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All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Evidence of chaotic pattern in solar flux through a reproducible sequence of period-doubling-type bifurcations

Presented here is a preliminary study of the limits to solar flux intensity prediction, and of whether the general lack of predictability in the solar flux arises from the nonlinear chaotic nature of the Sun's physical activity. Statistical analysis of a chaotic signal can extract only its most gross features, and detailed physical models fail, since even the simplest equations of motion for a nonlinear system can exhibit chaotic behavior. A recent theory by Feigenbaum suggests that nonlinear systems that can be led into chaotic behavior through a sequence of period-doubling bifurcations will exhibit a universal behavior. As the control parameter is increased, the bifurcation points occur in such a way that a proper ratio of these will approach the universal Feigenbaum number. Experimental evidence supporting the applicability of the Feigenbaum scenario to solar flux data is sparse. However, given the hypothesis that the Sun's convection zones are similar to a Rayleigh-Bernard mechanism, we can learn a great deal from the remarkable agreement observed between the prediction by theory (period doubling - a universal route to chaos) and the amplitude decrease of the signal's regular subharmonics. The authors show that period-doubling-type bifurcation is a possible route to a chaotic pattern of solar flux that is distinguishable from the logarithm of its power spectral density. This conclusion is the first positive step toward a reformulation of solar flux by a nonlinear chaotic approach. The ultimate goal of this research is to be able to predict an estimate of the upper and lower bounds for solar flux within its predictable zones. Naturally, it is an important task to identify the time horizons beyond which predictability becomes incompatible with computability.

Ashrafi, S.↗
NASA NTRS1991

Evidence of chaotic pattern in solar flux through a reproducible sequence of period-doubling-type bifurcations

A preliminary study of the limits to solar flux intensity prediction, and of whether the general lack of predictability in the solar flux arises from the nonlinear chaotic nature of the Sun's physical activity is presented. Statistical analysis of a chaotic signal can extract only its most gross features, and detailed physical models fail, since even the simplest equations of motion for a nonlinear system can exhibit chaotic behavior. A recent theory by Feigenbaum suggests that nonlinear systems that can be led into chaotic behavior through a sequence of period-doubling bifurcations will exhibit a universal behavior. As the control parameter is increased, the bifurcation points occur in such a way that a proper ratio of these will approach the universal Feigenbaum number. Experimental evidence supporting the applicability of the Feigenbaum scenario to solar flux data is sparse. However, given the hypothesis that the Sun's convection zones are similar to a Rayleigh-Bernard mechanism, we can learn a great deal from the remarkable agreement observed between the prediction by theory (period doubling - a universal route to chaos) and the amplitude decrease of the signal's regular subharmonics. It is shown that period-doubling-type bifurcation is a possible route to a chaotic pattern of solar flux that is distinguishable from the logarithm of its power spectral density. This conclusion is the first positive step toward a reformulation of solar flux by a nonlinear chaotic approach. The ultimate goal of this research is to be able to predict an estimate of the upper and lower bounds for solar flux within its predictable zones. Naturally, it is an important task to identify the time horizons beyond which predictability becomes incompatible with computability.

Ashrafi, S.↗
NASA NTRS1994

Evolution of the Earth-Moon system

The tidal evolution of the Earth-Moon system is reexamined. Several models of tidal friction are first compared in an averaged Hamiltonian formulation of the dynamics. With one of these models, full integrations of the tidally evolving Earth-Moon system are carried out in the complete, fully interacting, and chaotically evolving planetary system. Classic results on the history of the lunar orbit are confirmed by our more general model. A detailed history of the obliquity of the Earth which takes into account the evolving lunar orbit is presented.

Touma, Jihad↗
NASA NTRS2016

Chaos in Kepler's Multiple Planet Systems and K2s Observations of the Atmospheres of Uranus Neptune

More than one-third of the 4700 planet candidates found by NASA's Kepler spacecraft during its prime mission are associated with target stars that have more than one planet candidate, and such "multis" account for the vast majority of candidates that have been verified as true planets. The large number of multis tells us that flat multiplanet systems like our Solar System are common. Virtually all of the candidate planetary systems are stable, as tested by numerical integrations that assume a physically motivated mass-radius relationship, but some of the systems lie in chaotic regions close to instability. The characteristics of some of the most interesting confirmed Kepler multi-planet systems will be discussed. The Kepler spacecraft's 'second life' in theK2 mission has allowed it to obtain long time-series observations of Solar System targets, including the giant planets Uranus & Neptune. These observations show variability caused by the chaotic weather patterns on Uranus & Neptune.

planet candidates↗
NASA NTRS2008

Jet Propulsion Laboratory: Annual Report 2007

Many milestones are celebrated in the business of space exploration, but one of them that arrived this year has particular meaning for us. Half a century ago, on January 31, 1958, the Jet Propulsion Laboratory was responsible for creating America's first satellite, Explorer 1, and joined with the Army to launch it into orbit. That makes 2007 the 50th year we have been sending robotic craft from Earth to explore space. No other event before or since has had such a profound effect on JPL's basic identity, setting it on the path to become the world's leader in robotic solar system exploration. It is not lost on historians that Explorer 1, besides being America's first satellite, was also the first spacecraft from any country to deliver scientific results in its case, the discovery of the Van Allen Radiation Belts that surround Earth. Science, of course, has been the prime motivator for all the dozens of missions that we have lofted into space in the half-century since then. JPL has sent spacecraft to every planet in the solar system from Mercury to Neptune, some of them very sophisticated machines. But in one way or another, they all owe their heritage to the 31-pound bullet-shaped probe JPL shot into space in 1958. Although we have ranged far and wide across the solar system, we have a very strong contingent of satellites and instruments dedicated, like Explorer, to the environment of our home planet. JPL missions have been providing much of the data to establish the facts of global warming - most especially, the melting of ice sheets in Greenland and Antarctica. During the past year, JPL and our parent organization, the California Institute of Technology, have created a task force to focus the special capabilities of the Laboratory and campus on ways to better understand the physics of global change. While Earth is a chaotic and dynamic system capable of large natural variations, evidence is mounting that human activities are playing an increasingly important role. A central piece of this effort is a search for novel energy sources to replace fossil fuels, the combustion of which adds carbon dioxide to our atmosphere. All of this is supported by our worldwide Deep Space Network, which provides the communication link between spacecraft and the ground. In addition, missions are infused with technologies developed by researchers working on projects for non-NASA sponsors as well as on pure research.

Jet Propulsion Laboratory (JPL)↗
NASA NTRS1985

Volcano/ground ice interactions in Elysium Planitia, Mars

The occurrence within Elysium Planitia of meltwater deposits, possible pseudocraters, collapse features within troughs, and outflow channels indicates that a layer of subsurface volatiles existed at the time of volcanic activity within this area. The pseudocraters are interpreted to be indicators of near-surface volatiles, while meltwater deposits and the degree of preservation of trough walls and floors are thought to signify greater volatile depths. A latitudinal variation in the distribution of these features indicates either that the depth to the volatile layer increased from less than about 50 m at 35 deg N to greater than 600 m at 24 deg N, or that an ice wedge that existed at 35 deg N thinned to nonexistence at 24 deg N. Braided distributary channel systems within the chaotic terrain north of Elysium Planitia show that ephemeral lakes were repeatedly created and drained at this locality. The existence of volatiles contemporaneous with volcanic activity permits a search to be made for explosively generated landforms predicted to exist by previous theoretical models. Morphological evidence for strombolian, vulcanian and plinian eruptions is lacking within western Elysium Planitia; there are no identifiable cinder cones, pyroclastic flow deposits, or mantled areas indicative of large airfall deposits at an image resolution of 50-150 m/pixel. However, the pseudocraters indicate that small-scale phreatomagmatic activity may have taken place.

Mouginis-Mark, P. J.↗
NASA NTRS1991

Plasma transport in the Io torus - The importance of microscopic diffusion

This paper considers the question of whether the distribution of mass in the Io plasma torus is consistent with the concept of interchange eddy transport. Specifically, the flux tube content exhibits a gradual decrease with increasing radial distance from the source near Io without any evidence for substantial density irregularity associated with the plasma source or loss. Using a simple one-dimensional numerical model to simulate macroscopic interchange eddy transport, it is demonstrated that this smooth equilibrium distribution of mass can occur but only with the inclusion of a minimal level of small scale microscopic mixing at a rate approaching Bohm diffusion. Otherwise, the system exhibits a chaotic appearance which never approaches an equilibrium distribution. Various physical mechanisms for the microscopic diffusion process which is required to provide a sufficiently rapid mixing of material between the macroscopic eddies are discussed.

Mei, YI↗
NASA NTRS1996

Intraseasonal and Interannual Variability of Mars Present Climate

This is a Final Report for a Joint Research Interchange (JRI) between NASA Ames Research Center and San Jose State University, Department of Meteorology. The focus of this JRI has been to investigate the nature of intraseasonal and interannual variability of Mars'present climate. We have applied a three-dimensional climate model based on the full hydrostatic primitive equations to determine the spatial, but primarily, the temporal structures of the planet's large-scale circulation as it evolves during a given seasonal advance, and, over multi-annual cycles. The particular climate model applies simplified physical parameterizations and is computationally efficient. It could thus easily be integrated in a perpetual season or advancing season configuration, as well as over many Mars years. We have assessed both high and low-frequency components of the circulation (i.e., motions having periods of Omicron(2-10 days) or greater than Omicron(10 days), respectively). Results from this investigation have explored the basic issue whether Mars' climate system is naturally 'chaotic' associated with nonlinear interactions of the large-scale circulation-regardless of any allowance for year-to-year variations in external forcing mechanisms. Titles of papers presented at scientific conferences and a manuscript to be submitted to the scientific literature are provided. An overview of a areas for further investigation is also presented.

Hollingsworth, Jeffery L.↗
NASA NTRS2002

Nonlinear Dynamic Models in Advanced Life Support

To facilitate analysis, ALS systems are often assumed to be linear and time invariant, but they usually have important nonlinear and dynamic aspects. Nonlinear dynamic behavior can be caused by time varying inputs, changes in system parameters, nonlinear system functions, closed loop feedback delays, and limits on buffer storage or processing rates. Dynamic models are usually cataloged according to the number of state variables. The simplest dynamic models are linear, using only integration, multiplication, addition, and subtraction of the state variables. A general linear model with only two state variables can produce all the possible dynamic behavior of linear systems with many state variables, including stability, oscillation, or exponential growth and decay. Linear systems can be described using mathematical analysis. Nonlinear dynamics can be fully explored only by computer simulations of models. Unexpected behavior is produced by simple models having only two or three state variables with simple mathematical relations between them. Closed loop feedback delays are a major source of system instability. Exceeding limits on buffer storage or processing rates forces systems to change operating mode. Different equilibrium points may be reached from different initial conditions. Instead of one stable equilibrium point, the system may have several equilibrium points, oscillate at different frequencies, or even behave chaotically, depending on the system inputs and initial conditions. The frequency spectrum of an output oscillation may contain harmonics and the sums and differences of input frequencies, but it may also contain a stable limit cycle oscillation not related to input frequencies. We must investigate the nonlinear dynamic aspects of advanced life support systems to understand and counter undesirable behavior.

Jones, Harry↗
NASA NTRS1985

Markov-Tree model of intrinsic transport in Hamiltonian systems

A particle in a chaotic region of phase space can spend a long time near the boundary of a regular region since transport there is slow. This 'stickiness' of regular regions is thought to be responsible for previous observations in numerical experiments of a long-time algebraic decay of the particle survival probability, i.e., survival probability approximately t to the (-z) power for large t. This paper presents a global model for transport in such systems and demonstrates the essential role of the infinite hierarchy of small islands interspersed in the chaotic region. Results for z are discussed.

Meiss, J. D.↗
NASA NTRS2002

Solar System Dynamics

In these 18 years, the research has touched every major dynamical problem in the solar system, including: the effect of chaotic zones on the distribution of asteroids, the delivery of meteorites along chaotic pathways, the chaotic motion of Pluto, the chaotic motion of the outer planets and that of the whole solar system, the delivery of short period comets from the Kuiper belt, the tidal evolution of the Uranian arid Galilean satellites, the chaotic tumbling of Hyperion and other irregular satellites, the large chaotic variations of the obliquity of Mars, the evolution of the Earth-Moon system, and the resonant core- mantle dynamics of Earth and Venus. It has introduced new analytical and numerical tools that are in widespread use. Today, nearly every long-term integration of our solar system, its subsystems, and other solar systems uses algorithms that was invented. This research has all been primarily Supported by this sequence of PGG NASA grants. During this period published major investigations of tidal evolution of the Earth-Moon system and of the passage of the Earth and Venus through non-linear core-mantle resonances were completed. It has published a major innovation in symplectic algorithms: the symplectic corrector. A paper was completed on non-perturbative hydrostatic equilibrium.

Wisdom, Jack↗
NASA NTRS1994

Topological analysis of chaotic orbits: Revisiting Hyperion

There is emerging interest in the possibility of chaotic evolution in astrophysical systems. To mention just one example, recent well-sampled ground-based observations of the Saturian satellite Hyperion strongly suggest that it is exhibiting chaotic behavior. We present a general technique, the method of close returns, for the analysis of data from astronomical objects believed to be exhibiting chaotic motion. The method is based on the extraction of pieces of the evolution that exhibit nearly periodic behavior-episodes during which the object stays near in phase space to some unstable periodic orbit. Such orbits generally act as skeletal features, tracing the topological organization of the manifold on which the chaotic dynamics takes place. This method does not require data sets as lengthy as other nonlinear analysis techniques do and is therefore well suited to many astronomical observing programs. Well sampled data covering between twenty and forty characteristic periods of the system have been found to be sufficient for the application of this technique. Additional strengths of this method are its robustness in the presence of noise and the ability for a user to clearly distinguish between periodic, random, and chaotic behavior by inspection of the resulting two-dimensional image. As an example of its power, we analyze close returns in a numerically generated data set, based on a model for Hyperion extensively studied in the literature, corresponding to nightly observations of the satellite. We show that with a small data set, embedded unstable periodic orbits can be extracted and that these orbits can be responsible for nearly periodic behavior lasting a substantial fraction of the observing run.

Boyd, Patricia T.↗
NASA NTRS1986

Is there a single origin of life?

The emergence of the first life on the earth is now established as an early event, closely related to the evolving earth. Lack of knowledge of the primitive terrestrial conditions contemporary with the evolving prebolic organic chemistry limits reconstruction techniques. The primitive earth's aqueous history is essential to unraveling this problem. Based on current knowledge of other planets of the solar system, no close analog to the early earth can be expected. It is still not known if there was a second origin or if only earth has life. This may depend upon the question of the survival of information-bearing chemical systems in a dynamic or chaotic environment and the chemical protection afforded within such a system. Water is the central molecule of controversy: the blessing and the curse of the chemist. New and novel chemical mechanisms and systems abound.

Soffen, Gerald A.↗
NASA NTRS1981

Chaotic behavior and fluid dynamics

It is shown that while fluids are very complicated systems having many degrees of freedom, the basic mechanism underlying the observed chaotic behavior of fluid turbulence may not require the consideration of many degrees of freedom. Simple dynamical systems display erratic and chaotic behavior reminiscent of turbulence, the key to which is the 'sensitivity to initial conditions' introduced by Ruelle (1978). Simple models which are sensitive to initial data and have permitted workers to study chaotic behavior are described, with attention to the Lorenz equations, Landau's idea of a continuous transition to turbulence via an infinite cascade of bifurcations, and one-dimensional maps.

Yorke, J. A.↗
NASA NTRS1994

Terminal Model Of Newtonian Dynamics

Paper presents study of theory of Newtonian dynamics of terminal attractors and repellers, focusing on issues of reversibility vs. irreversibility and deterministic evolution vs. probabilistic or chaotic evolution of dynamic systems. Theory developed called "terminal dynamics" emphasizes difference between it and classical Newtonian dynamics. Also holds promise for explaining irreversibility, unpredictability, probabilistic behavior, and chaos in turbulent flows, in thermodynamic phenomena, and in other dynamic phenomena and systems.

Zak, Michail↗
NASA NTRS1989

Chaotic Motion Of A Two-Link Planar Mechanism

Report discusses global instability in orbital motion of two-link planar mechanism. Principal objective, contributes to understanding of chaotic motions in robot manipulators and other deterministic mechanical systems. Discussion begins with brief review of previous studies of chaotic motion and introduces notion of orbital instability in nonlinear systems. Introduces geometric approach useful in representation of orbital instability.

Lokshin, Anatoly↗
NASA NTRS1984

Nonlinear problems in flight dynamics

A comprehensive framework is proposed for the description and analysis of nonlinear problems in flight dynamics. Emphasis is placed on the aerodynamic component as the major source of nonlinearities in the flight dynamic system. Four aerodynamic flows are examined to illustrate the richness and regularity of the flow structures and the nature of the flow structures and the nature of the resulting nonlinear aerodynamic forces and moments. A framework to facilitate the study of the aerodynamic system is proposed having parallel observational and mathematical components. The observational component, structure is described in the language of topology. Changes in flow structure are described via bifurcation theory. Chaos or turbulence is related to the analogous chaotic behavior of nonlinear dynamical systems characterized by the existence of strange attractors having fractal dimensionality. Scales of the flow are considered in the light of ideas from group theory. Several one and two degree of freedom dynamical systems with various mathematical models of the nonlinear aerodynamic forces and moments are examined to illustrate the resulting types of dynamical behavior. The mathematical ideas that proved useful in the description of fluid flows are shown to be similarly useful in the description of flight dynamic behavior.

Chapman, G. T.↗
NASA NTRS1992

Combustion noise and combustion instabilities in propulsion systems

This paper is concerned with some aspects of non-linear behavior of unsteady motions in combustion chambers. The emphasis is on conditions under which organized oscillations having discrete frequencies may exist in the presence of random motions. In order to treat the two types of motions together, and particularly to investigate coupling between noise and combustion instabilities, the unsteady field is represented as a synthesis of acoustic modes having time-varying amplitudes. Each of the amplitudes are written as the sum of two parts, one associated with the random field and the remainder representing the organized oscillations. After spatial averaging, the general problem is reduced to solution of a set of second-order ordinary differential equations whose structure depends on the sorts of nonlinear processes accounted for. This formulation accommodates any physical process; in particular, terms are included to represent noise sources, although only limited modeling is discussed. Our results suggest that random sources of noise have only small effects on combustion instabilities and seem not to be a cause of unstable motions. However, the coupling between the two sorts of unsteady motions may be important as an essential process in a proposed scheme for noise control. It is now a familiar observation that many nonlinear deterministic systems are capable of exhibiting apparently random motions called 'chaos.' This is a particularly interesting possibility for systems which also executed non-deterministic random motions. In combustion chambers, a nonlinear deterministic system (acoustical motions) exists in the presence of noise produced by flow separation, turbulent motions, and energy released by combustion processes. The last part of the paper is directed to the matter of discovering whether or not chaotic motions exist in combustion systems. Analysis has not progressed sufficiently far to answer the question. We report here recent results of processing data taken in one combustor to determine the dimensions of any attractors in the motions. No evidence has been found for chaos in the strict sense, but the method seems to be an important means of investigating the nonlinear behavior of combustion systems.

F. E. C. Culick↗