Search NASA⌕ Search

SEARCH · Search NASA

Results for “nonlinear mappings”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 379 records · Page 21
All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Application of Space Shuttle photography to studies of upper ocean dynamics

Three studies have been conducted using space shuttle imagery to explain the dynamics behavior of internal waves in the Atlantic and Indian Oceans and to derive tide-related parameters for Delaware Bay. By interpreting space shuttle photographs taken during mission STS-40, a total of 34 internal wave packets on the continental shelf of the Middle Atlantic Bight have been recognized. Using the finite-depth theory we derived that the maximum amplitude of solitons is 5.6 m, the phase speed 0.42 m/s, and the period 23.8 min. Deep-ocean internal waves in the western equatorial Indian Ocean on photographs taken during mission STS-44 were also interpreted and analyzed. The internal waves occurred in the form of a multisoliton packet in which there are about a dozen solitons. The average wavelength of the solitons is 1.8 +/- 0.5 km. The crest lines are mostly straight and reach as long as 100 km. The distance between two adjacent packets is about 66 km. Using the deepwater soliton theory, we derived that the mean amplitude of the solitons is 25 m, the nonlinear phase speed 1.7 m/s, and the average period 18 min. For both cases, the semidiural tides are the principal generating mechanism. The tide-related parameters of Delaware Bay were derived from space shuttle time-series photographs taken during mission STS-40. The water area in the bay were measured from interpretation maps of the photographs. The corresponding tidal levels were calculated using the exposure time. From these data, an approximate function relating the water area to the tidal level at a reference point was determined. Then, the water areas of the Delaware Bay at mean high water (MHW) and mean low water (MLW), below 0 m, for the tidal zone, and the tidal flux were inferred. All parameters derived were reasonable and compared well with results of previous investigations.

Zheng, Quanan↗
DOE OSTI2020

Physical, numerical, and computational challenges of modeling neutrino transport in core-collapse supernovae

The proposal that core collapse supernovae are neutrino driven is still the subject of active investigation more than 50 years after the seminal paper by Colgate and White. The modern version of this paradigm, which we owe to Wilson, proposes that the supernova shock wave is powered by neutrino heating, mediated by the absorption of electron-flavor neutrinos and antineutrinos emanating from the proto-neutron star surface, or neutrinosphere. Neutrino weak interactions with the stellar core fluid, the theory of which is still evolving, are flavor and energy dependent. The associated neutrino mean free paths extend over many orders of magnitude and are never always small relative to the stellar core radius. Thus, neutrinos are never always fluid like. Instead, a kinetic description of them in terms of distribution functions that determine the number density of neutrinos in the six-dimensional phase space of position, direction, and energy, for both neutrinos and antineutrinos of each flavor, or in terms of angular moments of these neutrino distributions that instead provide neutrino number densities in the four-dimensional phase-space subspace of position and energy, is needed. In turn, the computational challenge is twofold: (i) to map the kinetic equations governing the evolution of these distributions or moments onto discrete representations that are stable, accurate, and, perhaps most important, respect physical laws such as conservation of lepton number and energy and the Fermi–Dirac nature of neutrinos and (ii) to develop efficient, supercomputer-architecture-aware solution methods for the resultant nonlinear algebraic equations. In this review, we present the current state of the art in attempts to meet this challenge.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Constraints on primordial non-Gaussianity from the cross-correlation of DESI luminous red galaxies and Planck CMB lensing

We use the angular cross-correlation between a luminous red galaxy (LRG) sample from the Dark Energy Spectroscopic Instrument (DESI) Legacy Survey data release DR9 and the Planck cosmic microwave background (CMB) lensing maps to constrain the local primordial non-Gaussianity parameter, f NL , using the scale-dependent galaxy bias effect. The galaxy sample covers approximately 40% of the sky, contains galaxies up to redshift z ∼ 1.4, and is calibrated with the LRG spectra that have been observed for DESI Year 1 (Y1). We apply a nonlinear imaging systematics treatment based on neural networks to remove observational effects that could potentially bias the f NL measurement. Our measurement is performed without blinding, but the full analysis pipeline is tested with simulations including systematics. Using the two-point angular cross-correlation between LRG and CMB lensing only, we find f NL = 39 −38 +40 at the 68% confidence level, and our result is robust in terms of systematics and cosmological assumptions. If we combine this information with the autocorrelation of LRG, applying a scale cut to limit the impact of systematics, we find f NL = 24 −21 +20 at the 68% confidence level. Our results motivate the use of CMB lensing cross-correlations to measure f NL with future datasets, given its stability in terms of observational systematics compared to the angular autocorrelation. Furthermore, performing accurate systematics mitigation is crucially important in order to achieve competitive constraints on f NL from CMB lensing cross-correlation in combination with the tracers’ autocorrelation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Approach to nonlinear magnetohydrodynamic simulations in stellarator geometry

The capability to model the nonlinear magnetohydrodynamic (MHD) evolution of stellarator plasmas is developed by extending the M3D-C 1 code to allow non-axisymmetric domain geometry. We introduce a set of logical coordinates, in which the computational domain is axisymmetric, to utilize the existing finite-element framework of M3D-C 1 . A C 1 coordinate mapping connects the logical domain to the non-axisymmetric physical domain, where we use the M3D-C 1 extended MHD models essentially without modifications. We present several numerical verifications on the implementation of this approach, including simulations of the heating, destabilization, and equilibration of a stellarator plasma with strongly anisotropic thermal conductivity, and of the relaxation of stellarator equilibria to integrable and non-integrable magnetic field configurations in realistic geometries.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1988

Deformations and strains in a thick adherend lap joint

Displacement fields in a thick adherend lap joint were measured by high-sensitivity moire interferometry. Contour maps of in-plane U and V displacements were obtained across adhesive and adherend surfaces. Loads ranged from a modest load to a near-failure load. Quantitative results are given for displacements and strains in the adhesive and along the adhesive/adherend boundary lines. The results show nearly constant shear strain in the adhesive, nonlinear strains as a function of load or average shear stress, and viscoelastic or time-dependent response. Longitudinal normal strains in the adhesive are nearly two orders of magnitude less than the shear strains. With its subwavelength displacement resolution and high spatial resolution, moire interferometry is especially well suited for deformation studies of adhesive joints.

Post, D.↗
DOE OSTI2020

Planck 2018 Results - II. Low Frequency Instrument data processing

We present a final description of the data-processing pipeline for the Planck Low Frequency Instrument (LFI), implemented for the 2018 data release. Several improvements have been made with respect to the previous release, especially in the calibration process and in the correction of instrumental features such as the effects of nonlinearity in the response of the analogue-to-digital converters. We provide a brief pedagogical introduction to the complete pipeline, as well as a detailed description of the important changes implemented. Self-consistency of the pipeline is demonstrated using dedicated simulations and null tests. We present the final version of the LFI full sky maps at 30, 44, and 70 GHz, both in temperature and polarization, together with a refined estimate of the solar dipole and a final assessment of the main LFI instrumental parameters.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Train Like a (Var)Pro: Efficient Training of Neural Networks with Variable Projection

Deep neural networks (DNNs) have achieved state-of-the-art performance across a variety of traditional machine learning tasks, e.g., speech recognition, image classification, and segmentation. The ability of DNNs to efficiently approximate high-dimensional functions has also motivated their use in scientific applications, e.g., to solve partial differential equations and to generate surrogate models. In this paper, we consider the supervised training of DNNs, which arises in many of the above applications. We focus on the central problem of optimizing the weights of the given DNN such that it accurately approximates the relation between observed input and target data. Devising effective solvers for this optimization problem is notoriously challenging due to the large number of weights, nonconvexity, data sparsity, and nontrivial choice of hyperparameters. To solve the optimization problem more efficiently, we propose the use of variable projection (VarPro), a method originally designed for separable nonlinear least-squares problems. Our main contribution is the Gauss--Newton VarPro method (GNvpro) that extends the reach of the VarPro idea to nonquadratic objective functions, most notably cross-entropy loss functions arising in classification. These extensions make GNvpro applicable to all training problems that involve a DNN whose last layer is an affine mapping, which is common in many state-of-the-art architectures. In our four numerical experiments from surrogate modeling, segmentation, and classification, GNvpro solves the optimization problem more efficiently than commonly used stochastic gradient descent (SGD) schemes. Finally, GNvpro finds solutions that generalize well, and in all but one example better than well-tuned SGD methods, to unseen data points.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Disentangling multiple scattering with deep learning: application to strain mapping from electron diffraction patterns

Abstract A fast, robust pipeline for strain mapping of crystalline materials is important for many technological applications. Scanning electron nanodiffraction allows us to calculate strain maps with high accuracy and spatial resolutions, but this technique is limited when the electron beam undergoes multiple scattering. Deep-learning methods have the potential to invert these complex signals, but require a large number of training examples. We implement a Fourier space, complex-valued deep-neural network, FCU-Net, to invert highly nonlinear electron diffraction patterns into the corresponding quantitative structure factor images. FCU-Net was trained using over 200,000 unique simulated dynamical diffraction patterns from different combinations of crystal structures, orientations, thicknesses, and microscope parameters, which are augmented with experimental artifacts. We evaluated FCU-Net against simulated and experimental datasets, where it substantially outperforms conventional analysis methods. Our code, models, and training library are open-source and may be adapted to different diffraction measurement problems.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Brighter-fatter Effect in Near-infrared Detectors—III. Fourier-domain Treatment of Flat Field Correlations and Application to WFIRST

Weak gravitational lensing has emerged as a leading probe of the growth of cosmic structure. However, the shear signal is very small and accurate measurement depends critically on our ability to understand how non-ideal instrumental effects affect astronomical images. The Wide-Field Infrared Survey Telescope (WFIRST) will fly a focal plane containing 18 Teledyne H4RG-10 near-infrared detector arrays, which present different instrument calibration challenges from previous weak lensing observations. Previous work [Paper I: Hirata & Choi, PASP, 132, 014501 (2020); and Paper II: Choi & Hirata, PASP, 132, 014502 (2020)] has shown that correlation functions of flat field images, including cross-correlations between different time slices that are enabled by the non-destructive read capability of the infrared detectors, are effective tools for disentangling linear and nonlinear inter-pixel capacitance (IPC) and the brighter-fatter effect (BFE). Here we present a Fourier-domain treatment of the flat field correlations, which allows us to expand the previous formalism to all orders in IPC, BFE, and classical nonlinearity. We show that biases in simulated flat field analyses in Paper I are greatly reduced through the use of this formalism. We then apply this updated formalism to flat field data from three WFIRST flight candidate detectors, and explore the robustness to variations in the analysis. We find that the BFE is present in all three detectors, and that its contribution to the flat field correlations dominates over the nonlinear IPC, in accordance with the results from Paper II on a development detector. The magnitude of the BFE is such that the effective area of a pixel is increased by (3.54 ± 0.03) × 10 -7 for every electron deposited in a neighboring pixel (sensor chip assembly [SCA] 20829, statistical error, not IPC-deconvolved). We compare IPC maps from flat field autocorrelation measurements to those obtained from the single pixel reset method and find a median difference of 0.113% for SCA 20829. After further diagnosis of this difference, we ascribe it largely to an additional source of cross-talk, the vertical trailing pixel effect, and recommend further work to develop a model for this effect. These results represent a significant step toward calibration of the non-ideal effects in WFIRST detectors.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1985

Contributions on the Subject of Longitudinal Movements of Aircraft in Wind Shears

The effect of downburst-type wind shears on the longitudinal dynamic behavior of an unguided aircraft is simulated numerically on the basis of published meteorological data and the flight characteristics of an A300-B passenger jet. The nonlinear differential equations of the aircraft motion are linearized by conventional methods, and the wind effects are introduced via the linear derivatives of the wind components referred to the wind gradients to obtain simplified technical models of the longitudinal response to all possible types of constant-gradient wind shears during the first 20-60 sec. Graphs, maps, and diagrams are provided, and a number of accidents presumed to have involved wind shears are analyzed in detail.

Krauspe, P.↗
NASA NTRS1997

Dynamic Forms: Application to Aircraft Guidance - Part 2

The paper describes a method for guiding a dynamic system through a given set of points. The paradigm is a fully automatic aircraft subject to air traffic control (ATC). The ATC provides a sequence of waypoints through which the aircraft trajectory must pass. The waypoints typically specify time, position, and velocity. The guidance problem is to synthesize a system state trajectory that satisfies both the ATC and aircraft constraints. Complications arise because the controlled process is multidimensional, multiaxis, nonlinear, highly coupled, and the state space is not flat. In addition, there is a multitude of operating modes, which may number in the hundreds. Each such mode defines a distinct state space model of the process by specifying the state space coordinatization, the partition of the controls into active controls and configuration controls, and the output map. Furthermore, mode transitions are required to be smooth. The proposed guidance algorithm is based on the inversion of the pure feedback approximation, followed by correction for the effects of zero dynamics. The paper describes the structure and major modules of the algorithm, and the performance is illustrated by several example aircraft maneuvers.

Meyer, George↗
NASA NTRS1987

Particle simulation of plasmas on the massively parallel processor

Particle simulations, in which collective phenomena in plasmas are studied by following the self consistent motions of many discrete particles, involve several highly repetitive sets of calculations that are readily adaptable to SIMD parallel processing. A fully electromagnetic, relativistic plasma simulation for the massively parallel processor is described. The particle motions are followed in 2 1/2 dimensions on a 128 x 128 grid, with periodic boundary conditions. The two dimensional simulation space is mapped directly onto the processor network; a Fast Fourier Transform is used to solve the field equations. Particle data are stored according to an Eulerian scheme, i.e., the information associated with each particle is moved from one local memory to another as the particle moves across the spatial grid. The method is applied to the study of the nonlinear development of the whistler instability in a magnetospheric plasma model, with an anisotropic electron temperature. The wave distribution function is included as a new diagnostic to allow simulation results to be compared with satellite observations.

Gledhill, I. M. A.↗
NASA NTRS1992

The spectral world coordinate systems in IRAF/NOAO

The world coordinate system (WCS) for dispersion calibrated spectra used in the IRAF/NOAO spectroscopy packages is described. In particular, the image header keywords which define the coordinates in an 'image' pixel array. These keywords appear both as part of the IRAF image structure and map directly to FITS format. The types of spectra include multidimensional images with spectral dispersion as one axis, one dimensional images, and a special 'multispec' format consisting of multiple, semi-independent, one dimensional spectra in two or three dimensional images. The types of coordinate systems include multidimensional linear coordinates with individual keywords and one dimensional linear and nonlinear coordinates for the 'multispec' images stored in IRAF WCS attributes. The nonlinear world coordinate systems include polynomial, spline, sampled table, and look-up table function representations.

Valdes, F.↗
NASA NTRS1996

Guidance of Nonlinear Systems

The paper describes a method for guiding a dynamic system through a given set of points. The paradigm is a fully automatic aircraft subject to air traffic control (ATC). The ATC provides a sequence of way points through which the aircraft trajectory must pass. The way points typically specify time, position, and velocity. The guidance problem is to synthesize a system state trajectory which satisfies both the ATC and aircraft constraints. Complications arise because the controlled process is multi-dimensional, multi-axis, nonlinear, highly coupled, and the state space is not flat. In addition, there is a multitude of possible operating modes, which may number in the hundreds. Each such mode defines a distinct state space model of the process by specifying the state space coordination, the partition of the controls into active controls and configuration controls, and the output map. Furthermore, mode transitions must be smooth. The guidance algorithm is based on the inversion of the pure feedback approximations, which is followed by iterative corrections for the effects of zero dynamics. The paper describes the structure and modules of the algorithm, and the performance is illustrated by several example aircraft maneuvers.

Meyer, George↗
NASA NTRS1997

Guidance of Nonlinear Systems

The paper describes a method for guiding a dynamic system through a given set of points. The paradigm is a fully automatic aircraft subject to air traffic control (ATC). The ATC provides a sequence of way points through which the aircraft trajectory must pass. The way points typically specify time, position, and velocity. The guidance problem is to synthesize a system state trajectory which satisfies both the ATC and aircraft constraints. Complications arise because the controlled process is multi-dimensional, multi-axis, nonlinear, highly coupled, and the state space is not flat. In addition, there is a multitude of possible operating modes, which may number in the hundreds. Each such mode defines a distinct state space model of the process by specifying the state space coordinatization, the partition of the controls into active controls and configuration controls, and the output map. Furthermore, mode transitions must be smooth. The guidance algorithm is based on the inversion of the pure feedback approximations, which is followed by iterative corrections for the effects of zero dynamics. The paper describes the structure and modules of the algorithm, and the performance is illustrated by several example aircraft maneuvers.

Meyer, George↗
DOE OSTI2022

Electro-Thermal Characterization of Dynamical VO 2 Memristors via Local Activity Modeling

We report translating the surging interest in neuromorphic electronic components, such as those based on nonlinearities near Mott transitions, into large-scale commercial deployment faces steep challenges in the current lack of means to identify and design key material parameters. These issues are exemplified by the difficulties in connecting measurable material properties to device behavior via circuit element models. Here, the principle of local activity is used to build a model of VO 2 /SiN Mott threshold switches by sequentially accounting for constraints from a minimal set of quasistatic and dynamic electrical and high-spatial-resolution thermal data obtained via in situ thermoreflectance mapping. By combining independent data sets for devices with varying dimensions, the model is distilled to measurable material properties, and device scaling laws are established. The model can accurately predict electrical and thermal conductivities and capacitances and locally active dynamics (especially persistent spiking self-oscillations). The systematic procedure by which this model is developed has been a missing link in predictively connecting neuromorphic device behavior with their underlying material properties, and should enable rapid screening of material candidates before employing expensive manufacturing processes and testing procedures.

36 MATERIALS SCIENCE↗
NASA NTRS2004

On Nonlinear Combustion Instability in Liquid Propellant Rocket Motors

All liquid propellant rocket instability calculations in current use have limited value in the predictive sense and serve mainly as a correlating framework for the available data sets. The well-known n-t model first introduced by Crocco and Cheng in 1956 is still used as the primary analytical tool of this type. A multitude of attempts to establish practical analytical methods have achieved only limited success. These methods usually produce only stability boundary maps that are of little use in making critical design decisions in new motor development programs. Recent progress in understanding the mechanisms of combustion instability in solid propellant rockets"' provides a firm foundation for a new approach to prediction, diagnosis, and correction of the closely related problems in liquid motor instability. For predictive tools to be useful in the motor design process, they must have the capability to accurately determine: 1) time evolution of the pressure oscillations and limit amplitude, 2) critical triggering pulse amplitude, and 3) unsteady heat transfer rates at injector surfaces and chamber walls. The method described in this paper relates these critical motor characteristics directly to system design parameters. Inclusion of mechanisms such as wave steepening, vorticity production and transport, and unsteady detonation wave phenomena greatly enhance the representation of key features of motor chamber oscillatory behavior. The basic theoretical model is described and preliminary computations are compared to experimental data. A plan to develop the new predictive method into a comprehensive analysis tool is also described.

Sims, J. D.↗
DOE OSTI2022

Detection of Forced Change Within Combined Climate Fields Using Explainable Neural Networks

Abstract Assessing forced climate change requires the extraction of the forced signal from the background of climate noise. Traditionally, tools for extracting forced climate change signals have focused on one atmospheric variable at a time, however, using multiple variables can reduce noise and allow for easier detection of the forced response. Following previous work, we train artificial neural networks to predict the year of single‐ and multi‐variable maps from forced climate model simulations. To perform this task, the neural networks learn patterns that allow them to discriminate between maps from different years—that is, the neural networks learn the patterns of the forced signal amidst the shroud of internal variability and climate model disagreement. When presented with combined input fields (multiple seasons, variables, or both), the neural networks are able to detect the signal of forced change earlier than when given single fields alone by utilizing complex, nonlinear relationships between multiple variables and seasons. We use layer‐wise relevance propagation, a neural network explainability tool, to identify the multivariate patterns learned by the neural networks that serve as reliable indicators of the forced response. These “indicator patterns” vary in time and between climate models, providing a template for investigating inter‐model differences in the time evolution of the forced response. This work demonstrates how neural networks and their explainability tools can be harnessed to identify patterns of the forced signal within combined fields.

54 ENVIRONMENTAL SCIENCES↗