SEARCH · Search NASA
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.
A generalized applied group theory is developed, and it is shown that phenomena from a number of diverse disciplines may be included under the umbrella of a single theoretical formulation based upon the concept of a group consistent with the usual definition of this term.
Group theory is applied to obtain generalized differential equations from the Hopf bifurcation theory on branching to periodic solutions. The conditions under which the symmetry group will admit imaginary eigenvalues are delimited. The action of the symmetry group on the circle group are explored and the Liapunov-Schmidt reduction is used to prove the Hopf theorem in the symmetric case. The emphasis is on simplifying calculations of the stability of bifurcating branches. The resulting general theory is demonstrated in terms of O(2) acting on a plane, O(n) in n-space, and O(3) and an irreducible model for spherical harmonics.
This paper presents a rational approach to modelling the triple velocity correlations that appear in the transport equations for the Reynolds stresses. All existing models of these correlations have largely been formulated on phenomenological grounds and are defective in one important aspect: they all neglect to allow for the dependence of these correlations on the local gradients of mean velocity. The mathematical necessity for this dependence will be demonstrated in the paper. The present contribution lies in the novel use of Group Representation Theory to determine the most general tensorial form of these correlations in terms of all the second- and third-order tensor quantities that appear in the exact equations that govern their evolution. The requisite representation did not exist in the literature and therefore had to be developed specifically for this purpose by Professor G. F. Smith. The outcome of this work is a mathematical framework for the construction of algebraic, explicit, and rational models for the triple velocity correlations that are theoretically consistent and include all the correct dependencies. Previous models are reviewed, and all are shown to be an incomplete subset of this new representation, even to lowest order.
Metric theories of gravity are compiled and classified according to the types of gravitational fields they contain, and the modes of interaction among those fields. The gravitation theories considered are classified as (1) general relativity, (2) scalar-tensor theories, (3) conformally flat theories, and (4) stratified theories with conformally flat space slices. The post-Newtonian limit of each theory is constructed and its Parametrized Post-Newtonian (PPN) values are obtained by comparing it with Will's version of the formalism. Results obtained here, when combined with experimental data and with recent work by Nordtvedt and Will and by Ni, show that, of all theories thus far examined by our group, the only currently viable ones are general relativity, the Bergmann-Wagoner scalar-tensor theory and its special cases (Nordtvedt; Brans-Dicke-Jordan), and a recent, new vector-tensor theory by Nordtvedt, Hellings, and Will.
The phenomenon of vortex breakdown is believed to be associated with a finite amplitude wave that has become trapped at the critical or breakdown location. The conditions at which the propagating waves become trapped at a certain axial location were examined by use of a group-velocity criterion implied by Landahl's general theory of wave trapping. An ideal vortex having constant vorticity and uniform axial velocity at the inlet of a slowly diverging duct was studied. The linear wave propagation analysis is applied to the base flow at several axial stations for several values of the ratio of swirl velocity to axial velocity at the inlet of the divergent duct, assuming a locally parallel flow. The dipsersion relations and hence the group velocities of both the symmetric (n = 0) and asymmetric modes (n = + or - 1) were investigated. The existence of a critical state in the flow (at which the group velocity vanishes), and its relationship to the stagnation point on the axis of the duct and to the occurrence of an irregular singularity in the equations governing wave propagation in the flow field are discussed.
Motion sickness is the general term describing a group of common nausea syndromes originally attributed to motion-induced cerebral ischemia, stimulation of abdominal organ afferent, or overstimulation of the vestibular organs of the inner ear. Sea-, car-, and airsicknesses are the most commonly experienced examples. However, the discovery of other variants such as Cinerama-, flight simulator-, spectacle-, and space sickness in which the physical motion of the head and body is normal or absent has led to a succession of sensory conflict theories which offer a more comprehensive etiologic perspective. Implicit in the conflict theory is the hypothesis that neutral and/or humoral signals originate in regions of the brain subversing spatial orientation, and that these signals somehow traverse to other centers mediating sickness symptoms. Unfortunately, the present understanding of the neurophysiological basis of motion sickness is far from complete. No sensory conflict neuron or process has yet been physiologically identified. To what extent can the existing theory be reconciled with current knowledge of the physiology and pharmacology of nausea and vomiting. The stimuli which causes sickness, synthesizes a contemporary Observer Theory view of the Sensory Conflict hypothesis are reviewed, and a revised model for the dynamic coupling between the putative conflict signals and nausea magnitude estimates is presented. The use of quantitative models for sensory conflict offers a possible new approach to improving the design of visual and motion systems for flight simulators and other virtual environment display systems.
Investigations of several problems of gravitation are discussed. The question of the existence of black holes is considered. While black holes like those in Einstein's theory may not exist in other gravity theories, trapped surfaces implying such black holes certainly do. The theories include those of Brans-Dicke, Lightman-Lee, Rosen, and Yang. A similar two-tensor theory of Yilmaz is investigated and found inconsistent and nonviable. The Newman-Penrose formalism for Riemannian geometries is adapted to general gravity theories and used to implement a search for twisting solutions of the gravity theories for empty and nonempty spaces. The method can be used to find the gravitational fields for all viable gravity theories. The rotating solutions are of particular importance for strong field interpretation of the Stanford/Marshall gyroscope experiment. Inhomogeneous cosmologies are examined in Einstein's theory as generalizations of homogeneous ones by raising the dimension of the invariance groups by one more parameter. The nine Bianchi classifications are extended to Rosen's theory of gravity for homogeneous cosmological models.
This report contains the 1989 annual progress reports of the Research Fellows of the Center for Turbulence Research. It is intended as a year end report to NASA, Ames Research Center which supports this group through core funding and by making available physical and intellectual resources. The Center for Turbulence Research is devoted to the fundamental study of turbulent flows; its objectives are to simulate advances in the physical understanding of turbulence, in turbulence modeling and simulation, and in turbulence control. The reports appearing in the following pages are grouped in the general areas of modeling, experimental research, theory, simulation and numerical methods, and compressible and reacting flows.
The paper demonstrates that the concept of turbulent constitutive relations can be used to construct general models for various turbulent correlations. Some of the Generalized Cayley-Hamilton formulas for relating tensor products of higher extension to tensor products of lower extension are introduced. The combination of dimensional analysis and invariant theory can lead to 'turbulent constitutive relations' (or general turbulence models) for, in principle, any turbulent correlations. As examples, the constitutive relations for Reynolds stresses and scalar fluxes are derived. The results are consistent with ones from Renormalization Group (RNG) theory and two-scale Direct-Interaction Approximation (DIA) method, but with a more general form.
Covariance groups and role of space-time coordinates in relativity theory
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.
It is shown that the usual one- and two-mode squeezing are based on reducible representations of the SU(1,1) group. Generalized squeezing is introduced with the use of different SU(1,1) rotations on each irreducible sector. Two-mode squeezing entangles the modes and information theory methods are used to study this entanglement. The entanglement of three modes is also studied with the use of the strong subadditivity property of the entropy.
I was recently tasked to work on an FAA funded task to investigate how the introduction of adaptive systems into air space management or avionics would impact software safety. Talking to control theory experts got a control theory answer, not a software answer and talking to software people got me answers about software in general. In this talk I discuss these two different viewpoints. Where the views of each group fall in the DO-178 process and how the collision of software and control theory cultures showed up when writing a new standard for Model Based Design. Some slides contain opinions and I hope the audience will feel free to respond with their own observations.
The Beta Cephei stars are a group of variables of spectral type B, whose light and radial velocity periods lie between about three and seven hours. An up-to-date summary of the observational data for individual stars considered to be members of the Beta Cephei group is provided. The general properties of Beta Cephei stars as determined from a comparison between theory and observation are considered, taking into account location in the HR diagram and evolutionary state, physical properties, statistics and galactic distribution, and period-luminosity relation and pulsation mode. Recent trends concerning the observation of Beta Cephei stars are examined, giving attention to a search for new variables, ultraviolet observations from spacecraft, and high-resolution studies of profile variations.
A general method described by Hermann and Martin (1976) for the study of the feedback invariants of linear systems is considered. It is shown that this method, which makes use of ideas of topology and algebraic geometry, is very useful in the investigation of feedback problems for which the classical methods are not suitable. The transfer function as a curve in the Grassmanian is examined. The general concepts studied in the context of specific systems and applications are organized in terms of the theory of Lie groups and algebraic geometry. Attention is given to linear systems which have a structure group, linear mechanical systems, and feedback invariants. The investigation shows that Lie group techniques are powerful and useful tools for analysis of the feedback structure of linear systems.
The author gives a summary of the conference proceedings. The conference began with the presentation of the basic data sets on pairs, groups, and interacting galaxies with the latter being further discussed with respect to both global properties and properties of the galactic nuclei. Then followed the theory, modelling and interpretation using analytic techniques, simulations and general modelling for spirals and ellipticals, starbursts and active galactic nuclei. Before the conference the author wrote down the three questions concerning pairs, groups and interacting galaxies that he hoped would be answered at the meeting: (1) How do they form, including the role of initial conditions, the importance of subclustering, the evolution of groups to compact groups, and the fate of compact groups; (2) How do they evolve, including issues such as relevant timescales, the role of halos and the problem of overmerging, the triggering and enhancement of star formation and activity in the galactic nuclei, and the relative importance of dwarf versus giant encounters; and (3) Are they important, including the frequency of pairs and interactions, whether merging and interactions are very important aspects of the life of a normal galaxy at formation, during its evolution, in forming bars, shells, rings, bulges, etc., and in the formation and evolution of active galaxies? Where possible he focuses on these three central issues in the summary.
Several sets of related Adage utility programs are described. A general description of the software group, instructions on how to use the programs, and a programmers description of the theory of operation are given along with a printed example of the program in use and a listing of the program.
An outstanding issue in computational analysis of time dependent problems is the imposition of appropriate radiation boundary conditions at artificial boundaries. Accurate conditions are developed which are based on the asymptotic analysis of wave propagation over long ranges. Employing the method of steepest descents, dominant wave groups are identified and simple approximations to the dispersion relation are considered in order to derive local boundary operators. The existence of a small number of dominant wave groups may be expected for systems with dissipation. Estimates of the error as a function of domain size are derived under general hypotheses, leading to convergence results. Some practical aspects of the numerical construction of the asymptotic boundary operators are also discussed.