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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
NASA NTRS1987

Algebraic multigrid

The state of the art in algebraic multgrid (AMG) methods is discussed. The interaction between the relaxation process and the coarse grid correction necessary for proper behavior of the solution probes is discussed in detail. Sufficient conditions on relaxation and interpolation for the convergence of the V-cycle are given. The relaxation used in AMG, what smoothing means in an algebraic setting, and how it relates to the existing theory are considered. Some properties of the coarse grid operator are discussed, and results on the convergence of two-level and multilevel convergence are given. Details of an algorithm particularly studied for problems obtained by discretizing a single elliptic, second order partial differential equation are given. Results of experiments with such problems using both finite difference and finite element discretizations are presented.

Ruge, J. W.↗
NASA NTRS1991

An algebra of discrete event processes

This report deals with an algebraic framework for modeling and control of discrete event processes. The report consists of two parts. The first part is introductory, and consists of a tutorial survey of the theory of concurrency in the spirit of Hoare's CSP, and an examination of the suitability of such an algebraic framework for dealing with various aspects of discrete event control. To this end a new concurrency operator is introduced and it is shown how the resulting framework can be applied. It is further shown that a suitable theory that deals with the new concurrency operator must be developed. In the second part of the report the formal algebra of discrete event control is developed. At the present time the second part of the report is still an incomplete and occasionally tentative working paper.

Heymann, Michael↗
NASA NTRS1990

Embedded Multiprocessor Technology for VHSIC Insertion

Viewgraphs on embedded multiprocessor technology for VHSIC insertion are presented. The objective was to develop multiprocessor system technology providing user-selectable fault tolerance, increased throughput, and ease of application representation for concurrent operation. The approach was to develop graph management mapping theory for proper performance, model multiprocessor performance, and demonstrate performance in selected hardware systems.

Hayes, Paul J.↗
NASA NTRS1993

Next generation initiation techniques

Four-dimensional data assimilation strategies can generally be classified as either current or next generation, depending upon whether they are used operationally or not. Current-generation data-assimilation techniques are those that are presently used routinely in operational-forecasting or research applications. They can be classified into the following categories: intermittent assimilation, Newtonian relaxation, and physical initialization. It should be noted that these techniques are the subject of continued research, and their improvement will parallel the development of next generation techniques described by the other speakers. Next generation assimilation techniques are those that are under development but are not yet used operationally. Most of these procedures are derived from control theory or variational methods and primarily represent continuous assimilation approaches, in which the data and model dynamics are 'fitted' to each other in an optimal way. Another 'next generation' category is the initialization of convective-scale models. Intermittent assimilation systems use an objective analysis to combine all observations within a time window that is centered on the analysis time. Continuous first-generation assimilation systems are usually based on the Newtonian-relaxation or 'nudging' techniques. Physical initialization procedures generally involve the use of standard or nonstandard data to force some physical process in the model during an assimilation period. Under the topic of next-generation assimilation techniques, variational approaches are currently being actively developed. Variational approaches seek to minimize a cost or penalty function which measures a model's fit to observations, background fields and other imposed constraints. Alternatively, the Kalman filter technique, which is also under investigation as a data assimilation procedure for numerical weather prediction, can yield acceptable initial conditions for mesoscale models. The third kind of next-generation technique involves strategies to initialize convective scale (non-hydrostatic) models.

Warner, Tom↗
NASA NTRS1995

On the nonlinear stability of the unsteady, viscous flow of an incompressible fluid in a curved pipe

The stability of the flow of an incompressible, viscous fluid through a pipe of circular cross-section curved about a central axis is investigated in a weakly nonlinear regime. A sinusoidal pressure gradient with zero mean is imposed, acting along the pipe. A WKBJ perturbation solution is constructed, taking into account the need for an inner solution in the vicinity of the outer bend, which is obtained by identifying the saddle point of the Taylor number in the complex plane of the cross-sectional angle co-ordinate. The equation governing the nonlinear evolution of the leading order vortex amplitude is thus determined. The stability analysis of this flow to periodic disturbances leads to a partial differential system dependent on three variables, and since the differential operators in this system are periodic in time, Floquet theory may be applied to reduce this system to a coupled infinite system of ordinary differential equations, together with homogeneous uncoupled boundary conditions. The eigenvalues of this system are calculated numerically to predict a critical Taylor number consistent with the analysis of Papageorgiou. A discussion of how nonlinear effects alter the linear stability analysis is also given, and the nature of the instability determined.

Shortis, Trudi A.↗
NASA NTRS2007

The Crew Earth Observations Experiment: Earth System Science from the ISS

This viewgraph presentation reviews the use of Astronaut Photography (AP) as taken from the International Space Station (ISS) in Earth System Science (ESS). Included are slides showing basic remote sensing theory, data characteristics of astronaut photography, astronaut training and operations, crew Earth observations group, targeting sites and acquisition, cataloging and database, analysis and applications for ESS, image analysis of particular interest urban areas, megafans, deltas, coral reefs. There are examples of the photographs and the analysis.

Stefanov, William L.↗
NASA NTRS2006

Volumetric Acoustic Vector Intensity Probe

A new measurement tool capable of imaging the acoustic intensity vector throughout a large volume is discussed. This tool consists of an array of fifty microphones that form a spherical surface of radius 0.2m. A simultaneous measurement of the pressure field across all the microphones provides time-domain near-field holograms. Near-field acoustical holography is used to convert the measured pressure into a volumetric vector intensity field as a function of frequency on a grid of points ranging from the center of the spherical surface to a radius of 0.4m. The volumetric intensity is displayed on three-dimensional plots that are used to locate noise sources outside the volume. There is no restriction on the type of noise source that can be studied. The sphere is mobile and can be moved from location to location to hunt for unidentified noise sources. An experiment inside a Boeing 757 aircraft in flight successfully tested the ability of the array to locate low-noise-excited sources on the fuselage. Reference transducers located on suspected noise source locations can also be used to increase the ability of this device to separate and identify multiple noise sources at a given frequency by using the theory of partial field decomposition. The frequency range of operation is 0 to 1400Hz. This device is ideal for the study of noise sources in commercial and military transportation vehicles in air, on land and underwater.

Klos, Jacob↗
NASA NTRS2009

Prediction of Turbulence-Generated Noise in Unheated Jets: JeNo Users' Manual (Version 1.0) - Part 2

JeNo (Version 1.0) is a Fortran90 computer code that calculates the far-field sound spectral density produced by axisymmetric, unheated jets at a user specified observer location and frequency range. The user must provide a structured computational grid and a mean flow solution from a Reynolds-Averaged Navier Stokes (RANS) code as input. Turbulence kinetic energy and its dissipation rate from a k-epsilon or k-omega turbulence model must also be provided. JeNo is a research code, and as such, its development is ongoing. The goal is to create a code that is able to accurately compute far-field sound pressure levels for jets at all observer angles and all operating conditions. In order to achieve this goal, current theories must be combined with the best practices in numerical modeling, all of which must be validated by experiment. Since the acoustic predictions from JeNo are based on the mean flow solutions from a RANS code, quality predictions depend on accurate aerodynamic input.This is why acoustic source modeling, turbulence modeling, together with the development of advanced measurement systems are the leading areas of research in jet noise research at NASA Glenn Research Center.

Khavaran, Abbas↗
NASA NTRS2013

Enhanced Schapery Theory Software Development for Modeling Failure of Fiber-Reinforced Laminates

Progressive damage and failure analysis (PDFA) tools are needed to predict the nonlinear response of advanced fiber-reinforced composite structures. Predictive tools should incorporate the underlying physics of the damage and failure mechanisms observed in the composite, and should utilize as few input parameters as possible. The purpose of the Enhanced Schapery Theory (EST) was to create a PDFA tool that operates in conjunction with a commercially available finite element (FE) code (Abaqus). The tool captures the physics of the damage and failure mechanisms that result in the nonlinear behavior of the material, and the failure methodology employed yields numerical results that are relatively insensitive to changes in the FE mesh. The EST code is written in Fortran and compiled into a static library that is linked to Abaqus. A Fortran Abaqus UMAT material subroutine is used to facilitate the communication between Abaqus and EST. A clear distinction between damage and failure is imposed. Damage mechanisms result in pre-peak nonlinearity in the stress strain curve. Four internal state variables (ISVs) are utilized to control the damage and failure degradation. All damage is said to result from matrix microdamage, and a single ISV marks the micro-damage evolution as it is used to degrade the transverse and shear moduli of the lamina using a set of experimentally obtainable matrix microdamage functions. Three separate failure ISVs are used to incorporate failure due to fiber breakage, mode I matrix cracking, and mode II matrix cracking. Failure initiation is determined using a failure criterion, and the evolution of these ISVs is controlled by a set of traction-separation laws. The traction separation laws are postulated such that the area under the curves is equal to the fracture toughness of the material associated with the corresponding failure mechanism. A characteristic finite element length is used to transform the traction-separation laws into stress-strain laws. The ISV evolution equations are derived in a thermodynamically consistent manner by invoking the stationary principle on the total work of the system with respect to each ISV. A novel feature is the inclusion of both pre-peak damage and appropriately scaled, post-peak strain softening failure. Also, the characteristic elements used in the failure degradation scheme are calculated using the element nodal coordinates, rather than simply the square root of the area of the element.

Pineda, Evan J.↗
NASA NTRS2014

Fault Management Design Strategies

Development of dependable systems relies on the ability of the system to determine and respond to off-nominal system behavior. Specification and development of these fault management capabilities must be done in a structured and principled manner to improve our understanding of these systems, and to make significant gains in dependability (safety, reliability and availability). Prior work has described a fundamental taxonomy and theory of System Health Management (SHM), and of its operational subset, Fault Management (FM). This conceptual foundation provides a basis to develop framework to design and implement FM design strategies that protect mission objectives and account for system design limitations. Selection of an SHM strategy has implications for the functions required to perform the strategy, and it places constraints on the set of possible design solutions. The framework developed in this paper provides a rigorous and principled approach to classifying SHM strategies, as well as methods for determination and implementation of SHM strategies. An illustrative example is used to describe the application of the framework and the resulting benefits to system and FM design and dependability.

systems engineering↗
DOE OSTI2024

Symmetry-Based Structured Matrices for Efficient Approximately Equivariant Networks

There has been much recent interest in designing symmetry-aware neural networks (NNs) exhibiting relaxed equivariance. Such NNs aim to interpolate between being exactly equivariant and being fully flexible, affording consistent performance benefits. In a separate line of work, certain structured parameter matrices -- those with displacement structure, characterized by low displacement rank (LDR) -- have been used to design small-footprint NNs. Displacement structure enables fast function and gradient evaluation, but permits accurate approximations via compression primarily to classical convolutional neural networks (CNNs). In this work, we propose a general framework -- based on a novel construction of symmetry-based structured matrices -- to build approximately equivariant NNs with significantly reduced parameter counts. Our framework integrates the two aforementioned lines of work via the use of so-called Group Matrices (GMs), a forgotten precursor to the modern notion of regular representations of finite groups. GMs allow the design of structured matrices -- resembling LDR matrices -- which generalize the linear operations of a classical CNN from cyclic groups to general finite groups and their homogeneous spaces. We show that GMs can be employed to extend all the elementary operations of CNNs to general discrete groups. Further, the theory of structured matrices based on GMs provides a generalization of LDR theory focussed on matrices with cyclic structure, providing a tool for implementing approximate equivariance for discrete groups. We test GM-based architectures on a variety of tasks in the presence of relaxed symmetry. We report that our framework consistently performs competitively compared to approximately equivariant NNs, and other structured matrix-based compression frameworks, sometimes with a one or two orders of magnitude lower parameter count.

Samudre, Ashwin↗
DOE OSTI2024

Gravitational form factors of glueballs in Yang-Mills theory

This work presents preliminary results of the first determination of the energy-momentum tensor form factors of the scalar glueball, referred to as gravitational form factors (GFFs). The calculation has been carried out in lattice Yang-Mills theory at a single lattice spacing. Using variationally optimized operators, the matrix elements are extracted from ratios of three-point functions to two-point functions. The glueball GFFs and their kinematic dependence are compared to those of other hadrons from previous calculations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1972

Respiratory protective device design using control system techniques

The feasibility of a control system analysis approach to provide a design base for respiratory protective devices is considered. A system design approach requires that all functions and components of the system be mathematically identified in a model of the RPD. The mathematical notations describe the operation of the components as closely as possible. The individual component mathematical descriptions are then combined to describe the complete RPD. Finally, analysis of the mathematical notation by control system theory is used to derive compensating component values that force the system to operate in a stable and predictable manner.

Burgess, W. A.↗
NASA NTRS1974

Power conversion in electrical networks

Aspects of dc to dc conversion were studied in terms of a class of switching voltage regulators from a stability viewpoint. Background concepts of nonlinear system theory were considered, including the problem of obtaining suitable realizations for a class of positive operators. It is shown that the state evolution equations for a power conversion network are in general of bilinear form, and that the theory of lie groups and lie algebras is useful in analyzing such systems. The feedback stabilization of a class of bilinear systems whose state space is a manifold is also discussed.

Wood, J. R.↗
NASA NTRS1984

Unsteady aerodynamics in time and frequency domains for finite time arbitrary motion of rotary wings in hover and forward flight

Several incompressible finite-time arbitrary-motion airfoil theories suitable for coupled flap-lag-torsional aeroelastic analysis of helicopter rotors in hover and forward flight are derived. These theories include generalized Greenberg's theory, generalized Loewy's theory, and a staggered cascade theory. The generalized Greenberg's and staggered cascade theories were derived directly in Laplace domain considering the finite length of the wake and using operational methods. The load expressions are presented in Laplace, frequency, and time domains. Approximate time domain loads for the various generalized theories, discussed in the paper, are obtained by developing finite state models using the Pade approximant of the appropriate lift deficiency functions. Three different methods for constructing Pade approximants of the lift deficiency functions were considered and the more flexible one was used. Pade approximants of Loewy's lift deficiency function, for various wake spacing and radial location parameters of a helicopter typical rotor blade section, are presented.

Dinyavari, M. A. H.↗
DOE OSTI2022

Improved Architectures and Training Algorithms for Deep Operator Networks

Operator learning techniques have recently emerged as a powerful tool for learning maps between infinite-dimensional Banach spaces. Trained under appropriate constraints, they can also be effective in learning the solution operator of partial differential equations (PDEs) in an entirely self-supervised manner. In this work we analyze the training dynamics of deep operator networks (DeepONets) through the lens of Neural Tangent Kernel theory, and reveal a bias that favors the approximation of functions with larger magnitudes. To correct this bias we propose to adaptively re-weight the importance of each training example, and demonstrate how this procedure can effectively balance the magnitude of back-propagated gradients during training via gradient descent. We also propose a novel network architecture that is more resilient to vanishing gradient pathologies. Taken together, our developments provide new insights into the training of DeepONets and consistently improve their predictive accuracy by a factor of 10-50x, demonstrated in the challenging setting of learning PDE solution operators in the absence of paired input-output observations.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1991

Task reports on developing techniques for scattering by 3D composite structures and to generate new solutions in diffraction theory using higher order boundary conditions

There are two tasks described in this report. First, an extension of a two dimensional formulation is presented for a three dimensional body of revolution. A Fourier series expansion of the vector electric and magnetic fields is employed to reduce the dimensionality of the system, and an exact boundary condition is employed to terminate the mesh. The mesh termination boundary is chosen such that it leads to convolutional boundary operators for low O(n) memory demand. Second, rigorous uniform geometrical theory of diffraction (UTD) diffraction coefficients are presented for a coated convex cylinder simulated with generalized impedance boundary conditions. Ray solutions are obtained which remain valid in the transition region and reduce uniformly those in the deep lit and shadow regions. A uniform asymptotic solution is also presented for observations in the close vicinity of the cylinder.

Volakis, John L.↗