Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Complexity theory”

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 1,081 records · Page 60
All sourcesNASA NTRSDOE OSTI
NASA NTRS2022

Uncertainty Models for the Hybrid Parametric Variation Method of Uncertainty Quantification; Analysis

There is some level of uncertainty in every finite element model (FEM), which flows to a level of uncertainty in predicted results. The purpose of uncertainty quantification (UQ) is to provide statistical bounds on prediction accuracy based on model uncertainty. This is distinct from model updating, which attempts to modify models to improve their accuracy. UQ does not improve the accuracy of models, but accepts that the models are inherently inaccurate and attempts to quantify the impact of that inaccuracy on predicted results. Previously, an alternate method for UQ, called the Hybrid Parametric Variation (HPV) method, was applied to Space Launch System (SLS) Hurty/Craig-Bampton (HCB) components to predict system-level statistics for launch vehicle attitude control transfer functions and core stage section loads due to buffet. The HPV method combines a parametric variation of the HCB fixed-interface (FI) modal frequencies with a nonparametric variation (NPV) method that randomly varies the HCB mass and stiffness matrices as Wishart random matrix distributions using random matrix theory (RMT). Alternatively, the most common method for modeling uncertainty in the structural dynamics community is a parametric approach, which varies physical parameters in the model. However, there are several disadvantages associated with the parametric method. Determining a reduced set of parameters that have a significant impact on the system response can be time consuming, and the selected parameter probability distributions are rarely reliably known. Therefore, in practice, the parameters are surrogates for the actual errors, and the link to parameter uncertainty is unknown. Another major drawback is that the uncertainty that can be represented is limited to the form of the nominal FEM. It is the experience of the authors that based on numerous aerospace programs, almost all FEM errors are in form rather than parameter values. This hypothesis is supported by the observation of the authors that it is almost never possible to ‘tune’ a FEM to match modal test results by only modifying model parameters. Model-form uncertainty cannot be directly represented by FEM input parameters nor included in a parametric approach. However, model-form uncertainty can be modeled using RMT, where a probability distribution is developed for the matrix ensemble of interest. The major advantage of the NPV method is that it covers errors in model form. The HPV method anchors uncertainty at the HCB component level to component modal test results by matching the HCB and test modes based on mode descriptions or other methods, and then applying differing levels of frequency variation. The specific variations depend on the confidence to which a component FEM has been validated through modal testing. The NPV method is layered on the frequency variation to match modal test self-orthogonality and cross-orthogonality (XO) results. Once the component uncertainty models are identified, they are assembled, and the uncertainty is propagated to the system level using a Monte Carlo (MC) analysis approach that generates statistics for system-level predictions This provides a UQ method that can be traced to test data, which can be updated as additional data and improved correlated models become available. The purpose of this paper is to collect and present all of the theory for HPV that has been previously published in reports and papers and to present examples of its application. Specifically, component uncertainty models based on the dispersion of corresponding mass and stiffness matrices using proposed test/analysis correlation metrics are investigated. The first example is purely academic so that the true answers are known, and the validity of the HPV method and the corresponding uncertainty models can be determined. The purpose of this paper is to collect and present all of the theory for HPV that has been previously published in reports and papers and to present examples of its application. Specifically, component uncertainty models based on the dispersion of corresponding mass and stiffness matrices using proposed test/analysis correlation metrics are investigated. The first example is purely academic so that the true answers are known, and the validity of the HPV method and the corresponding uncertainty models can be determined. The second example is an application to a component that is design specific to the SLS. Based on this work and other assessments, the HPV method provides another tool to the toolset used for complex system UQ analysis. From experience gathered to date using the HPV method, additional design specific applications must be investigated to provide further confidence in the validity of the HPV method of UQ analysis.

Uncertainty quantification↗
NASA NTRS1985

Finite-time arbitrary-motion unsteady cascade airfoil theory for helicopter rotors in hover

A complete and detailed derivation of finite-time arbitrary-motion cascade theory is presented for both Laplace and frequency domains. This theory includes the effect of returning wakes for both single- and multibladed rotors. The generalized cascade lift-deficiency function (CLDF) is shown to be consistent with the generalized Theodorsen lift-deficiency function when the wake spacing approaches infinity or when the reduced frequency tends to infinity. This function predicts correct zero-reduced-frequency limit. Accurate and efficient numerical procedures are presented for the evaluation of the CLDF. Numerical examples comparing the CLDF with Loewy's lift deficiency function in frequency domain are presented. Accurate Pade approximants of the CLDF are constructed using a Bode-plot approach which allows for complex poles.

Dinyavari, M. A. H.↗
NASA NTRS1994

Coronal mass ejections and major solar flares: The great active center of March 1989

The solar flare and coronal mass ejection (CME) events associated with the large and complex March 1989 active region are discussed. This active region gave us a chance to study the relation of CME with truly major solar flares. The work concentrates on questions of the relation of CMEs and flares to one another and to other types of activity on the Sun. As expected, some major (X-3B class) flares had associated CMEs. However, an unexpected finding is that others did not. In fact, there is strong evidence that the X4-4B flare of March 9th had no CME. This lack of a CME for such an outstanding flare event has important implications to theories of CME causation.Apparently, not all major flares cause CMEs or are caused by CMEs. The relations between CMEs and other types of solar activity are also discussed. No filament disappearances are reported for major CMEs studied here. Comparing these results with other studies, CMEs occur in association with flares and with erupting prominences, but neither are required for a CME. The relation between solar structures showing flaring without filament eruptions and structures showing filament eruptions without flares becomes important. The evolutionary relation between an active flaring sunspot region and extensive filaments without sunspots is reviewed, and the concept of an 'evolving magnetic structure' (EMS) is introduced. It is suggested that all CMEs arise in EMSs and that CMEs provide a major path through which azimuthal magnetic fields escape form the Sun during the solar cycle.

Feynman, Joan↗
NASA NTRS1975

Frequency stability requirements for two way range rate tracking

Accuracy limitations to two way range rate Doppler tracking due to master (reference) oscillator frequency instabilities are discussed. Theory is developed to treat both the effects of random and nonrandom oscillator instabilities. The nonrandom instabilities treated are drift, environmental effects, and coherent phase modulation. The effects of random instabilities on range rate accuracy are shown to be describable in terms of sigma y (2, T, tau). For the typical noise processes encountered in precision oscillators, range rate error is related to the more familiar sigma y (tau) and script L (f). Three examples are discussed to show how to determine range rate error from given sigma y (tau) or script L (f) curves, and approximations are developed to simplify the treatment of complex systems. An error analysis of range determined from rate data is also given.

Reinhardt, V.↗
NASA NTRS1997

The Topology of Symmetric Tensor Fields

Combinatorial topology, also known as "rubber sheet geometry", has extensive applications in geometry and analysis, many of which result from connections with the theory of differential equations. A link between topology and differential equations is vector fields. Recent developments in scientific visualization have shown that vector fields also play an important role in the analysis of second-order tensor fields. A second-order tensor field can be transformed into its eigensystem, namely, eigenvalues and their associated eigenvectors without loss of information content. Eigenvectors behave in a similar fashion to ordinary vectors with even simpler topological structures due to their sign indeterminacy. Incorporating information about eigenvectors and eigenvalues in a display technique known as hyperstreamlines reveals the structure of a tensor field. The simplify and often complex tensor field and to capture its important features, the tensor is decomposed into an isotopic tensor and a deviator. A tensor field and its deviator share the same set of eigenvectors, and therefore they have a similar topological structure. A a deviator determines the properties of a tensor field, while the isotopic part provides a uniform bias. Degenerate points are basic constituents of tensor fields. In 2-D tensor fields, there are only two types of degenerate points; while in 3-D, the degenerate points can be characterized in a Q'-R' plane. Compressible and incompressible flows share similar topological feature due to the similarity of their deviators. In the case of the deformation tensor, the singularities of its deviator represent the area of vortex core in the field. In turbulent flows, the similarities and differences of the topology of the deformation and the Reynolds stress tensors reveal that the basic addie-viscosity assuptions have their validity in turbulence modeling under certain conditions.

Levin, Yingmei↗
NASA NTRS2002

The Retrospective Iterated Analysis Scheme for Nonlinear Chaotic Dynamics

Atmospheric data assimilation is the name scientists give to the techniques of blending atmospheric observations with atmospheric model results to obtain an accurate idea of what the atmosphere looks like at any given time. Because two pieces of information are used, observations and model results, the outcomes of data assimilation procedure should be better than what one would get by using one of these two pieces of information alone. There is a number of different mathematical techniques that fall under the data assimilation jargon. In theory most these techniques accomplish about the same thing. In practice, however, slight differences in the approaches amount to faster algorithms in some cases, more economical algorithms in other cases, and even give better overall results in yet some other cases because of practical uncertainties not accounted for by theory. Therefore, the key is to find the most adequate data assimilation procedure for the problem in hand. In our Data Assimilation group we have been doing extensive research to try and find just such data assimilation procedure. One promising possibility is what we call retrospective iterated analysis (RIA) scheme. This procedure has recently been implemented and studied in the context of a very large data assimilation system built to help predict and study weather and climate. Although the results from that study suggest that the RIA scheme produces quite reasonable results, a complete evaluation of the scheme is very difficult due to the complexity of that problem. The present work steps back a little bit and studies the behavior of the RIA scheme in the context of a small problem. The problem is small enough to allow full assessment of the quality of the RIA scheme, but it still has some of the complexity found in nature, namely, its chaotic-type behavior. We find that the RIA performs very well for this small but still complex problem which is a result that seconds the results of our early studies.

Todling, Ricardo↗
NASA NTRS1990

Modeling the pressure-strain correlation of turbulence: An invariant dynamical systems approach

The modeling of the pressure-strain correlation of turbulence is examined from a basic theoretical standpoint with a view toward developing improved second-order closure models. Invariance considerations along with elementary dynamical systems theory are used in the analysis of the standard hierarchy of closure models. In these commonly used models, the pressure-strain correlation is assumed to be a linear function of the mean velocity gradients with coefficients that depend algebraically on the anisotropy tensor. It is proven that for plane homogeneous turbulent flows the equilibrium structure of this hierarchy of models is encapsulated by a relatively simple model which is only quadratically nonlinear in the anisotropy tensor. This new quadratic model - the SSG model - is shown to outperform the Launder, Reece, and Rodi model (as well as more recent models that have a considerably more complex nonlinear structure) in a variety of homogeneous turbulent flows. Some deficiencies still remain for the description of rotating turbulent shear flows that are intrinsic to this general hierarchy of models and, hence, cannot be overcome by the mere introduction of more complex nonlinearities. It is thus argued that the recent trend of adding substantially more complex nonlinear terms containing the anisotropy tensor may be of questionable value in the modeling of the pressure-strain correlation. Possible alternative approaches are discussed briefly.

Speziale, Charles G.↗
NASA NTRS1991

Modelling the pressure-strain correlation of turbulence - An invariant dynamical systems approach

The modeling of the pressure-strain correlation of turbulence is examined from a basic theoretical standpoint with a view toward developing improved second-order closure models. Invariance considerations along with elementary dynamical systems theory are used in the analysis of the standard hierarchy of closure models. In these commonly used models, the pressure-strain correlation is assumed to be a linear function of the mean velocity gradients with coefficients that depend algebraically on the anisotropy tensor. It is proven that for plane homogeneous turbulent flows the equilibrium structure of this hierarchy of models is encapsulated by a relatively simple model which is only quadratically nonlinear in the anisotropy tensor. This new quadratic model - the SSG model - is shown to outperform the Launder, Reece, and Rodi model (as well as more recent models that have a considerably more complex nonlinear structure) in a variety of homogeneous turbulent flows. Some deficiencies still remain for the description of rotating turbulent shear flows that are intrinsic to this general hierarchy of models and, hence, cannot be overcome by the mere introduction of more complex nonlinearities. It is thus argued that the recent trend of adding substantially more complex nonlinear terms containing the anisotropy tensor may be of questionable value in the modeling of the pressure-strain correlation. Possible alternative approaches are discussed briefly.

Speziale, Charles G.↗
NASA NTRS1996

Aerodynamic Shape Optimization of Supersonic Aircraft Configurations via an Adjoint Formulation on Parallel Computers

This work describes the application of a control theory-based aerodynamic shape optimization method to the problem of supersonic aircraft design. The design process is greatly accelerated through the use of both control theory and a parallel implementation on distributed memory computers. Control theory is employed to derive the adjoint differential equations whose solution allows for the evaluation of design gradient information at a fraction of the computational cost required by previous design methods. The resulting problem is then implemented on parallel distributed memory architectures using a domain decomposition approach, an optimized communication schedule, and the MPI (Message Passing Interface) Standard for portability and efficiency. The final result achieves very rapid aerodynamic design based on higher order computational fluid dynamics methods (CFD). In our earlier studies, the serial implementation of this design method was shown to be effective for the optimization of airfoils, wings, wing-bodies, and complex aircraft configurations using both the potential equation and the Euler equations. In our most recent paper, the Euler method was extended to treat complete aircraft configurations via a new multiblock implementation. Furthermore, during the same conference, we also presented preliminary results demonstrating that this basic methodology could be ported to distributed memory parallel computing architectures. In this paper, our concern will be to demonstrate that the combined power of these new technologies can be used routinely in an industrial design environment by applying it to the case study of the design of typical supersonic transport configurations. A particular difficulty of this test case is posed by the propulsion/airframe integration.

Reuther, James↗
NASA NTRS2002

Multiagent Work Practice Simulation: Progress and Challenges

Modeling and simulating complex human-system interactions requires going beyond formal procedures and information flows to analyze how people interact with each other. Such work practices include conversations, modes of communication, informal assistance, impromptu meetings, workarounds, and so on. To make these social processes visible, we have developed a multiagent simulation tool, called Brahms, for modeling the activities of people belonging to multiple groups, situated in a physical environment (geographic regions, buildings, transport vehicles, etc.) consisting of tools, documents, and computer systems. We are finding many useful applications of Brahms for system requirements analysis, instruction, implementing software agents, and as a workbench for relating cognitive and social theories of human behavior. Many challenges remain for representing work practices, including modeling: memory over multiple days, scheduled activities combining physical objects, groups, and locations on a timeline (such as a Space Shuttle mission), habitat vehicles with trajectories (such as the Shuttle), agent movement in 3d space (e.g., inside the International Space Station), agent posture and line of sight, coupled movements (such as carrying objects), and learning (mimicry, forming habits, detecting repetition, etc.).

Clancey, William J.↗
NASA NTRS2010

Current Sheets in the Corona and the Complexity of Slow Wind

The origin of the slow solar wind has long been one of the most important problems in solar/heliospheric physics. Two observational constraints make this problem especially challenging. First, the slow wind has the composition of the closed-field corona, unlike the fast wind that originates on open field lines. Second, the slow wind has substantial angular extent, of order 30 degrees, which is much larger than the widths observed for streamer stalks or the widths expected theoretically for a dynamic heliospheric current sheet. We propose that the slow wind originates from an intricate network of narrow (possibly singular) open-field corridors that emanate from the polar coronal hole regions. Using topological arguments, we show that these corridors must be ubiquitous in the solar corona. The total solar eclipse in August 2008, near the lowest point of cycle 23 affords an ideal opportunity to test this theory by using the ultra-high resolution Predictive Science's (PSI) eclipse model for the corona and wind. Analysis of the PSI eclipse model demonstrates that the extent and scales of the open-field corridors can account for both the angular width of the slow wind and its closed-field composition. We discuss the implications of our slow wind theory for the structure of the corona and heliosphere at solar minimum and describe further observational and theoretical tests.

Antiochos, Spiro↗
NASA NTRS1987

Analysis of a parallelized nonlinear elliptic boundary value problem solver with application to reacting flows

A parallelized finite difference code based on the Newton method for systems of nonlinear elliptic boundary value problems in two dimensions is analyzed in terms of computational complexity and parallel efficiency. An approximate cost function depending on 15 dimensionless parameters is derived for algorithms based on stripwise and boxwise decompositions of the domain and a one-to-one assignment of the strip or box subdomains to processors. The sensitivity of the cost functions to the parameters is explored in regions of parameter space corresponding to model small-order systems with inexpensive function evaluations and also a coupled system of nineteen equations with very expensive function evaluations. The algorithm was implemented on the Intel Hypercube, and some experimental results for the model problems with stripwise decompositions are presented and compared with the theory. In the context of computational combustion problems, multiprocessors of either message-passing or shared-memory type may be employed with stripwise decompositions to realize speedup of O(n), where n is mesh resolution in one direction, for reasonable n.

Keyes, David E.↗
NASA NTRS2001

Multiagent Work Practice Simulation: Progress and Challenges

Modeling and simulating complex human-system interactions requires going beyond formal procedures and information flows to analyze how people interact with each other. Such work practices include conversations, modes of communication, informal assistance, impromptu meetings, workarounds, and so on. To make these social processes visible, we have developed a multiagent simulation tool, called Brahms, for modeling the activities of people belonging to multiple groups, situated in a physical environment (geographic regions, buildings, transport vehicles, etc.) consisting of tools, documents, and a computer system. We are finding many useful applications of Brahms for system requirements analysis, instruction, implementing software agents, and as a workbench for relating cognitive and social theories of human behavior. Many challenges remain for representing work practices, including modeling: memory over multiple days, scheduled activities combining physical objects, groups, and locations on a timeline (such as a Space Shuttle mission), habitat vehicles with trajectories (such as the Shuttle), agent movement in 3D space (e.g., inside the International Space Station), agent posture and line of sight, coupled movements (such as carrying objects), and learning (mimicry, forming habits, detecting repetition, etc.).

Clancey, William J.↗
NASA NTRS2004

Random Matrix Approach to Quantum Adiabatic Evolution Algorithms

We analyze the power of quantum adiabatic evolution algorithms (Q-QA) for solving random NP-hard optimization problems within a theoretical framework based on the random matrix theory (RMT). We present two types of the driven RMT models. In the first model, the driving Hamiltonian is represented by Brownian motion in the matrix space. We use the Brownian motion model to obtain a description of multiple avoided crossing phenomena. We show that the failure mechanism of the QAA is due to the interaction of the ground state with the "cloud" formed by all the excited states, confirming that in the driven RMT models. the Landau-Zener mechanism of dissipation is not important. We show that the QAEA has a finite probability of success in a certain range of parameters. implying the polynomial complexity of the algorithm. The second model corresponds to the standard QAEA with the problem Hamiltonian taken from the Gaussian Unitary RMT ensemble (GUE). We show that the level dynamics in this model can be mapped onto the dynamics in the Brownian motion model. However, the driven RMT model always leads to the exponential complexity of the algorithm due to the presence of the long-range intertemporal correlations of the eigenvalues. Our results indicate that the weakness of effective transitions is the leading effect that can make the Markovian type QAEA successful.

Boulatov, Alexei↗
NASA NTRS1983

Theory of interstellar medium diagnostics

The theoretical interpretation of observed interplanetary resonance luminescence patterns is used as one of the must promising methods to determine the state of the local interstellar medium (LISM). However, these methods lead to discrepant results that would be hard to understand in the framework of any physical LISM scenario. Assuming that the observational data are reliable, two possibilities which could help to resolve these discrepancies are discussed: (1) the current modeling of resonance luminescence patterns is unsatisfactory and has to be improved, and (2) the extrapolated interstellar parameters are not indicative of the unperturbed LISM state, but rather designate an intermediate state attained in the outer regions of the solar system. It is shown that a quantitative treatment of the neutral gas-plasma interaction effects in the interface between the heliospheric and the interstellar plasmas is of major importance for the correct understanding of the whole complex.

Fahr, H. J.↗
NASA NTRS1983

Pair Production and Annihilation in Strong Magnetic Fields

Electromagnetic phenomena occurring in the presence of strong magnetic fields are currently of great interest in high-energy astrophysics. In particular, the process of pair production by single photons in the presence of fields of order 10 to the 12th power Gauss is of importance in cascade models of pulsar gamma ray emission, and may also become significant in theories of other radiation phenomena whose sources may be neutron stars (e.g., gamma ray bursts). In addition to pair production, the inverse process of pair annihilation is greatly affected by the presence of superstrong magnetic fields. The most significant departures from annihilation processes in free space are a reduction in the total rate for annihilation into two photons, a broadening of the familiar 511-keV line for annihilation at rest, and the possibility for annihilation into a single photon (which dominates the two-photon annihilation for B ( 10 the 13th power Gauss). The physics of these pair conversion processes, which is reviewed briefly, can become quite complex in the teragauss regime, and can involve calculations which are technically difficult to incorporate into models of emission mechanisms in neutron star magnetospheres. However, theoretical work, especially the case of pair annihilation, also suggests potential techniques for more direct measurements of field strengths near the stellar surface.

Daugherty, J. K.↗
NASA NTRS1983

Pair production and annihilation in strong magnetic fields

Electromagnetic phenomena occurring in the presence of strong magnetic fields are currently of great interest in high-energy astrophysics. In particular, the process of pair production by single photons in the presence of fields of order 10 to the 12th power Gauss is of importance in cascade models of pulsar gamma ray emission, and may also become significant in theories of other radiation phenomena whose sources may be neutron stars (e.g., gamma ray bursts). In addition to pair production, the inverse process of pair annihilation is greatly affected by the presence of superstrong magnetic fields. The most significant departures from annihilation processes in free space are a reduction in the total rate for annihilation into two photons, a broadening of the familiar 511-keV line for annihilation at rest, and the possibility for annihilation into a single photon which dominates the two-photon annihilation for B (10 to 13th power Gauss) The physics of these pair conversion processes, which is reviewed briefly, can become quite complex in the teragauss regime, and can involve calculations which are technically difficult to incorporate into models of emission mechanisms in neutron star magnetospheres. However, theoretical work, especially the case of pair annihilation, also suggests potential techniques for more direct measurements of field strengths near the stellar surface.

Daugherty, J. K.↗
NASA NTRS1985

The space station and human productivity: An agenda for research

Organizational problems in permanent organizations in outer space were analyzed. The environment of space provides substantial opportunities for organizational research. Questions about how to organize professional workers in a technologically complex setting with novel dangers and uncertainties present in the immediate environment are examined. It is suggested that knowledge from organization theory/behavior is an underutilized resource in the U.S. space program. A U.S. space station will be operable by the mid-1990's. Organizational issues will take on increasing importance, because a space station requires the long term organization of human and robotic work in the isolated and confined environment of outer space. When an organizational analysis of the space station is undertaken, there are research implications at multiple levels of analysis: for the individual, small group, organizational, and environmental levels of analysis. The research relevant to organization theory and behavior is reviewed.

Schoonhoven, C. B.↗