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NASA NTRS1994

Green's formula and variational principles for cosmic-ray transport with application to rotating and shearing flows

Green's theorem and Green's formula for the diffusive cosmic-ray transport equation in relativistic flows are derived. Green's formula gives the solution of the transport equation in terms of the Green's function of the adjoint transport equation, and in terms of distributed sources throughout the region R of interest, plus terms involving the particle intensity and streaming on the boundary. The adjoint transport equation describes the time-reversed particle transport. An Euler-Lagrange variational principle is then obtained for both the mean scattering frame distribution function f, and its adjoint f(dagger). Variations of the variational functional with respect to f(dagger) yield the transport equation, whereas variations of f yield the adjoint transport equation. The variational principle, when combined with Noether's theorem, yields the conservation law associated with Green's theorem. An investigation of the transport equation for steady, azimuthal, rotating flows suggests the introduction of a new independent variable H to replace the comoving frame momentum variable p'. For the case of rigid rotating flows, H is conserved and is shown to be analogous to the Hamiltonian for a bead on a rigidly rotating wire. The variable H corresponds to a balance between the centrifugal force and the particle inertia in the rotating frame. The physical interpretation of H includes a discussion of nonrelativistic and special relativistic rotating flows as well as the cases of aziuthal, differentially rotating flows about Schwarzs-child and Kerr black holes. Green's formula is then applied to the problem of the acceleration of ultra-high-energy cosmic rays by galactic rotation. The model for galactic rotation assumes an angular velocity law Omega = Omega(sub 0)(omega(sub 0)/omega), where omega denotes radial distance from the axis of rotation. Green's functions for the galactic rotation problem are used to investigate the spectrum of accelerated particles arising from monoenergetic and truncated power-law sources. We conclude that it is possible to accelerate particles beyond the knee by galactic rotation, but not in sufficient number to adequately explain the observed spectrum.

Webb, G. M.↗

NASA NTRS1994

Formation, early evolution, and gravitational stability of protoplanetary disks

The formation, viscous evolution, and gravitational stability of protoplanetary disks are investigated. The formation process is parameterized by the angular velocity of the molecular cloud core omega, while the viscous evolution is parameterized by the viscosity parameter alpha in the disk; in this study we consider a range of (0.4-6) x 10(exp -14)/s for omega and from 10(exp -5) to 10(exp -1) for alpha. The axisymmetric gravitational stabilities of the disks are checked using Toomre's criterion. The resulting disk surface temperature distribution, (d log T(sub s)/d log R) approximately = -0.6 (R is the cylindrical radius), can be attributed to two heating sources: the viscous heating dominant in the inner disk region, and the accretion shock heating dominant in the outer disk region. This surface temperature distribution matches that observed in many disks around young stellar objects. During the infall stage, disks with alpha less than 10(exp -1.5) become gravitationally unstable independent of omega. The gravitational instabilities occur at radii ranging from 5 to 40 AU. The ratio of the disk mass to the central star mass ranges from 0.2 to 0.5 at the times of instability, about 4 x 10(exp -5) x (omega/10(exp -14)/s)(exp -0.67) yr. Most disks with low alpha and high omega become gravitationally unstable during their formation phase.

Nakamoto, Taishi↗

NASA NTRS1994

Local shear instabilities in weakly ionized, weakly magnetized disks

We extend the analysis of axisymmetric magnetic shear instabilities from ideal magnetohydrodynamic (MHD) flows to weakly ionized plasmas with coupling between ions and neutrals caused by collisions, ionization, and recombination. As part of the analysis, we derive the single-fluid MHD dispersion relation without invoking the Boussinesq approximation. This work expands the range of applications of these instabilities from fully ionized accretion disks to molecular disks in galaxies and, with somewhat more uncertainty, to protostellar disks. Instability generally requires the angular velocity to decrease outward, the magnetic field strengths to be subthermal, and the ions and neutrals to be sufficiently well coupled. If ionization and recombination processes can be neglected on an orbital timescale, adequate coupling is achieved when the collision frequency of a given neutral with the ions exceeds the local epicyclic freqency. When ionization equilibrium is maintained on an orbital timescale, a new feature is present in the disk dynamics: in contrast to a single-fluid system, subthermal azimuthal fields can affect the axisymmetric stability of weakly ionized two-fluid systems. We discuss the underlying causes for this behavior. Azimuthal fields tend to be stabilizing under these circumstances, and good coupling between the neutrals and ions requires the collision frequency to exceed the epicyclic frequency by a potentially large secant factor related to the magnetic field geometry. When the instability is present, subthermal azimuthal fields may also reduce the growth rate unless the collision frequency is high, but this is important only if the field strengths are very subthermal and/or the azimuthal field is the dominant field component. We briefly discuss our results in the context of the Galactic center circumnuclear disk, and suggest that the shear instability might be present there, and be responsible for the observed turbulent motions.

Blaes, Omer M.↗

NASA NTRS1994

Asymptotic domination of cold relativistic MHD winds by kinetic energy flux

We study the conditions which lead to the conversion of most Poynting flux into kinetic energy flux in cold, relativistic hydromagnetic winds. It is shown that plasma acceleration along a precisely radial flow is extremely inefficient due to the near cancellation of the toroidal magnetic pressure and tension forces. However, if the flux tubes in a flow diverge even slightly faster than radially, the fast magnetosonic point moves inward from infinity to a few times the light cylinder radius. Once the flow becomes supermagnetosonic, further divergence of the flux tubes beyond the fast point can accelerate the flow via the 'magnetic nozzle' effect, thereby further converting Poynting flux to kinetic energy flux. We show that the Grad-Shafranov equation admits a generic family of kinetic energy-dominated asymptotic wind solutions with finite total magnetic flux. The Poynting flux in these solutions vanishes logarithmically with distance. The way in which the flux surfaces are nested within the flow depends only on the ratio of angular velocity to poliodal 4-velocity as a function of magnetic flux. Radial variations in flow structure can be expressed in terms of a pressure boundary condition on the outermost flux surface, provided that no external toriodal field surrounds the flow. For a special case, we show explicitly how the flux surfaces merge gradually to their asymptotes. For flows confined by an external medium of pressure decreasing to zero at infinity we show that, depending on how fast the ambient pressure declines, the final flow state could be either a collimated jet or a wind that fills the entire space. We discuss the astrophysical implications of our results for jets from active galactic nuclei and for free pulsar winds such as that believed to power the Crab Nebula.

Begelman, Mitchell C.↗

NASA NTRS1994

Low-frequency modes and nonbarotropic effects in pseudo-Newtonian accretion disks

A recently developed formalism is used to reexamine the question of the existence of hydrodynamical modes that pulsate with very low frequencies in the inner regions of accretion disks. The formalism is valid in an exact sense for the adiabatic pulsations of rotating Newtonian fluids that are generally nonbarotropic (such as those with 'nonadiabatic temperature gradients,' for example), and hence its application in the present context represents an improvement over previous analyses that are more approximate. The formalism is applied to thin non-self-gravitating disks, with the gravitational potential of the central source modified in the usual way in order to simulate relativistic effects. In the barotropic limit, the analyses indicate that in many cases nearly Keplerian disks exhibit nonaxisymmetric modes of pulsation that are trapped in the inner disk regions, with pulsation periods much longer than the dynamical timescale. These results are similar to those of earlier calculations that assume disks pulsate without changing the temperature distribution. A method is developed for including lowest order nonbarotropic effects. Previous analyses have been incapable of accurately treating the nonbarotropic regime. The application of the present method to the low-frequency modes reveals that, due to unexpected cancellations among terms, the nonbarotropic correction to the pusation frequency omega is only of order tilde-omega(sub BV exp 2) omega, where tilde-omega(sub BV) is the appropriate dimensionless Brunt-Vaisala frequency. This correction is much smaller than the expected correction of order tilde-omega(sub BV) Omega, where Omega is the rotation angular velocity. The important conclusion drawn from this is that nonbarotropic corrections are generally small and hence that low-frequency modes persist into the nonbarotropic regime. For disk temperatures appropriate to X-ray emission, the adiabatic frequencies of trapped modes are of the same order as the frequencies associated with quasi-periodic oscillations (QPOs) of certain low-mass X-ray binaries and other X-ray sources. It is suggested that further consideration be given to the possiblity that modulation of emission processes by these modes can explain at least some of the QPO phenomena.

Ipser, James R.↗

NASA NTRS1993

A model for the motion of the Philippine Sea plate consistent with NUVEL-1 and geological data

We investigate angular velocity vectors of the Philippine Sea (PH) plate relative to the adjacent major plates, Eurasia (EU) and Pacific (PA), and the smaller Caroline (CR) plate. Earthquake slip vector data along the Philippine Sea plate are inverted, subject to the constraint that EU-PA motion equals that predicted by the global relative plate model NUVEL-1. The resulting solution fails to satisfy geological constraints along the Caroline-Pacific boundary: convergence along the Mussau Trench and divergence along the Sorol Trough. We then seek solutions satisfying both the CR-PA boundary conditions and the Philippine Sea slip vector data, by adjusting the PA-PH and EU-PH best fitting poles within their error ellipses. We also consider northern Honshu to be part of the North American plate and impose the constraint that the Philippine Sea plate subducts beneath northern Honshu along the Sagmi Trough in a NNW-NW direction. Of the solutions satisfying these conditions, we select the best EU-PH as 48.2 deg N, 157.0 deg E, 1.09 deg/my, corresponding to a pole far from Japan and south of Kamchatka, and PA-PH, 1.2 deg N, 134.2 deg E, 1.00 deg/my. Predicted NA-PH and EU-PH convergence rates in central Honshu are consistent with estimated seismic slip rates. Previous estimates of the EU-PH pole close to central Honshu are inconsistent with extension within the Bonin backarc implied by earthquake slip vectors and NNW-NW convergence of the Bonin forearc at the Sagami Trough.

Seno, Tetsuzo↗

NASA NTRS1992

Responses of heart rate and blood pressure to KC-135 hyper-gravity

Many investigators have clarified the effects of hyper gravitational-inertial forces (G) upon the cardiovascular system, using the centrifugal apparatus with short rotating radius. We investigated the cardiovascular responses to KC-135 hyper-G flight with negligibly small angular velocity. Six normal, healthy subjects 29 to 40 years old (5 males and 1 female) took part in this experiment. Hyper gravitational-inertial force was generated by the KC-135 hyper-G flight, flown in a spiral path with a very long radius of 1.5 miles. Hyper-G was sustained for 3 minutes with 1.8 +Gz in each session and was repeatedly exposed to very subject sitting on a chair 5 times. The preliminary results of blood pressure and R-R interval are discussed. An exposure of 1.8 +Gz stress resulted in a remarkable increase of systolic and diastolic blood pressure, while the pulse pressure did not change and remained equal to the control level regardless of an exposure of hyper-G. These results in blood pressure indicate an increase of resistance in the peripheral vessels, when an exposure of hyper-G was applied. The R-R interval was calculated from ECG. R-R interval in all subjects was changed but not systematically, and R-R interval became obviously shorter during the hyper-G period than during the 1 +Gz control period although R-R interval varied widely in some cases. The coefficient of variation of R-R interval was estimated to determine the autonomic nerve activity, but no significant change was detectable.

Satake, Hirotaka↗

NASA NTRS1995

Auxiliary Control Mechanisms For RUM Actuators

RUM actuator proposed device mounted on gimbaled, pivoted, or freely floating instrument and used to make instrument oscillate about one or more axes. Includes one or more (typically, two) unbalanced masses (e.g., lump masses on arms) for each axis about which oscillation desired. Unbalanced masses driven to rotate at constant angular velocity to produce oscillating centrifugal forces, which, in turn, exerts cyclic torques that make instrument oscillate about desired axis. Used in both terrestrial and spacecraft applications: for example, to oscillate instruments as diverse as x-ray telescopes, magnetometers, accelerometers, and agricultural spraying nozzles in variety of scan patterns that include linear, circular, and raster. Weights, power demands, and costs reduced.

Polites, Michael E.↗

NASA NTRS1995

Touchdown dynamics

Aircraft tire wear results from operating conditions that are quite different from those encountered in land vehicles. One of the most important of these is touchdown, where the tire suddenly spins up from zero to a large angular velocity. This phenomenon is studied from both the analytical and experimental points of view. The analysis is basic, using elementary properties of the tire and wheel. It results in a new dimensionless description of the process. The experimental study consists primarily of small scale laboratory data, although limited full scale tire data is also presented. The data show increasing weight loss during touchdown as the dimensionless severity increases.

Clark, Samuel K.↗

NASA NTRS1995

Helioseismology: A probe of the solar interior, atmosphere, and activity cycle

Helioseismology began in earnest in the mid 1970's. In the two decades which have elapsed since that time this branch of solar physics has become a mature field of research. Helioseismology has demonstrated that the solar convection zone is about twice as deep as was generally thought to be the case before 1977. Helioseismology has also provided measurements of the solar internal angular velocity over much of the sun's interior. Helioseismology has also ruled out models which would solve the solar neutrino problem by a lowering of the temperature of the core. Recently, some of the seismic properties of the sun have been demonstrated to vary with changing levels of solar activity. Also, helioseismology has recently provided evidence for helical flow patterns in the shallow, sub-photosphere layers. The techniques of helioseismology are also expanding to include seismic probes of solar active regions. Some work is also being conducted into the possible contributions of the solar acoustic models to the heating of the solar atmosphere. In this talk I will highlight a few of the above results and concentrate on current areas of research in the field.

Rhodes, E. J., Jr.↗

NASA NTRS1995

Performance and operational considerations in the design of vehicle antennas for mobile satellite communications

This paper examines the vehicle antenna requirements for mobile satellite systems. The antenna parameters are discussed in the light of the requirements and the limitations in performance imposed by the physical constraints of antenna and by vehicle geometries. Measurements of diffraction and antenna noise temperature in an operational environment are examined, as well as their effects on system margins. Mechanical versus electronic designs are compared with regards to performance, cost, reliability, and design complexity. Comparisons between open-loop and close-loop tracking systems are made and the effects of bandwidth, sidelobe levels, operational constraints, vehicle angular velocity, and acceleration are discussed. Some consideration is given to the use of hybrid systems employing both open and closed-loop tracking. Changes to antenna/terminal specifications are recommended which will provide greater design flexibility and increase the likelihood of meeting the performance and operational requirements.

Milne, R.↗

NASA NTRS1996

Satellite Angular Rate Estimation From Vector Measurements

This paper presents an algorithm for estimating the angular rate vector of a satellite which is based on the time derivatives of vector measurements expressed in a reference and body coordinate. The computed derivatives are fed into a spacial Kalman filter which yields an estimate of the spacecraft angular velocity. The filter, named Extended Interlaced Kalman Filter (EIKF), is an extension of the Kalman filter which, although being linear, estimates the state of a nonlinear dynamic system. It consists of two or three parallel Kalman filters whose individual estimates are fed to one another and are considered as known inputs by the other parallel filter(s). The nonlinear dynamics stem from the nonlinear differential equation that describes the rotation of a three dimensional body. Initial results, using simulated data, and real Rossi X ray Timing Explorer (RXTE) data indicate that the algorithm is efficient and robust.

Azor, Ruth↗

NASA NTRS1996

Geostationary Operational Environmental Satellite (GOES) Gyro Temperature Model

The geostationary Operational Environmental Satellite (GOES) 1/M series of spacecraft are geostationary weather satellites that use the latest in weather imaging technology. The inertial reference unit package onboard consists of three gyroscopes measuring angular velocity along each of the spacecraft's body axes. This digital integrating rate assembly (DIRA) is calibrated and used to maintain spacecraft attitude during orbital delta-V maneuvers. During the early orbit support of GOES-8 (April 1994), the gyro drift rate biases exhibited a large dependency on gyro temperature. This complicated the calibration and introduced errors into the attitude during delta-V maneuvers. Following GOES-8, a model of the DIRA temperature and drift rate bias variation was developed for GOES-9 (May 1995). This model was used to project a value of the DIRA bias to use during the orbital delta-V maneuvers based on the bias change observed as the DIRA warmed up during the calibration. The model also optimizes the yaw reorientation necessary to achieve the correct delta-V pointing attitude. As a result, a higher accuracy was achieved on GOES-9 leading to more efficient delta-V maneuvers and a propellant savings. This paper summarizes the: Data observed on GOES-8 and the complications it caused in calibration; DIRA temperature/drift rate model; Application and results of the model on GOES-9 support.

Rowe, J. N.↗

NASA NTRS1997

Efficient Sequential Attitude Estimation from Vector Observations

This paper presents a computationally efficient, sequential method for attitude matrix estimation using gyro and vector measurements. The method is based on a recently introduced, minimal-parameter third-order method for solving the orthogonal matrix differential equation in R(sup n). In the three-dimensional case, these third-order attitude parameters can be interpreted as temporal-integrals of the body-frame angular velocity components. A nonlinear algorithm is developed, which uses this minimal set of three parameters to estimate the nine-parameter direction-cosine matrix. Having an extremely simple kinematic equation, these parameters render the resulting estimator highly computationally efficient. An orthogonalization procedure, incorporated into the measurement processing stage, enhances the accuracy and stability of the resulting algorithm, yet retains reasonable simplicity. The performance of the estimator is demonstrated via a Monte Carlo simulation study.

Oshman, Yaakov↗

NASA NTRS1997

Human Powered Centrifuge

A human powered centrifuge has independently established turntable angular velocity and human power input. A control system allows excess input power to be stored as electric energy in a battery or dissipated as heat through a resistors. In a mechanical embodiment, the excess power is dissipated in a friction brake.

Mulenburg, Gerald M.↗

NASA NTRS1992

Effects of Centrifuge Diameter and Operation on Rodent Adaptation to Chronic Centrifugation

This study examined the responses of rats to centrifugation in a constant acceleration field (1.5 G). Centrifuge diameter (1.8m, 2.5m or 6.0m) and schedule of operation (Daily or weekly stop) varied between groups. Body mass, food consumption, water consumption and neurovestibular function were measured weekly. Body temperature and activity were continuously monitored using telemetry. A subset of subjects were videotaped (50 minutes per day) to allow for movement analysis. Exposure to a hyperdynamic field of this magnitude did cause the expected depression in the physiological variables monitored. Recovery was accomplished within a relatively rapid time frame; all variables returned to precentrifugation levels. In general, the magnitudes of the changes and the rate of recovery were similar at different centrifuge diameters and stopping frequency. There were cases, however, in which the magnitude of the response and/or the rate of recovery to a new steady-state were altered as a result of centrifuge diameter. In summary, these results indicate that stopping frequency has little, if any, effect on adaptation to chronic centrifugation. However, the angular velocity (omega), and therefore centrifuge diameter is an important consideration in the adaptation of an organism to chronic centrifugation.

Fuller, Charles A.↗

NASA NTRS1997

Effects of Centrifuge Diameter and Operation on Rodent Adaptation to Chronic Centrifugation

Fuller, Charles A.↗

NASA NTRS1998

Turbulent Compressible Convection with Rotation: Mean Flows and Differential Rotation - 2

The effects of rotation on turbulent, compressible convection within stellar envelopes are studied through three-dimensional numerical simulations conducted within a local f-plane model. This work seeks to understand the types of differential rotation that can be established in convective envelopes of stars like the Sun, for which recent helioseismic observations suggest an angular velocity profile with depth and latitude at variance with many theoretical predictions. This paper analyzes the mechanisms that are responsible for the mean (horizontally averaged) zonal and meridional flows that are produced by convection influenced by Coriolis forces. The compressible convection is considered for a range of Rayleigh, Taylor, and Prandtl (and thus Rossby) numbers encompassing both laminar and turbulent flow conditions under weak and strong rotational constraints. When the nonlinearities are moderate, the effects of rotation on the resulting laminar cellular convection leads to distinctive tilts of the cell boundaries away from the vertical. These yield correlations between vertical and horizontal motions that generate Reynolds stresses that can drive mean flows, interpretable as differential rotation and meridional circulations. Under more vigorous forcing, the resulting turbulent convection involves complicated and contorted fluid particle trajectories, with few clear correlations between vertical and horizontal motions, punctuated by an evolving and intricate downflow network that can extend over much of the depth of the layer. Within such networks are some coherent structures of vortical downflow that tend to align with the rotation axis. These yield a novel turbulent alignment mechanism, distinct from the laminar tilting of cellular boundaries, that can provide the principal correlated motions and thus Reynolds stresses and subsequently mean flows. The emergence of such coherent structures that can persist amidst more random motions is a characteristic of turbulence with symmetries broken by rotation and stratification. Such structure is here found to play a crucial role in defining the mean zonal and meridional flows that coexist with the convection. Though they are subject to strong inertial oscillations, the strength and type of the mean flows are determined by a combination of the laminar tilting and the turbulent alignment mechanisms. Varying the parameters produces a wide range of mean motions. Among these, some turbulent solutions exhibit a mean zonal velocity profile that is nearly constant with depth, much as deduced by helioseismology at midlatitudes within the Sun. The solutions exhibit a definite handedness, with the direction of the persistent mean flows often prescribing a spiral with depth near the boundaries, also in accord with helioseismic deductions. The mean helicity has a profile that is positive in the upper portion of the domain and negative in the lower portion, a property bearing on magnetic dynamo processes that may be realized within such rotating layers of turbulent convection.

Brummell, Nicholas H.↗