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NASA NTRS2000

Terrestrial planet and asteroid formation in the presence of giant planets. I. Relative velocities of planetesimals subject to Jupiter and Saturn perturbations

We investigate the orbital evolution of 10(13)- to 10(25) -g planetesimals near 1 AU and in the asteroid belt (near 2.6 AU) prior to the stage of evolution when the mutual perturbations between the planetesimals become important. We include nebular gas drag and the effects of Jupiter and Saturn at their present masses and in their present orbits. Gas drag introduces a size-dependent phasing of the secular perturbations, which leads to a pronounced dip in encounter velocities (Venc) between bodies of similar mass. Plantesimals of identical mass have Venc approximately 1 and approximately 10 m s-1 (near 1 and 2.6 AU, respectively) while bodies differing by approximately 10 in mass have Venc approximately 10 and approximately 100 m s-1 (near 1 and 2.6 AU, respectively). Under these conditions, growth, rather than erosion, will occur only by collisions of bodies of nearly the same mass. There will be essentially no gravitational focusing between bodies less than 10(22) to 10(25) g, allowing growth of planetary embryos in the terrestrial planet region to proceed in a slower nonrunaway fashion. The environment in the asteroid belt will be even more forbidding and it is uncertain whether even the severely depleted present asteroid belt could form under these conditions. The perturbations of Jupiter and Saturn are quite sensitive to their semi-major axes and decrease when the planets' heliocentric distances are increased to allow for protoplanet migration. It is possible, though not clearly demonstrated, that this could produce a depleted asteroid belt but permit formation of a system of terrestrial planet embryos on a approximately 10(6)-year timescale, initially by nonrunaway growth and transitioning to runaway growth after approximately 10(5) years. The calculations reported here are valid under the condition that the relative velocities of the bodies are determined only by Jupiter and Saturn perturbations and by gas drag, with no mutual perturbations between planetesimals. If, while subject to these conditions, the bodies become large enough for their mutual perturbations to influence their velocity and size evolution significantly, the problem becomes much more complex. This problem is under investigation.

NASA Discipline Exobiology↗

NASA NTRS1986

Carbon dioxide evolution rate as a method to monitor and control an aerobic biological waste treatment system

An experimental system was developed to study the microbial growth kinetic of an undefined mixed culture in an erobic biological waste treatment process. The experimental results were used to develop a mathematical model that can predict the performance of a bioreactor. The bioreactor will be used to regeneratively treat waste material which is expected to be generated during a long term manned space mission. Since the presence of insoluble particles in the chemically undefined complex media made estimating biomass very difficult in the real system, a clean system was devised to study the microbial growth from the soluble substrate.

Lee, S. S.↗

NASA NTRSDate not supplied

From Research to Reality -- Challenges and Opportunities in Complex System Design

The scope and scale of our interconnected society requires that we view the world through a complex system lens, where numerous parts interact, and emergent behaviors are the norm. Understanding complex systems is critical for decision-making and policy development in domains such as ecological systems, financial markets, supply chains, and global transportation systems, where decision-makers need reliable information to predict the impact of decisions that may play out over decades. Traditional approaches to the research that produces this information are often insufficient, where hypotheses are tested in an isolated environment, and where the results may not carry over to the integrated system. There are a multitude of advancements in system engineering, artificial intelligence, and test and evaluation that are emerging to meet the challenge. Approaches such as agile development, model-based system engineering, design of experiments, large language models, and formal ontologies are providing ways to manage complexity and increase our collective ability to make the changes that we want to see in the world. In this talk I will provide a few examples related to the architecture of the National Airspace System (NAS), where we have investigated the use of large language models, basic formal ontology, and applied category theory to help researchers and system engineers be more effective in this complex design space. Bio: Dr. Ian Levitt’s current research focus is on the complex evolution of the National Airspace System. Prior to joining NASA in 2020, he was with the FAA leading international standards and national laboratory development for the agency. Dr. Levitt earned his PhD in mathematics from Rutgers University in 2009. His mission is to promote a healthy and continuous transformation of society through open information and cooperation.

Ian Levitt↗

NASA NTRS1983

Applications of state estimation in aircraft flight-data analysis

This paper traces the evolution of the use of state estimation in the analysis of aircraft flight data and discusses some recent applications associated with airline turbulence upsets and high-angle-of-attack flight tests. A unifying mathematical framework for state estimation is reviewed, and several examples are shown that illustrate a general approach for estimating variables that are difficult to measure. It is hoped that the diversity of the applications discussed and the examples presented will make the flight-data analyst mindful of the potential advantages of using state estimation methods.

Bach, R. E., Jr.↗

NASA NTRS1987

Theory of collapse and protostar formation

Interstellar clouds must increase in density by a factor of more than 10 to the 20th in order to form stars. Because observations of the phases intermediate between dense interstellar clouds and pre-main-sequence stars are difficult, theoretical solutions presently provide the primary means for exploring the collapse phase of protostellar formation. The mathematical formulation of the protostellar collapse problem is presented, and various methods employed in solving the equations are outlined. This tutorial emphasizes the numerical approach to the study of the nonlinear time-dependent evolution of collapsing interstellar clouds, including self-gravitation, rotation, and radiative transfer. Results are summarized for the restricted cases of spherical and axisymmetric symmetry, as well as for fully three-dimensional evolutions, and briefly compared to observations of star formation.

Boss, A. P.↗

NASA NTRS1986

multiplex gas chromatography: A novel analytical technique for future planetary studies

Determination of molecular species comprised of the biogenic elements in the atmospheres of planets and moons of the solar system is one the foremost requirements of the exobiologist studying chemical evolution and the origin of life. Multiplex chromatography is a technique where many samples are pseudo-randomly introduced to the chromatograph without regard to elution of preceding components. The resulting data are then reduced using mathematical techniques such as cross correlation or Fourier Transforms. To demonstrate the utility of this technique for future solar system exploration, chemical modulators were developed. Several advantages were realized from this technique in combination with these modulators: improvement in detection limits of several orders of magnitude, improvement in the analysis of complex mixtures by selectively modulating some of the components present in the sample, increase in the number of analyses that can be conducted in a given period of time, and reduction in the amount of expendables needed to run an analysis. In order to apply this technique in a real application, methane in ambient air was monitored continuously over a period of one week. By using ambient air as its own carrier all expendables beyond power were eliminated.

Valentin, J. R.↗

NASA NTRS2002

Plasmasphere Empirical Modeling with the IMAGE Mission

Empirical models of plasmaspheric properties date from the pioneering work of Storey where he developed the analysis of ground whistler observations that lead to his estimate for the equatorial plasma density at L=3. The most recent in situ satellite study takes us to 1000 CRRES satellite passes and a statistical analysis of the plasmapause location at all local times and for varying geomagnetic conditions by Moldwin et al. These and many other studies over the intervening 49 years have given us a strong familiarity with the distribution of cold plasmaspheric ions throughout the magnetosphere. The major components of inner plasmasphere, nightside bulge, sunward convection tail, and plasmapause are all well established. Storm-time erosion and the resulting ionospheric refilling has been encompassed, even if not completely understood. Small-scale density variations near the plasmapause and extending at least to geosynchronous orbit have been characterized in a variety of ways, even though we do not yet understand their origin. This paper will present early empirical modeling results from the inversion of IMAGE/EW global intensity images to density distributions. Densities are obtained in this initial study through use of forward image modeling with a simple 3-parameter plasmaspheric and plasmapause mathematical model. Individual interior plasmaspheric density profiles and plasmapause locations are obtained every 10 degrees in magnetic local time for each E W image analyzed. Derived profile parameters are statistically characterized in the context of storm magnitude and evolution. Identified patterns in the appearance of plasmaspheric structures, plasmapause erosion, and refilling will be presented. Comparisons to existing empirical plasmaspheric models and the implications for new modeling will be presented. Additional information is included in the original extended abstract.

Gallagher, D. L.↗

NASA NTRS1989

A priori predictions of the rotational constants for HC13N, HC15N, C5O

Ab initio molecular orbital theory is used to estimate the rotational constant for several carbon-chain molecules that are candidates for discovery in interstellar space. These estimated rotational constants can be used in laboratory or astronomical searches for the molecules. The rotational constant for HC13N is estimated to be 0.1073 +/- 0.0002 GHz and its dipole moment 5.4 D. The rotational constant for HC15N is estimated to be 0.0724 GHz, with a somewhat larger uncertainty. The rotational constant of C5O is estimated to be 1.360 +/- 2% GHz and its dipole moment 4.4. D.

NASA Discipline Exobiology↗

NASA NTRS2003

Active State Model for Autonomous Systems

The concept of the active state model (ASM) is an architecture for the development of advanced integrated fault-detection-and-isolation (FDI) systems for robotic land vehicles, pilotless aircraft, exploratory spacecraft, or other complex engineering systems that will be capable of autonomous operation. An FDI system based on the ASM concept would not only provide traditional diagnostic capabilities, but also integrate the FDI system under a unified framework and provide mechanism for sharing of information between FDI subsystems to fully assess the overall health of the system. The ASM concept begins with definitions borrowed from psychology, wherein a system is regarded as active when it possesses self-image, self-awareness, and an ability to make decisions itself, such that it is able to perform purposeful motions and other transitions with some degree of autonomy from the environment. For an engineering system, self-image would manifest itself as the ability to determine nominal values of sensor data by use of a mathematical model of itself, and selfawareness would manifest itself as the ability to relate sensor data to their nominal values. The ASM for such a system may start with the closed-loop control dynamics that describe the evolution of state variables. As soon as this model was supplemented with nominal values of sensor data, it would possess self-image. The ability to process the current sensor data and compare them with the nominal values would represent self-awareness. On the basis of self-image and self-awareness, the ASM provides the capability for self-identification, detection of abnormalities, and self-diagnosis.

Park, Han↗

NASA NTRS1993

Adjoint-Operator Learning For A Neural Network

Electronic neural networks made to synthesize initially unknown mathematical models of time-dependent phenomena or to learn temporally evolving patterns by use of algorithms based on adjoint operators. Algorithms less complicated, involve less computation and solve learning equations forward in time possibly simultaneously with equations of evolution of neural network, thereby both increasing computational efficiency and making real-time applications possible.

Barhen, Jacob↗

NASA NTRS2006

A Computational and Experimental Investigation of Shear Coaxial Jet Atomization

The instability and subsequent atomization of a viscous liquid jet emanated into a high-pressure gaseous surrounding is studied both computationally and experimentally. Liquid water issued into nitrogen gas at elevated pressures is used to simulate the flow conditions in a coaxial shear injector element relevant to liquid propellant rocket engines. The theoretical analysis is based on a simplified mathematical formulation of the continuity and momentum equations in their conservative form. Numerical solutions of the governing equations subject to appropriate initial and boundary conditions are obtained via a robust finite difference scheme. The computations yield real-time evolution and subsequent breakup characteristics of the liquid jet. The experimental investigation utilizes a digital imaging technique to measure resultant drop sizes. Data were collected for liquid Reynolds number between 2,500 and 25,000, aerodynamic Weber number range of 50-500 and ambient gas pressures from 150 to 1200 psia. Comparison of the model predictions and experimental data for drop sizes at gas pressures of 150 and 300 psia reveal satisfactory agreement particularly for lower values of investigated Weber number. The present model is intended as a component of a practical tool to facilitate design and optimization of coaxial shear atomizers.

Ibrahim, Essam A.↗

NASA NTRS1999

Pulse Phase Thermography for Defect Detection and Visualization

Pulse Phase Thermography (PPT) has been reported as a novel powerful technique of the thermal NDE. It employs application of the Discrete Fourier Transform (DFT) to thermal images obtained following flash heating of the front surface of a specimen. The computed phasegrams are excellent for defect visualization in a wide range of materials. This is in part due to their low sensitivity to uneven heating. This work is an attempt to analyze advantages and limitations of PPT. Results of application of the DFT to simulated temperature decays are presented. The temperature evolution on a surface has been simulated based on an analytical solution of the one-dimensional heat diffusion problem. A more sophisticated study has been done for different sizes of defects using numerical solution of the three-dimensional mathematical model. Capabilities of PPT for in-depth scanning and for monitoring of the material loss are discussed. The recommendations for the practical application of the PPT are presented. Experimental results obtained following these recommendations are reported.

Marinetti, Sergio↗

NASA NTRS1995

Radiation Pressure, Poynting-Robertson Drag, and Solar Wind Drag in the Restricted Three-Body Problem

In this paper, we examine the effects of radiation pressure, Poynting-Robertson (PR) drag, and solar wind drag on dust grains trapped in mean motion resonances with the Sun and Jupiter in the restricted (negligible dust mass) three-body Problem. We especially examine the evolution of dust grains in the 1:1 resonance. As a first step, the Sun and Jupiter are idealized to both be in circular orbit about a common center of mass (circular restricted three-body problem). From the equation of motion of the dust particle in the rotating reference frame, the drag-induced time rate of change of its Jacobi "constant," C, is then derived and expressed in spherical coordinates. This new mathematical expression in spherical coordinates shows that C, in the 1:1 resonance, both oscillates and secularly increases with increasing time. The new expression gives rise to an easy understanding of how an orbit evolves when the radiation force and solar wind drag are included. All dust grain orbits are unstable in time when PR and solar wind drag are included in the Sun-Jupiter-dust system. Tadpole orbits evolve into horseshoe orbits; and these orbits continuously expand in size to lead to close encounters with Jupiter. Permanent trapping is impossible. Orbital evolutions of a dust grain trapped in the 1:1 resonance in the planar circular, an inclined case, an eccentric case, and the actual Sun-Jupiter case are numerically simulated and compared with each other and show grossly similar time behavior. Resonances other than 1:1 are also explored with the new expression. Stable exterior resonance trapping may be possible under certain conditions. One necessary condition for such a trap is derived. Trapping in interior resonances is shown to be always unstable.

Liou, Jer-Chyi↗

NASA NTRS1982

The intercrater plains of Mercury and the Moon: Their nature, origin and role in terrestrial planet evolution. Measurement and errors of crater statistics

Planetary imagery techniques, errors in measurement or degradation assignment, and statistical formulas are presented with respect to cratering data. Base map photograph preparation, measurement of crater diameters and sampled area, and instruments used are discussed. Possible uncertainties, such as Sun angle, scale factors, degradation classification, and biases in crater recognition are discussed. The mathematical formulas used in crater statistics are presented.

Leake, M. A.↗

NASA NTRS2004

EHW Approach to Temperature Compensation of Electronics

Efforts are under way to apply the concept of evolvable hardware (EHW) to compensate for variations, with temperature, in the operational characteristics of electronic circuits. To maintain the required functionality of a given circuit at a temperature above or below the nominal operating temperature for which the circuit was originally designed, a new circuit would be evolved; moreover, to obtain the required functionality over a very wide temperature range, there would be evolved a number of circuits, each of which would satisfy the performance requirements over a small part of the total temperature range. The basic concepts and some specific implementations of EHW were described in a number of previous NASA Tech Briefs articles, namely, "Reconfigurable Arrays of Transistors for Evolvable Hardware" (NPO-20078), Vol. 25, No. 2 (February 2001), page 36; Evolutionary Automated Synthesis of Electronic Circuits (NPO- 20535), Vol. 26, No. 7 (July 2002), page 37; "Designing Reconfigurable Antennas Through Hardware Evolution" (NPO-20666), Vol. 26, No. 7 (July 2002), page 38; "Morphing in Evolutionary Synthesis of Electronic Circuits" (NPO-20837), Vol. 26, No. 8 (August 2002), page 31; "Mixtrinsic Evolutionary Synthesis of Electronic Circuits" (NPO-20773) Vol. 26, No. 8 (August 2002), page 32; and "Synthesis of Fuzzy-Logic Circuits in Evolvable Hardware" (NPO-21095) Vol. 26, No. 11 (November 2002), page 38. To recapitulate from the cited prior articles: EHW is characterized as evolutionary in a quasi-genetic sense. The essence of EHW is to construct and test a sequence of populations of circuits that function as incrementally better solutions of a given design problem through the selective, repetitive connection and/or disconnection of capacitors, transistors, amplifiers, inverters, and/or other circuit building blocks. The connection and disconnection can be effected by use of field-programmable transistor arrays (FPTAs). The evolution is guided by a search-andoptimization algorithm (in particular, a genetic algorithm) that operates in the space of possible circuits to find a circuit that exhibits an acceptably close approximation of the desired functionality. The evolved circuits can be tested by mathematical modeling (that is, computational simulation) only, tested in real hardware, or tested in combinations of computational simulation and real hardware.

Stoica, Adrian↗

NASA NTRS1994

Limits to randomness in paleobiologic models: the case of Phanerozoic species diversity

The question of how random, or unconstrained, paleobiologic models should be is examined with a case study: Signor's (1982, 1985) inverse calculation of levels of marine species diversity through the Phanerozoic. His calculation involved an ingenious model that estimated species numbers and species abundances in the world oceans of the past by correcting known numbers of fossil species for variations in sedimentary rocks available for sampling and in effort paleontologists might devote to sampling. The model proves robust to changes in possible shapes of species-abundance distributions, but it is sensitive to alterations in the assumption that paleontologists collect fossils at random. If it is assumed that ease of collecting varies with age of sediment (with the Cenozoic offering easy sampling) or that paleontologists tend to seek out rarer fossils, results of the inverse calculation change. In particular, the magnitude of the calculated Cenozoic diversity increase always declines from the factor of about seven as originally reported to something considerably smaller. This leaves open the problem of the magnitude of Cenozoic increase in marine species diversity, awaiting better empirical data and, perhaps, more exacting models, random or otherwise.

Non-NASA Center↗

NASA NTRS2004

Complexity of life via collective mind

e mind is introduced as a set of simple intelligent units (say, neurons, or interacting agents), which can communicate by exchange of information without explicit global control. Incomplete information is compensated by a sequence of random guesses symmetrically distributed around expectations with prescribed variances. Both the expectations and variances are the invariants characterizing the whole class of agents. These invariants are stored as parameters of the collective mind, while they contribute into dynamical formalism of the agents' evolution, and in particular, into the reflective chains of their nested abstract images of the selves and non-selves. The proposed model consists of the system of stochastic differential equations in the Langevin form representing the motor dynamics, and the corresponding Fokker-Planck equation representing the mental dynamics (Motor dynamics describes the motion in physical space, while mental dynamics simulates the evolution of initial errors in terms of the probability density). The main departure of this model from Newtonian and statistical physics is due to a feedback from the mental to the motor dynamics which makes the Fokker-Planck equation nonlinear. Interpretation of this model from mathematical and physical viewpoints, as well as possible interpretation from biological, psychological, and social viewpoints are discussed. The model is illustrated by the dynamics of a dialog.

collective intelligence↗

NASA NTRS1983

A unified mathematical theory of electrophoretic processes

A mathematical theory is presented which shows that each of the four classical electrophoretic modes (zone electrophoresis, moving boundary electrophoresis, isotachophoresis, and isoelectric focusing) is based on the same general principles and can collectively be described in terms of a single set of equations. This model can predict the evolution of the four electrophoretic modes as a function of time. The model system is one-dimensional, neglecting the effects of electroosmosis, temperature gradients, and any bulk flows of liquid. The model is based on equations which express the components' dissociation equilibria, the mass transport due to electromigration and diffusion, electroneutrality, and the conservation of mass and charge. The model consists of a system of coupled partial differential and nonlinear algebraic equations which can be solved numerically by use of a computer. The versatility of this model was verified using an example of a three-component system containing cacodylate, tris hydroxylmethylaminomethane, and histidine. Results show that this model not only correctly predicts the characteristic features of each electrophoretic mode, but also gives details of the concentration, pH, and conductivity profiles not easily amenable to direct experimental measurement.

Bier, M.↗