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NASA NTRS1990

Distributed deformation and block rotation in 3D

The authors address how block rotation and complex distributed deformation in the Earth's shallow crust may be explained within a stationary regional stress field. Distributed deformation is characterized by domains of sub-parallel fault-bounded blocks. In response to the contemporaneous activity of neighboring domains some domains rotate, as suggested by both structural and paleomagnetic evidence. Rotations within domains are achieved through the contemporaneous slip and rotation of the faults and of the blocks they bound. Thus, in regions of distributed deformation, faults must remain active in spite of their poor orientation in the stress field. The authors developed a model that tracks the orientation of blocks and their bounding faults during rotation in a 3D stress field. In the model, the effective stress magnitudes of the principal stresses (sigma sub 1, sigma sub 2, and sigma sub 3) are controlled by the orientation of fault sets in each domain. Therefore, adjacent fault sets with differing orientations may be active and may display differing faulting styles, and a given set of faults may change its style of motion as it rotates within a stationary stress regime. The style of faulting predicted by the model depends on a dimensionless parameter phi = (sigma sub 2 - sigma sub 3)/(sigma sub 1 - sigma sub 3). Thus, the authors present a model for complex distributed deformation and complex offset history requiring neither geographical nor temporal changes in the stress regime. They apply the model to the Western Transverse Range domain of southern California. There, it is mechanically feasible for blocks and faults to have experienced up to 75 degrees of clockwise rotation in a phi = 0.1 strike-slip stress regime. The results of the model suggest that this domain may first have accommodated deformation along preexisting NNE-SSW faults, reactivated as normal faults. After rotation, these same faults became strike-slip in nature.

Scotti, Oona↗

NASA NTRS1989

A Study of Strong Stability of Distributed Systems

The strong stability of distributed systems is studied and the problem of characterizing strongly stable semigroups of operators associated with distributed systems is addressed. Main emphasis is on contractive systems. Three different approaches to characterization of strongly stable contractive semigroups are developed. The first one is an operator theoretical approach. Using the theory of dilations, it is shown that every strongly stable contractive semigroup is related to the left shift semigroup on an L(exp 2) space. Then, a decomposition for the state space which identifies strongly stable and unstable states is introduced. Based on this decomposition, conditions for a contractive semigroup to be strongly stable are obtained. Finally, extensions of Lyapunov's equation for distributed parameter systems are investigated. Sufficient conditions for weak and strong stabilities of uniformly bounded semigroups are obtained by relaxing the equivalent norm condition on the right hand side of the Lyanupov equation. These characterizations are then applied to the problem of feedback stabilization. First, it is shown via the state space decomposition that under certain conditions a contractive system (A,B) can be strongly stabilized by the feedback -B(*). Then, application of the extensions of the Lyapunov equation results in sufficient conditions for weak, strong, and exponential stabilizations of contractive systems by the feedback -B(*). Finally, it is shown that for a contractive system, the first derivative of x with respect to time = Ax + Bu (where B is any linear bounded operator), there is a related linear quadratic regulator problem and a corresponding steady state Riccati equation which always has a bounded nonnegative solution.

Cataltepe, Tayfun↗

NASA NTRS1990

Explaining compact groups as change alignments

The physical nature of the apparently densest groups of galaxies, known as compact groups is a topic of some recent controversy, despite the detailed observations of a well-defined catalog of 100 isolated compact groups compiled by Hickson (1982). Whereas many authors have espoused the view that compact groups are bound systems, typically as dense as they appear in projection on the sky (e.g., Williams & Rood 1987; Sulentic 1987; Hickson & Rood 1988), others see them as the result of chance configurations within larger systems, either in 1D (chance alignments: Mamon 1986; Walke & Mamon 1989), or in 3D (transient cores: Rose 1979). As outlined in the companion review to this contribution (Mamon, in these proceedings), the implication of Hickson's compact groups (HCGs) being dense bound systems is that they would then constitute the densest isolated systems of galaxies in the Universe and the privileged site for galaxy interactions. In a previous paper (Mamon 1986), the author reviewed the arguments given for the different theories of compact groups. Since then, a dozen papers have been published on the subject, including a thorough and perceptive review by White (1990), thus more than doubling the amount written on the subject. Here, the author first enumerates the arguments that he brought up in 1986 substantiating the chance alignment hypothesis, then he reviews the current status of the numerous recent arguments arguing against chance alignments and/or for the bound dense group hypothesis (both for the majority of HCGs but not all of them), and finally he reconsiders each one of these anti-chance alignment arguments and shows that, rather than being discredited, the chance alignment hypothesis remains a fully consistent explanation for the nature of compact groups.

Mamon, Gary A.↗

NASA NTRS1990

Reliability of voting in fault-tolerant software systems for small output spaces

Under a voting strategy in a fault-tolerant software system there is a difference between correctness and agreement. An independent N-version programming reliability model is proposed for treating small output spaces which distinguishes between correctness and agreement. System reliability is investigated using analytical relationships and simulation. A consensus majority voting stratey is proposed and its performance is analyzed and compared with other voting strategies. A consensus voting strategy automatically adapts the voting to diffeerent component reliability and output space cardinality characteristics. It is shown that absolute majority voting strategy provides a lower bound on the reliability provided by the consensus majority, and the 2-of-n voting strategy an upper bound. If r is the cardinality of output space it is proved that 1/r is a lower bound on the average reliability of fault-tolerant system components below which the system reliability begins to deteriorate as more versions are added.

Mcallister, David F.↗

NASA NTRS1991

Kinetics and continuum emission of negative atomic ions in partially ionized plasmas

Kinetics and continuum emission of negative ions are studied in stationary atomic hydrogen, nitrogen, and oxygen plasmas. The intensity of the negative-ion emission was found to be neglibible when compared to those of bound-bound and free-bound emission at low and medium particle densities. However, the negative-ion continuum emission can contribute significantly in certain parts of the emission spectrum at high particle densities.

Soon, W. H.↗

NASA NTRS1991

Vibrational relaxation and dissociation in nitrogen

Calculations of the vibrational and dissociation transition probabilities are made for N2-N2 and N2-N collisions by means of a semiclassical N-state approximation. The flaws in previous techniques are reviewed, with special attention given to the prediction of overtones. The method presented ignores the effects of molecular rotation and employs a revised extended Rydberg intermolecular potential to describe diatom-diatom and diatom-atom collisions. The collision velocities investigated exhibit probabilities of less than unity by means of the N-state method. The continuum is quantized to treat dissociation, and the collision results demonstrate probability enhancements for V-V-T transitions in both bound-bound and bound-free transitions. The technique is of particular interest for the theoretical modeling of reentry flows such as those encountered in aerobraking maneuvers.

Varghese, Philip L.↗

NASA NTRS1992

Development of an algebraic turbulence model for analysis of propulsion flows

A simple turbulence model that will be applicable to propulsion flows having both wall bounded and unbounded regions was developed and installed within the PARC Navier-Stokes code by linking two existing algebraic turbulence models. The first is the Modified Mixing Length (MML) model which is optimized for wall bounded flows. The second is the Thomas model, the standard algebraic turbulence model in PARC which has been used to calculate both bounded and unbounded turbulent flows but was optimized for the latter. This paper discusses both models and the method employed to link them into one model (referred to as the MMLT model). The PARC code with the MMLT model was applied to two dimensional turbulent flows over a flat plate and over a backward facing step to validate and optimize the model and to compare its predictions to those obtained with the three turbulence models already available in PARC.

Georgiadis, N. J.↗

NASA NTRS1991

Limits on static shape control for space structures

This paper deals with correction of shape distortion due to zero-mean normally distributed errors in structural sizes. The concept of ideal actuators - actuators that can produce any desired displacement field - is introduced. Using this concept, a bound on the possible improvement in the expected value of the root-mean-square shape error is obtained. The shape correction associated with the ideal actuators is also characterized. An actuator effectiveness index is developed by comparing the displacement field generated by the actuator to the ideal. The results are specialized to a simple form for truss structures composed of nominally identical members. The bound and effectiveness index are tested on a 55-m radiometer antenna truss structure. It is found that previously obtained results for optimum actuators had a performance close to the bound obtained here. Also, it is found that large numbers of actuators are needed for large reductions in shape errors. Furthermore, the actuators associated with the optimum design are shown to have high effectiveness indices. Since only a small fraction of truss elements tend to have high effectiveness indices, the use of the effectiveness index can greatly reduce the number of truss members that need to be considered actuator sites.

Haftka, Raphael T.↗

NASA NTRS1992

Limits of Gaussian fluctuations in the cosmic microwave background at 19.2 GHz

The Northern Hemisphere data from the 19.2 GHz full sky survey are analyzed to place limits on the magnitude of Gaussian fluctuations in the cosmic microwave background implied by a variety of correlation functions. Included among the models tested are the monochromatic and Gaussian-shaped families, and those with power-law spectra for n values between -2 and 1. An upper bound is placed on the quadrupole anisotropy of Delta T/T less than 3.2 x 10 exp -5 rms, and an upper bound on scale-invariant (n = 1) fluctuations of a2 less than 4.5 x 10 exp -5 (95 percent confidence level). There is significant contamination of these data from Galactic emission, and improvement of the modeling of the Galaxy could yield a significant reduction of these upper bounds.

Boughn, S. P.↗

NASA NTRS1992

Rotational relaxation of molecular H2 at moderate temperatures

A coupled rotation-vibration-dissociation model is used to compute the rotational relaxation times for molecular hydrogen as a function of final temperatures (500-5000 K) in a hypothetical scenario of sudden compression. The theoretical model is based on a master equation solver. The bound-bound and bound-free transition rates have been computed using a quasi-classical trajectory method. A review of the available experimental data on the rotational relaxation of hydrogen is presented, with a critical overview of the method of measurements and data reduction, including the sources of errors. The experimental data are compared with the computed results.

Sharma, S. P.↗

NASA NTRS1992

Development of an algebraic turbulence model for analysis of propulsion flows

Georgiadis, N. J.↗

NASA NTRS1992

Recent advances in carbon-carbon substrate technology at NASA. Langley Research Center

A comparison of specific strengths of candidate high-temperature materials as a function of temperature is shown. From this comparison, it is apparent why there is an interest in carbon-carbon composites for applications as a strong, light-weight thermal protection system (TPS), or as hot structure, for applications above 2500 F. The lower bound of the carbon-carbon band is representative of the tensile strength of cross-ply Advanced Carbon-Carbon (ACC). The upper bound represents capabilities of various experimental carbon-carbon composites. Thin carbon-carbon composites, such as would be used as TPS panels or hot aero-structure, are usually constructed of layups of 2-D fabrics of carbon-fiber yarns (tows). Although the in-plane strengths of these composites can be very attractive, a major problem area is low interlaminar strength. The low interlaminar strength is the result of a relatively weak carbon matrix and poor interaction between the fibers and matrix. The purpose of this paper is to discuss strategies being employed to improve the interlaminar strengths of the materials at the upper bound of the carbon-carbon band, and to present some recent encouraging results. The emphasis of these strategies is to improve interlaminar shear and tensile strengths while maintaining, or even improving, the inplane properties.

Ransone, Philip O.↗

NASA NTRS1992

Palinspastic reconstruction of southeastern California and southwestern Arizona for the middle Miocene

A paleogeographic reconstruction of southeastern California and southwestern Arizona at 10 Ma was made based on available geologic and geophysical data. Clockwise rotation of 39 deg was reconstructed in the eastern Transverse Ranges, consistent with paleomagnetic data from late Miocene volcanic rocks, and with slip estimates for left-lateral faults within the eastern Transverse Ranges and NW-trending right lateral faults in the Mojave Desert. This domain of rotated rocks is bounded by the Pinto Mountain fault on the north. In the absence of evidence for rotation of the San Bernardino Mountains or for significant right slip faults within the San Bernardino Mountains, the model requires that the late Miocene Pinto Mountain fault become a thrust fault gaining displacement to the west. The Squaw Peak thrust system of Meisling and Weldon may be a western continuation of this fault system. The Sheep Hole fault bounds the rotating domain on the east. East of this fault an array of NW-trending right slip faults and south-trending extensional transfer zones has produced a basin and range physiography while accumulating up to 14 km of right slip. This maximum is significantly less than the 37.5 km of right slip required in this region by a recent reconstruction of the central Mojave Desert. Geologic relations along the southern boundary of the rotating domain are poorly known, but this boundary is interpreted to involve a series of curved strike slip faults and non-coaxial extension, bounded on the southeast by the Mammoth Wash and related faults in the eastern Chocolate Mountains. Available constraints on timing suggest that Quaternary movement on the Pinto Mountain and nearby faults is unrelated to the rotation of the eastern Transverse Ranges, and was preceded by a hiatus during part of Pliocene time which followed the deformation producing the rotation. The reconstructed Clemens Well fault in the Orocopia Mountains, proposed as a major early Miocene strand of the San Andreas fault, projects eastward towards Arizona, where early Miocene rocks and structures are continuous across its trace. The model predicts a 14 deg clockwise rotation and 55 km extension along the present trace of the San Andreas fault during late Miocene and early Pliocene time. Palinspastic reconstructions of the San Andreas system based on this proposed reconstruction may be significantly modified from current models.

Richard, Stephen M.↗

NASA NTRS1991

mu analysis with real parametric uncertainty

The authors give a broad overview, from a LFT (linear fractional transformation)/mu perspective, of some of the theoretical and practical issues associated with robustness in the presence of real parametric uncertainty, with a focus on computation. Recent results on the properties of mu in the mixed case are reviewed, including issues of NP completeness, continuity, computation of bounds, the equivalence of mu and its bounds, and some direct comparisons with Kharitonov-type analysis methods. In addition, some advances in the computational aspects of the problem, including a novel branch and bound algorithm, are briefly presented together with numerical results. The results suggest that while the mixed mu problem may have inherently combinatoric worst-case behavior, practical algorithms with modest computational requirements can be developed for problems of medium size (less than 100 parameters) that are of engineering interest.

Young, Peter M.↗

NASA NTRS1992

Stellar encounters involving neutron stars in globular cluster cores

Encounters between a 1.4 solar mass neutron star and a 0.8 solar mass red giant (RG) and between a 1.4 solar mass neutron star (NS) and an 0.8 solar mass main-sequence (MS) star have been successfully simulated. In the case of encounters involving an RG, bound systems are produced when the separation at periastron passage R(MIN) is less than about 2.5 R(RG). At least 70 percent of these bound systems are composed of the RG core and NS forming a binary engulfed in a common envelope of what remains of the former RG envelope. Once the envelope is ejected, a tight white dwarf-NS binary remains. For MS stars, encounters with NSs will produce bound systems when R(MIN) is less than about 3.5 R(MS). Some 50 percent of these systems will be single objects with the NS engulfed in a thick disk of gas almost as massive as the original MS star. The ultimate fate of such systems is unclear.

Davies, M. B.↗

NASA NTRS1992

Practical computation of the mixed mu problem

The computational aspects of the recently developed upper and lower bounds for the mixed mu problem are examined. In particular, a practical algorithm is developed to compute the bounds. This has been implemented as a Matlab function (m-file) and will be available in a test version in conjunction with the mu-Tools toolbox. The algorithm performance is very encouraging, in terms of both accuracy of the resulting bounds and growth rate in required computation with problem size. In particular, it appears that one can handle medium-size problems (less than 100 perturbations) with reasonable computational requirements.

Young, Peter M.↗

NASA NTRS1991

Limits on Gaussian fluctuations in the cosmic microwave background at 19.2 GHz

The Northern Hemisphere data from the 19.2 GHz full sky survey are analyzed to place limits on the magnitude of Gaussian fluctuations in the cosmic microwave background implied by a variety of correlation functions. Included among the models tested are the monochromatic and Gaussian-shaped families, and those with power law spectra for n from -2 to 1. We place an upper bound on the quadrupole anisotropy of DeltaT/T less than 3.2 x 10 exp -5 rms, and an upper bound on scale-invariant (n = 1) fluctuations of a2 less than 4.5 x 10 exp -5 (95 percent confidence level). There is significant contamination of these data from Galactic emission, and improvement of our modeling of the Galaxy could yield a significant reduction of these upper bounds.

Boughn, S. P.↗

NASA NTRS1993

The isolation limits of stochastic vibration

The vibration isolation problem is formulated as a 1D kinematic problem. The geometry of the stochastic wall trajectories arising from the stroke constraint is defined in terms of their significant extrema. An optimal control solution for the minimum acceleration return path determines a lower bound on platform mean square acceleration. This bound is expressed in terms of the probability density function on the significant maxima and the conditional fourth moment of the first passage time inverse. The first of these is found analytically while the second is found using a Monte Carlo simulation. The rms acceleration lower bound as a function of available space is then determined through numerical quadrature.

Knopse, C. R.↗