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At least 163 records · Page 9

Evaluation of current tropospheric mapping functions by Deep Space Network very long baseline interferometry

To compare the validity of current algorithms that map zenith tropospheric delay to arbitrary elevation angles, 10 different tropospheric mapping functions are used to analyze the current data base of Deep Space Network Mark 3 intercontinental very long baseline interferometric (VLBI) data. This analysis serves as a stringent test because of the high proportion of low-elevation observations necessitated by the extremely long baselines. Postfit delay and delay-rate residuals are examined, as well as the scatter of baseline lengths about the time-linear model that characterizes tectonic motion. Among the functions that utilize surface meteorological data as input parameters, the Lanyi 1984 mapping shows the best performance both for residuals and baselines, through the 1985 Davis function is statistically nearly identical. The next best performance is shown by the recent function of Niell, which is based on an examination of global atmospheric characteristics as a function of season and uses no weather data at the time of the measurements. The Niell function shows a slight improvement in residuals relative to Lanyi, but also an increase in baseline scatter that is significant for the California-Spain baseline. Two variants of the Chao mapping function, as well as the Chao tables used with the interpolation algorithm employed in the Orbit Determination Program software, show substandard behavior for both VLBI residuals and baseline scatter. The length of the California-Australia baseline (10,600 km) in the VLBI solution can vary by as much as 5 to 10 cm for the 10 mapping functions.

Sovers, O. J.↗

Near-surface ice on Mercury and the Moon: A topographic thermal model

A thermal model that can be easily adapted to craters of arbitrary shape is developed and applied to high-latitude impact craters on Mercury and the Moon, Chao Meng Fu crater at -87.5 deg L on Mercury, an unnamed bowl-shaped crater at 86.7 deg L on Mercury, and Peary crater at 88.6 deg L on the Moon. For an assumed input topography and grid of surface elements, the model computes for each element the irradiation from direct insolation and reflected and emitted radiation from other elements, taking into account shadowing by walls of the crater, partial obscuration of the solar disk near the poles and the diurnal, orbital, and seasonal cycles. Temperatures are computed over the surface grid as functions of depth and time from the surface to a specified depth and over the pertinent astronomical cycles, including the effects of direct and indirect surface irradiation, infrared radiation, heat conduction, and interior heating. Vapor fluxes and ice recession times are computed as functions of ice depth over the surface grid. Temperatures profiles, vapor fluxes, and ice recession times were computed for flat surfaces not associated with craters near the poles of Mercury and the Moon. It was found that water ice could have existed throughout geologic time within the maximum radar detection depth of recent observation of Mercury (J. K. Harmon and M. A. Slade, 1992, Science 258, 640-643) poleward of approximately 87 - 88 deg L on Mercury and poleward of approximately 73 deg L on the Moon. For Chao Meng Fu crater it was found that approximately 40% of the crater floor is permanently shadowed from direct solar insolation, while the remainder of the crater floor is periodically illuminated by a partially obscured Sun. Temperatures at the upper levels of the south wall can slightly exceed 550 K. Surface temperatures in the permanently shadowed region of the crater floor are under approximately 130 K, which could have allowed water ice to exist throughout geologic time within the radar detection depth of recent observation of Mercury. For small bowl-shaped crater on Mercury, it was found that most of the crater is permanently shadowed from direct solar radiation, except for a narrow semicircular band bordering the north rim. However, temperatures in the permanently shadowed region periodically reach a maximum near approximately 315 K due to efficient heating of the small crater by thermal emission and reflection from the small sunlit region, which periodically reaches temperatures exceeding 630 K. Water ice could not have existed throughout geologic time anywhere in this crater within the radar detection depth. For Peary crater on the Moon, the entire crater floor is permanently shadowed from direct solar insolation with maximum temperature under 120 K. The upper level of the north wall periodically reaches a maximum temperature near 310 K. The low temperatures on the crater floor would have allowed water ice to exist near the surface throughout geologic time, provided that the Moon's obliquity was always as low as it is at present.

Salvail, James R.↗

Physical Models of Cognition

This paper presents and discusses physical models for simulating some aspects of neural intelligence, and, in particular, the process of cognition. The main departure from the classical approach here is in utilization of a terminal version of classical dynamics introduced by the author earlier. Based upon violations of the Lipschitz condition at equilibrium points, terminal dynamics attains two new fundamental properties: it is spontaneous and nondeterministic. Special attention is focused on terminal neurodynamics as a particular architecture of terminal dynamics which is suitable for modeling of information flows. Terminal neurodynamics possesses a well-organized probabilistic structure which can be analytically predicted, prescribed, and controlled, and therefore which presents a powerful tool for modeling real-life uncertainties. Two basic phenomena associated with random behavior of neurodynamic solutions are exploited. The first one is a stochastic attractor ; a stable stationary stochastic process to which random solutions of a closed system converge. As a model of the cognition process, a stochastic attractor can be viewed as a universal tool for generalization and formation of classes of patterns. The concept of stochastic attractor is applied to model a collective brain paradigm explaining coordination between simple units of intelligence which perform a collective task without direct exchange of information. The second fundamental phenomenon discussed is terminal chaos which occurs in open systems. Applications of terminal chaos to information fusion as well as to explanation and modeling of coordination among neurons in biological systems are discussed. It should be emphasized that all the models of terminal neurodynamics are implementable in analog devices, which means that all the cognition processes discussed in the paper are reducible to the laws of Newtonian mechanics.

Zak, Michail↗

Postinstability Models in Dynamics

This paper is devoted to the concept of instability in dynamical systems with the main emphasis on orbital, Hadamard, and Reynolds instabilities. It demonstrates that the requirement about differentiability in dynamics in some cases is not consistent with the physical nature of motions, and may lead to unrealistic solutions. Special attention is paid to the fact that instability is not an invariant of motion: it depends upon frames of reference, the metric of configuration space, and classes of functions selected for mathematical models of physical phenomena. This leads to the possibility of elimination of certain types of instabilities (in particular, those which lead to chaos and turbulence) by enlarging the class of functions using the Reynolds-type transformation in combination with the stabilization principle: the additional terms (the so-called Reynolds stresses) are found from the conditions that they suppress the original instability. Based upon these ideas, a new approach to chaos and turbulence as well as a new mathematical formalism for nonlinear dynamics are discussed.

Zak, Michail↗

Stereo Imaging Velocimetry of Mixing Driven by Buoyancy Induced Flow Fields

Mixing of two fluids generated by steady and particularly g-jitter acceleration is fundamental towards the understanding of transport phenomena in a microgravity environment. We propose to carry out flight and ground-based experiments to quantify flow fields due to g-jitter type of accelerations using Stereo Imaging Velocimetry (SIV), and measure the concentration field using laser fluorescence. The understanding of the effects of g-jitter on transport phenomena is of great practical interest to the microgravity community and impacts the design of experiments for the Space Shuttle as well as the International Space Station. The aim of our proposed research is to provide quantitative data to the community on the effects of g-jitter on flow fields due to mixing induced by buoyancy forces. The fundamental phenomenon of mixing occurs in a broad range of materials processing encompassing the growth of opto-electronic materials and semiconductors, (by directional freezing and physical vapor transport), to solution and protein crystal growth. In materials processing of these systems, crystal homogeneity, which is affected by the solutal field distribution, is one of the major issues. The understanding of fluid mixing driven by buoyancy forces, besides its importance as a topic in fundamental science, can contribute towards the understanding of how solutal fields behave under various body forces. The body forces of interest are steady acceleration and g-jitter acceleration as in a Space Shuttle environment or the International Space Station. Since control of the body force is important, the flight experiment will be carried out on a tunable microgravity vibration isolation mount, which will permit us to precisely input the desired forcing function to simulate a range of body forces. To that end, we propose to design a flight experiment that can only be carried out under microgravity conditions to fully exploit the effects of various body forces on fluid mixing. Recent flight experiments, by the P.I. through collaboration with the Canadian Space Agency (STS-85, August 1997), aimed at determining the stability of the interface between two miscible liquids inside an enclosure show that a long liquid column (5 cm) under microgravity isolation conditions can be stable, i.e. the interface remains sharp and vertical over a short time scale; thus transport occurs by molecular mass diffusion. On the other hand, when the two liquids were excited from a controlled vibration source (Microgravity Vibration Isolation Mount) two to four mode large amplitude quasi-stationary waves were observed. The data was limited to CCD recording of the dynamics of the interface between the two fluids. We propose to carry out flight experiments to quantify the dynamics of the flow field using Stereo Imaging Velocimetry and measure the concentration field using laser fluorescence. The results will serve as a basis to understand effects of g-jitter on transport phenomena, in this case mass diffusion. As the measurement of the kinematics of the flow field will shed light on the instability mechanism. The research will allow measurement of the flow field in microgravity environment to prove two hypotheses: (1) Maxwell's hypothesis: finite convection always exists in diffusing systems, and (2) Quasi-stationary waves inside a bounded enclosure in a microgravity environment is generated by Kelvin-Helmholtz instability; resonance of the interface which produces incipient mixing is due to Rayleigh-Taylor instability. The first hypothesis can be used as a benchmark experiment to illustrate diffusive mixing. The second hypothesis will lead to the understanding of g-jitter effects on buoyancy driven flow fields which occur in many situations involving materials processing, and other basic fluid physics phenomena. In addition, the second hypothesis will also provide insight in how Rayleigh-Taylor and Kelvin-Helmholtz instabilities propagate concentration fronts during mixing. Measurement of the flow field using SIV is important because it is the flow field which causes instability at the interface between the two fluids. Mixing driven by buoyancy induced flow fields will be addressed both experimentally and computationally. The experimental effort will address the kinematics of mixing: stretching, transport and chaos. Quantification of the mechanisms of mixing will consists of measuring the flow field using the SIV system at Glenn and capturing the dynamics of the interface, to measure mass transport, using a CCD camera. These experiments will be carried out within the framework of Earth's gravity and g-jitter microgravity acceleration as in a Space Shuttle environment or the International Space Station. The g-jitter will be induced and controlled using a tunable vibration isolation platform to isolate against vibration as well as input periodic and random vibration to the system. The parametric range of the microgravity experiment will be extended from the experiments on STS-85 to investigate higher mode quasi-stationary waves (8 to 12), as well as resonance regions which leads to chaos and turbulence. Ground-based experiments will focus on effects of vibration on stably stratified fluid layers in order to scale for possible scenarios in a microgravity environment. These vibrations will be subjected perpendicular to the concentration field on the ground since the parallel case can only be carried out in a microgravity environment. The concept of dynamical similarity will be applied to tune the experiments as closely as possible to a Space Shuttle environment or the International Space Station. The computational effort will take advantage of the Computational Laboratory at Glenn to corroborate the experimental findings with predictions of the dynamics of the flow field using the codes FLUENT (finite difference based) and FIDAP (finite element based). We will investigate two important cases, single-fluid model to address dilute systems with negligible jump in viscosity and the more general two-fluid model which accounts for finite jump in viscosity. Apart from its microgravity relevance, this experiment is well suited to study dynamics in nonlinear systems.

Duval, W. M. B.↗

Long-Term Dynamics of Small Bodies in the Solar System

As part of the NASA Planetary Geology and Geophysics program, Prof. Norm Murray (CITA (Canadian Institute of Theoretical Astrophysics)) and I have been conducting investigations of the long-term dynamics of small bodies in the outer solar system. This grant, and its successor NAG5-10365, supports travel for collaboration by the Investigators and also supports Murray during an annual one month visit to the CfA (Harvard-Smithsonian Center for Astrophysics) for further collaboration. In the course of this grant we made a number of advances in solar system dynamics. For example, we developed an analytic model for the origin and consequence of chaos associated with three-body resonances in the asteroid belt. This has been shown to be important for the delivery of near Earth objects (NEO). We later extended this model to three-body resonances among planets. We were able to show that the numerically identified chaos among the outer planets results from a three-body resonance involving Jupiter, Saturn, and Uranus. The resulting paper was awarded the 1999 Newcomb Cleveland award from the AAAS (American Association for the Advancement of Science). This award singles out one paper published in Science each year for distinction. A list of grant-related publications is presented, with abstracts included.

Holman, Matthew J.↗

Uncertainty Propagation for Turbulent, Compressible Flow in a Quasi-1D Nozzle Using Stochastic Methods

This paper describes a fully spectral, Polynomial Chaos method for the propagation of uncertainty in numerical simulations of compressible, turbulent flow, as well as a novel stochastic collocation algorithm for the same application. The stochastic collocation method is key to the efficient use of stochastic methods on problems with complex nonlinearities, such as those associated with the turbulence model equations in compressible flow and for CFD schemes requiring solution of a Riemann problem. Both methods are applied to compressible flow in a quasi-one-dimensional nozzle. The stochastic collocation method is roughly an order of magnitude faster than the fully Galerkin Polynomial Chaos method on the inviscid problem.

Zang, Thomas A.↗

Ariadnes-Gorgonum Knob Fields of North-Western Terra Sirenum, Mars

Fields of knobs and small mesas outcrop principally in five adjacent basins in northwestern Terra Sirenum (~32-43 S, 166-192 W). Several of these knob fields (the largest) have names. East to west they are: Gorgonum Chaos, Atlantis Chaos, and Ariadnes Colles. These three largest knob fields are on order of 200 km across and are roughly equant but with very irregular boundaries in plan view . There are several smaller knob fields in smaller nearby basins; some as small as 20 km across. Knob material, where unmantled, is relatively brighter than its surroundings. The largest individual knobs are almost invariably mesas with typical plan dimensions of ~10 km and relief > 200 m. Knob profiles transition from mesas to rounded mounds with decreasing size. Individual knobs range in size down to ~100 m in plan view and relief < 10 m where seen on some MOC NA images.

Moore, J. M.↗

Long-Term Dynamics of Small Bodies in the Solar System

As part of the NASA Planetary Geology and Geophysics program Prof. Norm Murray (CITA) and I have been conducting investigations of the long-term dynamics of small bodies in the outer solar system. This grant, and its predecessor NAG5- 7761, supports travel for collaboration by the Investigators and also supports Murray during an annual one month visit to the CfA for further collaboration. In the course of this grant we made a number of advances in solar system dynamics. For example, we developed an analytic model for the origin and consequence of chaos associated with three-body resonances in the asteroid belt. This has been shown to be important for the delivery of near Earth objects. We later extended this model to three- body resonances among planets. We were able to show that the numerically identified chaos among the outer planets results from a three-body resonance involving Jupiter, Saturn, and Uranus. The resulting paper was awarded the 1999 Newcomb Cleveland award from the AAAS. This award singles out one paper published in Science each year for distinction.

Holman, Matthew J.↗

Lunar and Planetary Science XXXV: Icy Worlds: Moving and Grooving

Reports from the conference session entitled Icy Worlds: Moving and Grooving, include:Mass Anomalies on Ganymede; Europan Chaos and Lenticulae: A Synthesis of Size, Spacing, and Areal Density Analyses; Thermal and Topographic Tests of Europa Chaos Formation Models; Flexure of Europa s Lithosphere Due to Ridge-Loading; Ridges on Europa: Origin by Incremental Ice-Wedging ; Convergent Boundaries on Europa: a Numerical Approach to Euler Pole Analysis and Its' Implications for Plate Reconstruction; Numerical Simulations of Subsolidus Convection in the Ice Shell of Europa: Implications for the Thermal Evolution and Present State; Effects of Plasticity on Convection in an Ice Shell: Implications for Europa; Non-Newtonian Convection and Compositional Buoyancy: Advances in Modeling Convection and Dome Formation on Europa; Convective Instability in Ice I: Application to Callisto and Ganymede; Crater Size Distributions on Callisto: A Galileo SSI Summary; Neutron Diffraction Studies of Planetary Ices; and H2O2 Synthesis Induced by Irradiation of H2O with Energetic H+ and Ar+ Ions at Various Temperatures.

Source record↗

Lunar and Planetary Science XXXV: Ancient Mars Water and Landforms

Titles in this section include: 1) Giant Lowland Polygons: Relics of an Ancient Martian Ocean? 2) Lake Shorelines: Earth Analogs for Hypothesized Martian Coastal Features; 3) Complex Evolution of Paleolacustrine Systems on Mars: An Example from the Holden Crater; 4) Geomorphology and Hydraulics of Ma'adim Vallis, Mars, During a Noachian/Hesperian Boundary Paleoflood; 5) Geologic Evolution of Dao Vallis, Mars; 6) Advances in Reconstructing the Geologic History of the Chryse Region Outflow Channels on Mars; 7) Ravi Vallis, Mars - Paleoflood Origin and Genesis of Secondary Chaos Zones; 8) Walla Walla Vallis and Wallula Crater: Two Recently Discovered Martian Features Record Aqueous History; 9) Tharsis Recharge: a Source of Groundwater for Martian Outflow Channels; 10) Factors Controlling Water Volumes and Release Rates in Martian Outflow Channels; 11) Significance of Confined Cavernous Systems for Outflow Channel Water Sources, Reactivation Mechanisms and Chaos Formation; 12) Systematic Differences in Topography of Martian and Terrestrial Drainage Basins; 13) Waves on Seas of Mars and Titan: Wind-Tunnel Experiments on Wind-Wave Generation in Extraterrestrial Atmospheres.

Source record↗

Detection of chaotic determinism in time series from randomly forced maps

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

Non-NASA Center↗

Long-Term Dynamics of Small Bodies in the Solar System

As part of the NASA Planetary Geology and Geophysics program Prof. Norm Murray (CITA) and I have been conducting investigations of the long-term dynamics of small bodies in the outer solar system. This grant, and its predecessor NAG5-7761, supported travel for collaboration by the Investigators and also supports Murray during an annual one month visit to the CfA for further collaboration. In the course of this grant we made a number of advances in solar system dynamics. For example, we developed an analytic model for the origin and consequence of chaos associated with three-body resonances in the asteroid belt. This has been shown to be important for the delivery of near Earth objects. We later extended this model to three-body resonances among planets. We were able to show that the numerically identified chaos among the outer planets results from a three-body resonance involving Jupiter, Saturn, and Uranus. The resulting paper was awarded the 1999 Newcomb Cleveland award from the AAAS. This award singles out one paper published in Science each year for distinction. This grant has also supported, in part, my participate in other solar system dynamics projects. The results from those collaborations are also listed.

Saunders, Steve↗

Innovative Trajectory Designs to meet Exploration Challenges

This document is a viewgraph presentation of the conference paper. Missions incorporated into NASA's Vision for Space Exploration include many different destinations and regions; are challenging to plan; and need new and innovative trajectory design methods to enable them. By combining proven methods with chaos dynamics, exploration goals that require maximum payload mass or minimum duration can be achieved. The implementation of these innovative methods, such as weak stability boundaries, has altered NASA's approach to meet exploration challenges and is described to show how exploration goals may be met in the next decade. With knowledge that various perturbations play a significant role, the mission designer must rely on both traditional design strategies as well as these innovative methods. Over the past decades, improvements have been made that would at first glance seem dramatic. This paper provides a brief narrative on how a fundamental shift has occurred and how chaos dynamics improve the design of exploration missions with complex constraints.

Folta, David C.↗

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↗

Multifidelity Uncertainty Quantification of a Commercial Supersonic Transport

The objective of this work was to develop a multifidelity uncertainty quantification approach for efficient analysis of a commercial supersonic transport concept. An approach based on point-collocation, non-intrusive polynomial chaos was formulated in which a low-fidelity model could be corrected using multiple higher-fidelity models. The formulation and methodology also allows for the addition of uncertainty sources not present in the lower fidelity models. To demonstrate the applicability and potential computational savings of the multifidelity polynomial chaos approach, two model problems were explored. The first was a supersonic airfoil with three levels of modeling fidelity, each capturing a gradual increase in modeling of the underlying flow physics. As much as 50% computational cost reduction was observed using the mutlifidelity approach, while predicting nearly the same amount of uncertainty in drag. The second problem was a commercial supersonic transport. This model had three levels of fidelity that included two different modeling approaches and the addition of physics between the fidelity levels. Results of this analysis yielded nearly a 70% computational savings to predict a comparable amount of uncertainty in ground noise. Both problems illustrate the applicability and significant computational savings of the multifidelity method for efficient and accurate uncertainty quantification.

Thomas K. West IV↗

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.

Joanna N Schmidt↗