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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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At least 91 records · Page 5

FORESTR: Finding, Organizing, Representing, Explaining, Summarizing, and Thinning Random forests

Random forests have become popular models used for data driven predictions. As a result, random forests are currently used or being considered for high-consequence mission applications in national security, such as the prediction of yield from optical signals and malware detection. While random forests may provide accurate predictions, the complexity of the algorithm causes a lack of interpretability. Random forests are an ensemble of regression or decision trees. Individual regression and decision trees are interpretable, but ensembles are inherently difficult to interpret due to the compilation of many models. We aim to increase the interpretability of random forests by finding patterns in the ensemble of trees that can be used to “thin” (or remove) trees. As a starting point, in this report, we develop a new distance metric for quantifying the similarity between trees based on their topologies (i.e., shapes). We base the metric on a novel distance metric for graphs that is a proper mathematical distance, is invariant to transformations, has registration between graphs, and computes topological evolutions between graphs. We use the tree distance metric to compute tree statistics such as a “mean tree” and to identify clusters of trees. We apply the developed methodology to a toy dataset and a mission relevant product inspection dataset to demonstrate how the metric can provide insight into random forests. Furthermore, we discuss the limitations of the approach and ideas for future research into how the metric could be used as a thinning tool to develop less complex models.

97 MATHEMATICS AND COMPUTING↗

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↗

Comparison of analytical and physical modeling of planetesimal accumulation

Three cases for which the analytic solutions to the planetary embryo coagulation equation are known, namely those of constant coagulation rate, of rate proportional to the sum of the masses of the two colliding bodies, and of rate proportional to the product of their masses, are presently used to test the mathematical validity of the Wetherill and Stewart (1989) physical model for the evolution of planetary embryos' mass distribution. In all cases, excellent agreement is found between numerical physical modeling results and those of the analytic solutions. The treatment of the runaway case can proceed via extension of the efforts of Trubnikov (1971).

Wetherill, George W.↗

Life in the Universe: Foundation for exciting multidisciplinary science activities for middle and elementary school classes

Young students find extra-terrestrial life one of the most intriguing of all topics. A project funded by the National Science Foundation and NASA, and administered by the SETI Institute, is underway to devise science lessons for grades 3-9 that draw upon this fascination. The lessons are designed by teachers and persons with long experience at curriculum design, tested in classrooms, revised and retested. Six guides, each containing some 6-10 science lessons, will be finished by summer, 1994.The theme Life in the Universe lends itself naturally to integrated treatment of facts and concepts from many scientific disciplines. The lessons for two completed guides span the origin of planet systems, evolution of complex life, chemical makeup of life, astronomy, spectroscopy, continental drift, mathematics and SETI (Search for Extra-Terrestrial Intelligence). All lessons are hands-on, interesting, and successful.

Milne, D.↗

Examination of Haines Jump in Microfluidic Experiments via Evolution Graphs and Interface Tracking

This work examines a type of rapid pore-filling event in multiphase flow through permeable media that is better known as Haines Jump. While existing microfluidic experiments on Haines Jump mostly seek to maintain quasi-steady states through very low bulk flow rates over long periods of time, this work explores the combined use of a highly structured microscale transport network, high-speed fluorescent microscopy, displacement front segmentation algorithms, and a tracking algorithm to build evolution graphs that track displacement fronts as they evolve through high-speed video recording. The resulting evolution graph allows the segmentation of a high-speed recording in both space and time, potentially facilitating topology-cognitive computation on the transport network. Occurrences of Haines Jump are identified in the microfluidic displacement experiments and their significance in bulk flow rates is qualitatively analyzed. The bulk flow rate has little effect on the significance of Haines Jump during merging and splitting, but large bulk flow rates may obscure small bursts at the narrowest part of the throat.

permeable media↗

Injection Characteristics of Non-Swirling and Swirling Annular Liquid Sheets

A simplified mathematical model, based on body-fitted coordinates, is formulated to study the evolution of non-swirling and swirling liquid sheet emanated from an annular nozzle in a quiescent surrounding medium. The model provides predictions of sheet trajectory, thickness and velocity at various liquid mass flow rates and liquid-swirler angles. It is found that a non-swirling annular sheet converges toward its centerline and assumes a bell shape as it moves downstream from the nozzle. The bell radius, and length are more pronounced at higher liquid mass flow rates. The thickness of the non-swirling annular sheet increases while its stream-wise velocity decreases with an increase in mass flow rate. The introduction of swirl results in the formation of a diverging hollow-cone sheet. The hollow-cone divergence from its centerline is enhanced by an increase in liquid mass flow rate or liquid-swirler angle. The hollow- cone sheet its radius, curvature and stream-wise velocity increase while its thickness and tangential velocity decrease as a result of increasing the mass flow rate or liquid-swirler angle. The present results are compared with previous studies and conclusions are drawn.

Harper, Brent↗

Mathematical Analysis and Optimization of Infiltration Processes

A variety of infiltration techniques can be used to fabricate solid materials, particularly composites. In general these processes can be described with at least one time dependent partial differential equation describing the evolution of the solid phase, coupled to one or more partial differential equations describing mass transport through a porous structure. This paper presents a detailed mathematical analysis of a relatively simple set of equations which is used to describe chemical vapor infiltration. The results demonstrate that the process is controlled by only two parameters, alpha and beta. The optimization problem associated with minimizing the infiltration time is also considered. Allowing alpha and beta to vary with time leads to significant reductions in the infiltration time, compared with the conventional case where alpha and beta are treated as constants.

Chang, H.-C.↗

Modeling of Alkane Oxidation Using Constituents and Species

It is currently not possible to perform simulations of turbulent reactive flows due in particular to complex chemistry, which may contain thousands of reactions and hundreds of species. This complex chemistry results in additional differential equations, making the numerical solution of the equation set computationally prohibitive. Reducing the chemical kinetics mathematical description is one of several important goals in turbulent reactive flow modeling. A chemical kinetics reduction model is proposed for alkane oxidation in air that is based on a parallel methodology to that used in turbulence modeling in the context of the Large Eddy Simulation. The objective of kinetic modeling is to predict the heat release and temperature evolution. This kinetic mechanism is valid over a pressure range from atmospheric to 60 bar, temperatures from 600 K to 2,500 K, and equivalence ratios from 0.125 to 8. This range encompasses diesel, HCCI, and gas-turbine engines, including cold ignition. A computationally efficient kinetic reduction has been proposed for alkanes that has been illustrated for n-heptane using the LLNL heptane mechanism. This model is consistent with turbulence modeling in that scales were first categorized into either those modeled or those computed as progress variables. Species were identified as being either light or heavy. The heavy species were decomposed into defined 13 constituents, and their total molar density was shown to evolve in a quasi-steady manner. The light species behave either in a quasi-steady or unsteady manner. The modeled scales are the total constituent molar density, Nc, and the molar density of the quasi-steady light species. The progress variables are the total constituent molar density rate evolution and the molar densities of the unsteady light species. The unsteady equations for the light species contain contributions of the type gain/loss rates from the heavy species that are modeled consistent with the developed mathematical forms for the total constituent molar density rate evolution; indeed, examination of these gain/loss rates shows that they also have a good quasi-steady behavior with a functional form resembling that of the constituent rate. This finding highlights the fact that the fitting technique provides a methodology that can be repeatedly used to obtain an accurate representation of full or skeletal kinetic models. Assuming success with the modified reduced model, the advantage of the modeling approach is clear. Because this model is based on the Nc rate rather than on that of individual heavy species, even if the number of species increases with increased carbon number in the alkane group, providing that the quasi-steady rate aspect persists, then extension of this model to higher alkanes should be conceptually straightforward, although it remains to be seen if the functional fits would remain valid or would require reconstruction.

Bellan, Jasette↗

Ion Atmosphere of Wormlike Micelles Profiled by Contrast Variation Small-Angle Neutron Scattering

Structural studies of wormlike micelles have so far mostly focused on the conformational properties of surfactant aggregates. The diffuse ionic atmosphere, which has a profound influence on various micellization phenomena such as thermodynamic stability and structural polymorphism, remains largely unexplored experimentally. In this report a strategy of contrast variation small-angle neutron scattering for this crucial structural study is outlined. Underlined by a general criterion established for unbiasedly identifying the length scale relevant to charge association from the spectral evolution, our analytical framework can provide a quantitative description of counterion distribution in a mathematically tractable manner. Overall, our method can be conveniently extended to facilitate structural studies of complex multicomponent systems using contrast variation neutron scattering.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Demand modelling of passenger air travel: An analysis and extension. Volume 1: Background and summary

The framework for a model of travel demand which will be useful in predicting the total market for air travel between two cities is discussed. Variables to be used in determining the need for air transportation where none currently exists and the effect of changes in system characteristics on attracting latent demand are identified. Existing models are examined in order to provide insight into their strong points and shortcomings. Much of the existing behavioral research in travel demand is incorporated to allow the inclusion of non-economic factors, such as convenience. The model developed is characterized as a market segmentation model. This is a consequence of the strengths of disaggregation and its natural evolution to a usable aggregate formulation. The need for this approach both pedagogically and mathematically is discussed.

Jacobson, I. D.↗

Demand modelling of passenger air travel: An analysis and extension, volume 2

Previous intercity travel demand models in terms of their ability to predict air travel in a useful way and the need for disaggregation in the approach to demand modelling are evaluated. The viability of incorporating non-conventional factors (i.e. non-econometric, such as time and cost) in travel demand forecasting models are determined. The investigation of existing models is carried out in order to provide insight into their strong points and shortcomings. The model is characterized as a market segmentation model. This is a consequence of the strengths of disaggregation and its natural evolution to a usable aggregate formulation. The need for this approach both pedagogically and mathematically is discussed. In addition this volume contains two appendices which should prove useful to the non-specialist in the area.

Jacobson, I. D.↗

A matched filter method for ground-based sub-noise detection of terrestrial extrasolar planets in eclipsing binaries: application to CM Draconis

The photometric detection of extrasolar planets by transits in eclipsing binary systems can be significantly improved by cross-correlating the observational light curves with synthetic models of possible planetary transit features, essentially a matched filter approach. We demonstrate the utility and application of this transit detection algorithm for ground-based detections of terrestrial-sized (Earth-to-Neptune radii) extrasolar planets in the dwarf M-star eclipsing binary system CM Draconis. Preliminary photometric observational data of this system demonstrate that the observational noise is well characterized as white and Gaussian at the observational time steps required for precision photometric measurements. Depending on planet formation scenarios, terrestrial-sized planets may form quite close to this low-luminosity system. We demonstrate, for example, that planets as small as 1.4 Earth radii with periods on the order of a few months in the CM Draconis system could be detected at the 99.9% confidence level in less than a year using 1-m class telescopes from the ground. This result contradicts commonly held assumptions limiting present ground-based efforts to, at best, detections of gas giant planets after several years of observation. This method can be readily extended to a number of other larger star systems with the utilization of larger telescopes and longer observing times. Its extension to spacecraft observations should also allow the determination of the presence of terrestrial-sized planets in nearly 100 other known eclipsing binary systems.

NASA Discipline Number 52-10↗