Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “chaotic systems”

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 73 records · Page 4

Section on Observed Impacts on El Nino

Agricultural applications of El Nino forecasts are already underway in some countries and need to be evaluated or re-evaluated. For example, in Peru, El Nino forecasts have been incorporated into national planning for the agricultural sector, and areas planted with rice and cotton (cotton being the more drought-tolerant crop) are adjusted accordingly. How well are this and other such programs working? Such evaluations will contribute to the governmental and intergovernmental institutions, including the Inter-American Institute for Global Change Research and the US National Ocean and Atmospheric Agency that are fostering programs to aid the effective use of forecasts. As El Nino climate forecasting grows out of the research mode into operational mode, the research focus shifts to include the design of appropriate modes of utilization. Awareness of and sensitivity to the costs of prediction errors also grow. For example, one major forecasting model failed to predict the very large El Nino event of 1997, when Pacific sea-surface temperatures were the highest on record. Although simple correlations between El Nino events and crop yields may be suggestive, more sophisticated work is needed to understand the subtleties of the interplay among the global climate system, regional climate patterns, and local agricultural systems. Honesty about the limitations of an forecast is essential, especially when human livelihoods are at stake. An end-to-end analysis links tools and expertise from the full sequence of ENSO cause-and-effect processes. Representatives from many disciplines are needed to achieve insights, e.g, oceanographers and atmospheric scientists who predict El Nino events, climatologists who drive global climate models with sea-surface temperature predictions, agronomists who translate regional climate connections in to crop yield forecasts, and economists who analyze market adjustments to the vagaries of climate and determine the value of climate forecasts. Methods include historical studies to understand past patterns and to test hindcasts of the prediction tools, crop modeling, spatial analysis and remote sensing. This research involves expanding, deepening, and applying the understanding of physical climate to the fields of agronomy and social science; and the reciprocal understanding of crop growth and farm economics to climatology. Delivery of a regional climate forecast with no information about how the climate forecast was derived limits its effectiveness. Explanation of a region's major climate driving forces helps to place a seasonal forecast in context. Then, a useful approach is to show historical responses to previous El Nino events, and projections, with uncertainty intervals, of crop response from dynamic process crop growth models. Regional ID forecasts should be updated with real-time weather conditions. Since every El Nino event is different, it is important to track, report and advise on each new event as it unfolds. The stability of human enterprises depends on understanding both the potentialities and the limits of predictability. Farmers rely on past experience to anticipate and respond to fluctuations in the biophysical systems on which their livelihoods depend. Now scientists are improving their ability to predict some major elements of climate variability. The improvements in the reliability of El Nino forecasts are encouraging, but seasonal forecasts for agriculture are not, and will probably never be completely infallible, due to the chaotic nature of the climate system. Uncertainties proliferate as we extend beyond Pacific sea-surface temperatures to climate teleconnections and agricultural outcomes. The goal of this research is to shed as a clear light as possible on these inherent uncertainties and thus to contribute to the development of appropriate responses to El Nino and other seasonal forecasts for a range of stakeholders, which, ultimately, includes food consumers everywhere.

Rosenzweig, Cynthia↗

Variations of the Milankovitch frequencies in time

The sensitivity of the amplitudes and frequencies in the development of the Earth's orbital and rotational elements involved in the astronomical theory of paleoclimates (eccentricity, obliquity, and climate precession), to the Earth-Moon distance and consequently to the length of the day and to the dynamical ellipticity of the Earth has been discussed for the last billions of years. The shortening of the Earth-Moon distance and of the length of the day, as well as the lengthening of the dynamical ellipticity of the Earth back in time induce a shortening of the fundamental astronomical periods for precession and obliquity. At the same time, the amplitudes of the different terms in the development of the obliquity are undergoing a relative enlargement of about 50 percent at 2 x 10(exp 9) yr BP but the independent term is increasing very weakly (less than 0.1 percent). In other words, the value of the obliquity, which lies within a range of 21.7 to 24.9 deg over the Quarternary was restricted to a range of 22.5 to 24.1 deg at 2 x 10(exp 9) yr BP. On the other hand, the amplitudes in the development of the climatic precession do not change. Moreover, these changes in the frequencies and amplitudes for both obliquity and climatic precession are larger for longer period terms. Finally, the periods in the eccentricity development are not influenced by the variation of the lunar distance. But the motion of the solar system, especially of the inner planets, was shown to be chaotic. It means that it is impossible to compute the exact motion of the planets over more than about 100 Myr, and the fundamental frequencies of the systems are not fixed quantities, but are slowly varying with time. As long as we consider the most important terms, the maximum deviation from the present-day value of the 19-kyr precessional period due to the chaotic motion of the solar system only does not reach more than a few tens of years around 80 Myr BP. Therefore the shortening of the obliquity and climatic precession periods is mostly driven by the change in the lunar distance and the consequent variations in the dynamical ellipticity of the Earth's angular speed. At first sight, the deviation in the period for the eccentricity can be neglected, as the chaotic behavior of the solar system implies a relative change of the main periods by less than 0.2 percent, 1.4 percent, and 1.9 percent respectively, this maximum change being achieved around 80 Myr BP. This implies, in particular, that the eccentricity periods for Quarternary climate studies may be considered more or less constant for pre-Quaternay times and equal to their Quaternary values.

Loutre, Marie-France↗

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↗

Dynamic Modeling of Off-Nominal Operation in Advanced Life Support Systems

System failures, off-nominal operation, or unexpected interruptions in processing capability can cause unanticipated instabilities in Advanced Life Support (ALS) systems, even long after they are repaired. Much current modeling assumes ALS systems are static and linear, but ALS systems are actually dynamic and nonlinear, especially when failures and off nominal operation are considered. Modeling and simulation provide a way to study the stability and time behavior of nonlinear dynamic ALS systems under changed system configurations or operational scenarios. The dynamic behavior of a nonlinear system can be fully explored only by computer simulation over the full range of inputs and initial conditions. Previous simulations of BIO-Plex in SIMULINK, a toolbox of Matlab, were extended to model the off-nominal operation and long-term dynamics of partially closed physical/chemical and bioregenerative life support systems. System nonlinearity has many interesting potential consequences. Different equilibrium points may be reached for different initial conditions. The system stability can depend on the exact system inputs and initial conditions. The system may oscillate or even in rare cases behave chaotically. Temporary internal hardware failures or external perturbations in ALS systems can lead to dynamic instability and total ALS system failure. Appropriate control techniques can restore reliable operation and minimize the effects of dynamic instabilities due to anomalies or perturbations in a life support system.

Jones, Harry↗

The rotation of Hyperion

For almost the entire range of dimensions of Hyperion allowed by uncertainties in the observations, the satellite cannot librate stably about a rotation rate which is synchronous with its orbital mean motion. Rather, the large gravitational torques on the asymmetric satellite coupled with the large eccentricity forced by the orbital resonance with Titan cause Hyperion to tumble in a random manner. Large changes in orientation of body axes relative to inertial space and in the instantaneous spin rate occur on timescales of the order of the orbit period. Numerical evaluation of the exponential divergence of nearby trajectories in the phase space of the motion verifies that the tumbling is truly chaotic. This newly defined state of chaotic rotation for Hyperion is likely to be the only example of confined, continuously observable chaotic motion in the solar system.

Peale, S. J.↗

Deterministic representation of chaos with application to turbulence

Chaotic motions of nonlinear dynamical systems are decomposed into mean components and fluctuations. The approach is based upon the concept that the fluctuations driven by the instability of the original (unperturbed) motion grow until a new stable state is approached. The Reynolds-type equations written for continuous as well as for finite-degrees-of-freedom dynamical systems are closed by using this stabilization principle. The theory is applied to conservative systems, to strange attractors and to turbulent motions.

Zak, M.↗

Dynamics of coorbital satellite rings

The dynamical behavior of a coorbital satellite ring is studied for N = 2-9 satellites, in terms of a simplified dynamical description, in which the motion is reduced to the separation angles between satellites. The number and stability of different kinds of stationary configurations is explored, revealing that equally spaced rings are not stable against small perturbations for N not greater than 6, while for N = 2-8 there exists another, stable compact solution. Integrations of exact equations confirm these results. Moreover, the systems are found to display chaotic characteristics for a certain range of energy. The behavior can be interpreted in terms of maximum velocity curves, defining the allowed region of the motion in the phase space.

Salo, H.↗

Nonlinear rotordynamics analysis

Effective analysis tools were developed for predicting the nonlinear rotordynamic behavior of the Space Shuttle Main Engine (SSME) turbopumps under steady and transient operating conditions. Using these methods, preliminary parametric studies were conducted on both generic and actual HPOTP (high pressure oxygen turbopump) models. In particular, a novel modified harmonic balance/alternating Fourier transform (HB/AFT) method was developed and used to conduct a preliminary study of the effects of fluid, bearing and seal forces on the unbalanced response of a multi-disk rotor in the presence of bearing clearances. The method makes it possible to determine periodic, sub-, super-synchronous and chaotic responses of a rotor system. The method also yields information about the stability of the obtained response, thus allowing bifurcation analyses. This provides a more effective capability for predicting the response under transient conditions by searching in proximity of resonance peaks. Preliminary results were also obtained for the nonlinear transient response of an actual HPOTP model using an efficient, newly developed numerical method based on convolution integration. Currently, the HB/AFT is being extended for determining the aperiodic response of nonlinear systems. Initial results show the method to be promising.

Noah, Sherif T.↗

A hybrid electromagnetic-acoustic levitator for the containerless processing of undercooled melts

The hybrid, acoustic-EM levitator discussed provides a small lifting force independently of its EM component by exciting an acoustic resonance that serves as a pressure node at the position of the EM-levitated specimen. The system also stabilizes and damps chaotic oscillations during specimen positioning, and can excite forced oscillations of levitated molten metals for drop-physics and thermophysical property measurements. Attention is given to the character and function of the atmosphere in the levitator. Noncontact temperature measurement is via single-color optical pyrometer.

Hmelo, Anthony B.↗

Stochastic Representation of Chaos using Terminal Attractors

A nonlinear version of the Liouville equation based upon terminal attractors is proposed for describing post-instability motions of dynamical systems with exponential divergence of trajectories such as those leading to chaos and turbulence. As a result, the post-instability motions are represented by expectations, variances, and higher moments of the state variables as functions of time. The proposed approach can be applied to conservative chaos, and in particular, to n-bodies problem, as well as to dissipative systems, and in particular, to chaotic attractors and turbulence.

stochastic processes↗

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.↗

Studies in astronomical time series analysis. IV - Modeling chaotic and random processes with linear filters

While chaos arises only in nonlinear systems, standard linear time series models are nevertheless useful for analyzing data from chaotic processes. This paper introduces such a model, the chaotic moving average. This time-domain model is based on the theorem that any chaotic process can be represented as the convolution of a linear filter with an uncorrelated process called the chaotic innovation. A technique, minimum phase-volume deconvolution, is introduced to estimate the filter and innovation. The algorithm measures the quality of a model using the volume covered by the phase-portrait of the innovation process. Experiments on synthetic data demonstrate that the algorithm accurately recovers the parameters of simple chaotic processes. Though tailored for chaos, the algorithm can detect both chaos and randomness, distinguish them from each other, and separate them if both are present. It can also recover nonminimum-delay pulse shapes in non-Gaussian processes, both random and chaotic.

Scargle, Jeffrey D.↗

Lyapunov exponents for infinite dimensional dynamical systems

Classically it was held that solutions to deterministic partial differential equations (i.e., ones with smooth coefficients and boundary data) could become random only through one mechanism, namely by the activation of more and more of the infinite number of degrees of freedom that are available to such a system. It is only recently that researchers have come to suspect that many infinite dimensional nonlinear systems may in fact possess finite dimensional chaotic attractors. Lyapunov exponents provide a tool for probing the nature of these attractors. This paper examines how these exponents might be measured for infinite dimensional systems.

Mhuiris, Nessan Mac Giolla↗

Evidence for chaotic fault interactions in the seismicity of the San Andreas fault and Nankai trough

The dynamical behavior introduced by fault interactions is examined here using a simple spring-loaded, slider-block model with velocity-weakening friction. The model consists of two slider blocks coupled to each other and to a constant-velocity driver by elastic springs. For an asymmetric system in which the frictional forces on the two blocks are not equal, the solutions exhibit chaotic behavior. The system's behavior over a range of parameter values seems to be generally analogous to that of weakly coupled segments of an active fault. Similarities between the model simulations and observed patterns of seismicity on the south central San Andreas fault in California and in the Nankai trough along the coast of southwestern Japan.

Huang, Jie↗

Linking "Smart" Modules by a Single Channel

System architecture brings order to potentially chaotic situation. New configuration allows many "smart" modules (each containing memory and microprocessor) to be linked by common data channel. Architecture allows each module to carry on operations at own data rate within block of time, while communications between modules occur in strict synchronism.

Kohl, W. H.↗

Demonstration of Detection and Ranging Using Solvable Chaos

Acoustic experiments demonstrate a novel approach to ranging and detection that exploits the properties of a solvable chaotic oscillator. This nonlinear oscillator includes an ordinary differential equation and a discrete switching condition. The chaotic waveform generated by this hybrid system is used as the transmitted waveform. The oscillator admits an exact analytic solution that can be written as the linear convolution of binary symbols and a single basis function. This linear representation enables coherent reception using a simple analog matched filter and without need for digital sampling or signal processing. An audio frequency implementation of the transmitter and receiver is described. Successful acoustic ranging measurements are presented to demonstrate the viability of the approach.

Corron, Ned J.↗

The Frequency of Giant Impacts on Earth-Like Worlds

The late stages of terrestrial planet formation are dominated by giant impacts that collectively influence the growth, composition, and habitability of any planets that form. Hitherto, numerical models designed to explore these late stage collisions have been limited by assuming that all collisions lead to perfect accretion, and many of these studies lack the large number of realizations needed to account for the chaotic nature of N-body systems. We improve on these limitations by performing 280 simulations of planet formation around a Sun-like star, half of which used an N-body algorithm that has recently been modified to include fragmentation and hit-and-run (bouncing) collisions. We find that when fragmentation is included, the final planets formed are comparable in terms of mass and number; however, their collision histories differ significantly and the accretion time approximately doubles. We explored impacts onto Earth-like planets, which we parameterized in terms of their specific impact energies. Only 15 of our 164 Earth-analogs experienced an impact that was energetic enough to strip an entire atmosphere. To strip about half of an atmosphere requires energies comparable to recent models of the Moon-forming giant impact. Almost all Earth-analogs received at least one impact that met this criteria during the 2 Gyr simulations and the median was three giant impacts. The median time of the final giant impact was 43 Myr after the start of the simulations, leading us to conclude that the time-frame of the Moon-forming impact is typical among planetary systems around Sun-like stars.

terrestrial planet formation↗

Chaos in the Solar System

The physical basis of chaos in the solar system is now better understood: In all cases investigated so far, chaotic orbits result from overlapping resonances. Perhaps the clearest examples are found in the asteroid belt. Overlapping resonances account for its kirkwood gaps and were used to predict and find evidence for very narrow gaps in the outer belt. Further afield, about one new "short-peroid" comet is discovered each year. They are believed to come from the "Kuiper Belt" (at 40 AU or more) via chaotic orbits produced by mean-motion and secular resonances with Neptune. Finally, the planetary system itself is not immune from chaos. In the inner solar system, overlapping secular resonances have been identified as the possible source of chaos. For example, Mercury in 1012 years, may suffer a close encounter with Venus or plunge into the Sun. In the outer solar system, three-body resonances have been identified as a source of chaos, but on an even longer time scale of 109 times the age of the solar system. On the human time scale, the planets do follow their orbits in a stately procession, and we can predict their trajectories for hundreds of thousands of years. That is because the mavericks, with shorter instability times, have long since been ejected. The solar system is not stable; it is just old!

Lecar, Myron↗