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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 NTRS2010

Physics of Life: A Model for Non-Newtonian Properties of Living Systems

This innovation proposes the reconciliation of the evolution of life with the second law of thermodynamics via the introduction of the First Principle for modeling behavior of living systems. The structure of the model is quantum-inspired: it acquires the topology of the Madelung equation in which the quantum potential is replaced with the information potential. As a result, the model captures the most fundamental property of life: the progressive evolution; i.e. the ability to evolve from disorder to order without any external interference. The mathematical structure of the model can be obtained from the Newtonian equations of motion (representing the motor dynamics) coupled with the corresponding Liouville equation (representing the mental dynamics) via information forces. All these specific non-Newtonian properties equip the model with the levels of complexity that matches the complexity of life, and that makes the model applicable for description of behaviors of ecological, social, and economical systems. Rather than addressing the six aspects of life (organization, metabolism, growth, adaptation, response to stimuli, and reproduction), this work focuses only on biosignature ; i.e. the mechanical invariants of life, and in particular, the geometry and kinematics of behavior of living things. Living things obey the First Principles of Newtonian mechanics. One main objective of this model is to extend the First Principles of classical physics to include phenomenological behavior on living systems; to develop a new mathematical formalism within the framework of classical dynamics that would allow one to capture the specific properties of natural or artificial living systems such as formation of the collective mind based upon abstract images of the selves and non-selves; exploitation of this collective mind for communications and predictions of future expected characteristics of evolution; and for making decisions and implementing the corresponding corrections if the expected scenario is different from the originally planned one. This approach postulates that even a primitive living species possesses additional, non-Newtonian properties that are not included in the laws of Newtonian or statistical mechanics. These properties follow from a privileged ability of living systems to possess a self-image (a concept introduced in psychology) and to interact with it. The proposed mathematical system is based on the coupling of the classical dynamical system representing the motor dynamics with the corresponding Liouville equation describing the evolution of initial uncertainties in terms of the probability density and representing the mental dynamics. The coupling is implemented by the information-based supervising forces that can be associated with self-awareness. These forces fundamentally change the pattern of the probability evolution, and therefore, lead to a major departure of the behavior of living systems from the patterns of both Newtonian and statistical mechanics. This innovation is meant to capture the signature of life based only on observable behavior, not on any biochemistry. This will not prevent the use of this model for developing artificial living systems, as well as for studying some general properties of behavior of natural, living systems.

Zak, Michail↗
NASA NTRS1993

Analysis of the distribution of pitch angles in model galactic disks - Numerical methods and algorithms

An automated mathematical method capable of successfully isolating the many different features in prototype and observed spiral galaxies and of accurately measuring the pitch angles and lengths of these individual features is developed. The method is applied to analyze the evolution of specific features in a prototype galaxy exhibiting flocculent spiral structure. The mathematical-computational method was separated into two components. Initially, the galaxy was partitioned into dense regions constituting features using two different methods. The results obtained using these two partitioning algorithms were very similar, from which it is inferred that no numerical biasing was evident and that capturing of the features was consistent. Standard least-squares methods underestimated the true slope of the cloud distribution and were incapable of approximating an orientation of 45 deg. The problems were overcome by introducing a superior fit least-squares method, developed with the intention of calculating true orientation rather than a regression line.

Russell, William S.↗
NASA NTRS1994

Adiabatic invariants in stellar dynamics. 1: Basic concepts

The adiabatic criterion, widely used in astronomical dynamics, is based on the harmonic oscillator. It asserts that the change in action under a slowly varying perturbation is exponentially small. Recent mathematical results that precisely define the conditions for invariance show that this model does not apply in general. In particular, a slowly varying perturbation may cause significant evolution stellar dynamical systems even if its time scale is longer than any internal orbital time scale. This additional 'heating' may have serious implications for the evolution of star clusters and dwarf galaxies which are subject to long-term environmental forces. The mathematical developments leading to these results are reviewed, and the conditions for applicability to and further implications for stellar systems are discussed. Companion papers present a computational method for a general time-dependent disturbance and detailed example.

Weinberg, Martin D.↗
NASA NTRS1976

Equivalence of equations describing trace element distribution during equilibrium partial melting

It is shown that four equations used for calculating the evolution of trace-element abundances during equilibrium partial melting are mathematically equivalent. The equations include those of Hertogen and Gijbels (1976), Shaw (1970), Schilling (1971), and O'Nions and Clarke (1972). The general form to which all these equations reduce is presented, and an analysis is performed to demonstrate their mathematical equivalence. It is noted that the utility of the general equation flows from the nature of equilibrium (i.e., the final state is independent of the path by which that state is attained).

Consolmagno, G. J.↗
NASA NTRS1999

Direct Numerical Simulation of Wetting and Spreading Behavior on Heterogeneous and Roughened Substrates

A method of calculation is presented that allows the simulation of the time-dependent three-dimensional motion of thin liquid layers on solid substrates for systems with finite equilibrium contact angles. The contact angle is a prescribed function of position on the substrate. Similar mathematical models are constructed for substrates with a pattern of roughness. Evolution equations are given, using the lubrication approximation, that include viscous, capillary and disjoining forces. Motion to and from dry substrate regions is made possible by use of a thin energetically-stable wetting layer. We simulate motion on heterogeneous substrates with periodic arrays of high contact-angle patches. Two different problems are treated for heterogenous substrates. The first is spontaneous motion driven only by wetting forces. If the contact-angle difference is sufficiently high, the droplet can find several different stable positions, depending on the previous history of the motion. A second simulation treats a forced cyclical motion. Energy dissipation per cycle for a heterogeneous substrate is found to be larger than for a uniform substrate with the same total energy. The Landau-Levich solution for plate removal from a liquid bath is extended to account for a pattern of roughness on the plate.

Schwartz, Leonard W.↗
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 NTRS1990

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.↗
NASA NTRS1994

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.↗
NASA NTRS2004

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↗
NASA NTRS1997

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.↗
NASA NTRS2010

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↗
NASA NTRS1978

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.↗
NASA NTRS1978

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.↗
NASA NTRS1996

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↗
NASA NTRS2019

Complex Dynamics of Air Traffic Flow

Air traffic in the United States has continued to grow at a steady pace since 1980, except for a dip immediately after the tragic events of September 11, 2001. There are different growth scenarios associated both with the magnitude and the composition of the future air traffic. The Terminal Area Forecast (TAF), prepared every year by the FAA, projects the growth of traffic in the United States. Both Boeing and Airbus publish market outlooks for air travel annually. Although predicting the future growth of traffic is difficult, there are two significant trends: heavily congested major airports continue to see an increase in traffic, and the emergence of regional jets and other smaller aircraft with fewer passengers operating directly between non-major airports. The interaction between air traffic demand and the ability of the system to provide the necessary airport and airspace resources can be modeled as a network. The size of the resulting network varies depending on the choice of its nodes. It would be useful to understand the properties of this network to guide future design and development. Many questions, such as the growth of delay with increasing traffic demand and impact of the en route weather on future air traffic, require a systematic understanding of the properties of the air traffic network. There has been a major advance in the understanding of the behavior of networks with a large number of components. Several theories have been advanced about the evolution of large biological and engineering networks by authors in diversified disciplines like physics, mathematics, biology and computer science. Several networks exhibit a scale-free property in the sense that the probabilistic distribution of their nodes as a function of connections decreases slower than an exponential. These networks are characterized by the fact that a small number of components have a disproportionate influence on the performance of the network. Scale-free networks are tolerant to random failure of components, but are vulnerable to selective attack on components. This paper examines two network representations for the baseline air traffic system. A network defined with the 40 major airports as nodes and with standard flight routes as links has a characteristic scale: all nodes have 60 or more links and no node has more than 460 links. Another network is defined with baseline aircraft routing structure exhibits an exponentially truncated scale-free behavior. Its degree ranges from 2 connections to 2900 connections, and 225 nodes have more than 250 connections. Furthermore, those high-degree nodes are homogeneously distributed in the airspace. A consequence of this scale-free behavior is that the random loss of a single node has little impact, but the loss of multiple high-degree nodes (such as occurs during major storms in busy airspace) can adversely impact the system. Two future scenarios of air traffic growth are used to predict the growth of air traffic in the United States. It is shown that a three-times growth in the overall traffic may result in a ten-times impact on the density of traffic in certain parts of the United States.

Scale-free Networks↗
NASA NTRS2001

Mathematical Modeling of Ni/H2 and Li-Ion Batteries

The modelling effort outlined in this viewgraph presentation encompasses the following topics: 1) Electrochemical Deposition of Nickel Hydroxide; 2) Deposition rates of thin films; 3) Impregnation of porous electrodes; 4) Experimental Characterization of Nickel Hydroxide; 5) Diffusion coefficients of protons; 6) Self-discharge rates (i.e., oxygen-evolution kinetics); 7) Hysteresis between charge and discharge; 8) Capacity loss on cycling; 9) Experimental Verification of the Ni/H2 Battery Model; 10) Mathematical Modeling Li-Ion Batteries; 11) Experimental Verification of the Li-Ion Battery Model; 11) Integrated Power System Models for Satellites; and 12) Experimental Verification of Integrated-Systems Model.

Weidner, John W.↗