/telescope collimation and observing procedures. The present results include data from an additional 13 quarterly observing runs since 1985. We continue to find that the apparent velocity of integrated sunlight is variable, in the sense of having a greater reshift at solar maximum. This is supported by the temporal dependence of the integrated light velocity, and by the presence of a correlation between velocity and the disk-averaged magnetic flux derived from Kitt Peak magnetograms. The indicated peak-to-peak apparent velocity amplitude over a solar cycle is approximately the same as the velocity amplitude of the Sun's motion about the solar system barycenter. This represents about half the amplitude which we inferred in Paper I (Deming et al. 1987), but the present result has a much greater statistical significance. Our results have implications for those investigations which search for the Doppler signatures of planetary-mass companions to solar-type stars. We contrast our results to the recent finding by McMillan et al. 1993 that solar absorption lines in the violet spectral region are wavelength-stable over the solar cycle.

Deming, Drake↗
DOE OSTI2024

Empowering Scientific Innovation Through An Integrated Research Infrastructure: The Role of the Advanced Computing Ecosystem

As the landscape of computational science evolves, the Department of Energy (DOE) is reimagining the roles of its large-scale computing facilities to meet emerging research challenges. The Integrated Research Infrastructure (IRI) program aims to transform how experiments are designed, conducted, and shared, with significant impacts on all stakeholders. In response, the Oak Ridge Leadership Computing Facility (OLCF) has established the Advanced Computing Ecosystem (ACE), a strategic framework to prepare its hardware, software, and experimental capabilities for the IRI era. ACE focuses on integrating novel compute environments, orchestrating advanced workflows, and developing foundational technologies, ensuring a seamless transition to IRI while accelerating scientific discovery. This paper outlines ACE's role in advancing OLCF's mission and its impact on the future of computational science.

Widener, Patrick↗
NASA NTRS1999

Human responses to upright tilt: a window on central autonomic integration

1. We examined interactions between haemodynamic and autonomic neural oscillations during passive upright tilt, to gain better insight into human autonomic regulatory mechanisms. 2. We recorded the electrocardiogram, finger photoplethysmographic arterial pressure, respiration and peroneal nerve muscle sympathetic activity in nine healthy young adults. Subjects breathed in time with a metronome at 12 breaths min-1 (0.2 Hz) for 5 min each, in supine, and 20, 40, 60, 70 and 80 deg head-up positions. We performed fast Fourier transform (and autoregressive) power spectral analyses and integrated low-frequency (0.05-0.15 Hz) and respiratory-frequency (0. 15-0.5 Hz) spectral powers. 3. Integrated areas of muscle sympathetic bursts and their low- and respiratory-frequency spectral powers increased directly and significantly with the tilt angle. The centre frequency of low-frequency sympathetic oscillations was constant before and during tilt. Sympathetic bursts occurred more commonly during expiration than inspiration at low tilt angles, but occurred equally in expiration and inspiration at high tilt angles. 4. Systolic and diastolic pressures and their low- and respiratory-frequency spectral powers increased, and R-R intervals and their respiratory-frequency spectral power decreased progressively with the tilt angle. Low-frequency R-R interval spectral power did not change. 5. The cross-spectral phase angle between systolic pressures and R-R intervals remained constant and consistently negative at the low frequency, but shifted progressively from positive to negative at the respiratory frequency during tilt. The arterial baroreflex modulus, calculated from low-frequency cross-spectra, decreased at high tilt angles. 6. Our results document changes of baroreflex responses during upright tilt, which may reflect leftward movement of subjects on their arterial pressure sympathetic and vagal response relations. The intensity, but not the centre frequency of low-frequency cardiovascular rhythms, is modulated by the level of arterial baroreceptor input. Tilt reduces respiratory gating of sympathetic and vagal motoneurone responsiveness to stimulatory inputs for different reasons; during tilt, sympathetic stimulation increases to a level that overwhelms the respiratory gate, and vagal stimulation decreases to a level below that necessary for maximal respiratory gating to occur.

Non-NASA Center↗
NASA NTRS1985

The Toda lattice as a forced integrable system

The analytic properties of the Jost functions for the inverse scattering transform associated with the forced Toda lattice are shown to determine the time evolution of this particular boundary value problem. It is suggested that inverse scattering methods may be used generally to analyze forced integrable systems. Thus an extension of the applicability of the inverse scattering transform is indicated.

Hansen, P. J.↗
DOE OSTI2025

Explainable AI for Multivariate Time Series Pattern Exploration: Latent Space Visual Analytics With Temporal Fusion Transformer and Variational Autoencoders in Power Grid Event Diagnosis

Detecting and analyzing complex patterns in multivariate time-series data is crucial for decision-making in urban and environmental system operations. However, challenges arise from the high dimensionality, intricate complexity, and interconnected nature of complex patterns, which hinder the understanding of their underlying physical processes. Existing AI methods often face limitations in interpretability, computational efficiency, and scalability, reducing their applicability in real-world scenarios. This paper proposes a novel visual analytics framework that integrates two generative AI models, Temporal Fusion Transformer (TFT) and Variational Autoencoders (VAEs), to reduce complex patterns into lower-dimensional latent spaces and visualize them in 2D using dimensionality reduction techniques such as PCA, t-SNE, and UMAP with DBSCAN. These visualizations, presented through coordinated and interactive views and tailored glyphs, enable intuitive exploration of complex multivariate temporal patterns, identifying patterns’ similarities and uncover their potential correlations for a better interpretability of the AI outputs. The framework is demonstrated through a case study on power grid signal data, where it identifies multi-label grid event signatures, including faults and anomalies with diverse root causes. Additionally, novel metrics and visualizations are introduced to validate the models and assess the performance, efficiency, and consistency of latent maps generated by VAE, which have been utilized in prior studies for latent space cartography and used as a benchmark in this study, and the emerging TFT architecture under various configurations. These analyses provide actionable insights for model parameter tuning and reliability improvements. Comparative results highlight that TFT achieves shorter run times and superior scalability to diverse time-series data shapes compared to VAE. This work advances fault diagnosis in multivariate time series, fostering explainable AI to support critical system operations.

Explainable AI↗
NASA NTRS1988

Transformational derivation of programs using the Focus system

A program derivation support system called Focus is being constructed. It will formally derive programs using the paradigm of program transformation. The following issues are discussed: (1) the integration of validation and program derivation activities in the Focus system; (2) its tree-based user interface; (3) the control of search spaces in program derivation; and (4) the structure and organization of program derivation records. The inference procedures of the system are based on the integration of functional and logic programming principles. This brings about a synthesis of paradigms that were heretofore considered far apart, such as logical and executable specifications and constructive and transformational approaches to program derivation. A great emphasis has been placed, in the design of Focus, on achieving small search spaces during program derivation. The program manipulation operations such as expansion, simplification and rewriting were designed with this objective. The role of operations that are expensive in search spaces, such as folding, has been reduced. Program derivations are documented in Focus in a way that the high level descriptions of derivations are expressed only using program level information. All the meta-level information, together with dependencies between derivations of program components, is automatically recorded by the system at a lower level of description for its own use in replay.

Reddy, Uday S.↗
DOE OSTI2026

A Discrete Hankel Transform Approach to Nuclear Data Processing for Fusion Applications

This study introduces advancements to the numerical solutions employed in the processing of nuclear data for fusion applications. It leverages the convolution theorem and Fourier transform techniques to enhance computational efficiency and broaden applicability. Building upon a previously reported discrete Hankel transform approach for Doppler broadening, this work refines the solution of convolution integrals central to these applications. The methodology provides a general and unified framework for evaluating any convolution operation, regardless of whether the underlying problem involves temperature effects in nuclear reactions. The applicability to the nuclear data processing for fusion is demonstrated by deriving the convolution integrals for some of the fusion-related quantities. As before, the convolution operation utilizes a Gaussian-based kernel; however, the discrete Hankel transform of order $𝛼$ = $\frac{1}{2}$ is now applied to the forward Fourier transform of the nonkernel argument, rather than the inverse Fourier transform. This modification eliminates the need for the integration of the nonkernel, cross section–based function, which is a step that posed challenges for certain pointwise cross-section representations. It also removes the requirement for cross-section linearization. Optimized for graphics processing unit architectures, the approach significantly improves computational performance. These advancements are currently under evaluation as the foundation for the next-generation thermonuclear data file processing codes being developed at Lawrence Livermore National Laboratory.

Nuclear science and engineering↗
NASA NTRS2018

An Integrated Platform for Mission Performance: Goddard Space Flight Center's Meta Information System

Successful management of NASA Goddard Space Flight Centers portfolio of mission projects (i.e. spacecraft, spacecraft instruments / subsystems, and ground systems) depends upon numerous processes, data and information resources coming together throughout the life-cycle of the projects to enable sound decision-making, risk reduction, conformance with requirements and continual improvement. In the summer of 2012, GSFC SMA management recognized that the set of legacy data systems used to support the SMA mission and responsibilities at GSFC were not effective, integrated nor on par with best practices. Accordingly, GSFC SMA management launched a project to transform the GSFC electronic management system to create and deploy an integrated, state-of-the-market information system for process performance, data management and analytics that is currently operating in support of GSFC overall mission performance. The information system, known as Meta, provides controlled, process-based applications, integrated data management, and analytics for a robust set of integrated applications. Since the inception of the project, a lean, award-winning SMA project team has thus far designed, configured and managed the system to serve as an integrated platform for 18 applications that support key processes for GSFC and the Science Mission Directorate at NASA headquarters, such as internal Management System assessments, Supplier Assessments, Supplier Research & Analysis, Problem Reporting for in-house mission projects, On-orbit Anomaly Reporting for GSFC-operated spacecraft, GSFC Project Life-Cycle Reviews, Risk Management and Reporting, and SMA Project Team Reporting. The system has experienced steady growth in utilization with 1,917 users (NASA employees and support contractor personnel) and 44 gigabytes of data and related files managed by the system as of the end of April 2018. Overall, Meta has achieved increasing levels of process management and real-time data / information integration to enable improved process performance, richer analytics and informed decision-making. This paper will present and examine the need, goals, approach and design driving the management and operation of the Meta information system and its ongoing growth as an integrated platform for advancing NASA mission performance.

Integration↗
NASA NTRSDate not supplied

Human Interfaces and Management of Information (HIMI) Challenges for “In-time” Aviation Safety Management Systems (IASMS)

The envisioned transformation of the National Airspace System to integrate an In-time Aviation Safety Management System(IASMS)to assure safety in Advanced Air Mobility(AAM)brings unprecedented challenges to the design of human interfaces and management of safety information. Safety in design and operational safety assurance are critical factors for how humans will interact with increasingly autonomous systems. The IASMS Concept of Operations builds from traditional commercial operator safety management and scales in complexity to AAM. The transformative changes in future aviation systems pose potential new critical safety risks with novel types of aircraft and other vehicles having different performance capabilities, flying in increasingly complex airspace, and using adaptive contingencies to manage normal and non-normal operations. These changes compel development of new and emerging capabilities that enable innovative ways for humans to interact with data and manage information. In-creasing complexity of AAM corresponds with use of predictive modeling, data analytics, machine learning, and artificial intelligence to effectively address known hazards and emergent risks. The roles of humans will dynamically evolve in increments with this technological and operational evolution. The interfaces for how humans will interact with increasingly complex and assured systems designed to operate autonomously and how information will need to be presented are important challenges to be resolved.

Lawrence J Prinzel↗
DOE OSTI2026

AstraAI v1

AstraAI is an open-source, structure-aware AI coding agent designed for large scientific and DOE-HPC codebases such as AMReX-based applications. Unlike general-purpose coding assistants, AstraAI combines retrieval-augmented generation (RAG) with compiler-level Abstract Syntax Tree (AST) analysis to perform precise, scope-constrained code modifications. It identifies exact function spans, enforces locality of edits, and maintains cross-file invariants, enabling deterministic and build-safe transformations in complex C++/GPU environments. AstraAI is intended for developers working on large, evolving HPC frameworks where correctness, reproducibility, and structural integrity are critical. Typical use cases include modifying physics kernels, updating GPU device lambdas, and performing multi-file refactors without breaking compilation or runtime semantics. Compared to conventional LLM-based coding agents - even those with repository access - AstraAI provides structural guarantees rather than free-form text patches. It minimizes unintended diffs, prevents scope drift, preserves formatting and build stability, and reduces structural hallucinations. By integrating compiler tooling directly into the generation loop, AstraAI transforms AI-assisted coding from probabilistic text editing into deterministic, structure-preserving program transformation suitable for mission-critical scientific software.

Natarajan, Mahesh [Lawrence Berkeley National Labo↗
DOE OSTI2026

AGFormer: Adaptive Spatiotemporal graph informed transformer for multi-reservoir inflow forecasting

Accurate reservoir inflow forecasting is crucial for effective water resource management, yet most machine learning models focus on single-reservoir prediction and overlook spatial dependencies among hydrologically connected reservoirs. Here, we propose AGFormer (Adaptive Graph-Informed Transformer), an end-to-end framework that integrates adaptive graph learning with temporal sequence modeling for multi-reservoir inflow forecasting. A shared encoder and graph attention mechanism generate reservoir-specific embeddings, which are then processed by the Transformer-based encoder–decoder for multi-step inflow forecasting. We also introduce a pretraining paradigm to learn robust temporal embeddings from misaligned historical records. Evaluated on 30 reservoirs in the Upper Colorado River Basin, AGFormer achieves superior seven-day-ahead forecasts, with NSE > 0.75 for 20 reservoirs—outperforming Encoder–Decoder LSTM, GCN+LSTM, and Transformer baselines. Adaptive graph learning captures dynamic inter-reservoir dependencies, and feature attribution aligns with snowmelt-driven hydrology. Incorporating forecasted meteorological inputs further enhances accuracy, demonstrating AGFormer’s potential to support reservoir management under dynamic hydrological conditions.

Adaptive graph learning↗
NASA NTRS1977

The intermediate anomaly

Time transformations of the equation dt = cr to the n ds, where s is a variable called the intermediate anomaly, are known to reduce global error in the solution of gravitational systems obtained by numerical integration. Attention is given to the Sundman time transformation, and its relation to equations of Keplerian elliptical motion.

Nacozy, P.↗
NASA NTRSDate not supplied

NASA and Advanced Air Mobility (AAM) National Campaign (NC) Tech Talk: Integrated Data Product

NASA Advanced Air Mobility (AAM) National Campaign has hosted multiple flight tests in a effort to promote public confidence and accelerate the realization of emerging aviation markets for passenger and cargo transportation in urban, suburban, rural, and regional environments. The goals and objectives for each flight test are intended to assess the performance of the vehicle’s capacity to operate safely, efficiently, and sustainably in urban areas. The Airspace Test and Infrastructure (ATI) team processes the flight data to evaluate the effectiveness of air vehicle and airspace management integration, while its analysis capabilities support the assessment of the efficacy of proposed vehicles and ground systems required to enable the vehicles’ operations. The ATI data services team creates many products from the data, first by transforming and merging the data into a single Integrated Data Product (IDP). This aligns data from many sources by time, so that, for example, the winds that impacted a flight can be aligned with its ground track and speed. A detailed IDP enables many types of statistical computation and visualizations that help researchers understand what transpired during the flight and how it can be explained. This Tech Talk will give an overview of the IDP process, including examples of the resulting products created by the data services team. It will also share an application that will allow participants to perform their own data analysis.

National Campaign, Advanced Air Mobility, Integrat↗
NASA NTRS1976

CCD correlation techniques

Two CCD techniques were discussed for performing an N-point sampled data correlation between an input signal and an electronically programmable reference function. The design and experimental performance of an implementation of the direct time correlator utilizing two analog CCDs and MOS multipliers on a single IC were evaluated. The performance of a CCD implementation of the chirp z transform was described, and the design of a new CCD integrated circuit for performing correlation by multiplication in the frequency domain was presented. This chip provides a discrete Fourier transform (DFT) or inverse DFT, multipliers, and complete support circuitry for the CCD CZT. The two correlation techniques are compared.

Hewes, C. R.↗
NASA NTRS1989

Multicenter molecular integrals for Slater orbitals of higher principal quantum numbers

As was shown earlier by Tai (1979), by using the Fourier-transform technique and properly coupling a pair of two-center exchange integrals, the multicenter molecular integrals can be cast into a simple expression upon which numerical procedures can be directly applied. In this paper, the procedure of Tai is extended to integrals involving orbitals with arbitrarily higher principal quantum number. The derivation is outlined, and the explicit expressions are presented for a three-center nuclear attraction integral and a four-center two-electron Coulomb repulsion integral of arbitrary higher states.

Tai, H.↗
NASA NTRS2013

A T Matrix Method Based upon Scalar Basis Functions

A surface integral formulation is developed for the T matrix of a homogenous and isotropic particle of arbitrary shape, which employs scalar basis functions represented by the translation matrix elements of the vector spherical wave functions. The formulation begins with the volume integral equation for scattering by the particle, which is transformed so that the vector and dyadic components in the equation are replaced with associated dipole and multipole level scalar harmonic wave functions. The approach leads to a volume integral formulation for the T matrix, which can be extended, by use of Green's identities, to the surface integral formulation. The result is shown to be equivalent to the traditional surface integral formulas based on the VSWF basis.

wave functions↗
DOE OSTI2024

Integrable symplectic maps with a polygon tessellation

Identifying integrable dynamics remains a formidable challenge, and despite centuries of research, only a handful of examples are known to date. In this article, we explore a distinct form of area-preserving (symplectic) mappings derived from the stroboscopic Poincaré cross section of a kicked rotator—an oscillator subjected to an external force periodically switched on in short pulses. The significance of this class of problems extends to various applications in physics and mathematics, including particle accelerators, crystallography, and studies of chaos. Notably, Suris's theorem constrains the integrability within this category of mappings, outlining potential scenarios with analytic invariants of motion. In this paper, we challenge the assumption of the analyticity of the invariant by exploring piecewise linear transformations on a torus ( T 2 ) and associated systems on the plane ( R 2 ), incorporating arithmetic quasiperiodicity and discontinuities. Introducing a new automated technique, we discovered previously unknown scenarios featuring polygonal invariants that form perfect tessellations and, moreover, fibrations of the plane or torus. This work reveals a novel category of planar tilings characterized by discrete symmetries that emerge from the invertibility of transformations and are intrinsically linked to the presence of integrability. Our algorithm relies on the analysis of the Poincaré rotation number and its piecewise monotonic nature for integrable cases, contrasting with the noisy behavior in the case of chaos, thereby allowing for clear separation. Some of the newly discovered systems exhibit the peculiar behavior of “integrable diffusion,” characterized by infinite and quasirandom hopping between tiles while being confined to a set of invariant segments. Finally, through the implementation of a smoothening procedure, all mappings can be generalized to quasi-integrable scenarios with suppressed volume occupied by chaotic trajectories, thereby opening doors to potential practical applications. Published by the American Physical Society 2024

43 PARTICLE ACCELERATORS↗