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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.

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NASA NTRS1996

Seismic Excitation of the Polar Motion

The mass redistribution in the earth as a result of an earthquake faulting changes the earth's inertia tensor, and hence its rotation. Using the complete formulae developed by Chao and Gross (1987) based on the normal mode theory, we calculated the earthquake-induced polar motion excitation for the largest 11,015 earthquakes that occurred during 1977.0-1993.6. The seismic excitations in this period are found to be two orders of magnitude below the detection threshold even with today's high precision earth rotation measurements. However, it was calculated that an earthquake of only one tenth the size of the great 1960 Chile event, if happened today, could be comfortably detected in polar motion observations. Furthermore, collectively these seismic excitations have a strong statistical tendency to nudge the pole towards approx. 140 deg E, away from the actually observed polar drift direction. This non-random behavior, similarly found in other earthquake-induced changes in earth rotation and low-degree gravitational field by Chao and Gross (1987), manifests some geodynamic behavior yet to be explored.

Chao, Benjamin Fong↗
NASA NTRS1996

Seismic Excitation of the Polar Motion, 1977-1993

The mass redistribution in the earth as a result of an earthquake faulting changes the earth's inertia tensor, and hence its rotation. Using the complete formulae developed by CHAO and GROSS (1987) based on the normal mode theory, we calculated the earthquake-induced polar motion excitation for the largest 11,015 earthquakes that occurred during 1977.0-1993.6. The seismic excitations in this period are found to be two orders of magnitude below the detection threshold even with today's high precision earth rotation measurements. However, it was calculated that an earthquake of only one tenth the size of the great 1960 Chile event, if happened today, could be comfortably detected in polar motion observations. Furthermore, collectively these seismic excitations have a strong statistical tendency to nudge the pole towards approximately 140deg E, away from the actual observed polar drift direction. This non-random behavior, similarly found in other earthquake-induced changes in earth rotation and low-degree gravitational field by CHAO and GROSS (1987), manifests some geodynamic behavior yet to be explored.

Chao, Benjamin Fong↗
NASA NTRS2008

The Role of Continental-scale Landmass in Monsoons-A GCM Investigation

It was argued by Chao and Chen (2001) that land-sea thermal contrast on the continental scale is not a necessary condition for monsoons and that a monsoon is an ITCZ that have moved into the subtropics in its annual cycle of latitudinal movement. Chao and Chen supported their contention by GCM experiments in which they replaced landmass by ocean and were able to generate monsoons. However, land-sea thermal contrast does exist and must play a role in monsoonal rainfall distribution. Land-sea thermal contrast is one facet of continental-scale landmass. The other important characteristic of landmass is its topography. In this article the roles of landmass in monsoonal rainfall distribution and in middle latitude storm tracks are examined through GCM experiments. Comparison of a set of two GCM experiments in which the sea surface temperature (SST) from observations is prescribed from observations with and without a six-month delay reveals the role of Land-sea thermal contrast. Another set of experiments, which repeats the first set but with topography of all landmass reduced to zero, reveals the role of topography of landmass. These experiments confirm that land-sea thermal contrast is not a necessary condition for monsoons and that a monsoon should be viewed as an ITCZ displaced into the subtropics, instead of a continent-sized giant sea breeze. However, land-sea thermal contrast does have influence on the distribution of monsoonal rainfall. The temperature rise over south Asia as the season moves into summer helps the Asian monsoon to start early. However, this role is not the same as that of the land-sea thermal contrast as in the conventional explanation for the cause of monsoon. The heated landmass in summer contributes to the displacement of ITCZ into the subtropics. Also, the heated landmass in summer, by drawing moisture toward itself, limits the range of the summer storm tracks in the middle latitude oceans. On the ether hand, in winter the landmass does not present a competition for rainfall and thus allow middle latitude storm tracks to expand over the ocean.

Chao, Winston↗
NASA NTRS2008

The Role of Continental-scale Landmass in Monsoonal and Global Precipitation Distribution

It was argued by Chao and Chen (20011) that land-sea thermal contrast on the continental scale is not a necessary condition for monsoons and that a monsoon is an ITCZ that have moved into the subtropics in its annual cycle of latitudinal movement. Chao and Chen supported their contention by GCM experiments in which they replaced landmass by ocean and were able to generate monsoons. However, land-sea thermal contrast does exist and must play a role in monsoonal rainfall distribution. Land-sea thermal contrast is one facet of continental-scale landmass. in this article the roles of land-sea thermal contrast in monsoonal rainfall distribution and in middle latitude storm tracks are examined through GCM experiments. Comparison of a set of two GCM experiments in which the sea surface temperature (SST) from observations is prescribed from observations with and without a six-month delay reveals the role of land-sea thermal contrast. These experiments confirm that land-sea thermal contrast is not a necessary condition for monsoons and that a monsoon should be viewed as an ITCZ displaced into the subtropics, instead of a continent-sized giant sea breeze. However, land-sea thermal contrast does have influence on the distribution of monsoonal rainfall. The temperature rise over south Asia as the season moves into summer helps the Asian monsoon to start early. However, this role is not the same as that of the land-sea thermal contrast as in the conventional explanation for the cause of monsoon. The heated Landmass in summer contributes to the displacement of 1TCZ into the subtropics Also, the heated landmass in summer, by drawing moisture toward itself, limits the range of the summer storm tracks in the middle latitude oceans. On the other band, in winter the landmass does not present a competition for rainfall and thus allow middle latitude storm tracks to expand over the ocean.

Chao, Winston C.↗
NASA NTRS2010

The Origin of Monsoons: The Role of Continental-Scale Landmass

In a challenge to the traditional explanation for the cause of monsoons Chao and Chen (JAS 2001) argued that land-sea thermal contrast is not necessary for the existence of monsoons. However, the question of whether land-sea thermal contrast plays any modifying role still exists. This study tries to answer that question. The result is a more complete theory of the origin of monsoons than that proposed by Chao and Chen. Two criticisms of the traditional explanation for the cause of monsoons do not apply to this theory. They are: 1) no explanation for monsoon onset and retreat, let alone the fact that monsoon onset is much faster than monsoon retreat, and 2) for the South Asian monsoon, land-sea thermal contrast is greatest just prior to monsoon onset, not at the height of the monsoon season. Land-sea thermal contrast acts as a facilitator for monsoon onset. If it does not exist, monsoon onset can still occur but at a later time. Our results are supported by GCM experiments.

Chao, Winston↗
NASA NTRSDate not supplied

Design Under Uncertainty with Design-Dependent Uncertain Variables

Uncertainty quantification (UQ) can provide a more robust understanding of a system, leading to better informed decisions earlier in the design process. The additional information that UQ provides can be leveraged during a design optimization process known as design under uncertainty that, when incorporated with multidisciplinary design and optimization, can become computationally infeasible due to the large number of responses required for meaningful results. Previous work addressed reducing the computational expense in design under uncertainty by incorporating analytic derivatives throughout polynomial chaos expansion. Although this allows design under uncertainty to be feasible for more systems, some multidisciplinary systems have design-dependent uncertain variables. This paper details an implementation of design dependent uncertain variables in a manner than preserves derivatives required for efficient gradient-based optimization throughout the process. Two analytic examples of design-dependent uncertain variables are given: the first transforms a uniform uncertain variable with one design variable and the second transforms a normal uncertain variable with two design variables. The polynomial chaos expansion (PCE) results are comparable to both the Monte Carlo (MC) results and the analytic results for the two examples. A case study that maximizes the lift-to-drag ratio with a design-dependence between the wing leading edge sweep angle and uncertain parameter percentage of laminar flow is compared to a MC and alternative optimization formulations. This paper demonstrates that design-dependent uncertain variables are valid and hold throughout PCE.

robust design↗
NASA NTRS1979

Laminar boundary-layer flow of non-Newtonian fluid

A solution for the two-dimensional and axisymmetric laminar boundary-layer momentum equation of power-law non-Newtonian fluid is presented. The analysis makes use of the Merk-Chao series solution method originally devised for the flow of Newtonian fluid. The universal functions for the leading term in the series are tabulated for n from 0.2 to 2. Equations governing the universal functions associated with the second and the third terms are provided. The solution together with either Lighthill's formula or Chao's formula constitutes a simple yet general procedure for the calculation of wall shear and surface heat transfer rate. The theory was applied to flows over a circular cylinder and a sphere and the results compared with published data.

Lin, F. N.↗
NASA NTRS1985

Relative Time-scale for Channeling Events Within Chaotic Terrains, Margaritifer Sinus, Mars

A relative time scale for ordering channel and chaos forming events was constructed for areas within the Margaritifer Sinus region of Mars. Transection and superposition relationships of channels, chaotic terrain, and the surfaces surrounding them were used to create the relative time scale; crater density studies were not used. Channels and chaos in contact with one another were treated as systems. These systems were in turn treated both separately (in order to understand internal relationships) and as members of the suite of Martian erosional forms (in order to produce a combined, master time scale). Channeling events associated with chaotic terrain development occurred over an extended geomorphic period. The channels can be divided into three convenient groups: those that pre-date intercrater plains development post-plains, pre-chasma systems; and those associated with the development of the Vallis Marineris chasmata. No correlations with cyclic climatic changes, major geologic events in other regions on Mars, or triggering phenomena (for example, specific impact events) were found.

Janke, D.↗
NASA NTRS1987

Part 1: The geomorphic evolution of Eastern Margaritifer Sinus, Mars

Geomorphic mapping, crater counts on selected surfaces, and a detailed study of drainage basins, were used to trace the geologic evolution of Margaritifer Sinus Quandrangle. The oldest dated surface covering these basins evolved during the period of intense bombardment. Since that time four resurfacing events have occurred. The first three were all of regional extent, while the fourth, occurred locally, filling basins. Valley networks, incised in the third event unit, are always buried by the fourth event unit when present. A peak in geomorphic activity occurred from 10,000 to 5000. Events during this period included the formation of Uzboi/Ladon Valles with deposition in Ladon Basin, and the formation of Samara and Parana/Loire Valles in MC19SE. Flow out of Ladon Basin and to a lesser extent Samara and Parana/Loire Valles created etched terrain at their confluence that was synchronous with initiation of Margaritifer and Iani Chaos. The range of dates for the chaos may be due to periodic collapse. The extensive, well integrted nature of Samara and Parana/Loire Valles requires the existence of a long period of favorable climatic conditions to allow their formation. Development of these two systems was probably through sapping processes.

Grant, John A., III↗
NASA NTRS1988

A numerical study of bifurcations in a barotropic shear flow

In the last few years, more and more evidence has emerged suggesting that transition to turbulence may be viewed as a succession of bifurcations to deterministic chaos. Most experimental and numerical observations have been restricted to Rayleigh-Benard convection and Taylor-Couette flow between concentric cylinders. An attempt is made to accurately describe the bifurcation sequence leading to chaos in a 2-D temporal free shear layer on the beta-plane. The beta-plane is a locally Cartesian reduction of the equations describing the dynamicss of a shallow layer of fluid on a rotating spherical planet. It is a valid model for large scale flows of interest in meteorology and oceanography.

Huerre, P.↗
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 NTRS1991

Research highlights: June 1990 - May 1991

Linear instability calculations at MSFC have suggested that the Geophysical Fluid Flow Cell (GFFC) should exhibit classic baroclinic instability at accessible parameter settings. Interest was in the mechanisms of transition to temporal chaos and the evolution of spatio-temporal chaos. In order to understand more about such transitions, high resolution numerical experiments for the physically simplest model of two layer baroclinic instability were conducted. This model has the advantage that the numerical code is exponentially convergent and can be efficiently run for very long times, enabling the study of chaotic attractors without the often devastating effects of low-order trunction found in many previous studies. Numerical algorithms for implementing an empirical orthogonal function (EOF) analysis of the high resolution numerical results were completed. Under conditions of rapid rotation and relatively low differential heating, convection in a spherical shell takes place as columnar banana cells wrapped around the annular gap, but with axes oriented along the axis of rotation; these were clearly evident in the GFFC experiments. The results of recent numerical simulations of columnar convection and future research plans are presented.

Source record↗
NASA NTRS1991

An unpredictable-dynamics approach to neural intelligence

The theoretical basis for a dynamic neural network architecture that takes advantage of the notion of terminal chaos to process information in a way that is phenomenologically similar to brain activity is presented. The architecture exploits the phenomenology of nonlinear dynamic systems as an alternative to the traditional paradigm of finite-state machines. It is based on some effects of non-Lipschitzian dynamics. The nonlinear phenomenon of terminal chaos and its relevance to brain activity are examined.

Zak, Michail↗
NASA NTRS1992

Detecting and disentangling nonlinear structure from solar flux time series

Interest in solar activity has grown in the past two decades for many reasons. Most importantly for flight dynamics, solar activity changes the atmospheric density, which has important implications for spacecraft trajectory and lifetime prediction. Building upon the previously developed Rayleigh-Benard nonlinear dynamic solar model, which exhibits many dynamic behaviors observed in the Sun, this work introduces new chaotic solar forecasting techniques. Our attempt to use recently developed nonlinear chaotic techniques to model and forecast solar activity has uncovered highly entangled dynamics. Numerical techniques for decoupling additive and multiplicative white noise from deterministic dynamics and examines falloff of the power spectra at high frequencies as a possible means of distinguishing deterministic chaos from noise than spectrally white or colored are presented. The power spectral techniques presented are less cumbersome than current methods for identifying deterministic chaos, which require more computationally intensive calculations, such as those involving Lyapunov exponents and attractor dimension.

Ashrafi, S.↗
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↗
NASA NTRS1992

Turbulence: The chief outstanding difficulty of our subject

A review of interesting current topics in turbulence research is decorated with examples of popular fallacies about the behavior of turbulence. Topics include the status of the Law of the Wall, especially in compressible flow; analogies between the effects of Reynolds numbers, pressure gradient, unsteadiness and roughness change; the status of Kolmogorov's universal equilibrium theory and local isotropy of the small eddies; turbulence modelling, with reference to universality, pressure-strain modelling and the dissipation equation; and chaos. Fallacies include the mixing-length concept; the effect of pressure gradient on Reynolds shear stress; the separability of time and space derivatives; models of the dissipation equation; and chaos.

Bradshaw, Peter↗
NASA NTRS1993

Desktop chaotic systems: Intuition and visualization

This paper presents a dynamic study of the Wildwood Pendulum, a commercially available desktop system which exhibits a strange attractor. The purpose of studying this chaotic pendulum is twofold: to gain insight in the paradigmatic approach of modeling, simulating, and determining chaos in nonlinear systems; and to provide a desktop model of chaos as a visual tool. For this study, the nonlinear behavior of this chaotic pendulum is modeled, a computer simulation is performed, and an experimental performance is measured. An assessment of the pendulum in the phase plane shows the strange attractor. Through the use of a box-assisted correlation dimension methodology, the attractor dimension is determined for both the model and the experimental pendulum systems. Correlation dimension results indicate that the pendulum and the model are chaotic and their fractal dimensions are similar.

Bright, Michelle M.↗
NASA NTRS1993

Using emergent order to shape a space society

A fast-growing movement in the scientific community is reshaping the way that we view the world around us. The short-hand name for this movement is 'chaos'. Chaos is a science of the global, nonlinear nature of systems. The center of this set of ideas is that simple, deterministic systems can breed complexity. Systems as complex as the human body, ecology, the mind or a human society. While it is true that simple laws can breed complexity, the other side is that complex systems can breed order. It is the latter that I will focus on in this paper. In the past, nonlinear was nearly synonymous with unsolvable because no general analytic solutions exist. Mathematically, an essential difference exists between linear and nonlinear systems. For linear systems, you just break up the complicated system into many simple pieces and patch together the separated solutions for each piece to form a solution to the full problem. In contrast, solutions to a nonlinear system cannot be added to form a new solution. The system must be treated in its full complexity. While it is true that no general analytical approach exists for reducing a complex system such as a society, it can be modeled. The technical involves a mathematical construct called phase space. In this space stable structures can appear which I use as analogies for the stable structures that appear in a complex system such as an ecology, the mind or a society. The common denominator in all of these systems is that they rely on a process called feedback loops. Feedback loops link the microscopic (individual) parts to the macroscopic (global) parts. The key, then, in shaping a space society, is in effectively using feedback loops. This paper will illustrate how one can model a space society by using methods that chaoticists have developed over the last hundred years. And I will show that common threads exist in the modeling of biological, economical, philosophical, and sociological systems.

Graps, Amara L.↗