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Results for “representation theoretic methods”

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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Bounds on spectral gaps of Hyperbolic spin surfaces

We describe a method for constraining Laplacian and Dirac spectra of two dimensional compact orientable hyperbolic spin manifolds and orbifolds. The key ingredient is an infinite family of identities satisfied by the spectra. These spectral identities follow from the consistency between 1) the spectral decomposition of functions on the spin bundle into irreducible representations of SL(2,R) and 2) associativity of pointwise multiplication of functions. Applying semidefinite programming methods to our identities produces rigorous upper bounds on the Laplacian spectral gap as well as on the Dirac spectral gap conditioned on the former. In several examples, our bounds are nearly sharp; a numerical algorithm based on the Selberg trace formula shows that the [0;3,3,5] orbifold, a particular surface with signature [1;3], and the Bolza surface nearly saturate the bounds at genus 0, 1 and 2 respectively. Under additional assumptions on the number of harmonic spinors carried by the spin-surface, we obtain more restrictive bounds on the Laplacian spectral gap. In particular, these bounds apply to hyperelliptic surfaces. We also determine the set of Laplacian spectral gaps attained by all compact orientable two-dimensional hyperbolic spin orbifolds. We show that this set is upper bounded by 12.13798; this bound is nearly saturated by the [0;3,3,5] orbifold, whose first non-zero Laplacian eigenvalue is λ^(0)_1 ≈ 12.13623.

Spectral theory↗
DOE OSTI2022

Graph-Based Similarity Metrics for Comparing Simulation Model Causal Structures

The causal structure of a simulation is a major determinant of both its character and behavior, yet most methods we use to compare simulations focus only on simulation outputs. We introduce a method that combines graphical representation with information theoretic metrics to quantitatively compare the causal structures of models. The method applies to agent-based simulations as well as system dynamics models and facilitates comparison within and between types. Comparing models based on their causal structures can illuminate differences in assumptions made by the models, allowing modelers to (1) better situate their models in the context of existing work, including highlighting novelty, (2) explicitly compare conceptual theory and assumptions to simulated theory and assumptions, and (3) investigate potential causal drivers of divergent behavior between models. We demonstrate the method by comparing two epidemiology models at different levels of aggregation.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1976

Crack-opening displacements in center-crack, compact, and crack-line wedge-loaded specimens

The theoretical crack-opening displacements for center-crack, compact, and crack-line wedge-loaded specimens (reported in the ASTM Proposed Recommended Practice for R-Curve Determination (1974)) disagree with experimental measurements in the literature. The disagreement is a result of using approximate specimen configurations and load representation to obtain the theoretical displacements. An improved method of boundary collocation is presented which was used to obtain the theoretical displacements in these three specimen types; the actual specimen configurations and more accurate load representation were used. In the analysis of crack-opening displacements in the compact and crack-line wedge-loaded specimens, the effects of the pin-loaded holes were also included. The theoretical calculations agree with the experimental measurements reported in the literature. Also examined are accurate polynomial expressions for crack-opening displacements in both compact and crack-line wedge-loaded specimens.

Newman, J. C., Jr.↗
NASA NTRS1978

Correlation of laser velocimeter measurements over a wing with results of two prediction techniques

The flow field at the center line of an unswept wing with an aspect ratio of eight was determined using a two dimensional viscous flow prediction technique for the flow field calculation, and a three dimensional potential flow panel method to evaluate the degree of two dimensionality achieved at the wing center line. The analysis was made to provide an acceptable reference for comparison with velocity measurements obtained from a fringe type laser velocimeter optics systems operating in the backscatter mode in the Langley V/STOL tunnel. Good agreement between laser velocimeter measurements and theoretical results indicate that both methods provide a true representation of the velocity field about the wing at angles of attack of 0.6 and 4.75 deg.

Hoad, D. R.↗
NASA NTRS1974

Data compression

An approach to data compression is discussed in which the effect achieved by compression is evaluated by the closeness of the approach to the minimum possible volume. An attempt is made to systematize the known results on data compression. The review contains: description of methods of data compression based on statistical coding and information theory; application of methods of interpolation and extrapolation; a specific compression method (related to description of the histogram of a sample); some criteria of effectiveness and methods of service information representation; and discussion of models suggested for theoretical analysis.

Babkin, V. F.↗
DOE OSTI2022

Netostat: analyzing dynamic flow patterns in high-speed networks

Understanding flow traffic patterns in networks, such as the Internet or service provider networks, is crucial to improving their design and building them robustly. However, as networks grow and become more complex, it is increasingly cumbersome and challenging to study how the many flow patterns, sizes and the continually changing source-destination pairs in the network evolve with time. Here, we present Netostat, a visualization-based network analysis tool that uses visual representation and a mathematics framework to study and capture flow patterns, using graph theoretical methods such as clustering, similarity and difference measures. Netostat generates an interactive graph of all traffic patterns in the network, to isolate key elements that can provide insights for traffic engineering. We present results for U.S. and European research networks, ESnet and GEANT, demonstrating network state changes, to identify major flow trends, potential points of failure, and bottlenecks.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1975

Reduction of wind tunnel wall interference by controlled wall flow

An alternate method of testing was developed in which flow through the porous walls of the tunnel was actively controlled so as to approximate free air conditions in the neighborhood of the model during the test. The amount and distribution of the controlled flow through the walls is computed using a potential flow representation of the model based on the measured lift. Theoretical analysis is presented to prove the convergence of the method to free air conditions and to substantiate the general three-dimensional theory of operation when the normal flow distribution is continuous. A two-dimensional tunnel was constructed to evaluate the concept. Results show that substantial reduction of wall interference may be achieved with relatively low values of porosity of actively controlled walls.

Bernstein, S.↗
NASA NTRS1976

Reduction of wind-tunnel wall interference by controlled wall flow

Corrections for wind tunnel wall interferences are applied successfully to high lift models when the model to tunnel size ratio is small. The accuracy of the corrections becomes poorer when larger models are tested. An alternate method of testing was developed in which flow through the porous walls of the tunnel was actively controlled so as to approximate free air conditions in the neighborhood of the model during the test. The amount and distribution of the controlled flow through the walls is computed using a potential flow representation of the model based on the measured lift. Theoretical analysis is presented to prove the convergence of the method to free air conditions and to substantiate the general three dimensional theory of operation when the normal flow distribution is continuous. A two dimensional tunnel was constructed to evaluate the concept. Results show that substantial reduction of wall interference may be achieved with relatively low values of porosity of actively controlled walls.

Bernstein, S.↗
NASA NTRS1987

An analysis of flux-split algorithms for Euler's equations with real gases

An analysis of flux-splitting procedures for the solution of Euler's equations with real gas effects is presented. An alternative real-gas flux-splitting is derived which can easily be implemented into existing codes. This approach, which takes the form of an 'equivalent' gamma representation is not an ad hoc model, but is based on theoretical considerations. Details of this method with the Steger-Warming and Van Leer flux vector splittings and the Roe flux-difference splitting are given. Applications of the method to several high Mach number, high temperature flows are presented for one and two space dimensions.

Grossman, B.↗
NASA NTRS1995

Real-time value-driven diagnosis

Diagnosis is often thought of as an isolated task in theoretical reasoning (reasoning with the goal of updating our beliefs about the world). We present a decision-theoretic interpretation of diagnosis as a task in practical reasoning (reasoning with the goal of acting in the world), and sketch components of our approach to this task. These components include an abstract problem description, a decision-theoretic model of the basic task, a set of inference methods suitable for evaluating the decision representation in real-time, and a control architecture to provide the needed continuing coordination between the agent and its environment. A principal contribution of this work is the representation and inference methods we have developed, which extend previously available probabilistic inference methods and narrow, somewhat, the gap between probabilistic and logical models of diagnosis.

Dambrosio, Bruce↗
NASA NTRS1997

Interfacing Relativistic and Nonrelativistic Methods: A Systematic Sequence of Approximations

A systematic sequence of approximations for the introduction of relativistic effects into nonrelativistic molecular finite-basis set calculations is described. The theoretical basis for the approximations is the normalized elimination of the small component (ESC) within the matrix representation of the modified Dirac equation. The key features of the normalized method are the retention of the relativistic metric and the ability to define a single matrix U relating the pseudo-large and large component coefficient matrices. This matrix is used to define a modified set of one- and two-electron integrals which have the same appearance as the integrals of the Breit-Pauli Hamiltonian. The first approximation fixes the ratios of the large and pseudo-large components to their atomic values, producing an expansion in atomic 4-spinors. The second approximation defines a local fine-structure constant on each atomic centre, which has the physical value for centres considered to be relativistic and zero for nonrelativistic centres. In the latter case, the 4-spinors are the positive-energy kinetic al ly-balanced solutions of the Levy-Leblond equation, and the integrals involving pseudo-large component basis functions on these centres, are set to zero. Some results are presented for test systems to illustrate the various approximations.

Dyall, Ken↗
DOE OSTI2024

Accelerate microstructure evolution simulation using graph neural networks with adaptive spatiotemporal resolution

Abstract Surrogate models driven by sizeable datasets and scientific machine-learning methods have emerged as an attractive microstructure simulation tool with the potential to deliver predictive microstructure evolution dynamics with huge savings in computational costs. Taking 2D and 3D grain growth simulations as an example, we present a completely overhauled computational framework based on graph neural networks with not only excellent agreement to both the ground truth phase-field methods and theoretical predictions, but enhanced accuracy and efficiency compared to previous works based on convolutional neural networks. These improvements can be attributed to the graph representation, both improved predictive power and a more flexible data structure amenable to adaptive mesh refinement. As the simulated microstructures coarsen, our method can adaptively adopt remeshed grids and larger timesteps to achieve further speedup. The data-to-model pipeline with training procedures together with the source codes are provided.

36 MATERIALS SCIENCE↗
NASA NTRS1988

Advancements in frequency-domain methods for rotorcraft system identification

A new method for frequency-domain identification of rotorcraft dynamics is presented. Nonparametric frequency-response identification and parametric tranfer-function modeling methods are extended to allow the extraction of state-space (stability and control derivative) representations. An interactive computer program DERIVID is described for the iterative solution of the multi-input/multi-output frequency-response matching approach used in the identification. Theoretical accuracy methods are used to determine the appropriate model structure and degree-of-confidence in the identified parameters. The method is applied to XV-15 tilt-rotor aircraft data in hover. Bare-airframe stability and control derivatives for the lateral/directional dynamics are shown to compare favorably with models previously obtained using time-domain identification methods and the XV-15 simulation program.

Tischler, Mark B.↗
NASA NTRS1989

Advancements in frequency-domain methods for rotorcraft system identification

A new method for frequency-domain identification of rotorcraft dynamics is presented. Nonparametric frequency-response identification and parametric transfer-function modeling methods are extended to allow the extraction of state-space (stability and control derivative) representations. An interactive computer program DERIVID is described for the iterative solution of the multi-input/multi-output frequency-response matching approach used in the identification. Theoretical accuracy methods are used to determine the appropriate model structure and degree-of-confidence in the identified parameters. The method is applied to XV-15 tilt-rotor aircraft data in hover. Bare-airframe stability and control derivatives for the lateral/directional dynamics are shown to compare favorably with models previously obtained using time-domain identification methods and the XV-15 simulation program.

Tischler, Mark B.↗
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 OSTI2020

A Method for Extrapolating CMM Data

This report provides a method for evaluating coordinate measuring machine (CMM) data and extrapolating the data to estimate the dimensions of a cylindrical component beyond the sampled measurements. The theoretical basis is provided, and a calculational method is presented. The report also provides detailed, formatted, printed, and plotted representations.

36 MATERIALS SCIENCE↗
NASA NTRS1983

A theoretical investigation of the sound radiation fields associated with a Bellmouth inlet

Analytical results are obtained by numerical integration of a cylindrically symmetric integral representation of the external solutions of the Helmholtz equation. The accuracy of this method is checked by comparisons of computed results with 'exact' solutions generated by the point source method. In all cases, the average error for the amplitude and phase of the points calculated in the field is found to be less than ten percent. Theoretical studies which model experiments run for the NASA Langely Bellmouth inlet configuration are presented and comparisons are made with the experimental results. In all cases very good agreement is obtained between the experimental and theoretically calculated values.

Meyer, W. L.↗
NASA NTRS1996

There aren't Non-Standard Solutions for the Braid Group Representations of the QYBE Associated with 10-D Representations of SU(4)

It is well known that the quantum Yang-Baxter equations (QYBE) play an important role in various theoretical and mathematical physics, such as completely integrable system in (1 + 1)-dimensions, exactly solvable models in statistical mechanics, the quantum inverse scattering method and the conformal field theories in 2-dimensions. Recently, much remarkable progress has been made in constructing the solutions of the QYBE associated with the representations of lie algebras. It is shown that for some cases except the standard solutions, there also exist new solutions, but the others have not non-standard solutions. In this paper by employing the weight conservation and the diagrammatic techniques we show that the solution associated with the 10-D representations of SU (4) are standard alone.

Yijun, Huang↗