Search NASA⌕ Search

SEARCH · Search NASA

Results for “chaotic states”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1997

Beyond the Ionosphere: Fifty Years of Satellite Communication

The three overlapping stages of satellite communications development outlined provide the three-part framework for the organization of the papers contained in this book. Part 1, 'Passive Origins,' treats the first stage of satellite communications development, extending from the 1940s into the early 1960s, when passive artificial and natural satellites funded by the military and private enterprise established the field. Part 2, 'Creating the Global, Regional, and National Systems,' addresses events that constituted the second stage of development. Early in this stage, which stretched from the 1960s into the 1970s, satellite systems began to make their appearance in the United States, while domestic and international efforts sought to bring order to this new but chaotic, field in the form of Comsat and Intelsat. Part 3, 'The Unfolding of the World System,' explores the development of satellite communications in the remainder of the world, with a strong emphasis on Asia.

Butrica, Andrew J.↗
NASA NTRS2002

Differential Flatness and Cooperative Tracking in the Lorenz System

In this paper the control of the Lorenz system for both stabilization and tracking problems is studied via feedback linearization and differential flatness. By using the Rayleigh number as the control, only variable physically tunable, a barrier in the controllability of the system is incidentally imposed. This is reflected in the appearance of a singularity in the state transformation. Composite controllers that overcome this difficulty are designed and evaluated. The transition through the manifold defined by such a singularity is achieved by inducing a chaotic response within a boundary layer that contains it. Outside this region, a conventional feedback nonlinear control is applied. In this fashion, the authority of the control is enlarged to the whole. state space and the need for high control efforts is mitigated. In addition, the differential parametrization of the problem is used to track nonlinear functions of one state variable (single tracking) as well as several state variables (cooperative tracking). Control tasks that lead to integrable and non-integrable differential equations for the nominal flat output in steady-state are considered. In particular, a novel numerical strategy to deal with the non-integrable case is proposed. Numerical results validate very well the control design.

Crespo, Luis G.↗
NASA NTRS2003

Probable Disastrous Consequences of Collision Between Unknown Small (100 m) Asteroids with Known (Approximately 1 km) Near Earth Orbiting (NEO) Asteroids

The long-term stability of the Solar System is not well understood. Ironically its stability is taken for granted even though our knowledge of all the constituents [comets, asteroids. (The Asteroid Belt between Mars and Jupiter, Trojan Asteroids, Kuiper belt, Ort Cloud), planetoids, planets, moons, etc], and its long-term dynamics cannot be easily computed. At best one might say that the solar system is chaotic, but much of the time it seems to exists near a quasi-stationary state. An asteroid that passes near the Earth regularly returns with clock-like precision. Taking into account every known detail of its path through the solar system, its orbit is calculated forward thousands of years with no untoward calamity on the horizon. And then one day, this passive visitor slams into the Earth during a sunny afternoon picnic! Can this happen? Unfortunately, this is a real possibility in the ordinary history of the solar system. In fact our knowledge of the solar system in the small is sketchy, as will be pointed out. Events, which lie outside our awareness, can precipitate disasters that we may perceive when it's too late to launch effective counter measures. In this work, one such scenario is described and the direct consequences for the Earth are calculated.

Smalley, Larry↗
NASA NTRS1989

Low Reynolds number numerical solutions of chaotic flow

Numerical computations of two-dimensional flow past an airfoil at low Mach number, large angle of attack, and low Reynolds number are reported which show a sequence of flow states leading from single-period vortex shedding to chaos via the period-doubling mechanism. Analysis of the flow in terms of phase diagrams, Poincare sections, and flowfield variables are used to substantiate these results. The critical Reynolds number for the period-doubling bifurcations is shown to be sensitive to mesh refinement and the influence of large amounts of numerical dissipation. In extreme cases, large amounts of added dissipation can delay or completely eliminate the chaotic response. The effect of artificial dissipation at these low Reynolds numbers is to produce a new effective Reynolds number for the computations.

Pulliam, Thomas H.↗
NASA NTRS1987

Revision of the Martian relative age chronology

This study has provided a more detailed chronology than currently exists in the literature and has created some changes to the currently accepted geological evolutionary sequence of Mars. The period of heavy bombardment, although dominated by impact processes, experienced many forms of volcanic activity and at least one episode of intense fracturing. Most small volcanic constructs and the ridged plains regions are found to date from this early period, contrary to common belief. The fracturing and dissection of the highlands helps to provide further constraints on the timing of events such as the formation of the hemispheric dichotomy and the formation of the Tharsis Bulge. The northern plains are found to consist of a number of differently aged regions. The difference in age between the chaotic terrain and the outflow channels together with differences in the distribution curves among craters of various erosional states found on the channels support the theory of episodic periods of flooding.

Barlow, Nadine G.↗
NASA NTRS1988

A physical model for earthquakes. I - Fluctuations and interactions. II - Application to southern California

The idea that earthquakes represent a fluctuation about the long-term motion of plates is expressed mathematically through the fluctuation hypothesis, under which all physical quantities which pertain to the occurance of earthquakes are required to depend on the difference between the present state of slip on the fault and its long-term average. It is shown that under certain circumstances the model fault dynamics undergo a sudden transition from a spatially ordered, temporally disordered state to a spatially disordered, temporally ordered state, and that the latter stages are stable for long intervals of time. For long enough faults, the dynamics are evidently chaotic. The methods developed are then used to construct a detailed model for earthquake dynamics in southern California. The result is a set of slip-time histories for all the major faults, which are similar to data obtained by geological trenching studies. Although there is an element of periodicity to the events, the patterns shift, change and evolve with time. Time scales for pattern evolution seem to be of the order of a thousand years for average recurring intervals of about a hundred years.

Rundle, John B.↗
NASA NTRS1987

Chaotic nature of the spin-glass phase

The microscopic structure of the ordered phase of spin glasses is investigated theoretically in the framework of the T = 0 fixed-point model (McMillan, 1984; Fisher and Huse, 1986; and Bray and Moore, 1986). The sensitivity of the ground state to changes in the interaction strengths at T = 0 is explored, and it is found that for sufficiently large length scales the ground state is unstable against arbitrarily weak perturbations to the bonds. Explicit results are derived for d = 1, and the implications for d = 2 and d = 3 are considered in detail. It is concluded that there is no hidden order pattern for spin glasses at all T less than T(C), the ordered-phase spin correlations being chaotic functions of spin separation at fixed temperature or of temperature (for a given pair of spins) at scale lengths L greater than (T delta T) exp -1/zeta, where zeta = d(s)/2 - y, d(s) is the interfacial fractal dimension, and -y is the thermal eigenvalue at T = 0.

Bray, A. J.↗
NASA NTRS2010

A Machine-Checked Proof of A State-Space Construction Algorithm

This paper presents the correctness proof of Saturation, an algorithm for generating state spaces of concurrent systems, implemented in the SMART tool. Unlike the Breadth First Search exploration algorithm, which is easy to understand and formalise, Saturation is a complex algorithm, employing a mutually-recursive pair of procedures that compute a series of non-trivial, nested local fixed points, corresponding to a chaotic fixed point strategy. A pencil-and-paper proof of Saturation exists, but a machine checked proof had never been attempted. The key element of the proof is the characterisation theorem of saturated nodes in decision diagrams, stating that a saturated node represents a set of states encoding a local fixed-point with respect to firing all events affecting only the node s level and levels below. For our purpose, we have employed the Prototype Verification System (PVS) for formalising the Saturation algorithm, its data structures, and for conducting the proofs.

Catano, Nestor↗
NASA NTRS1989

An introduction to chaotic and random time series analysis

The origin of chaotic behavior and the relation of chaos to randomness are explained. Two mathematical results are described: (1) a representation theorem guarantees the existence of a specific time-domain model for chaos and addresses the relation between chaotic, random, and strictly deterministic processes; (2) a theorem assures that information on the behavior of a physical system in its complete state space can be extracted from time-series data on a single observable. Focus is placed on an important connection between the dynamical state space and an observable time series. These two results lead to a practical deconvolution technique combining standard random process modeling methods with new embedded techniques.

Scargle, Jeffrey D.↗
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.↗
NASA NTRS1995

Chaotic Rotation of Nereid

The shape and spin of Neptune's outermost satellite Nereid are still unknown. Ground-based photometry indicates large brightness variations, but different observers report very different lightcurve amplitudes and periods. On the contrary, Voyager 2 images spanning 12 days show no evidence of variations greater than 0.1 mag. The latter suggest either that Nereid is nearly spherical, or that it is rotating slowly. We propose that tides have already despun Nereid's rotation to a period of a few weeks, during the time before the capture of Triton when Nereid was closer to Neptune. Since Nereid reached its present orbit, tides have further despun Nereid to a period on the order of a month. For Nereid's orbital eccentricity of 0.75, tidal evolution ceases when the spin period is still approximately 1/8 of the orbital period. Furthermore, the synchronous resonance becomes quite weak for such high eccentricities, along with other low-order spin orbit commensurabilities. In contrast, high-order resonances become very strong particularly the 6:1, 6.5:1, 7:1, 7.5:1, and 8:1 spin states. If Nereid departs by more than approximately 1% from a sphere, however, these resonances overlap, generating chaos. Our simulations show that Nereid is likely to be in chaotic rotation for any spin period longer than about 2 weeks.

Dobrovolskis, Anthony R.↗
NASA NTRS1990

Interesting examples of supervised continuous variable systems

The authors analyze two simple deterministic flow models for multiple buffer servers which are examples of the supervision of continuous variable systems by a discrete controller. These systems exhibit what may be regarded as the two extremes of complexity of the closed loop behavior: one is eventually periodic, the other is chaotic. The first example exhibits chaotic behavior that could be characterized statistically. The dual system, the switched server system, exhibits very predictable behavior, which is modeled by a finite state automaton. This research has application to multimodal discrete time systems where the controller can choose from a set of transition maps to implement.

Chase, Christopher↗
NASA NTRS2010

A Modeling and Verification Study of Summer Precipitation Systems Using NASA Surface Initialization Datasets

One of the most challenging weather forecast problems in the southeastern U.S. is daily summertime pulse-type convection. During the summer, atmospheric flow and forcing are generally weak in this region; thus, convection typically initiates in response to local forcing along sea/lake breezes, and other discontinuities often related to horizontal gradients in surface heating rates. Numerical simulations of pulse convection usually have low skill, even in local predictions at high resolution, due to the inherent chaotic nature of these precipitation systems. Forecast errors can arise from assumptions within parameterization schemes, model resolution limitations, and uncertainties in both the initial state of the atmosphere and land surface variables such as soil moisture and temperature. For this study, it is hypothesized that high-resolution, consistent representations of surface properties such as soil moisture, soil temperature, and sea surface temperature (SST) are necessary to better simulate the interactions between the surface and atmosphere, and ultimately improve predictions of summertime pulse convection. This paper describes a sensitivity experiment using the Weather Research and Forecasting (WRF) model. Interpolated land and ocean surface fields from a large-scale model are replaced with high-resolution datasets provided by unique NASA assets in an experimental simulation: the Land Information System (LIS) and Moderate Resolution Imaging Spectroradiometer (MODIS) SSTs. The LIS is run in an offline mode for several years at the same grid resolution as the WRF model to provide compatible land surface initial conditions in an equilibrium state. The MODIS SSTs provide detailed analyses of SSTs over the oceans and large lakes compared to current operational products. The WRF model runs initialized with the LIS+MODIS datasets result in a reduction in the overprediction of rainfall areas; however, the skill is almost equally as low in both experiments using traditional verification methodologies. Output from object-based verification within NCAR s Meteorological Evaluation Tools reveals that the WRF runs initialized with LIS+MODIS data consistently generated precipitation objects that better matched observed precipitation objects, especially at higher precipitation intensities. The LIS+MODIS runs produced on average a 4% increase in matched precipitation areas and a simultaneous 4% decrease in unmatched areas during three months of daily simulations.

Jonathan L. Case↗
NASA NTRS1990

Non-linear dynamics of a spur gear pair

The backlash nonlinearity excited primarily by transmission error between spur gear pairs is studied for both external and internal excitations. The digital simulation technique and the method of harmonic balance are used to develop steady state solutions for the internal sinuosidal excitations. The analytic predictions agreed well with available experimental data. Digital simulation is used to observe that at the chaotic and subharmonic resonances may exist in a gear pair depending on the mean or design load, mean to alternating force ratio, damping, and backlash.

Kahraman, A.↗
NASA NTRS2009

Examining the Impacts of High-Resolution Land Surface Initialization on Model Predictions of Convection in the Southeastern U.S.

One of the most challenging weather forecast problems in the southeastern U.S. is daily summertime pulse convection. During the summer, atmospheric flow and forcing are generally weak in this region; thus, convection typically initiates in response to local forcing along sea/lake breezes, and other discontinuities often related to horizontal gradients in surface heating rates. Numerical simulations of pulse convection usually have low skill, even in local predictions at high resolution, due to the inherent chaotic nature of these precipitation systems. Forecast errors can arise from assumptions within physics parameterizations, model resolution limitations, as well as uncertainties in both the initial state of the atmosphere and land surface variables such as soil moisture and temperature. For this study, it is hypothesized that high-resolution, consistent representations of surface properties such as soil moisture and temperature, ground fluxes, and vegetation are necessary to better simulate the interactions between the land surface and atmosphere, and ultimately improve predictions of local circulations and summertime pulse convection. The NASA Short-term Prediction Research and Transition (SPORT) Center has been conducting studies to examine the impacts of high-resolution land surface initialization data generated by offline simulations of the NASA Land Informatiot~ System (LIS) on subsequent numerical forecasts using the Weather Research and Forecasting (WRF) model (Case et al. 2008, to appear in the Journal of Hydrometeorology). Case et al. presents improvements to simulated sea breezes and surface verification statistics over Florida by initializing WRF with land surface variables from an offline LIS spin-up run, conducted on the exact WRF domain and resolution. The current project extends the previous work over Florida, focusing on selected case studies of typical pulse convection over the southeastern U.S., with an emphasis on improving local short-term WRF simulations over the Mobile, AL and Miami, FL NWS county warning areas. Future efforts may involve examining the impacts of assimilating remotely-sensed soil moisture data, and/or introducing weekly greenness vegetation fraction composites (as opposed to monthly climatologies) into ol'fline NASA LIS runs. Based on positive impacts, the offline LIS runs could be transitioned into an operational mode, providing land surface initialization data to NWS forecast offices in real time.

Case, Jonathan L.↗
NASA NTRS1985

A note on the loop thermosyphon with mixed boundary conditions

This paper presents a one-dimensional model for flow in a toroidal fluid loop in which the wall heat transfer coefficient is constant over one half of the loop, and zero over the other. A mathematically low-dimensional form of the model gives reasonably accurate predictions of the steady state mass flow, stability, and the nature of nonsteady motions. Numerical computations with a high-dimensional model illustrate the effects of mixed boundaries and axial heat conduction on the chaotic solutions. Comparisons are made with previous low-dimensional models that are exact only for a spatially uniform heat transfer coefficient.

Hart, J. E.↗
NASA NTRS1997

Detection of "noisy" chaos in a time series

Time series from biological system often displays fluctuations in the measured variables. Much effort has been directed at determining whether this variability reflects deterministic chaos, or whether it is merely "noise". The output from most biological systems is probably the result of both the internal dynamics of the systems, and the input to the system from the surroundings. This implies that the system should be viewed as a mixed system with both stochastic and deterministic components. We present a method that appears to be useful in deciding whether determinism is present in a time series, and if this determinism has chaotic attributes. The method relies on fitting a nonlinear autoregressive model to the time series followed by an estimation of the characteristic exponents of the model over the observed probability distribution of states for the system. The method is tested by computer simulations, and applied to heart rate variability data.

Non-NASA Center↗
NASA NTRS1993

Intraseasonal variability in a barotropic model with seasonal forcing

It has recently been suggested that oscillatory topographic instability could contribute to low-frequency variability over the Northern Hemisphere midlatitudes. A barotropic potential vorticity model, with a hierarchy of forcing and topography configurations on the sphere, is used to investigate the nature of low-frequency oscillations induced by such instabilities. Steady-state solutions of the model include multiple unstable equilibria that sustain oscillatory instabilities with periods of 10 - 15 days, and 150 - 180 days, for a realistic forcing pattern, Time-dependent solutions exhibit chaotic behavior with episodic oscillations, featuring both the intraseasonal (35 - 50 day) and biweekly (10 - 15 day) modes. The former is dominated by standing spatial patterns, the latter by traveling wave patterns. The phases of the intraseasonal oscillation are robust for all cases, exhibiting a clear oscillatory exchange of atmospheric angular momentum with the solid earth via mountain troque. It is demonstrated, through linear stability analysis on the sphere, that the intraseasonal oscillations are induced by topographic instabilities. The role of the seasonal cycle is studied by prescribing an annual cycle in the forcing. In this case, the winter forcing is more favorable than the summer for the occurrence of episodic intraseasonal oscillations. Recent observations are consistent with this model result.

Strong, Christopher M.↗