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All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Dimensional analysis of acoustically propagated signals

Traditionally, long term measurements of atmospherically propagated sound signals have consisted of time series of multiminute averages. Only recently have continuous measurements with temporal resolution corresponding to turbulent time scales been available. With modern digital data acquisition systems we now have the capability to simultaneously record both acoustical and meteorological parameters with sufficient temporal resolution to allow us to examine in detail relationships between fluctuating sound and the meteorological variables, particularly wind and temperature, which locally determine the acoustic refractive index. The atmospheric acoustic propagation medium can be treated as a nonlinear dynamical system, a kind of signal processor whose innards depend on thermodynamic and turbulent processes in the atmosphere. The atmosphere is an inherently nonlinear dynamical system. In fact one simple model of atmospheric convection, the Lorenz system, may well be the most widely studied of all dynamical systems. In this paper we report some results of our having applied methods used to characterize nonlinear dynamical systems to study the characteristics of acoustical signals propagated through the atmosphere. For example, we investigate whether or not it is possible to parameterize signal fluctuations in terms of fractal dimensions. For time series one such parameter is the limit capacity dimension. Nicolis and Nicolis were among the first to use the kind of methods we have to study the properties of low dimension global attractors.

Hansen, Scott D.↗
NASA NTRS1995

Lyapunov exponents from CHUA's circuit time series using artificial neural networks

In this paper we present the general problem of identifying if a nonlinear dynamic system has a chaotic behavior. If the answer is positive the system will be sensitive to small perturbations in the initial conditions which will imply that there is a chaotic attractor in its state space. A particular problem would be that of identifying a chaotic oscillator. We present an example of three well known different chaotic oscillators where we have knowledge of the equations that govern the dynamical systems and from there we can obtain the corresponding time series. In a similar example we assume that we only know the time series and, finally, in another example we have to take measurements in the Chua's circuit to obtain sample points of the time series. With the knowledge about the time series the phase plane portraits are plotted and from them, by visual inspection, it is concluded whether or not the system is chaotic. This method has the problem of uncertainty and subjectivity and for that reason a different approach is needed. A quantitative approach is the computation of the Lyapunov exponents. We describe several methods for obtaining them and apply a little known method of artificial neural networks to the different examples mentioned above. We end the paper discussing the importance of the Lyapunov exponents in the interpretation of the dynamic behavior of biological neurons and biological neural networks.

Gonzalez, J. Jesus↗
NASA NTRS1994

Bias properties of extragalactic distance indicators. 3: Analysis of Tully-Fisher distances for the Mathewson-Ford-Buchhorn sample of 1355 galaxies

The observational selection bias properties of the large Mathewson-Ford-Buchhorn (MFB) sample of axies are demonstrated by showing that the apparent Hubble constant incorrectly increases outward when determined using Tully-Fisher (TF) photometric distances that are uncorreted for bias. It is further shown that the value of H(sub 0) so determined is also multivlaued at a given redshift when it is calculated by the TF method using galaxies with differenct line widths. The method of removing this unphysical contradiction is developed following the model of the bias set out in Paper II. The model developed further here shows that the appropriate TF magnitude of a galaxy that is drawn from a flux-limited catalog not only is a function of line width but, even in the most idealistic cases, requires a triple-entry correction depending on line width, apparent magnitude, and catalog limit. Using the distance-limited subset of the data, it is shown that the mean intrinsic dispersion of a bias-free TF relation is high. The dispersion depends on line width, decreasing from sigma(M) = 0.7 mag for galaxies with rotational velocities less than 100 km s(exp-1) to sigma(M) = 0.4 mag for galaxies with rotational velocities greater than 250 km s(exp-1). These dispersions are so large that the random errors of the bias-free TF distances are too gross to detect any peculiar motions of individual galaxies, but taken together the data show again the offset of 500 km s(exp-1) fond both by Dressler & Faber and by MFB for galaxies in the direction of the putative Great Attractor but described now in a different way. The maximum amplitude of the bulk streaming motion at the Local Group is approximately 500 km s(exp-1) but the perturbation dies out, approaching the Machian frame defined by the CMB at a distance of approximately 80 Mpc (v is approximately 4000 km s(exp -1)). This decay to zero perturbation at v is approximately 4000 km s(exp -1) argues against existing models with a single attraction at approximately 4500 km s(exp -1) (the Great Attactor model) pulling the local region. Rather, the cause of the perturbation appears to be the well-known clumpy mass distribution within 4000 km s(exp -1) in the busy directions of Hydra, Centaurus, Antila and Dorado, as postulated earlier (Tammann & Sandage 1985).

Federspiel, Martin↗
NASA NTRS1996

Dimension Determination of Precursive Stall Events in a Single Stage High Speed Compressor

This paper presents a study of the dynamics for a single-stage, axial-flow, high speed compressor core, specifically, the NASA Lewis rotor stage 37. Due to the overall blading design for this advanced core compressor, each stage has considerable tip loading and higher speed than most compressor designs, thus, the compressor operates closer to the stall margin. The onset of rotating stall is explained as bifurcations in the dynamics of axial compressors. Data taken from the compressor during a rotating stall event is analyzed. Through the use of a box-assisted correlation dimension methodology, the attractor dimension is determined during the bifurcations leading to rotating stall. The intent of this study is to examine the behavior of precursive stall events so as to predict the entrance into rotating stall. This information may provide a better means to identify, avoid or control the undesirable event of rotating stall formation in high speed compressor cores.

Bright, Michelle M.↗
NASA NTRS1996

Turbulent Fluid Motion 6: Turbulence, Nonlinear Dynamics, 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, 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.

Deissler, Robert G.↗
NASA NTRS2001

Single and Double ITCZ in Aqua-Planet Models with Globally Uniform Sea Surface Temperature and Solar Insolation: An Interpretation

It has been known for more than a decade that an aqua-planet model with globally uniform sea surface temperature and solar insolation angle can generate ITCZ (intertropical convergence zone). Previous studies have shown that the ITCZ under such model settings can be changed between a single ITCZ over the equator and a double ITCZ straddling the equator through one of several measures. These measures include switching to a different cumulus parameterization scheme, changes within the cumulus parameterization scheme, and changes in other aspects of the model design such as horizontal resolution. In this paper an interpretation for these findings is offered. The latitudinal location of the ITCZ is the latitude where the balance of two types of attraction on the ITCZ, both due to earth's rotation, exists. The first type is equator-ward and is directly related to the earth's rotation and thus not sensitive to model design changes. The second type is poleward and is related to the convective circulation and thus is sensitive to model design changes. Due to the shape of the attractors, the balance of the two types of attractions is reached either at the equator or more than 10 degrees away from the equator. The former case results in a single ITCZ over the equator and the latter case a double ITCZ straddling the equator.

Chao, Winston C.↗
NASA NTRS2002

Galvanic Liquid Applied Coating System For Protection of Embedded Steel Surfaces from Corrosion

Corrosion of reinforcing steel in concrete is an insidious problem facing Kennedy Space Center (KSC), other Government Agencies, and the general public. These problems include KSC launch support structures, highway bridge infrastructure, and building structures such as condominium balconies. Due to these problems, the development of a Galvanic Liquid Applied Coating System would be a breakthrough technology having great commercial value for the following industries: Transportation, Infrastructure, Marine Infrastructure, Civil Engineering, and the Construction Industry. This sacrificial coating system consists of a paint matrix that may include metallic components, conducting agents, and moisture attractors. Similar systems have been used in the past with varying degrees of success. These systems have no proven history of effectiveness over the long term. In addition, these types of systems have had limited success overcoming the initial resistance between the concrete/coating interface. The coating developed at KSC incorporates methods proven to overcome the barriers that previous systems could not achieve. Successful development and continued optimization of this breakthrough system would produce great interest in NASA/KSC for corrosion engineering technology and problem solutions. Commercial patents on this technology would enhance KSC's ability to attract industry partners for similar corrosion control applications.

Curran, Joseph↗
NASA NTRS2002

Single and Double ITCZ in Aqua-Planet Models with Globally and Temporally Uniform Sea Surface Temperature and Solar Insolation: An Interpretation

Previous studies (Chao 2000, Chao and Chen 2001, Kirtman and Schneider 2000, Sumi 1992) have shown that, by means of one of several model design changes, the structure of the ITCZ in an aqua-planet model with globally uniform SST and solar angle (U-SST-SA) can change between a single ITCZ at the equator and a double ITCZ straddling the equator. These model design changes include switching to a different cumulus parameterization scheme (e.g., from relaxed Arakawa Schubert scheme (RAS) to moist convective adjustment scheme (MCA)), changes within the cumulus parameterization scheme, and changes in other aspects of the model, such as horizontal resolution. Sometimes only one component of the double ITCZ shows up; but still this is an ITCZ away from the equator, quite distinct from a single ITCZ over the equator. Since these model results were obtained by different investigators using different models which have yielded reasonable general circulation, they are considered as reliable. Chao and Chen (2001; hereafter CC01) have made an initial attempt to interpret these findings based on the concept of rotational ITCZ attractors that they introduced. The purpose of this paper is to offer a more complete interpretation.

Chao, Winston C.↗
NASA NTRS2003

CIZA: The First Systematic X-Ray Search for Clusters of Galaxies Behind the Milky Way

The aim of the CIZA project (Clusters In the Zone of Avoidance) was to take the first step toward a complete X-ray census of clusters of galaxies behind the plane of the Galaxy (the absolute value of b less than or equal to 20 degrees), the historical Zone of Avoidance of optical extragalactic surveys. Finding these heavily obscured clusters in ROSAT All-Sky Survey data would allow us to: 1. Construct the first truly all-sky, statistically complete, X-ray flux limited sample of galaxy clusters; 2. Use this sample to obtain an improved measurement of the cluster dipole (both amplitude and direction); 3. Chart large-scale structure across the plane of the Milky Way as traced by galaxy clusters; 4. Identify potential massive galaxy clusters contributing to the observed large-scale flow pattern in the local universe, specifically in the region around the Great Attractor; and 5. Use least-action modelling to deduce the gravitational fields created by galaxy clusters and compare this reconstruction with the one obtained from local galaxy surveys. Our project was highly successful in demonstrating the feasibility of this undertaking and allowed substantial progress toward achieving the stated science goals.

Ebeling, Harald↗
NASA NTRS2002

Factors Affecting the Latitudinal Location of the Intertropical Convergence Zone in a GCM

The dominant role of the latitudinal peak of the sea surface temperature (SST) in determining the latitudinal location of the intertropical convergence zone (ITCZ) is well-known. However, the roles of the other factors are less well-known and are the topic of this study. These other factors include the inertial stability, the interaction between convection and surface fluxes and the interaction between convection and radiation. Since these interactions involve convection, in a model they involve the cumulus parameterization scheme. These factors are studied with a general circulation model with uniform SST and solar angle. Under the aforementioned model settings, the latitudinal location of the ITCZ is the latitude where the balance of two types of attraction on the ITCZ, both due to earth's rotation, exists. Directly related to the Coriolis parameter, the first type pulls the ITCZ toward the equator and is not sensitive to model design changes. Related to the convective circulation, the second type pulls the ITCZ poleward and is sensitive to model design changes. Due to the shape and the magnitude of the attractors, the balance of the two types of attractions is reached either at the equator or more than 10 degrees away from the equator. The former case results in a single ITCZ over the equator and the latter case a double ITCZ straddling the equator.

Chao, Winston C.↗
NASA NTRS1996

Consumption, supply and transport: self-organization without direct communication

Swimming bacteria of the species Bacillus subtilis require and consume oxygen. In static liquid cultures the cells' swimming behaviour leads them to accumulate up oxygen concentration gradients generated by consumption and supply. Since the density of bacterial cells exceeds that of the fluid in which they live, fluid regions where cells have accumulated are denser than depleted regions. These density variations cause convection. The fluid motion is dynamically maintained by the swimming of the cells toward regions of attraction: the air-fluid interface and the fluctuating advecting attractors, gradients of oxygen concentration that are embedded in the convecting fluid. Because of the fluid dynamical conservation laws, these complex physical and biological factors generate patterns ordered over distances > 10000 bacterial cell diameters. The convection enhances long-range transport and mixing of oxygen, cells and extracellular products by orders of magnitude. Thus, through the interplay of physical and biological factors, a population of undifferentiated selfish cells creates functional dynamic patterns. Populations of bacteria that have organised themselves into regularly patterned regions of vigorous convection and varying cell concentration interact with their environment as if they were one purposeful, coherent multicellular individual. The mathematical and experimental ingredients of these remarkable phenomena are presented here.

Non-NASA Center↗
NASA NTRS2001

Dynamical networks with topological self-organization

Coupled evolution of state and topology of dynamical networks is introduced. Due to the well organized tensor structure, the governing equations are presented in a canonical form, and required attractors as well as their basins can be easily implanted and controlled.

neural net architecture self organizing feature ma↗
NASA NTRS2006

Projecting Future Urbanization with Prescott College's Spatial Growth Model to Promote Environmental Sustainability and Smart Growth, A Case Study in Atlanta, Georgia

Planning is an integral element of good management and necessary to anticipate events not merely respond to them. Projecting the quantity and spatial distribution of urban growth is essential to effectively plan for the delivery of city services and to evaluate potential environmental impacts. The major drivers of growth in large urban areas are increasing population, employment opportunities, and quality of life attractors such as a favorable climate and recreation opportunities. The spatial distribution of urban growth is dictated by the amount and location of developable land, topography, energy and water resources, transportation network, climate change, and the existing land use configuration. The Atlanta region is growing very rapidly both in population and the consumption of forestland or low-density residential development. Air pollution and water availability are significant ongoing environmental issues. The Prescott Spatial Growth Model (SGM) was used to make growth projections for the metropolitan Atlanta region to 2010,2020 and 2030 and results used for environmental assessment in both business as usual and smart growth scenarios. The Prescott SGM is a tool that uses an ESRI ArcView extension and can be applied at the parcel level or more coarse spatial scales and can accommodate a wide range of user inputs to develop any number of growth rules each of which can be weighted depending on growth assumptions. These projections were used in conjunction with meteorological and air quality models to evaluate future environmental impacts. This presentation will focus on the application of the SGM to the 13-County Atlanta Regional Commission planning jurisdiction as a case study. The SGM will be described, including how rule sets are developed and the decision process for allocation of future development to available land use categories. Data inputs required to effectively run the model will be discussed. Spatial growth projections for ten, twenty, and thirty year planning horizons will be presented and results discussed, including regional climate and air quality impacts.

Estes, Maurice G., Jr.↗
NASA NTRS2009

Complexity for Survival of Living Systems

A logical connection between the survivability of living systems and the complexity of their behavior (equivalently, mental complexity) has been established. This connection is an important intermediate result of continuing research on mathematical models that could constitute a unified representation of the evolution of both living and non-living systems. Earlier results of this research were reported in several prior NASA Tech Briefs articles, the two most relevant being Characteristics of Dynamics of Intelligent Systems (NPO- 21037), NASA Tech Briefs, Vol. 26, No. 12 (December 2002), page 48; and Self-Supervised Dynamical Systems (NPO- 30634) NASA Tech Briefs, Vol. 27, No. 3 (March 2003), page 72. As used here, living systems is synonymous with active systems and intelligent systems. The quoted terms can signify artificial agents (e.g., suitably programmed computers) or natural biological systems ranging from single-cell organisms at one extreme to the whole of human society at the other extreme. One of the requirements that must be satisfied in mathematical modeling of living systems is reconciliation of evolution of life with the second law of thermodynamics. In the approach followed in this research, this reconciliation is effected by means of a model, inspired partly by quantum mechanics, in which the quantum potential is replaced with an information potential. The model captures the most fundamental property of life - the ability to evolve from disorder to order without any external interference. The model incorporates the equations of classical dynamics, including Newton s equations of motion and equations for random components caused by uncertainties in initial conditions and by Langevin forces. The equations of classical dynamics are coupled with corresponding Liouville or Fokker-Planck equations that describe the evolutions of probability densities that represent the uncertainties. The coupling is effected by fictitious information-based forces that are gradients of the information potential, which, in turn, is a function of the probability densities. The probability densities are associated with mental images both self-image and nonself images (images of external objects that can include other agents). The evolution of the probability densities represents mental dynamics. Then the interaction between the physical and metal aspects of behavior is implemented by feedback from mental to motor dynamics, as represented by the aforementioned fictitious forces. The interaction of a system with its self and nonself images affords unlimited capacity for increase of complexity. There is a biological basis for this model of mental dynamics in the discovery of mirror neurons that learn by imitation. The levels of complexity attained by use of this model match those observed in living systems. To establish a mechanism for increasing the complexity of dynamics of an active system, the model enables exploitation of a chain of reflections exemplified by questions of the form, "What do you think that I think that you think...?" Mathematically, each level of reflection is represented in the form of an attractor performing the corresponding level of abstraction with more details removed from higher levels. The model can be used to describe the behaviors, not only of biological systems, but also of ecological, social, and economics ones.

Zak, Michail↗
NASA NTRS2010

Turbulence and the Stabilization Principle

Further results of research, reported in several previous NASA Tech Briefs articles, were obtained on a mathematical formalism for postinstability motions of a dynamical system characterized by exponential divergences of trajectories leading to chaos (including turbulence). To recapitulate: Fictitious control forces are introduced to couple the dynamical equations with a Liouville equation that describes the evolution of the probability density of errors in initial conditions. These forces create a powerful terminal attractor in probability space that corresponds to occurrence of a target trajectory with probability one. The effect in ordinary perceived three-dimensional space is to suppress exponential divergences of neighboring trajectories without affecting the target trajectory. Con sequently, the postinstability motion is represented by a set of functions describing the evolution of such statistical quantities as expectations and higher moments, and this representation is stable. The previously reported findings are analyzed from the perspective of the authors Stabilization Principle, according to which (1) stability is recognized as an attribute of mathematical formalism rather than of underlying physics and (2) a dynamical system that appears unstable when modeled by differentiable functions only can be rendered stable by modifying the dynamical equations to incorporate intrinsic stochasticity.

Zak, Michail↗
NASA NTRS2006

NASA Tech Briefs, May 2006

T-Shaped Emitter Metal Structures for HBTs Rigorous Estimation of SNR of a PSK Communication Link Advanced Ka-Band Transceiver With Monopulse Tracking EMI Filters for Low-Temperature Applications Lightweight Electronic Camera for Research on Clouds Pilot Weather Advisor System Waveguide Power-Amplifier Module for 80 to 150 GHz Better Back Contacts for Solar Cells on Flexible Substrates Topics covered include:Tunable, Highly Stable Lasers for Coherent Lidar; Improved Photon-Emission-Microscope System; Program Synthesizes UML Sequence Diagrams; Aspect-Oriented Subprogram Synthesizes UML Sequence Diagrams; Updated Computational Model of Cosmic Rays Near Earth; Software for Alignment of Segments of a Telescope Mirror; Simulation of Dropping of Cargo With Parachutes; DAVE-ML Utility Program; Robust Control for the Mercury Laser Altimeter; Thermally Stable Piezoelectric and Pyroelectric Polymers; Combustion Synthesis of Ca3(PO4)2 Net-Shape Surgical Implants; Stochastic Representation of Chaos Using Terminal Attractors; Two High-Temperature Foil Journal Bearings; Using Plates To Represent Fillets in Finite-Element Modeling; Repairing Chipped Silicide Coatings on Refractory Metal Substrates; Simplified Fabrication of Helical Copper Antennas; Graded-Index "Whispering-Gallery" Optical Microresonators; Optical Profilometers Using Adaptive Signal Processing; Manufacture of Sparse-Spectrum Optical Microresonators; Exact Tuning of High-Q Optical Microresonators by Use of UV; Automation for "Direct-to" Clearances in Air-Traffic Control; Improved Traps for Removing Gases From Coolant Liquids; and Lunar Constellation of Frozen Elliptical Inclined Orbits.

Source record↗
NASA NTRS2003

Self-Supervised Dynamical Systems

Some progress has been made in a continuing effort to develop mathematical models of the behaviors of multi-agent systems known in biology, economics, and sociology (e.g., systems ranging from single or a few biomolecules to many interacting higher organisms). Living systems can be characterized by nonlinear evolution of probability distributions over different possible choices of the next steps in their motions. One of the main challenges in mathematical modeling of living systems is to distinguish between random walks of purely physical origin (for instance, Brownian motions) and those of biological origin. Following a line of reasoning from prior research, it has been assumed, in the present development, that a biological random walk can be represented by a nonlinear mathematical model that represents coupled mental and motor dynamics incorporating the psychological concept of reflection or self-image. The nonlinear dynamics impart the lifelike ability to behave in ways and to exhibit patterns that depart from thermodynamic equilibrium. Reflection or self-image has traditionally been recognized as a basic element of intelligence. The nonlinear mathematical models of the present development are denoted self-supervised dynamical systems. They include (1) equations of classical dynamics, including random components caused by uncertainties in initial conditions and by Langevin forces, coupled with (2) the corresponding Liouville or Fokker-Planck equations that describe the evolutions of probability densities that represent the uncertainties. The coupling is effected by fictitious information-based forces, denoted supervising forces, composed of probability densities and functionals thereof. The equations of classical mechanics represent motor dynamics that is, dynamics in the traditional sense, signifying Newton s equations of motion. The evolution of the probability densities represents mental dynamics or self-image. Then the interaction between the physical and metal aspects of a monad is implemented by feedback from mental to motor dynamics, as represented by the aforementioned fictitious forces. This feedback is what makes the evolution of probability densities nonlinear. The deviation from linear evolution can be characterized, in a sense, as an expression of free will. It has been demonstrated that probability densities can approach prescribed attractors while exhibiting such patterns as shock waves, solitons, and chaos in probability space. The concept of self-supervised dynamical systems has been considered for application to diverse phenomena, including information-based neural networks, cooperation, competition, deception, games, and control of chaos. In addition, a formal similarity between the mathematical structures of self-supervised dynamical systems and of quantum-mechanical systems has been investigated.

Zak, Michail↗
NASA NTRS2010

Coarse, Intermediate and High Resolution Numerical Simulations of the Transition of a Tropical Wave Critical Layer to a Tropical Storm

Recent work has hypothesized that tropical cyclones in the deep Atlantic and eastern Pacific basins develop from within the cyclonic Kelvin cat's eye of a tropical easterly wave critical layer located equatorward of the easterly jet axis. The cyclonic critical layer is thought to be important to tropical cyclogenesis because its cat's eye provides (i) a region of cyclonic vorticity and weak deformation by the resolved flow, (ii) containment of moisture entrained by the developing flow and/or lofted by deep convection therein, (iii) confinement of mesoscale vortex aggregation, (iv) a predominantly convective type of heating profile, and (v) maintenance or enhancement of the parent wave until the developing proto-vortex becomes a self-sustaining entity and emerges from the wave as a tropical depression. This genesis sequence and the overarching framework for describing how such hybrid wave-vortex structures become tropical depressions/storms is likened to the development of a marsupial infant in its mother's pouch, and for this reason has been dubbed the "marsupial paradigm". Here we conduct the first multi-scale test of the marsupial paradigm in an idealized setting by revisiting the Kurihara and Tuleya problem examining the transformation of an easterly wave-like disturbance into a tropical storm vortex using the WRF model. An analysis of the evolving winds, equivalent potential temperature, and relative vertical vorticity is presented from coarse (28 km), intermediate (9 km) and high resolution (3.1 km) simulations. The results are found to support key elements of the marsupial paradigm by demonstrating the existence of rotationally dominant region with minimal strain/shear deformation near the center of the critical layer pouch that contains strong cyclonic vorticity and high saturation fraction. This localized region within the pouch serves as the "attractor" for an upscale "bottom up" development process while the wave pouch and proto-vortex move together.

Montgomery, M. T.↗