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At least 775 records · Page 43

On the Origin of Chaos in the Asteroid Belt

We consider the effect of gravitational perturbations from Jupiter on the dynamics of asteroids, when Jupiter is itself perturbed by Saturn. The presence of Saturn introduces a number of additional frequencies into Jupiters orbit. These frequencies in turn produce chaos in narrow regions on either side of the chaotic zones associated with the mean motion resonances between the asteroids and Jupiter. The resonant arguments of these three-body resonances contain the longitudes of Jupiter and the asteroid together with either the secular frequency 9-6, or the longitude of Saturn. Resonances involving the longitude of Saturn are analogs of the Laplace resonance in the Jovian satellite system. We show that many three-body resonances involving the longitude of Saturn are chaotic. We give simple expressions for the width of the chaotic region and the associated Lyapunov time. In some cases the chaos can produce a diffusive growth in the 4 eccentricity of the asteroid that leads to ejection of the asteroid on times shorter than the age of the solar system. We give simple estimates for the diffusion time. Finally, we present the results of numerical integrations testing the theory.

Murray, N.↗

A Coupled Aeroelastic Model for Launch Vehicle Stability Analysis

A technique for incorporating distributed aerodynamic normal forces and aeroelastic coupling effects into a stability analysis model of a launch vehicle is presented. The formulation augments the linear state-space launch vehicle plant dynamics that are compactly derived as a system of coupled linear differential equations representing small angular and translational perturbations of the rigid body, nozzle, and sloshing propellant coupled with normal vibration of a set of orthogonal modes. The interaction of generalized forces due to aeroelastic coupling and thrust can be expressed as a set of augmenting non-diagonal stiffness and damping matrices in modal coordinates with no penalty on system order. While the eigenvalues of the structural response in the presence of thrust and aeroelastic forcing can be predicted at a given flight condition independent of the remaining degrees of freedom, the coupled model provides confidence in closed-loop stability in the presence of rigid-body, slosh, and actuator dynamics. Simulation results are presented that characterize the coupled dynamic response of the Ares I launch vehicle and the impact of aeroelasticity on control system stability margins.

Orr, Jeb S.↗

Diagrammatic technique for calculating matrix elements of collective operators in superradiance

Adopting the so-called genealogical construction, one can express the eigenstates of collective operators corresponding to a specified mode for an N-atom system in terms of those for an (N-1) atom system. Using these Dicke states as bases and using the Wigner-Eckart theorem, a matrix element of a collective operator of an arbitrary mode can be written as the product of an m-dependent factor and an m-independent reduced matrix element (RME). A set of recursion formulas for the RME is obtained. A graphical representation of the RME on the branching diagram for binary irreducible representations of permutation groups is then introduced. This gives a simple and systematic way of calculating the RME. This method is especially useful when the cooperation number r is close to N/2, where almost exact asymptotic expressions can be obtained easily. The result shows explicity the geometry dependence of superradiance and the relative importance of r-conserving and r-nonconserving processes.

Lee, C. T.↗

CNS development under altered gravity: cerebellar glial and neuronal protein expression in rat neonates exposed to hypergravity

The future of space exploration depends on a solid understanding of the developmental process under microgravity, specifically in relation to the central nervous system (CNS). We have previously employed a hypergravity paradigm to assess the impact of altered gravity on the developing rat cerebellum. The present study addresses the molecular mechanisms involved in the cerebellar response to hypergravity. Specifically, the study focuses on the expression of selected glial and neuronal cerebellar proteins in rat neonates exposed to hypergravity (1.5 G) from embryonic day (E)11 to postnatal day (P)6 or P9 (the time of maximal cerebellar changes) comparing them against their expression in rat neonates developing under normal gravity. Proteins were analyzed by quantitative Western blots of cerebellar homogenates; RNA analysis was performed in the same samples using quantitative PCR. Densitometric analysis of Western blots suggested a reduction in glial (glial acidic protein, GFAP) and neuronal (neuronal cell adhesion molecule, NCAM-L1, synaptophysin) proteins, but the changes in individual cerebellar proteins in hypergravity-exposed neonates appeared both age- and gender-specific. RNA analysis suggested a reduction in GFAP and synaptophysin mRNAs on P6. These data suggest that exposure to hypergravity may interfere with the expression of selected cerebellar proteins. These changes in protein expression may be involved in mediating the effect of hypergravity on the developing rat cerebellum. c2003 COSPAR. Published by Elsevier Ltd. All rights reserved.

NASA Program Fundamental Space Biology↗

Data Integration Support for Data Served in the OPeNDAP and OGC Environments

NASA is coordinating a technology development project to construct a gateway between system components built upon the Open-source Project for a Network Data AcceSs Protocol (OPeNDAP) and those made available made available via interfaces specified by the Open Geospatial Consortium (OGC). This project is funded though the Advanced Collaborative Connections for Earth-Sun System Science (ACCESS) Program and is a NASA contribution to the Committee on Earth Satellites (CEOS) Working Group on Information Systems and Services (WGISS). The motivation for the project is the set of data integration needs that have been expressed by the Coordinated Enhanced Observing Period (CEOP), an international program that is addressing the study of the global water cycle. CEOP is assembling a large collection in situ and satellite data and mode1 results from a wide variety of sources covering 35 sites around the globe. The data are provided by systems based on either the OPeNDAP or OGC protocols but the research community desires access to the full range of data and associated services from a single client. This presentation will discuss the current status of the OPeNDAP/OGC Gateway Project. The project is building upon an early prototype that illustrated the feasibility of such a gateway and which was demonstrated to the CEOP science community. In its first year as an ACCESS project, the effort has been has focused on the design of the catalog and data services that will be provided by the gateway and the mappings between the metadata and services provided in the two environments.

McDonald, Kenneth R.↗

Skeletal Phenotype of Transgenic Mice Expressing the Beta1 Integrin Cytoplasmic Tail In Osteoblasts

To define the physiologic role of beta1 integrin in bone formation and mechanical loading, transgenic mice were generated by expressing the cytoplasmic tall and transmembrane domain of Beta1 integrin under the control of the osteocalcin promoter. In cultured cells, this truncated fragment of Beta1 can act as a dominant negative. Previously, the matrix of calvariae was shown to be abnormal in transgenic (TG) compared to wildtype (WT) mice. In this study, we analyzed appendicular bone in TG and WT, male and female mice at 14, 35, 63, 90 and 365 days old (n=8-12/gp). To assess beta1 integrin function in mechanical loading, a pilot study using hindlimb unloading by tail suspension was performed. 35d old TG and WT females were hindlimb unloaded for 4 wks (n=3-5). Body mass, bone mineral content, histomorphometric (distal femur) and biomechanical parameters were analyzed. Statistical significance (P less than.05) was defined by ANOVA using the Tukey-Kramer post-hoc test. We confirmed transgene expression by immunoprecipitating then immunoblotting bone lysates using an antibody against the beta1 tail. Body masses of TG mice at 63, 90 and 365d old were greater (16-25%) than WT. Some TG female mice at 365d appeared obese; mean abdominal fat mass was 415% greater in TG than WT mice. Tibiae were longer (5-7%) in TG than WT mice at 63 and 90d. Tibial mineral mass of 35d males was 7% lower in TG than WT mice, but at 63d was 21% higher. The % osteoblast surface in 35d TG mice was 20% higher than WT, and at 63d was 17% lower, while % osteoclast surface did not differ. In 365d mice, cancellous bone volume (125%) and endocortical mineral apposition rate (40%) were greater in TG than WT males but not females. In WT mice, hindlimb unloading caused a reduction in mineral mass of tibiae (-20%) and lumbar vertebrae (-22%) relative to normally loaded controls. Surprisingly, hindlimb unloading also caused a relative reduction (-13%) in humerus mass. The effects of hindlimb unloading on tibia and humerus mass were less obvious in TG than in WT mice. Since hindlimb unloading caused skeletal changes in both loaded and unloaded bones, systemic changes may contribute to bone responses observed using this animal model. In conclusion, transgene expression resulted in marked metabolic changes during growth and in the aged female. Our results demonstrate that expression of the Beta1 integrin cytoplasmic tail in vivo causes gender- and age-specific changes in select morphometric parameters, bone length, and bone mass.

Globus, R. K.↗

Semantically-Rigorous Systems Engineering Modeling Using Sysml and OWL

The Systems Modeling Language (SysML) has found wide acceptance as a standard graphical notation for the domain of systems engineering. SysML subsets and extends the Unified Modeling Language (UML) to define conventions for expressing structural, behavioral, and analytical elements, and relationships among them. SysML-enabled modeling tools are available from multiple providers, and have been used for diverse projects in military aerospace, scientific exploration, and civil engineering. The Web Ontology Language (OWL) has found wide acceptance as a standard notation for knowledge representation. OWL-enabled modeling tools are available from multiple providers, as well as auxiliary assets such as reasoners and application programming interface libraries, etc. OWL has been applied to diverse projects in a wide array of fields. While the emphasis in SysML is on notation, SysML inherits (from UML) a semantic foundation that provides for limited reasoning and analysis. UML's partial formalization (FUML), however, does not cover the full semantics of SysML, which is a substantial impediment to developing high confidence in the soundness of any conclusions drawn therefrom. OWL, by contrast, was developed from the beginning on formal logical principles, and consequently provides strong support for verification of consistency and satisfiability, extraction of entailments, conjunctive query answering, etc. This emphasis on formal logic is counterbalanced by the absence of any graphical notation conventions in the OWL standards. Consequently, OWL has had only limited adoption in systems engineering. The complementary strengths and weaknesses of SysML and OWL motivate an interest in combining them in such a way that we can benefit from the attractive graphical notation of SysML and the formal reasoning of OWL. This paper describes an approach to achieving that combination.

Web Ontology Language (OWL)↗

Physical interrelation between Fokker-Planck and random walk models with application to Coulomb interactions.

A model of the random walk is formulated to allow a simple computing procedure to replace the difficult problem of solution of the Fokker-Planck equation. The step sizes and probabilities of taking steps in the various directions are expressed in terms of Fokker-Planck coefficients. Application is made to many particle systems with Coulomb interactions. The relaxation of a highly peaked velocity distribution of particles to equilibrium conditions is illustrated.

Englert, G. W.↗

An error criterion for determining sampling rates in closed-loop control systems

The determination of an error criterion which will give a sampling rate for adequate performance of linear, time-invariant closed-loop, discrete-data control systems was studied. The proper modelling of the closed-loop control system for characterization of the error behavior, and the determination of an absolute error definition for performance of the two commonly used holding devices are discussed. The definition of an adequate relative error criterion as a function of the sampling rate and the parameters characterizing the system is established along with the determination of sampling rates. The validity of the expressions for the sampling interval was confirmed by computer simulations. Their application solves the problem of making a first choice in the selection of sampling rates.

Brecher, S. M.↗

Derivatives of eigenvalues and eigenvectors for a general matrix

Expressions are obtained for the derivatives of the eigenvalues and eigenvectors which are expressions of only one left-hand and one right-hand eigenvector. The approach described makes use of a Choleski decomposition or some other decomposition method. The method may be extended to find any order of derivative of the eigenvalue and eigenvector. The expressions obtained for finding the derivatives of eigenvalues and eigenvectors for nonself-adjoint systems may be applied to self-adjoint systems.

Rudisill, C. S.↗

Electrophoretic separator for purifying biologicals

Mathematical expressions were developed to describe the interrelationships between operating requirements (capabilities), cell parameters, and system constraints in terms of design criteria definition. The mathematical model was programmed for computer solution. The model was exercised to identify performance-limiting characteristics, and analyses were conducted to predict operation in space of an experiment involving separation of four components. An engineering model of a flowing electrophoretic separator was constructed. The design is directed toward verifying improvements in resolution and throughput of a thicker cell than can be used on earth.

Source record↗

A constructive approach to commutative ring theory

The development of a system in MACSYMA for solving ring problems is described. Fundamental algorithms are given for expressing ideals in canonical form, and concrete examples are demonstrated.

Spear, D. A.↗

Evolution of ion cyclotron instability in the plasma convection system of the magnetosphere

In the present paper, Liouville's theorem is used in combination with approximate, but extremely accurate, expressions which reflect the invariance of the magnetic moment and the longitudinal invariant to determine analytically the evolution of an adiabatically convecting energetic particle distribution. Features of the convecting distribution, reproduced by this model, include positive pitch angle anisotropy, regions in velocity space where the nonmonotonic perpendicular energy distribution is greater than zero, and the energy dependence of the degree of particle injection. The energy dependence of the injection yields upper and lower cutoffs to the distribution within the plasmasphere, and only an upper cutoff outside. This approach is used to study the evolution of ion cyclotron waves in a convecting particle distribution.

Kaye, S. M.↗

On the large-scale dynamics of rapidly rotating convection zones

The fact that the values of the eight basic waves present in turbulent flows in the presence of rotation prohibit a tilt of eddy towards the axis of rotation is incorporated into a formalism for rapidly rotating convection zones. Equations for turbulent velocities are defined in a rotating coordinate system, assuming that gravity and grad delta T act in a radial direction. An expression is derived for the lifetime of a basic wave and then for the average velocity vector. A real convective eddy is formulated and the wave vectors are calculated. The velocity amplitude and the stress tensor amplitude are integrated over the eddy domain. Applied to the solar convective zone, it is found that the convective cells are aligned along the axis of rotation at the poles and at the equator, a model that conflicts with nonrotating mixng length theory predictions.

Durney, B. R.↗

A performability solution method for degradable nonrepairable systems

The present performability model-solving algorithm identifies performance with 'reward', representing the state behavior of a system S by a finite-state stochastic process and determining reward by means of reward rates that are associated with the states of the base model. A general method is obtained for determining the probability distribution function of the performance (reward) variable, and therefore the performability, of the corresponding system. This is done for bounded utilization periods, and the result is an integral expression which is either analytically or numerically solvable.

Furchtgott, D. G.↗

An analytic solution for the state trajectories of a feedback control system

In connection with the normal process of control system design, the determination of the state trajectories for the controlled system is frequently required. The procedure involved in the determination is straightforward. However, extensive computations may be needed, if either time-varying control gains are used, or if small integration step sizes are required by the presence of high-frequency system dynamics. The present investigation is concerned with an approach for overcoming the computational difficulties, taking into account a change of variables for the close-loop system dynamics equation. This procedure makes it possible to obtain a closed-form expression for the state trajectories.

Turner, J. D.↗

Shuttle imaging radar-C science plan

The Shuttle Imaging Radar-C (SIR-C) mission will yield new and advanced scientific studies of the Earth. SIR-C will be the first instrument to simultaneously acquire images at L-band and C-band with HH, VV, HV, or VH polarizations, as well as images of the phase difference between HH and VV polarizations. These data will be digitally encoded and recorded using onboard high-density digital tape recorders and will later be digitally processed into images using the JPL Advanced Digital SAR Processor. SIR-C geologic studies include cold-region geomorphology, fluvial geomorphology, rock weathering and erosional processes, tectonics and geologic boundaries, geobotany, and radar stereogrammetry. Hydrology investigations cover arid, humid, wetland, snow-covered, and high-latitude regions. Additionally, SIR-C will provide the data to identify and map vegetation types, interpret landscape patterns and processes, assess the biophysical properties of plant canopies, and determine the degree of radar penetration of plant canopies. In oceanography, SIR-C will provide the information necessary to: forecast ocean directional wave spectra; better understand internal wave-current interactions; study the relationship of ocean-bottom features to surface expressions and the correlation of wind signatures to radar backscatter; and detect current-system boundaries, oceanic fronts, and mesoscale eddies. And, as the first spaceborne SAR with multi-frequency, multipolarization imaging capabilities, whole new areas of glaciology will be opened for study when SIR-C is flown in a polar orbit.

Source record↗

On-line replacement of program modules using AdaPT

One purpose of our research is the investigation of the effectiveness and expressiveness of AdaPT(1), a set of language extensions to Ada 83, for distributed systems. As a part of that effort, we are now investigating the subject of replacing, e.g., upgrading, software modules while the software system remains in operation. The AdaPT language extension provide a good basis for this investigation for several reasons: (1) they include the concept of specific, self-contained program modules which can be manipulated; (2) support for program configuration is included in the language; and (3) although the discussion will be in terms of the AdaPT language, the AdaPT to Ada 83 conversion methodology being developed as another part of this project will provide a basis for the application of our findings to Ada 83 systems. The purpose of this investigation is to explore the basic mechanisms to the replacement process. Thus, while replacement in the presence of real-time deadlines, heterogeneous systems, and unreliable networks is certainly a topic of interest, we will first gain an understanding of the basic processes in the absence of such concerns. The extension of the replacement process to more complex situations can be made later. This report will establish an overview of the on-line upgrade problem, and present a taxonomy of the various aspects of the replacement process.

Waldrop, Raymond S.↗