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NASA NTRS1995

Bounce-averaged Hamiltonian for charged particles in an axisymmetric but nondipolar model magnetosphere

Schulz, Michael↗

NASA NTRS1995

Bounce-Averaged Hamiltonian for Charged Particles in an Axisymmetric but Nondipolar Model Magnetosphere

In order to facilitate bounce-averaged guiding center simulations of geomagnetically trapped particles, we express the kinetic energy of a particle with magnetic coordinates (L,phi) as an analytic function of the first two adiabatic invariants (M, J) and the L value of the field line. The magnetic field model is axisymmetric, consisting of a dipolar B field plus a uniform southward magnetic field parallel to the dipole moment mu(sub E). This model magnetosphere is surrounded by a circular equatorial neutral line whose radius b is an adjustable parameter. The L value of a field line is (by definition) inversely proportional to the flux enclosed by the corresponding magnetic shell of equatorial radius r(sub 0), and the L value at the neutral line (r(sub 0) = b) is denoted L*. The azimuthal coordinate phi measures magnetic local time. The best functional representation found for the normalized difference (L(exp 3)a(exp 3)/mu(sub E))(B(sub m) - B(sub 0)) between mirror-point field B(sub m) and equatorial field B(sub 0) along any field line is a 5-term expansion in powers (2/3 through 6/3) of the quantity X equivalent to (La/mu(sub E))(exp 1/2)K, where K equivalent to (J(exp 2)/8m(sub 0)M)(exp 1/2) is an adiabatically conserved quantity independent of particle energy, m(sub 0) is the rest mass of the particle, and a is the radius of the Earth. This functional form is motivated by results for limiting cases in which particles mirror very near and very far from the magnetic equator. Expansion coefficients corresponding to various powers of X are obtained from least squares fits to numerically computed results for X as a function of L and B(sub m). These are accurately expressible as fourth-order polynomials in (r(sub 0)/b)(exp 3), hence indirectly as functions of L/L* = 3La/2b. This representation, which leads (except for a manageably small region of parameter space) to better than 1% accuracy in the specification of B(sub m) as a function of K and L, allows bounce-averaged guiding center simulations to be performed without actually tracing the bounce motions of individual particles. Bounce-averaged drifts L' (meridional) and phi' (azimuthal) are proportional to derivatives of the Hamiltonian H (sum of kinetic and potential energies) with respect to phi and L, respectively. Our formulation thus provides a computationally efficient method for tracing the bounce-averaged adiabatic motion (conserving all three invariants) and nonadiabatic transport (violating the third invariant while conserving the first two invariants) of geomagnetically trapped particles in the model magnetosphere.

Schulz, Michael↗

NASA NTRS1992

Symmetry as Bias: Rediscovering Special Relativity

This paper describes a rational reconstruction of Einstein's discovery of special relativity, validated through an implementation: the Erlanger program. Einstein's discovery of special relativity revolutionized both the content of physics and the research strategy used by theoretical physicists. This research strategy entails a mutual bootstrapping process between a hypothesis space for biases, defined through different postulated symmetries of the universe, and a hypothesis space for physical theories. The invariance principle mutually constrains these two spaces. The invariance principle enables detecting when an evolving physical theory becomes inconsistent with its bias, and also when the biases for theories describing different phenomena are inconsistent. Structural properties of the invariance principle facilitate generating a new bias when an inconsistency is detected. After a new bias is generated. this principle facilitates reformulating the old, inconsistent theory by treating the latter as a limiting approximation. The structural properties of the invariance principle can be suitably generalized to other types of biases to enable primal-dual learning.

Lowry, Michael R.↗

NASA NTRS1994

Higher-Order Neural Networks Applied to 2D and 3D Object Recognition

A Higher-Order Neural Network (HONN) can be designed to be invariant to geometric transformations such as scale, translation, and in-plane rotation. Invariances are built directly into the architecture of a HONN and do not need to be learned. Thus, for 2D object recognition, the network needs to be trained on just one view of each object class, not numerous scaled, translated, and rotated views. Because the 2D object recognition task is a component of the 3D object recognition task, built-in 2D invariance also decreases the size of the training set required for 3D object recognition. We present results for 2D object recognition both in simulation and within a robotic vision experiment and for 3D object recognition in simulation. We also compare our method to other approaches and show that HONNs have distinct advantages for position, scale, and rotation-invariant object recognition. The major drawback of HONNs is that the size of the input field is limited due to the memory required for the large number of interconnections in a fully connected network. We present partial connectivity strategies and a coarse-coding technique for overcoming this limitation and increasing the input field to that required by practical object recognition problems.

Spirkovska, Lilly↗

NASA NTRS1995

A Game Theoretic Fault Detection Filter

The fault detection process is modelled as a disturbance attenuation problem. The solution to this problem is found via differential game theory, leading to an H(sub infinity) filter which bounds the transmission of all exogenous signals save the fault to be detected. For a general class of linear systems which includes some time-varying systems, it is shown that this transmission bound can be taken to zero by simultaneously bringing the sensor noise weighting to zero. Thus, in the limit, a complete transmission block can he achieved, making the game filter into a fault detection filter. When we specialize this result to time-invariant system, it is found that the detection filter attained in the limit is identical to the well known Beard-Jones Fault Detection Filter. That is, all fault inputs other than the one to be detected (the "nuisance faults") are restricted to an invariant subspace which is unobservable to a projection on the output. For time-invariant systems, it is also shown that in the limit, the order of the state-space and the game filter can be reduced by factoring out the invariant subspace. The result is a lower dimensional filter which can observe only the fault to be detected. A reduced-order filter can also he generated for time-varying systems, though the computational overhead may be intensive. An example given at the end of the paper demonstrates the effectiveness of the filter as a tool for fault detection and identification.

Chung, Walter H.↗

NASA NTRS1996

On Betz' Method for Rollup of Vortex Sheets

A method introduced by Betz in 1932 relates the vortex sheet shed by one side of a lifting wing to the rolled-up vortex far downstream. The Betz rollup theory came into active use during the 1970's when the hazard posed by vortex wakes of subsonic transport aircraft became of concern at airports. Even though the method involves several simplifying assumptions, it provides insight into the rollup process and has proven to be a useful and reliable tool for the analysis and diagnosis of lift-generated wakes. As part of an ongoing effort to develop improved guidelines for the rollup process of complex vortex wakes, the research described is directed at the study of the two vortex invariants not used in the Betz formulation, and to find out if they can be used to determine the sequence of rollup or the center of vortices where rollup begins. It is found that the two unused vortex invariants are both conserved during rollup, but that they do not yield any information or guidance on rollup sequence or on the location of vortex centers. It is also found that the invariant for energy can be used to determine the rolled-up structure of vortices but the structure differs negligibly from that predicted by use of the invariant for the second moment of circulation.

Rossow, Vernon J.↗

NASA NTRS2011

Forty-Year Calibrated Record of Earth-Surface Reflected Radiance from Landsat: A Review

Sensors on Landsat satellites have been collecting images of the Earth's surface for nearly 40 years. These images have been invaluable for characterizing and detecting changes in the land cover and land use of the world. Although initially conceived as primarily picture generating sensors, even the early sensors were radiometrically calibrated and spectrally characterized prior to launch and incorporated some capabilities to monitor their radiometric calibration once on orbit. Recently, as the focus of studies has shifted to monitoring Earth surface parameters over significant periods of time, serious attention has been focused toward bringing the data from all these sensors onto a common radiometric scale over this 40-year period. This effort started with the most recent systems and then was extended back in time. Landsat-7 ETM+, the best-characterized sensor of the series prior to launch and once on orbit, and the most stable system to date, was chosen to serve as the reference. The Landsat-7 project was the first of the series to build an image assessment system into its ground system, allowing systematic characterization of its sensors and data. Second, the Landsat-5 TM (still operating at the time of the Landsat-7 launch and continues to operate) calibration history was reconstructed based on its internal calibrator, vicarious calibrations, pseudo-invariant sites and a tie to Landsat-7 ETM+ at the time of the commissioning of Landsat-7. This process was performed in two iterations: the earlier one relied primarily on the TM internal calibrator. When this was found to have some deficiencies, a revised calibration was based more on pseudo-invariant sites, though the internal calibrator was still used to establish the short-term variations in response due to icing build up on the cold focal plane. As time progressed, a capability to monitor the Landsat-5 TM was added to the image assessment system. The Landsat-4 TM, which operated from 1982-1992, was the third system to which the radiometric scale was extended. The limited and broken use of the Landsat-4 TM made this analysis more difficult. Eight-day separated image pairs from Landsat-5 combined with analysis of pseudo invariant sites established this history. The fourth and most challenging effort was making the Landsat-1 to -5 MSS sensors' data internally radiometrically consistent. This effort was particularly complicated by the age of the MSS data, varying formats and processing levels in the archive, limited datasets, and limited documentation available. Ultimately, pseudo-invariant sites were identified in North America and used for this effort. Note that most of the Landsat-MSS archived data had already been calibrated using the MSS internal calibrators, so this processing was imbedded in the result. The final effort was developing an absolute scale for Landsat MSS similar to what was already established for the "TM" sensors. This was accomplished by using simultaneous data from Landsat-5 MSS and Landsat-5 TM, accounting for spectral differences between the sensors using EO-1 Hyperion data. The recalibrated history of the Landsat data and implications to users are discussed. The key result from this work is a consistently calibrated Landsat data archive that spans nearly 40 years with total uncertainties on the order of 10% or less for most sensors and bands.

Markham, Brian↗

NASA NTRS2016

Characterizing Cometary Electrons with Kappa Distributions

The Rosetta spacecraft has escorted comet 67P/Churyumov-Gerasimenko since 6 August 2014 and has offered an unprecedented opportunity to study plasma physics in the coma. We have used this opportunity to make the first characterization of cometary electrons with kappa distributions. Two three-dimensional kappa functions were fit to the observations, which we interpret as two populations of dense and warm (density 10 cubic centimeters, temperature 2 times 10 (sup 5) degrees Kelvin, invariant kappa index 10 to 1000), and rarefied and hot (density equals 0.005 cubic centimeters, temperature 5 times 10 (sup 5) degrees Kelvin, invariant kappa index equals 1 to 10) electrons. We fit the observations on 30 October 2014 when Rosetta was 20 kilometers from 67P, and 3 Astronomical Units from the Sun. We repeated the analysis on 15 August 2015 when Rosetta was 300 kilometers from the comet and 1.3 Astronomical Units from the Sun. Comparing the measurements on both days gives the first comparison of the cometary electron environment between a nearly inactive comet far from the Sun and an active comet near perihelion. We find that the warm population density increased by a factor of 3, while the temperature cooled by a factor of 2, and the invariant kappa index was unaffected. We find that the hot population density increased by a factor of 10, while the temperature and invariant kappa index were unchanged. We conclude that the hot population is likely the solar wind halo electrons in the coma. The warm population is likely of cometary origin, but its mechanism for production is not known.

Broiles, T. W.↗

NASA NTRSDate not supplied

TPSAS-NF1676L-19788-DND

The calibration of the historical AVHRR visible channels has always been hindered by the degrading NOAA satellite orbits. The complete AVHRR record spans over three decades making it useful for cloud, aerosol, and land use climate studies. Studies that monitor long-term changes in these properties require climate quality calibration. The AVHRR sensors do not have any onboard visible calibration, unlike the IR channels. Many AVHRR post-launch calibration methods have been published. Some of these are based on the pseudo invariant targets such as desert and polar ice and others employ direct calibration transfer from a well-calibrated sensor such as MODIS. Most historical studies only employed only one method and reconciling calibration differences from multiple studies was difficult. This study employs multiple calibration approaches, which are then merged according to their individual uncertainty. Since the visible spectral response functions are similar across AVHRR sensor and that the morning and afternoon orbits usually degrade in the same manner, an afternoon and morning orbiter during the MODIS era is chosen as the reference AVHRR sensor. The reference AVHRR sensor is inter-calibrated with the Aqua-MODIS Collection 6 standard using simultaneous nadir overpass (SNO) radiance pairs. Three pseudo invariant target approaches are utilized, deserts, polar ice and deep convective clouds. These sites are characterized using reference AVHRR reflectances as a function of solar zenith angle. The multiple calibration approach is then validated with non-reference AVHRR sensor during the MODIS era, using AVHRR and MODIS SNO measurements. For historical AVHRR satellite having consistent calibration across invariant targets then validates the approach. This calibration effort is in sponsored by the NOAA CDR program to provide climate quality visible calibration coefficients to the remote sensing community. Each of the calibration approaches are unique and when utilized in tandem can accurately calibrate the AVHRR record. AVHRR calibration methods cannot rely on repeatable annual orbits for calibration model development. Inconsistent results prompt code and invariant target examinations that cannot be determined using only single method approaches. Results from this study will be presented at the meeting.

David Doelling↗

NASA NTRS1971

Equicontrollability and the model following problem

Equicontrollability and its application to the linear time-invariant model-following problem are discussed. The problem is presented in the form of two systems, the plant and the model. The requirement is to find a controller to apply to the plant so that the resultant compensated plant behaves, in an input-output sense, the same as the model. All systems are assumed to be linear and time-invariant. The basic approach is to find suitable equicontrollable realizations of the plant and model and to utilize feedback so as to produce a controller of minimal state dimension. The concept of equicontrollability is a generalization of control canonical (phase variable) form applied to multivariable systems. It allows one to visualize clearly the effects of feedback and to pinpoint the parameters of a multivariable system which are invariant under feedback. The basic contributions are the development of equicontrollable form; solution of the model-following problem in an entirely algorithmic way, suitable for computer programming; and resolution of questions on system decoupling.

Curran, R. T.↗

NASA NTRS1976

Magnetospheric whistler ducts observed by ISIS satellites

The latitudinal width of the magnetospheric whistler duct has been estimated by the first and final invariant latitudes of whistler echoes and the conservation of the magnetic flux for the centered dipole field, using 105 whistler echoes in ISIS VLF data received at Kashima, Japan for 1972-1973. The latitudinal distribution of whistler duct occurrence shows a maximum at invariant latitudes of 40-45 degrees near the maximum occurrence latitude of ground whistlers. The radial width of magnetospheric whistler duct in the geomagnetically equatorial plane increases with invariant latitude of the geomagnetic flux tube in which whistlers propagate.

Ondoh, T.↗

NASA NTRS1981

Estimation and correction of advection effects with single and multiple, conventional and Doppler radars

The laws of fluid motion are invariant under a Gallilean transformation. For a perfect observing system, the data analysis should, therefore, also be invariant under a Gallilean transformation. This invariance is often not preserved in practical observing systems. In this connection, it is often advisable to perform mesoscale analysis in a frame moving with respect to the earth's surface. In the present investigation the velocity of such a frame is referred to as an advection velocity. The investigation is concerned with remaining problems regarding the Gallilean transformation. The establishment of a frame of reference for the achievement of maximum coherence is considered, taking into account the case of given nonsimultaneous observations of scalars or Cartesian vectors. It is found that advection speed can be estimated objectively if a scalar or Cartesian vector can be observed directly and if, in addition, the time and position of each observation is approximately known.

Gal-Chen, T.↗

NASA NTRS1986

A geometric approach to failure detection and identification in linear systems

Using concepts of (C,A)-invariant and unobservability (complementary observability) subspaces, a geometric formulation of the failure detection and identification filter problem is stated. Using these geometric concepts, it is shown that it is possible to design a causal linear time-invariant processor that can be used to detect and uniquely identify a component failure in a linear time-invariant system, assuming: (1) The components can fail simultaneously, and (2) The components can fail only one at a time. In addition, a geometric formulation of Beard's failure detection filter problem is stated. This new formulation completely clarifies of output separability and mutual detectability introduced by Beard and also exploits the dual relationship between a restricted version of the failure detection and identification problem and the control decoupling problem. Moreover, the frequency domain interpretation of the results is used to relate the concepts of failure sensitive observers with the generalized parity relations introduced by Chow. This interpretation unifies the various failure detection and identification concepts and design procedures.

Massoumnia, M. A.↗

NASA NTRS1986

Methods for the solution of radiative transfer equation

To obtain an exact solution of the radiative-transfer equation in media where both absorption and scattering are significant, the usual approach is to use a numerical method. Three methods are known in the literature: invariant imbedding, eigenvalue-eigenfunction, and matrix doubling. This paper examines the practical application of these methods to the problem of emission from an inhomogeneous (Rayleigh) layer, the effects of layer parameters on the stability. It is found that invariant imbedding is most suitable for computing emission from an inhomogeneous layer with a temperature profile but tends to be unstable as the optical thickness of the layer increases beyond 0.5. On the other hand, the matrix-doubling method is stable for arbitrary optical thickness but is not suitable for handling multilayers. The eigenvalue-eigenfunction method is more stable than the invariant imbedding as optical thickness increases up to 2.0. It also permits temperature profile in the layer, but the computation is much more complicated. It is less stable than the matrix-doubling method when optical thickness is larger than 2.0. In general, the choice of a method is dependent on the nature of the problem.

Chen, M. F.↗

NASA NTRS1987

Observing rotation and deformation of sea ice with synthetic aperture radar

The ESA's ERS-1 satellite will carry SARs over the polar regions; an important component in the use of these data is an automated scheme for the extraction of sea ice velocity fields from a sequence of SAR images of the same geographical region. The image pyramid area-correlation hierarchical method is noted to be vulnerable to uncertainties for sea ice rotations greater than 10-15 deg between SAR observations. Rotation-invariant methods can successfully track isolated floes in the marginal ice zone. Hu's (1962) invariant moments are also worth considering as a possible basis for rotation-invariant tracking methods. Feature tracking is inherently robust for tracking rotating sea ice, but is limited when features are floe-lead boundaries. A variety of techniques appears neccessary.

Vesecky, J. F.↗

NASA NTRS1987

Covariance and the hierarchy of frame bundles

This is an essay on the general concept of covariance, and its connection with the structure of the nested set of higher frame bundles over a differentiable manifold. Examples of covariant geometric objects include not only linear tensor fields, densities and forms, but affinity fields, sectors and sector forms, higher order frame fields, etc., often having nonlinear transformation rules and Lie derivatives. The intrinsic, or invariant, sets of forms that arise on frame bundles satisfy the graded Cartan-Maurer structure equations of an infinite Lie algebra. Reduction of these gives invariant structure equations for Lie pseudogroups, and for G-structures of various orders. Some new results are introduced for prolongation of structure equations, and for treatment of Riemannian geometry with higher-order moving frames. The use of invariant form equations for nonlinear field physics is implicitly advocated.

Estabrook, Frank B.↗

NASA NTRS1989

Making A Circular-Harmonic Filter

Optical image-correlating system made rotationally invariant. Experiment shows circular-harmonic filter generated optically. Hologram made by phase-shifted-double-exposure procedure. Filter used in optical image-recognition system based on correlation between target (image to be recognized) and matched spatial filter. In addition to usual invariance under translation of target, circular harmonic filter invariant under rotation of target; peak intensity of illumination at origin of correlation plane does not vary when target rotated about optical axis.

Cheng, Yeou Yen↗

NASA NTRS1986

A multiaxial theory of viscoplasticity for isotropic materials

Many viscoplastic constitutive models for high temperature structural alloys are based exclusively on uniaxial test data. Generalization to multiaxial states of stress is made by assuming the stress dependence to be on the second principal invariant (J sub 2) of the deviatoric stress, frequently called the effective stress. If such a J sub 2 theory, based on uniaxial testing, is called upon to predict behavior under conditions other than uniaxial, e.g., pure shear, and it does so poorly, nothing is left to adjust in the theory. For a fully isotropic material whose inelastic deformation behavior is relatively independent of hydrostatic stress, the most general stress dependence is on the two (non-zero) principal invariants of the deviatoric stress, J sub 2 and J sub 3. These invariants constitute what is known as an integrity basis for the material. A time dependent constitutive theory with stress dependence on J sub 2 and J sub 3 is presented, that reduces to a known J sub 2 theory as a special case.

Robinson, D. N.↗