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At least 433 records · Page 24

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NASA NTRS1974

Cosmic ray anisotropies observed late in the decay phase of solar flare events

Data was obtained from instrumentation on Explorers 34 and 41 on cosmic-ray anisotropy and magnetic field vectors during five solar flare events. The analysis was conducted in the energy range from 0.7 to 7.6 MeV, of the late decay phase, to evaluate the dependence of net cosmic-ray anisotropy vector amplitude and direction on the magnetic field azimuth. Results showed that in the late decay phase the direction of the net cosmic-ray anisotropy vector was invariant in relation to the direction of the magnetic field, particle energy, and species. Within the statistical error of the available data the invariant direction was perpendicular to the mean magnetic field direction.

Allum, F. R.↗

NASA NTRS1975

The geometric approach to sets of ordinary differential equations and Hamiltonian dynamics

The calculus of differential forms is used to discuss the local integration theory of a general set of autonomous first order ordinary differential equations. Geometrically, such a set is a vector field V in the space of dependent variables. Integration consists of seeking associated geometric structures invariant along V: scalar fields, forms, vectors, and integrals over subspaces. It is shown that to any field V can be associated a Hamiltonian structure of forms if, when dealing with an odd number of dependent variables, an arbitrary equation of constraint is also added. Families of integral invariants are an immediate consequence. Poisson brackets are isomorphic to Lie products of associated CT-generating vector fields. Hamilton's variational principle follows from the fact that the maximal regular integral manifolds of a closed set of forms must include the characteristics of the set.

Estabrook, F. B.↗

NASA NTRS1975

Stored energy function and compressibility of compressible rubberlike materials under large strain

By using new invariants in the theory of finite elasticity an expression is obtained for the stored energy function of slightly compressible materials in which the effects of the distortional change (change of shape) and of the volume change are clearly separated. The volume-related terms are expressed as a function of the third invariant, the classical compressibility, and an induced anisotropy of the effective compressibility which is due to the large deformations. After evaluating the terms, using data on pressure, volume, uniaxial strain, and fractional volume change vs strain data on natural rubber from the literature, it is shown that the volume change contribution to the total stress observed in a simple tensile experiment can be clearly separated from the distortional contribution, even at finite strains.

Peng, S. T. J.↗

NASA NTRS1976

On the optimal minimum order observer-based compensator and the limited state variable feedback controller

Four design problems are considered: two on the optimal minimum order observer-based compensator design and two on the optimal limited state variable feedback controller. The problem of designing an optimal discrete time linear time-invariant observer-based compensator for the regulation of an n dimensional linear discrete time time-invariant plant with m independent outputs is considered. This is a stochastic design problem to the extent that the initial plant state is assumed to be a random vector with known first and second order statistics. The compensator parameters are obtained by minimizing the expectation, with respect to the initial conditions, of the standard cost, quadratic in the state and control vectors with the inclusion of cross terms.

Llorens-Ortiz, B.↗

NASA NTRS1977

'Disturbance zeros' in multivariable systems

Zeros of the transfer matrix relating the outputs to the disturbances ('disturbance zeros') of a linear time-invariant system are defined. It is shown that these zeros are invariant under output feedback to control inputs but not under state feedback to control inputs, and the effect of state feedback on disturbance zeros is studied. The results are used to develop an algorithm for assigning disturbance zeros and system poles by means of state feedback. As an application of the algorithm, it is shown that the disturbance zeros can be positioned such that the effect of a class of disturbances at the outputs is eliminated in the steady state. An example is given to illustrate the main results of the paper.

Patel, R. V.↗

NASA NTRS1978

ORACLS: A system for linear-quadratic-Gaussian control law design

A modern control theory design package (ORACLS) for constructing controllers and optimal filters for systems modeled by linear time-invariant differential or difference equations is described. Numerical linear-algebra procedures are used to implement the linear-quadratic-Gaussian (LQG) methodology of modern control theory. Algorithms are included for computing eigensystems of real matrices, the relative stability of a matrix, factored forms for nonnegative definite matrices, the solutions and least squares approximations to the solutions of certain linear matrix algebraic equations, the controllability properties of a linear time-invariant system, and the steady state covariance matrix of an open-loop stable system forced by white noise. Subroutines are provided for solving both the continuous and discrete optimal linear regulator problems with noise free measurements and the sampled-data optimal linear regulator problem. For measurement noise, duality theory and the optimal regulator algorithms are used to solve the continuous and discrete Kalman-Bucy filter problems. Subroutines are also included which give control laws causing the output of a system to track the output of a prescribed model.

Armstrong, E. S.↗

NASA NTRS1977

Low-energy particle observations in the quiet dayside cusp from AE-C and AE-D

AE-C and AE-D observations at low altitudes in the high-latitude region near magnetic local noon have revealed properties of low energy electrons and protons that are similar to those determined from earlier particle and field-aligned current observations. The principal feature determined in the present study is a well-defined boundary (less than a few km or 0.01 deg in invariant latitude) which appears only in the postnoon high-latitude region. Energy spectra of low energy electrons and protons show a distinctive softening at latitudes above this boundary. The region of soft particle precipitation above this boundary (located near 78 deg invariant latitude during moderately disturbed to quiet geomagnetic conditions) is identified as the dayside cusp.

Potemra, T. A.↗

NASA NTRS1978

Three-dimensional magnetohydrodynamic turbulence in cylindrical geometry

A theory is developed in which a perfectly conducting cylindrical wall is used to describe incompressible MHD turbulence. Dynamic equations of incompressible MHD and its associated fields are expanded in a system of vector eigenfunctions of the curl. The total energy, magnetic helicity, and cross helicity have simple quadratic expressions in the expansion coefficients. The invariants are temporally constant for a truncation at a large, but finite, number of coefficients. The invariants are used to construct canonical distributions. It is noted that for all initial conditions, including quiescent ones, the mean-square velocity fields have finite values. The stability problem is transformed into a search for values of the integral variants which minimize the mean-square velocity fields. This leads to an extremal helicity principle.

Montgomery, D.↗

NASA NTRS1979

Mikhailov Stability Criterion for Time-delayed Systems

The valid and invalid application of the Mikhailov criterion to linear, time-invariant systems with time delays is discussed. The Mikhailov criterion is a graphical procedure which was developed to examine the stability of linear, time-invariant systems with no time delays. Two equivalent formulations of the criterion are discussed. Results indicate that the first formulation remains valid for time-delayed systems of the retared type, with the understanding that the Mikhailov curve need not necessarily always rotate in the counterclockwise direction for a stable system. Erroneous results in the second formulation are formed when there are time delays in the systems.

Barker, L. K.↗

NASA NTRS1978

A method for determining the weak statistical stationarity of a random process

A method for determining the weak statistical stationarity of a random process is presented. The core of this testing procedure consists of generating an equivalent ensemble which approximates a true ensemble. Formation of an equivalent ensemble is accomplished through segmenting a sufficiently long time history of a random process into equal, finite, and statistically independent sample records. The weak statistical stationarity is ascertained based on the time invariance of the equivalent-ensemble averages. Comparison of these averages with their corresponding time averages over a single sample record leads to a heuristic estimate of the ergodicity of a random process. Specific variance tests are introduced for evaluating the statistical independence of the sample records, the time invariance of the equivalent-ensemble autocorrelations, and the ergodicity. Examination and substantiation of these procedures were conducted utilizing turbulent velocity signals.

Sadeh, W. Z.↗

NASA NTRS1978

Observations of low-energy electrons from AE-C in the south polar cusp during the geomagnetic storm of September 21, 1977

The present paper deals with the characteristics of low-energy electrons measured onboard the Atmosphere Explorer C (AE-C) satellite above the south polar cusp during the intense geomagnetic storm of September 21, 1977. The low-energy electron fluxes measured with the Photoelectron Spectrometer experiment indicate that the dayside polar cusp was displaced down to 69-72 deg invariant latitude during the storm. A region of intense fluxes of precipitating electrons was observed in the region near 1700 MLT between 66 and 69 deg invariant latitude, which statistically coincides with that of ascending field-alignment currents in the disturbed afternoon auroral region.

Potemra, T. A.↗

NASA NTRS1979

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.↗

NASA NTRS1980

Modal methods in optimal control synthesis

Efficient algorithms for solving linear smoother-follower problems with quadratic criteria are presented. For time-invariant systems, the algorithm consists of one backward integration of a linear vector equation and one forward integration of another linear vector equation. Furthermore, the backward and forward Riccati matrices can be expressed in terms of the eigenvalues and eigenvectors of the Euler-Lagrange equations. Hence, the gains of the forward and backward Kalman-Bucy filters and of the optimal state-feedback regulator can be determined without integration of matrix Riccati equations. A computer program has been developed, based on this method of determining the gains, to synthesize the optimal time-invariant compensator in the presence of random disturbance inputs and random measurement errors. The program also computes the rms state and control variables of the optimal closed-loop system.

Bryson, A. E., Jr.↗

NASA NTRS1980

Plasma convection in the high-latitude F-region

Plasma convection patterns in the high-latitude F region are examined, and their implications for F region plasma distributions and the magnetosphere-solar wind interaction are discussed. In-situ electric field measurements in the ionospheric plasma above invariant latitudes of 60 deg are presented which show that the dominant plasma motion is one of two-cell convection perpendicular to the magnetic field, with motion directed away from the sun at invariant latitudes above 70-75 deg and return flow at lower latitudes. AE-C data revealing the presence of eastward, rather than antisunward, convection in the polar cap region is also noted. Analysis of the F region plasma distributions that may result from the two convection patterns indicates that total ion concentrations may differ by two or three orders of magnitude in different signatures of the high-latitude F region, and may account for the mid-latitude F region trough. The F region patterns are also shown to imply that in an open magnetosphere, a region of reconnection extends across a substantial portion of the magnetotail, while in a closed magnetosphere, the viscous interaction may weaken as the plasma moves down the tail, or remain strong with the boundary layer extending down the tail. The importance of further measurements of the stability of the F region convection pattern is pointed out.

Heelis, R. A.↗

NASA NTRS1981

Local transformations for multi-input nonlinear systems

In this paper Brockett's feedback invariants of nonlinear systems are generalized to a larger class of transformations. In terms of these invariants, the recent results on linear equivalents of nonlinear systems to the multiple-input case have also been extended.

Hunt, L. R.↗

NASA NTRS1982

Two-and-a-half-dimensional magnetohydrodynamic turbulence

The homogeneous turbulence for which fluctuating magnetic fields and velocity fields are independent of one spatial coordinate but still possess all three components are studied to form a generalized two-and-half dimensional geometry. The integral of the z-vector potential and the magnetic helicity are shown to be ideal invariants, and the basic dynamical variables and the equations of uniform-density incompressible magnetohydrodynamics are defined. The possibility of simultaneous inverse cascades is considered, and Kolmogoroff dimensional analysis is employed to infer omnidirectional inverse cascade spectra. Implications of a selective decay hypothesis, where a tendency exists in the initial value problem for the ideal invariants directly cascaded to higher wavenumbers to be selectively dissipated, and the possibility of a dynamo action in the considered geometry, are examined.

Montgomery, D.↗

NASA NTRS1983

Magnetic neutral sheets in evolving fields. I - General theory. II - Formation of the solar corona

The problem of the hydrostatic equilibrium of a large-scale magnetic field embedded in a fluid with infinite electrical conductivity is considered. It is pointed out that a necessary condition for static equilibrium is the invariance of the small-scale pattern in the field along the large-scale direction. A varying topological pattern implies that no fluid pressure distribution exists for which the field is everywhere static. Magnetic neutral sheets form, and dynamical reconnection of the field takes place. It is shown here that the invariance is also a sufficient condition for the existence of a fluid pressure distribution producing static equilibrium. Even in the simplest cases, however, the requirements on the fluid pressure are extreme and, a priori, are unlikely. It is concluded that almost all twisted flux tubes packed together produce dynamical nonequilibrium and dissipation of their twisting. This is the basic effect underlying the long-standing conjecture that the shuffling of the footpoints of the bipolar magnetic fields in the sun is responsible for heating the active corona. Attention is then given to the consequences of this general dynamical dissipation in the magnetic fields that produce the active corona of the sun. The footpoints of the field are continually manipulated by the subphotospheric convection in such a way that the lines of force are continually wrapped and rotated about one another.

Parker, E. N.↗

NASA NTRS1984

Magnetopause structure and the question of particle accessibility

A simple plane model of the magnetopause is used to address the question of particle accessibility. Particle motion in the current sheet region is analyzed, showing that the concept of gyromotion is useful even when the electric and magnetic fields vary significantly over the gyroradius, as long as the variation is perpendicular to the drift direction. The first adiabatic invariant for particle motion is defined in such a way that it is preserved in regions of large field gradients, provided that the gradients are in a direction primarily perpendicular to the particle drifts. This generalized invariant provides an adiabatically conserved quantity that can be used to characterize particles as they move from a source region through the drift region and into the magnetopause itself, helping to resolve the accessibility question. Some preliminary results are given for the magnetopause structure based on the location of particle guiding points.

Whipple, E. C.↗