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It is shown that a simple two-link planar manipulator exhibits a phenomenon of global instability in a subspace of its configuration space. A numerical example, as well as results of a graphic simulation, is given.
It is proposed that chaotic attractors incorporated in neural net models can represent classes of patterns in the same way in which a set of static attractors represent unrelated patterns. Therefore, chaotic states of neuron activity are associated with higher level cognitive processes such as generalization and abstraction.
An analogue of the magnetosphere developed on the basis of Shaw's (1984) dripping faucet model was used to model the mechanisms of the magnetospheric response to energy transfer from the solar wind. It is demonstrated that geomagnetic activity results from nonlinearly coupled physical processes and that the strength and the nature of the coupling changes dramatically as the magnetosphere is driven harder and harder by increasing energy input. Based on initial results obtained from the model, is is suggested that a chaotic transition takes place in the analogue system as the loading rate is increased beyond a critical value. This model is able to explain many of the features in the results of linear prediction filtering techniques.
Recently Karachentsev's group at The Smithsonian Astrophysical Observatory (SAO) (6-meter Telescope Observatory) published a list of 84 triple systems of galaxies with their distances, radial (line of sight) velocities, and angular sizes (Karachentseva et al., 1988). This gives a new ground for studies of the dark matter problem which fills the gap between the large cosmic scales (White, 1987; Dekel and Rees, 1987, and Einasto et al., 1977) and the scale of individual galaxies (Erickson et al., 1987). The data on the typical velocity dispersions and linear dimension of the triplets indicate that they contain considerable amounts of dark matter (see also earlier work of Karachentseva et al., 1979). Numerical simulations show that the statistical characteristics of the Karachentsev triplets can be imitated by model ensembles of triple systems with dark matter masses M sub d = (1-3 x 10(exp 12) M sub O, which is almost ten times greater than the typical mass of stellar galaxies estimated by the standard mass-to-luminosity ration (Kiseleva and Chernin, 1988). Here, the authors report that important information can be drawn from the data on the visible configurations of these systems. The statistics of configurations provide an independent evidence for dark matter in the triplets; moreover, it enables one to argue that dark matter seems to be distributed over the whole volume of the typical triplet forming its common corona rather than concentrated within individual coronae (or haloes) of the member galaxies.
The magnetospheric response to the solar-wind input, as represented by the time-series measurements of the auroral electrojet (AE) index, has been examined using phase-space reconstruction techniques. The system was found to behave as a low-dimensional chaotic system with a fractal dimension of 3.6 and has Kolmogorov entropy less than 0.2/min. These indicate that the dynamics of the system can be adequately described by four independent variables, and that the corresponding intrinsic time scale is of the order of 5 min. The relevance of the results to magnetospheric modeling is discussed.
The variability of solar activity over long time scales, given semiquantitatively by measurements of sunspot numbers, is examined as a nonlinear dynamical system. First, a discussion of the data set used and the techniques utilized to reduce the noise and capture the long-term dynamics inherent in the data is presented. Subsequently, an attractor is reconstructed from the data set using the method of time delays. The reconstructed attractor is then used to determine both the dimension of the underlying system and also the largest Lyapunov exponent, which together indicate that the sunspot cycle is indeed chaotic and also low dimensional. In addition, recent techniques of exploiting chaotic dynamics to provide accurate, short-term predictions are utilized in order to improve upon current forecasting methods and also to place theoretical limits on predictability extent. The results are compared to chaotic solar-dynamo models as a possible physically motivated source of this chaotic behavior.
An ion heating mechanism is proposed of slow shocks, which is associated with the chaotic motion of particles in the downstream wave field. For a coherent electromagnetic wave propagating along the downstream magnetic field, corresponding to switch-off shocks, the particle motions are not chaotic. For an oblique wave, the interaction between the particles and the wave field may lead to chaotic particle motions. Such particles may be greatly thermalized within one wavelength after they are incident into the downstream wave field. The results can be used to explain the existence of the critical intermediate Mach number observed in the hybrid simulations.
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.
The dynamic response of an aircraft panel forced at resonance and off-resonance by plane acoustic waves at normal incidence is investigated experimentally and numerically. Linear, nonlinear (period doubling), and chaotic responses are obtained by increasing the sound pressure level of the excitation. The response time history is sensitive to the input level and to the frequency of excitation. The change in response behavior is due to a change in input conditions, triggered either naturally or by modulation of the bandwidth of the incident waves. Off-resonance bifurcation is diffused and difficult to maintain; thus the panel response drifts into a linear behavior. The acoustic pressure emanated by the panel is either linear or nonlinear as is the vibration response. The nonlinear effects accumulate during the propagation with distance. Results are also obtained on the control of the panel response using damping tape on an aluminum panel and a graphite epoxy panel having the same size and weight. Good agreement is obtained betwen the experimental and numerical results.
The dynamic response of an aircraft panel forced at resonance and off-resonance by plane acoustic waves at normal incidence is investigated experimentally and numerically. Linear, nonlinear (period doubling) and chaotic responses are obtained by increasing the sound pressure level of the excitation. The response time history is sensitive to the input level and to the frequency of excitation. The change in response behavior is due to a change in input conditions, triggered either naturally or by modulation of the bandwidth of the incident waves. Off-resonance, bifurcation is diffused and difficult to maintain, thus the panel response drifts into a linear behavior. The acoustic pressure emanated by the panel is either linear or nonlinear as is the vibration response. The nonlinear effects accumulate during the propagation with distance. Results are also obtained on the control of the panel response using damping tape on aluminum panel and using a graphite epoxy panel having the same size and weight. Good agreement is obtained between the experimental and numerical results.
We analyze two examples of the discrete control of a continuous variable system. These examples exhibit what may be regarded as the two extremes of complexity of the closed-loop behavior: one is eventually periodic, the other is chaotic. Our examples are derived from sampled deterministic flow models. These are of interest in their own right but have also been used as models for certain aspects of manufacturing systems. In each case, we give a precise characterization of the closed-loop behavior.
The hypothesis is that the global climate system, consisting of atmospheric dust interacting with the circulation, produces its own interannual variability when forced at the annual frequency. The model has two time-dependent variables representing the amount of atmospheric dust in the northern and southern hemispheres, respectively. Absorption of sunlight by the dust drives a cross-equatorial Hadley cell that brings more dust into the heated hemisphere. The circulation decays when the dust storm covers the globe. Interannual variability manifests itself either as a periodic solution in which the period is a multiple of the Martian year, or as an aperiodic (chaotic) solution that never repeats. Both kinds of solution are found in the model, lending support to the idea that interannual variability is an intrinsic property of the global climate system. The next step is to develop a hierarchy of dust-circulation models capable of being integrated for many years.
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, Liapunov exponents, power spectra, and strange attractors. Initially neighboring solutions for a low-Reynolds-number fully developed turbulence are compared. The turbulence is sustained by a nonrandom time-independent external force. The solutions, on the average, separate exponentially with time, having a positive Liapunov exponent. Thus, the turbulence is characterized as chaotic. In a search for solutions which contrast with the turbulent ones, the Reynolds number (or strength of the forcing) is reduced. Several qualitatively different flows are noted. These are, respectively, fully chaotic, complex periodic, weakly chaotic, simple periodic, and fixed-point. Of these, we classify only the fully chaotic flows as turbulent. Those flows have both a positive Liapunov exponent and Poincare sections without pattern. By contrast, the weakly chaotic flows, although having positive Liapunov exponents, have some pattern in their Poincare sections. The fixed-point and periodic flows are nonturbulent, since turbulence, as generally understood, is both time-dependent and aperiodic.
The stringent spin balance requirements arise from the predecessor of SSMIS, the SSMI. The SSMI sensor spinning portion weighed only 85 pounds and contained 7 channels of radiometric data. The Aerospace Corporation recommended to pass on the same requirements from the smaller SSMI to our larger SSMIS (with slight change for increased weight). The SSMIS spinning portion will weigh about 155 pounds and contain 24 channels of radiometeric data. The SSMIS, on orbit, spins a CCW direction at 31.6 RPM its own drive motor. The packaging of this SSMIS is unique, as it combines three sensor into one unit. This combination allows for concurrently reading data in one beam. The unit will have a polar orbit about 500 miles above the earths surface. One of the primary influences for our receipt of the follow-on contract for the next generation sensor, was the ability to package 24 channels of radiometeric data into about the some volume as its predecessor. The data from SSMIS will be used to measure the following: (1) Ocean surface wind speed, (2) Rain over land an ocean, (3) Cloud water over Ocean, (4) Soil moisture, (5) Ice Concentration, (6) Ice age, (7) Ice Edge and snow edge, (8) Water vapor over Ocean, (9) Surface type, (10) Snow water content, (11) Land surface Temperature, (12) Cloud amount over ocean.
The air on this mostly sunny January day is crisp and the wind is blustery. The morning's National Weather Service 6-hour forecast had accurately predicted these conditions for the Baltimore-Washington area and the 2-3 day extended outlook was almost perfect. The previous week, the National Center for Environmental Prediction's (NCEP) 6-10 day temperature and precipitation outlook for the general trends for the' region was correct as well. However, no forecast could have predicted specific details about this day. It is 28.5 F in the sunshine bright enough for dark sunglasses, and windy enough to blow off a hat. Such details are impossible to foresee with any accuracy and are outside the scope of routine weather prediction. Equally difficult is accurately forecasting weather beyond about 2 weeks.
Doctinary overlays on the definition of life can effectively be avoided by focusing discussion on microorganisms, their vital processes, and their genetic pedigree. To reach beyond these present and highly advanced forms of life and to inquire about its origin it is necessary to consider the requirements imposed by the environment. These requirements include geophysically and geochemically acceptable conjectures for the generation of source compounds, their concentration from dilute solution, and their selective combination into functional biomolecules. For vital function these macromolecules require programming in the form of specific sequence motifs. This critical programming constitutes the scientifically least understood process in the origin of life. Once this stage has been surpassed the laws of Darwinian evolution can operate in ways that are understood and experimentally demonstrated.
A light-toned interior layer deposit (ILD) on the floor of the deep martian depression Juventae Chasma is found to have a relatively high thermal inertia approx. 500 J m(exp -2) s(exp -1/2) K(exp -1). This could imply rock, but is also similar to the average value of thermal inertia found for north polar layered deposits. Furthermore, ILD-B is found to exhibit a bluff and terrace structure . A terrace structure arises naturally in model simulations of the sublimation of large ice deposits. Such a staircase terrain, of course, is a further characteristic of north polar layered terrain. Morphological similarity, thermal inertia in the range of thermal inertias of the north polar cap layered terrain, and relatively high albedo lead us to propose that the ILD-B may consist of residual water ice partially covered by, and perhaps mixed with, varying amounts of dust or sand. Other ILDs (A-C) are also found in Juventae Chasma. While these ILDs lack the close morphological resemblance to the north polar cap, they share many other common features and appear to be part of the same formation. Similar ILDs are found in chaotic terrain elsewhere in the martian tropics. This leads us to propose that water ice may exist in the martian tropics today and may be implicit in the formation of chaotic terrain.