Results for “Group Theory and Generalizations” — Page 4

NASA NTRS1999

The NASA/MSFC Coherent Lidar Technology Advisory Team

The SPAce Readiness Coherent Lidar Experiment (SPARCLE) mission was proposed as a low cost technology demonstration mission, using a 2-micron, 100-mJ, 6-Hz, 25-cm, coherent lidar system based on demonstrated technology. SPARCLE was selected in late October 1997 to be NASA's New Millennium Program (NMP) second earth-observing (EO-2) mission. To maximize the success probability of SPARCLE, NASA/MSFC desired expert guidance in the areas of coherent laser radar (CLR) theory, CLR wind measurement, fielding of CLR systems, CLR alignment validation, and space lidar experience. This led to the formation of the NASA/MSFC Coherent Lidar Technology Advisory Team (CLTAT) in December 1997. A threefold purpose for the advisory team was identified as: 1) guidance to the SPARCLE mission, 2) advice regarding the roadmap of post-SPARCLE coherent Doppler wind lidar (CDWL) space missions and the desired matching technology development plan 3, and 3) general coherent lidar theory, simulation, hardware, and experiment information exchange. The current membership of the CLTAT is shown. Membership does not result in any NASA or other funding at this time. We envision the business of the CLTAT to be conducted mostly by email, teleconference, and occasional meetings. The three meetings of the CLTAT to date, in Jan. 1998, July 1998, and Jan. 1999, have all been collocated with previously scheduled meetings of the Working Group on Space-Based Lidar Winds. The meetings have been very productive. Topics discussed include the SPARCLE technology validation plan including pre-launch end-to-end testing, the space-based wind mission roadmap beyond SPARCLE and its implications on the resultant technology development, the current values and proposed future advancement in lidar system efficiency, and the difference between using single-mode fiber optical mixing vs. the traditional free space optical mixing.

Kavaya, Michael J.↗

NASA NTRS1999

Pre-Launch End-to-End Testing Plans for the SPAce Readiness Coherent Lidar Experiment (SPARCLE)

The SPAce Readiness Coherent Lidar Experiment (SPARCLE) mission was proposed as a low cost technology demonstration mission, using a 2-micron, 100-mJ, 6-Hz, 25-cm, coherent lidar system based on demonstrated technology. SPARCLE was selected in late October 1997 to be NASA's New Millennium Program (NMP) second earth-observing (EO-2) mission. To maximize the success probability of SPARCLE, NASA/MSFC desired expert guidance in the areas of coherent laser radar (CLR) theory, CLR wind measurement, fielding of CLR systems, CLR alignment validation, and space lidar experience. This led to the formation of the NASA/MSFC Coherent Lidar Technology Advisory Team (CLTAT) in December 1997. A threefold purpose for the advisory team was identified as: 1) guidance to the SPARCLE mission, 2) advice regarding the roadmap of post-SPARCLE coherent Doppler wind lidar (CDWL) space missions and the desired matching technology development plan 3, and 3) general coherent lidar theory, simulation, hardware, and experiment information exchange. The current membership of the CLTAT is shown. Membership does not result in any NASA or other funding at this time. We envision the business of the CLTAT to be conducted mostly by email, teleconference, and occasional meetings. The three meetings of the CLTAT to date, in Jan. 1998, July 1998, and Jan. 1999, have all been collocated with previously scheduled meetings of the Working Group on Space-Based Lidar Winds. The meetings have been very productive. Topics discussed include the SPARCLE technology validation plan including pre-launch end-to-end testing, the space-based wind mission roadmap beyond SPARCLE and its implications on the resultant technology development, the current values and proposed future advancement in lidar system efficiency, and the difference between using single-mode fiber optical mixing vs. the traditional free space optical mixing. attitude information from lidar and non-lidar sensors, and pointing knowledge algorithms will meet this second requirement. The topic of this paper is the pre-launch demonstration of the first requirement, adequate sensitivity of the SPARCLE lidar.

Kavaya, Michael J.↗

NASA NTRS2004

Theoretical Astrophysics at Fermilab

The Theoretical Astrophysics Group works on a broad range of topics ranging from string theory to data analysis in the Sloan Digital Sky Survey. The group is motivated by the belief that a deep understanding of fundamental physics is necessary to explain a wide variety of phenomena in the universe. During the three years 2001-2003 of our previous NASA grant, over 120 papers were written; ten of our postdocs went on to faculty positions; and we hosted or organized many workshops and conferences. Kolb and collaborators focused on the early universe, in particular and models and ramifications of the theory of inflation. They also studied models with extra dimensions, new types of dark matter, and the second order effects of super-horizon perturbations. S tebbins, Frieman, Hui, and Dodelson worked on phenomenological cosmology, extracting cosmological constraints from surveys such as the Sloan Digital Sky Survey. They also worked on theoretical topics such as weak lensing, reionization, and dark energy. This work has proved important to a number of experimental groups [including those at Fermilab] planning future observations. In general, the work of the Theoretical Astrophysics Group has served as a catalyst for experimental projects at Fennilab. An example of this is the Joint Dark Energy Mission. Fennilab is now a member of SNAP, and much of the work done here is by people formerly working on the accelerator. We have created an environment where many of these people made transition from physics to astronomy. We also worked on many other topics related to NASA s focus: cosmic rays, dark matter, the Sunyaev-Zel dovich effect, the galaxy distribution in the universe, and the Lyman alpha forest. The group organized and hosted a number of conferences and workshop over the years covered by the grant. Among them were:

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NASA NTRS1984

Generalized bilateral control of robot arms

This paper summarizes the theory of a new form of bilateral or force-reflecting manual control of remote robot (slave) arms. The mathematics of workspace representation, command structure, kinematic and dynamic control coordination required for implementing the new form of generalized bilateral control through computer programs is presented. The paper concludes with a brief description of implementation organization of the new system using a six-degree-of-freedom backdrivable hand controller, a PUMA 560 robot arm and a distributed net of microcomputers organized in two groups: one at the remote work site and one at the control station.

Bejczy, A. K.↗

NASA NTRS1996

Relativistic Navigation: A Theoretical Foundation

We present a theoretical foundation for relativistic astronomical measurements in curved space-time. In particular, we discuss a new iterative approach for describing the dynamics of an isolated astronomical N-body system in metric theories of gravity. To do this, we generalize the Fock-Chandrasekhar method of the weak-field and slow-motion approximation (WFSMA) and develop a theory of relativistic reference frames (RF's) for a gravitationally bounded many-extended-body problem. In any proper RF constructed in the immediate vicinity of an arbitrary body, the N-body solutions of the gravitational field equations are formally presented as a sum of the Riemann-flat inertial space-time, the gravitational field generated by the body itself, the unperturbed solutions for each body in the system transformed to the coordinates of this proper RF, and the gravitational interaction term. We develop the basic concept of a general WFSMA theory of the celestial RF's applicable to a wide class of metric theories of gravity and an arbitrary model of matter distribution. We apply the proposed method to general relativity. Celestial bodies are described using a perfect fluid model; as such, they possess any number of internal mass and current multipole moments that explicitly characterize their internal structures. The obtained relativistic corrections to the geodetic equations of motion arise because of a coupling of the bodies' multiple moments to the surrounding gravitational field. The resulting relativistic transformations between the different RF's extend the Poincare group to the motion of deformable self-gravitating bodies. Within the present accuracy of astronomical measurements we discuss the properties of the Fermi-normal-like proper RF that is defined in the immediate vicinity of the extended compact bodies. We further generalize the proposed approximation method and include two Eddington parameters (gamma, Beta). This generalized approach was used to derive the relativistic equations of satellite motion in the vicinity of the extended bodies. Anticipating improvements in radio and laser tracking technologies over the next few decades, we apply this method to spacecraft orbit determination. We emphasize the number of feasible relativistic gravity tests that may be performed within the context of the parameterized WFSMA. Based on the planeto-centric equations of motion of a spacecraft around the planet, we suggested a new null test of the Strong Equivalence Principle (SEP). The experiment to measure the corresponding SEP violation effect could be performed with the future Mercury Orbiter mission. We discuss other relativistic effects, including the perihelion advance and the redshift and geodetic precession of the orbiter's orbital plane about Mercury, as well as the possible future implementation of the proposed formalism in software codes developed for solar-system orbit determination. All the important calculations are completely documented, and the references contain an extensive list of cited literature.

Turyshev, Slava G.↗

NASA NTRS1980

A theory for the origin of a self-replicating chemical system. I - Natural selection of the autogen from short, random oligomers

A general theory is presented for the origin of a self-replicating chemical system, termed an autogen, which is capable of both crude replication and translation (protein synthesis). The theory requires the availability of free energy and monomers to the system, a significant background low-yield synthesis of kinetically stable oligopeptides and oligonucleotides, the localization of the oligomers, crude oligonucleotide selectivity of amino acids during oligopeptide synthesis, crude oligonucleotide replication, and two short peptide families which catalyze replication and translation, to produce a localized group of at least one copy each of two protogenes and two protoenzymes. The model posits a process of random oligomerization, followed by the random nucleation of functional components and the rapid autocatalytic growth of the functioning autogen to macroscopic amounts, to account for the origin of the first self-replicating system. Such a process contains steps of such high probability and short time periods that it is suggested that the emergence of an autogen in a laboratory experiment of reasonable time scale may be possible.

White, D. H.↗

NASA NTRS1992

NASA/DOD Aerospace Knowledge Diffusion Research Project. Paper 22: Establishing a research agenda for Scientific and Technical Information (STI): Focus on the user

The goal is the creation of a generally accepted, systematically developed and implemented, but user focused, research agenda for the Advisory Group for Aerospace Research and Development (AGARD) and the Technical Information Panel (TIP) member countries. Information use seldom exists as an isolated incident. Information use usually takes place within organizational and interpersonal contexts. Therefore, it should not be studied in isolation, but rather in an holistic environment. Once implemented, this research agenda could be completed within 3 to 5 years. The results would be generalizable to AGARD member nations, would form the basis for the development of theory based practice, and would form a significant body of knowledge that can be used by AGARD information professionals for policy, practice, product, and systems development.

Pinelli, Thomas E.↗

NASA NTRS1975

Two-electron bond-orbital model. I

The one-electron bond-orbital model of Harrison (1973) for tetrahedrally coordinated solids is modified to a two-electron model using a generalization of Falicov and Harris' (1969) method for treating the hydrogen molecule. Expressions for nuclear-exchange and pseudodipolar interactions are obtained in terms of bond-orbital model parameters. The eigenfunctions and eigenvalues of the Hamiltonian are employed along with standard perturbation theory to calculate the energy shifts resulting from the application of an external electric field and induced by the magnetic interaction between the nuclear spins and the bond-electron spins. The quantitative predictions of the derived formulas are examined for real semiconductors involving elements and compounds from periodic groups III, IV, and V. It is concluded that the present two-electron model makes it possible to assess the quantitative effects of electron correlation in the anion-cation bond for both nonmagnetic properties (electric susceptibility, dielectric constant) and magnetic properties (nuclear-exchange and pseudodipolar interactions) of various materials.

Huang, C.↗

NASA NTRS1984

On the psychophysics of workload - Why bother with subjective measures?

Psychophysical functions describe the relationship between variations in the amplitude of a defined physical quantity and the psychological perception of these changes. Examples are brightness, loudness, and pain. The regularities of these relationships have been formulated into psychophysical laws. The measurement methodology of psychophysical scaling has been refined by the Harvard group led by Stevens (1957 and 1966), who proposed a power function as a general form for such laws. It is argued here that a similar scaling approach can be adapted to the measurement of workload and task demands based upon subjective estimates. The rationale is that these estimates, like other psychophysical judgments, reflect the individual's perception of the amount of processing resources that the subject invests to meet the demand imposed by a task. This approach was successfully applied to the assessment of 21 experimental conditions given to a group of 60 subjects. The paper discusses the main results of this effort and their implications to theory and application in human performance.

Gopher, D.↗

NASA NTRS1989

Computer simulation of the mathematical modeling involved in constitutive equation development: Via symbolic computations

Development of new material models for describing the high temperature constitutive behavior of real materials represents an important area of research in engineering disciplines. Derivation of mathematical expressions (constitutive equations) which describe this high temperature material behavior can be quite time consuming, involved and error prone; thus intelligent application of symbolic systems to facilitate this tedious process can be of significant benefit. A computerized procedure (SDICE) capable of efficiently deriving potential based constitutive models, in analytical form is presented. This package, running under MACSYMA, has the following features: partial differentiation, tensor computations, automatic grouping and labeling of common factors, expression substitution and simplification, back substitution of invariant and tensorial relations and a relational data base. Also limited aspects of invariant theory were incorporated into SDICE due to the utilization of potentials as a starting point and the desire for these potentials to be frame invariant (objective). Finally not only calculation of flow and/or evolutionary laws were accomplished but also the determination of history independent nonphysical coefficients in terms of physically measurable parameters, e.g., Young's modulus, was achieved. The uniqueness of SDICE resides in its ability to manipulate expressions in a general yet predefined order and simplify expressions so as to limit expression growth. Results are displayed when applicable utilizing index notation.

Arnold, S. M.↗

NASA NTRS1986

Circumstellar dust

The presence of dust in the general interstellar medium is inferred from the extinction, polarization, and scattering of starlight; the presence of dark nebulae; interstellar depletions; the observed infrared emission around certain stars and various types of interstellar clouds. Interstellar grains are subject to various destruction mechanisms that reduce their size or even completely destroy them. A continuous source of newly formed dust must therefore be present for dust to exist in the various phases of the interstellar medium (ISM). The working group has the following goals: (1) review the evidences for the formation of dust in the various sources; (2) examine the clues to the nature and composition of the dust; (3) review the status of grain formation theories; (4) examine any evidence for the processing of the dust prior to its injection into the interstellar medium; and (5) estimate the relative contribution of the various sources to the interstellar dust population.

Dwek, E.↗

NASA NTRS1985

Applications of Fuzzy Set Theory to Satellite Soundings

The introduction of an appropriate fuzzy setting for satellite soundings and its application to clustering methods via unimodal fuzzy sets in the future is proposed. Methods of hard clustering analysis and fuzzy partitioned clustering were applied on simulated data with very encouraging results. The proposed clustering technique is discussed. The notion of a unimodal fuzzy set was chosen to represent the partition of a data set for two reasons: (1) it detects all the locations in the vector space where highly concentrated clusters of points exist; and (2) the notion is general enough to represent clusters that exhibit quite general distributions of points. The technique detects all of the existing unimodal fuzzy sets and realizes the maximum separation among them. It is economical in memory space and computational time requirements and also detects groups that are fairly generally distributed in the feature space.

Munteanu, M. J.↗

NASA NTRS1977

The reality of comet groups and pairs

Although the common genetic origin of the Kreutz family of sun-grazing comets has generally been accepted, there remains uncertainty with regard to genetic identity among other groups of comets whose orbital elements are nearly alike. Porter (1952) has listed a number of such groups, and Opik (1971) has made a statistical study of the orbits of 472 comets with aphelion distances beyond Saturn. Opik lists 97 groups that show similarities among their three angular elements, calculates an overall probability of some 10 to the -39th power that these similarities could have occurred by chance, and thus concludes that 60% or more of such comets fall into genetic groups containing from two to seven members. This paper explores the statistical reality of Opik's groups utilizing the Monte Carlo method of statistics as well as ordinary probability theory. The conclusion is reached that except for a few pairs, the similarity among orbital elements within the groups is no greater than random expectation.

Whipple, F. L.↗

NASA NTRS1997

Solar-System Tests of Gravitational Theories

We are engaged in testing gravitational theory by means of observations of objects in the solar system. These tests include an examination of the Principle Of Equivalence (POE), the Shapiro delay, the advances of planetary perihelia, the possibility of a secular variation G in the "gravitational constant" G, and the rate of the de Sitter (geodetic) precession of the Earth-Moon system. These results are consistent with our preliminary results focusing on the contribution of Lunar Laser Ranging (LLR), which were presented at the seventh Marcel Grossmann meeting on general relativity. The largest improvement over previous results comes in the uncertainty for (eta): a factor of five better than our previous value. This improvement reflects the increasing strength of the LLR data. A similar analysis presented at the same meeting by a group at the Jet Propulsion Laboratory gave a similar result for (eta). Our value for (beta) represents our first such result determined simultaneously with the solar quadrupole moment from the dynamical data set. These results are being prepared for publication. We have shown how positions determined from different planetary ephemerides can be compared and how the combination of VLBI and pulse timing information can yield a direct tie between planetary and radio frames. We have continued to include new data in our analysis as they became available. Finally, we have made improvement in our analysis software (PEP) and ported it to a network of modern workstations from its former home on a "mainframe" computer.

Shapiro, Irwin↗

NASA NTRS1995

Comparisons between theory and observation of active region tilts

Active regions in the Sun are generally tilted relative to the azimuthal direction, with the leading side being closer to the equator than the following side. This tilts is known to increase with latitude. Recently, theoretical calculations of the dynamics of emerging, initially toroidal active-region flux tubes have been done, showing that the observed tilts can be explained by the Coriolis force acting on a diverging flow field in emerging flux loops. The calculations of Fan, Fisher, & McClymont predict that alpha proportional to Phi(exp 1/4) B(sub 0 exp -5/4) sin theta, where alpha is the tilt angle of the active region, B(sub 0) is the magnetic field strength of the active-region flux tube near the base of the convection zone, and phi is the amount of magnetic flux in the tube. We compare these theoretical predictions with the behavior of a sample of 24,701 sunspot groups observed at Mount Wilson over a period of 68 yr, using the polarity separation distance d as a proxy for phi. Our major findings are given.

Fisher, G. H.↗

NASA NTRS1987

Surface flaw reliability analysis of ceramic components with the SCARE finite element postprocessor program

The SCARE (Structural Ceramics Analysis and Reliability Evaluation) computer program on statistical fast fracture reliability analysis with quadratic elements for volume distributed imperfections is enhanced to include the use of linear finite elements and the capability of designing against concurrent surface flaw induced ceramic component failure. The SCARE code is presently coupled as a postprocessor to the MSC/NASTRAN general purpose, finite element analysis program. The improved version now includes the Weibull and Batdorf statistical failure theories for both surface and volume flaw based reliability analysis. The program uses the two-parameter Weibull fracture strength cumulative failure probability distribution model with the principle of independent action for poly-axial stress states, and Batdorf's shear-sensitive as well as shear-insensitive statistical theories. The shear-sensitive surface crack configurations include the Griffith crack and Griffith notch geometries, using the total critical coplanar strain energy release rate criterion to predict mixed-mode fracture. Weibull material parameters based on both surface and volume flaw induced fracture can also be calculated from modulus of rupture bar tests, using the least squares method with known specimen geometry and grouped fracture data. The statistical fast fracture theories for surface flaw induced failure, along with selected input and output formats and options, are summarized. An example problem to demonstrate various features of the program is included.

Gyekenyesi, John P.↗

NASA NTRS1987

Surface flaw reliability analysis of ceramic components with the SCARE finite element postprocessor program

The SCARE (Structural Ceramics Analysis and Reliability Evaluation) computer program on statistical fast fracture reliability analysis with quadratic elements for volume distributed imperfections is enhanced to include the use of linear finite elements and the capability of designing against concurrent surface flaw induced ceramic component failure. The SCARE code is presently coupled as a postprocessor to the MSC/NASTRAN general purpose, finite element analysis program. The improved version now includes the Weibull and Batdorf statistical failure theories for both surface and volume flaw based reliability analysis. The program uses the two-parameter Weibull fracture strength cumulative failure probability distribution model with the principle of independent action for poly-axial stress states, and Batdorf's shear-sensitive as well as shear-insensitive statistical theories. The shear-sensitive surface crack configurations include the Griffith crack and Griffith notch geometries, using the total critical coplanar strain energy release rate criterion to predict mixed-mode fracture. Weibull material parameters based on both surface and volume flaw induced fracture can also be calculated from modulus of rupture bar tests, using the least squares method with known specimen geometry and grouped fracture data. The statistical fast fracture theories for surface flaw induced failure, along with selected input and output formats and options, are summarized. An example problem to demonstrate various features of the program is included.

Gyekenyesi, J. P.↗

NASA NTRS1997

Infrared Spectra of Substituted Polycyclic Aromatic Hydrocarbons

Calculations are carried out using density functional theory (DFT) to determine the harmonic frequencies and intensities of 1-methylanthracene, 9-methylanthracene, 9-cyanoanthracene, 2-aminoanthracene, acridine, and their positive ions. The theoretical data are compared with matrix-isolation spectra for these species also reported in this work. The theoretical and experimental frequencies and relative intensities for the neutral species are in generally good agreement, whereas the positive ion spectra are only in qualitative agreement. Relative to anthracene, we find that substitution of amethyl or CN for a hydrogen does not significantly affect the spectrum other than to add the characteristic methyl C-H stretch and C-N stretch (near 2200/cm), respectively. However, addition of NH2 dramatically affects the spectrum of the neutral. Not only are the NH2 modes themselves strong, but this electron withdrawing group induces sufficient partial charge on the ring to give the neutral molecule characteristics of the anthracene cation spectrum. The sum of the absolute intensities is about four times larger for 2-aminoanthracene than for 9-cyanoanthracene. Substituting nitrogen in the ring at the nine position (acridine) does not greatly alter the spectrum compared with anthracene.

Bauschlicher, Charles W., Jr.↗