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At least 955 records · Page 53
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NASA NTRS1990

Chaos in driven Alfven systems

The chaos in a one-dimensional system, which would be nonlinear stationary Alfven waves in the absence of an external driver, is characterized. The evolution equations are numerically integrated for the transverse wave magnetic field amplitude and phase using the derivative nonlinear Schroedinger equation (DNLS), including resistive wave damping and a long-wavelength monochromatic, circularly polarized driver. A Poincare map analysis shows that, for the nondissipative (Hamiltonian) case, the solutions near the phase space (soliton) separatrices of this system become chaotic as the driver amplitude increases, and 'strong' chaos appears when the driver amplitude is large. The dissipative system exhibits a wealth of dynamical behavior, including quasiperiodic orbits, period-doubling bifurcations leading to chaos, sudden transitions to chaos, and several types of strange attractors.

Hada, T.↗
NASA NTRS1991

The O VII soft X-ray spectrum and its application to hot plasmas in astrophysics

The paper presents a revised theory and atomic model for the line intensities emitted by O VII, taking into account all of the processes responsible for the emission. This is used to provide a revision of the density measurements made for solar active regions and during flares, as well as an attempt to understand the spectrum of the Puppis A supernova remnant. In order to explain the strange intensity ratios observed from Puppis A, previous authors have proposed an interpretation based upon a high-temperature thermal plasma in a nonequilibrium ionization state. An alternative model is presented here, based upon the assumed presence of a proportion of fast, nonthermal electrons imbedded in an otherwise thermal plasma at a temperature below 10 to the 6th K. This can adequately explain the observations without the necessity of invoking departures from the ionization balance.

Gabriel, A. H.↗
NASA NTRS1992

Turbulence and deterministic chaos

Several turbulent and nonturbulent solutions of the Navier-Stokes equations are obtained. The unaveraged equations are used numerically in conjunction with tools and concepts from nonlinear dynamics, including time series, phase portraits, Poincare sections, largest Liapunov exponents, power spectra, and strange attractors. Initially neighboring solutions for a low Reynolds number fully developed turbulence are compared. Several flows are noted: fully chaotic, complex periodic, weakly chaotic, simple periodic, and fixed-point. Of these, only fully chaotic is classified as turbulent. Besides the sustained flows, a flow which decays as it becomes turbulent is examined. For the finest grid, 128(exp 3) points, the spatial resolution appears to be quite good. As a final note, the variation of the velocity derivatives skewness of a Navier-Stokes flow as the Reynolds number goes to zero is calculated numerically. The value of the skewness is shown to become small at low Reynolds numbers, in agreement with intuitive arguments that nonlinear terms should be negligible.

Deissler, Robert G.↗
NASA NTRS1992

Nonlinear techniques for forecasting solar activity directly from its time series

Numerical techniques for constructing nonlinear predictive models to forecast solar flux directly from its time series are presented. This approach makes it possible to extract dynamical invariants of our system without reference to any underlying solar physics. We consider the dynamical evolution of solar activity in a reconstructed phase space that captures the attractor (strange), given a procedure for constructing a predictor of future solar activity, and discuss extraction of dynamical invariants such as Lyapunov exponents and attractor dimension.

Ashrafi, S.↗
NASA NTRS1991

Nonlinear symmetric instability and intraseasonal oscillations in the tropical atmosphere

Symmetric inertial instability (SII) is studied as a mechanism for stratospheric and tropospheric phenomena in the equatorial regions. The linear and nonlinear dynamics of SII in a two-layer, zonally symmetric model on an equatorial beta plane, in the presence of a basic flow with horizontal and vertical shear, with and without dissipative effects are investigated. Linear symmetric instabilities are, in accordance with previously published results, purely exponential, that is, nonoscillatory. Nonlinear SII, studied here for the first time on a planetary scale, can produce finite-amplitude oscillatory behavior, periodic or chaotic. The period of oscillations in the inviscid case depends on the initial data. In the presence of dissipative effects, all solutions tend to a limit cycle or to a strange attractor. The dominant period in this case, over a wide range of parameters and whether vertical shear is present or not, is in the intraseasonal, 20-30-day range. It appears therefore that nonlinear SII might be a contributing mechanism to low-frequency oscillations in the tropical atmosphere.

Zhao, J.-X.↗
NASA NTRS1991

Cosmological gamma-ray bursts

The distribution in angle and flux of gamma-ray bursts indicates that the majority of gamma-ray bursters are at cosmological distances, i.e., at z of about 1. The rate is then about 10 exp -8/yr in a galaxy like the Milky Way, i.e., orders of magnitude lower than the estimated rate for collisions between neutron stars in close binary systems. The energy per burst is about 10 exp 51 ergs, assuming isotropic emission. The events appear to be less energetic and more frequent if their emission is strongly beamed. Some tests for the distance scale are discussed: a correlation between the burst's strength and its spectrum; the absorption by the Galactic gas below about 2 keV; the X-ray tails caused by forward scattering by the Galactic dust; about 1 month recurrence of some bursts caused by gravitational lensing by foreground galaxies; and a search for gamma-ray bursts in M31. The bursts appear to be a manifestation of something exotic, but conventional compact objects can provide an explanation. The best possibility is offered by a decay of a bindary composed of a spinning-stellar-mass black-hole primary and a neutron or a strange-quark star secondary. In the final phase the secondary is tidally disrupted, forms an accretion disk, and up to 10 exp 54 ergs are released. A very small fraction of this energy powers the gamma-ray burst.

Paczynski, Bohdan↗
NASA NTRS1990

A new finite element method for solving compressible Navier-Stokes equations based on an operator splitting method and h-p adaptivity

A new finite element method solving compressible Navier-Stokes equations is proposed. The method is based on a version of Strang's operator splitting and an h-p adaptive finite element approximation in space. This paper contains the formulation of the method with a detailed discussion of boundary conditions, a sample adaptive strategy and numerical examples involving compressible viscous flow over a flat plate with Reynolds number Re = 1000 and Re = 10,000.

Demkowicz, L.↗
NASA NTRS1992

Off-center nuclei in galaxies

The nucleus of a galaxy orbits around the mass centroid. Orbital motions appear overstable in numerical experiments started with a galaxy's nucleus at rest atop its mass centroid. The amplitude doubles in 6-10 orbital periods. Orbits precess, nutate, and change their amplitudes, but they keep fairly constant periods. Orbital periods are in resonance with local particle motions, and amplitudes reach a core radius. This resonance suggests that center motions are a local, rather than a global, phenomenon. The overstability implies that a galaxy cannot be formed in nature with its nucleus at rest atop its mass centroid, and that nuclei orbit the mass centroid in real galaxies. These center motions should show up observationally as a shift of the nucleus away from the center defined by nearby isophotes. Off-center nuclei have been reported in many galaxies (e.g., M33, M101, NGC 3379, NGC 3384). Other kinds of observations confirmed the picture of nonsteady galactic centers as well. Gas trapped in moving nuclear regions of a galaxy should show strange flow patterns with possible shocks. The nuclear regions of galaxies including Milky Way and of globular clusters are not likely to be in a static steady state.

Miller, R. H.↗
NASA NTRS1992

Is a pyrene-like molecular ion the cause of the 4,430-A diffuse interstellar absorption band?

The diffuse interstellar band (DIB) absorption features of astronomical spectra are suggested by recent results to be separable from the grains that cause visual extinction. Attention is presently given to laboratory measurements of the optical spectrum of the pyrene cation C16H10(+), which is one of the polycyclic aromatic hydrocarbon (PAH) molecular candidates proposed as carriers for DIBs. This ion exhibits an intense but strangely broad continuum similar to that of the naphthalene cation, so that this may be a common feature of all PAH cations and the basis of an explanation for PAHs' converting of an interstellar radiation fraction as large as that from the UV and visible range down to the IR.

Salama, F.↗
NASA NTRS1992

Self-organized rock textures and multiring structure in the Duolun crater

The Duolun impact crater is a multiring basin located 200 km north of Beijing. From the center to the edge of the crater there are innermost rim, inner ring, outer rim, and outermost ring. Recently, we have found some self-organized textures or chaos phenomena in shock-metamorphic rocks from the Duolun impact crater, such as turbulence in matrices of impact glass, oscillatory zoning, or chemical chaos of spherulites in spherulitic splashed breccia, fractal wavy textures or self-similar wavy textures with varied scaling in impact glass, and crystallite beams shaped like Lorentz strange attractors. The rare phenomena indicate that the shock-metamorphic rocks from Duolun crater are formed far from equilibrium. If impact cratering generates momentarily under high-pressure and superhigh-temperature, occurrence of those chaos phenomena in shock-metamorphic rock is not surprising.

Wu, Siben↗
NASA NTRS1993

Nonlinear techniques for forecasting solar activity directly from its time series

This paper presents numerical techniques for constructing nonlinear predictive models to forecast solar flux directly from its time series. This approach makes it possible to extract dynamical in variants of our system without reference to any underlying solar physics. We consider the dynamical evolution of solar activity in a reconstructed phase space that captures the attractor (strange), give a procedure for constructing a predictor of future solar activity, and discuss extraction of dynamical invariants such as Lyapunov exponents and attractor dimension.

Ashrafi, S.↗
NASA NTRS1992

Non-scalar uncertainty: Uncertainty in dynamic systems

The following point is stated throughout the paper: dynamic systems are usually subject to uncertainty, be it the unavoidable quantic uncertainty when working with sufficiently small scales or when working in large scales uncertainty can be allowed by the researcher in order to simplify the problem, or it can be introduced by nonlinear interactions. Even though non-quantic uncertainty can generally be dealt with by using the ordinary probability formalisms, it can also be studied with the proposed non-scalar formalism. Thus, non-scalar uncertainty is a more general theoretical framework giving insight into the nature of uncertainty and providing a practical tool in those cases in which scalar uncertainty is not enough, such as when studying highly nonlinear dynamic systems. This paper's specific contribution is the general concept of non-scalar uncertainty and a first proposal for a methodology. Applications should be based upon this methodology. The advantage of this approach is to provide simpler mathematical models for prediction of the system states. Present conventional tools for dealing with uncertainty prove insufficient for an effective description of some dynamic systems. The main limitations are overcome abandoning ordinary scalar algebra in the real interval (0, 1) in favor of a tensor field with a much richer structure and generality. This approach gives insight into the interpretation of Quantum Mechanics and will have its most profound consequences in the fields of elementary particle physics and nonlinear dynamic systems. Concepts like 'interfering alternatives' and 'discrete states' have an elegant explanation in this framework in terms of properties of dynamic systems such as strange attractors and chaos. The tensor formalism proves especially useful to describe the mechanics of representing dynamic systems with models that are closer to reality and have relatively much simpler solutions. It was found to be wise to get an approximate solution to an accurate model than to get a precise solution to a model constrained by simplifying assumptions. Precision has a very heavy cost in present physical models, but this formalism allows the trade between uncertainty and simplicity. It was found that modeling reality sometimes requires that state transition probabilities should be manipulated as nonscalar quantities, finding at the end that there is always a transformation to get back to scalar probability.

Martinez, Salvador Gutierrez↗
NASA NTRS1992

The dimension of attractors underlying periodic turbulent Poiseuille flow

A lower bound on the Liapunov dimenison, D-lambda, of the attractor underlying turbulent, periodic Poiseuille flow at a pressure-gradient Reynolds number of 3200 is calculated, on the basis of a coarse-grained (16x33x8) numerical solution, to be approximately 352. Comparison of Liapunov exponent spectra from this and a higher-resolution (16x33x16) simulation on the same spatial domain shows these spectra to have a universal shape when properly scaled. On the basis of these scaling properties, and a partial exponent spectrum from a still higher-resolution (32x33x32) simulation, it is argued that the actual dimension of the attractor underlying motion of the given computational domain is approximately 780. It is suggested that this periodic turbulent shear flow is deterministic chaos, and that a strange attractor does underly solutions to the Navier-Stokes equations in such flows.

Keefe, Laurence↗
NASA NTRS1992

Gamma-ray bursts from colliding neutron stars

Three distance scales to gamma-ray bursters are discussed: about 300 pc, about 2 - 50 kpc, and about 1 Gpc, corresponding to the Galactic disk, Galactic halo, and extragalactic origin. No compelling evidence is found in favor of any of them. The BATSE experiment on GRO should determine the distance scale by determining the angular distribution of very weak bursts. The rate of collisions between the neutron stars is about 0.0001/yr in our Galaxy, and about 10 exp 5/yr within the Hubble distance. The collisions are the final phases of binary orbit decay driven by gravitational radiation, and may produce gamma-ray bursts detectable at extra-galactic distances. If strange stars exist then their collisions must release about 10 exp 49 erg in gamma-rays over about 10 seconds. Such events should be detectable out to about 1 Gpc with the current instruments.

Paczynski, Bohdan↗
NASA NTRS1991

Why did Halley hiccup?

The outburst of Halley comet that occurred in February 1991 when the comet was over 14 AU from the sun, between the orbits of Saturn and Uranus, is described. This region of the solar system was known to be so cold that a comet nucleus would be totally inert there. On February 12th, 1991 Halley brightened by a factor of about 300, and a dust coma was observed around the nucleus. Different explanations of the comet's strange behavior are suggested.

Weissman, Paul↗
NASA NTRS1990

Mathematical theory of a relaxed design problem in structural optimization

Various attempts have been made to construct a rigorous mathematical theory of optimization for size, shape, and topology (i.e. layout) of an elastic structure. If these are represented by a finite number of parametric functions, as Armand described, it is possible to construct an existence theory of the optimum design using compactness argument in a finite dimensional design space or a closed admissible set of a finite dimensional design space. However, if the admissible design set is a subset of non-reflexive Banach space such as L(sup infinity)(Omega), construction of the existence theory of the optimum design becomes suddenly difficult and requires to extend (i.e. generalize) the design problem to much more wider class of design that is compatible to mechanics of structures in the sense of variational principle. Starting from the study by Cheng and Olhoff, Lurie, Cherkaev, and Fedorov introduced a new concept of convergence of design variables in a generalized sense and construct the 'G-Closure' theory of an extended (relaxed) optimum design problem. A similar attempt, but independent in large extent, can also be found in Kohn and Strang in which the shape and topology optimization problem is relaxed to allow to use of perforated composites rather than restricting it to usual solid structures. An identical idea is also stated in Murat and Tartar using the notion of the homogenization theory. That is, introducing possibility of micro-scale perforation together with the theory of homogenization, the optimum design problem is relaxed to construct its mathematical theory. It is also noted that this type of relaxed design problem is perfectly matched to the variational principle in structural mechanics.

Kikuchi, Noboru↗
NASA NTRS1992

Spectral analysis for automated exploration and sample acquisition

Future space exploration missions will rely heavily on the use of complex instrument data for determining the geologic, chemical, and elemental character of planetary surfaces. One important instrument is the imaging spectrometer, which collects complete images in multiple discrete wavelengths in the visible and infrared regions of the spectrum. Extensive computational effort is required to extract information from such high-dimensional data. A hierarchical classification scheme allows multispectral data to be analyzed for purposes of mineral classification while limiting the overall computational requirements. The hierarchical classifier exploits the tunability of a new type of imaging spectrometer which is based on an acousto-optic tunable filter. This spectrometer collects a complete image in each wavelength passband without spatial scanning. It may be programmed to scan through a range of wavelengths or to collect only specific bands for data analysis. Spectral classification activities employ artificial neural networks, trained to recognize a number of mineral classes. Analysis of the trained networks has proven useful in determining which subsets of spectral bands should be employed at each step of the hierarchical classifier. The network classifiers are capable of recognizing all mineral types which were included in the training set. In addition, the major components of many mineral mixtures can also be recognized. This capability may prove useful for a system designed to evaluate data in a strange environment where details of the mineral composition are not known in advance.

Eberlein, Susan↗
NASA NTRS1993

On the estimation of the correlation dimension and its application to radar reflector discrimination

Recently, system theorists have recognized that low order systems of nonlinear differential equations can give rise to solutions which are neither periodic, constant, nor predictable in steady state, but which are nonetheless bounded and deterministic. This behavior, which was first described in the study of weather systems, has been termed 'chaotic.' Much study of chaotic systems has concentrated on analysis of the systems' phase space attractors. It has been recognized that invariant measures of the attractor possess inherent information about the system. One such measure is the dimension of the attractors. The dimension of a chaotic attractor has been shown to be noninteger, leading to the term 'strange attractor;' the attractor is said to have a fractal structure. The correlation dimension has become one of the most popular measures of dimension. However, many problems have been identified in correlation dimension estimation from time sequences. The most common methods for obtaining the correlation dimension have been least squares curves fitting to find the slope of the correlation integral and the Takens Estimator. However, these estimates show unacceptable sensitivity to the upper limit on the distance chosen. Here, a new method is proposed which is shown to be rather insensitive to the upper limit and to perform in a very stable manner, at least in the absence of noise. The correlation dimension is also shown to be an effective discriminant in distinguishing between radar returns resulting from weather and those from the ground. The weather returns are shown to have a correlation dimension generally between 2.0 and 3.0, while ground returns have a correlation dimension exceeding 3.0.

Barnett, Kevin D.↗