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NASA NTRS1988

A micromechanics model for the effective Young's modulus of a piecewise-isotropic laminate with wavy patterns

A mathematical model based on the Euler-Bernoulli beam theory is proposed for predicting the effective Young's moduli of piece-wise isotropic composite laminates with wavy patterns in the main load-carrying layers. Strains in corrugated layers, in-phase layers, and out-of-phase layers are predicted for various geometries and material configurations by assuming matrix layers as elastic foundations. Experimental results obtained from corrugated aluminum specimens and aluminum/epoxy specimens with in-phase and out-of-phase wavy patterns coincide very well with the predictions. The work represents a preliminary effort toward further generalization of the model for two-dimensional anisotropic laminates containing wavy patterns in the main load-carrying layers.

Lee, Jong-Won↗

NASA NTRS2003

Intelligent Machines in the 21st Century: Automating the Processes of Inference and Inquiry

The last century saw the application of Boolean algebra toward the construction of computing machines, which work by applying logical transformations to information contained in their memory. The development of information theory and the generalization of Boolean algebra to Bayesian inference have enabled these computing machines. in the last quarter of the twentieth century, to be endowed with the ability to learn by making inferences from data. This revolution is just beginning as new computational techniques continue to make difficult problems more accessible. However, modern intelligent machines work by inferring knowledge using only their pre-programmed prior knowledge and the data provided. They lack the ability to ask questions, or request data that would aid their inferences. Recent advances in understanding the foundations of probability theory have revealed implications for areas other than logic. Of relevance to intelligent machines, we identified the algebra of questions as the free distributive algebra, which now allows us to work with questions in a way analogous to that which Boolean algebra enables us to work with logical statements. In this paper we describe this logic of inference and inquiry using the mathematics of partially ordered sets and the scaffolding of lattice theory, discuss the far-reaching implications of the methodology, and demonstrate its application with current examples in machine learning. Automation of both inference and inquiry promises to allow robots to perform science in the far reaches of our solar system and in other star systems by enabling them to not only make inferences from data, but also decide which question to ask, experiment to perform, or measurement to take given what they have learned and what they are designed to understand.

Knuth, Kevin H.↗

NASA NTRS1983

Aerothermal modeling, phase 1. Volume 1: Model assessment

Phase 1 was conducted as part of the overall NASA Hot Section Technology (HOST) Program. The purpose of this effort was to determine the predictive accuracy of and the deficiencies within the various analytical modules comprising the overall combustor aerothermal model used at General Electric, as well as to formulate recommendations for improvement where needed. This effort involved the assembly of a benchmark quality data base from selected available literature, and from General Electric engine and combustor component test data. This data base was supplemented with additional definitive data obtained from an experimental test program conducted as part of the Phase 1 effort. Using selections from this data base, assessment studies were conducted to evaluate the various modules. Assessment of the internal flow module was conducted using 2-D parabolic and ellipitic, as well as 3-D elliptic internal flow calculations of definitive test data selected from the assembled data base. The 2-D assessment provided methodical examination of the mathematical techniques and the physical submodules, while the 3-D assessment focused on usefulness as a design tool. Calculations of combustor linear metal temperatures, pressure loss performance, and airflow distribution were performed using aerothermal modules which were in general use for many years at General Electric. The results of these assessment provided for the identification of deficiencies within the modules. The deficiencies were addressed in some detail providing a foundation on which to formulate a prioritized list of recommendations for improvement.

Kenworthy, M. J.↗

NASA NTRS1981

Guy cable design and damping for vertical axis wind turbines

Guy cables are frequently used to support vertical axis wind turbines since guying the turbine reduces some of the structural requirements on the tower. The guys must be designed to provide both the required strength and the required stiffness at the top of the turbine. The axial load which the guys apply to the tower, bearings, and foundations is an undesirable consequence of using guys to support the turbine. Limiting the axial load so that it does not significantly affect the cost of the turbine is an important objective of the cable design. The lateral vibrations of the cables is another feature of the cable design which needs to be considered. These aspects of the cable design are discussed, and a technique for damping cable vibrations was mathematically analyzed and demonstrated with experimental data.

Carne, T. G.↗

NASA NTRS2010

STEM Education Efforts in the Ares Projects

According to the National Science Foundation, of the more than 4 million first university degrees awarded in science and engineering in 2006, students in China earned about 21%, those in the European Union earned about 19%, and those in the United States earned about 11%. Statistics like these are of great interest to NASA's Ares Projects, which are responsible for building the rockets for the U.S. Constellation Program to send humans beyond low-Earth orbit. Science, technology, engineering, and mathematics students are essential for the long-term sustainability of any space program. Since the Projects creation, the Ares Outreach Team has used a variety of STEM-related media, methods, and materials to engage students, educators, and the general public in Constellation's mission. Like Project Apollo, the nation s exploration destinations and the vehicles used to get there can inspire students to learn more about STEM. Ares has been particularly active in public outreach to schools in Northern Alabama; on the Internet via outreach and grade-specific educational materials; and in more informal social media settings such as YouTube and Facebook. These combined efforts remain integral to America s space program, regardless of its future direction.

Doreswamy, Rajiv↗

NASA NTRS1988

Cracking of a layered medium on an elastic foundation under thermal shock

The cladded pressure vessel under thermal shock conditions which is simulated by using two simpler models was studied. The first model (Model 1) assumes that, if the crack size is very small compared to the vessel thickness, the problem can be treated as a semi-infinite elastic medium bonded to a very thin layer of different material. However, if the crack size is of the same order as the vessel thickness, the curvature effects may not be negligible. In this case it is assumed that the relatively thin walled hollow cylinder with cladding can be treated as a composite beam on an elastic foundation (Model 2). In both models, the effect of surface cooling rate is studied by assuming the temperature boundary condition to be a ramp function. The calculated results include the transient temperature, thermal stresses in the uncracked medium and stress intensity factors which are presented as a function of time, and the duration of cooling ramp. The stress intensity factors are also presented as a function of the size and the location of the crack. The problem is solved for two bonded materials of different thermal and mechanical properties. The mathematical formulation results in two singular integral equations which are solved numerically. The results are given for two material pairs, namely an austenitic steel layer welded on a ferritic steel substrate, and a ceramic coating on ferritic steel. In the case of the yielded clad, the stress intensity factors for a crack under the clad are determined by using a plastic strip model and are compared with elastic clad results.

Rizk, Abd El-Fattah A.↗

NASA NTRS2001

Discrete-State Simulated Annealing For Traveling-Wave Tube Slow-Wave Circuit Optimization

Algorithms based on the global optimization technique of simulated annealing (SA) have proven useful in designing traveling-wave tube (TWT) slow-wave circuits for high RF power efficiency. The characteristic of SA that enables it to determine a globally optimized solution is its ability to accept non-improving moves in a controlled manner. In the initial stages of the optimization, the algorithm moves freely through configuration space, accepting most of the proposed designs. This freedom of movement allows non-intuitive designs to be explored rather than restricting the optimization to local improvement upon the initial configuration. As the optimization proceeds, the rate of acceptance of non-improving moves is gradually reduced until the algorithm converges to the optimized solution. The rate at which the freedom of movement is decreased is known as the annealing or cooling schedule of the SA algorithm. The main disadvantage of SA is that there is not a rigorous theoretical foundation for determining the parameters of the cooling schedule. The choice of these parameters is highly problem dependent and the designer needs to experiment in order to determine values that will provide a good optimization in a reasonable amount of computational time. This experimentation can absorb a large amount of time especially when the algorithm is being applied to a new type of design. In order to eliminate this disadvantage, a variation of SA known as discrete-state simulated annealing (DSSA), was recently developed. DSSA provides the theoretical foundation for a generic cooling schedule which is problem independent, Results of similar quality to SA can be obtained, but without the extra computational time required to tune the cooling parameters. Two algorithm variations based on DSSA were developed and programmed into a Microsoft Excel spreadsheet graphical user interface (GUI) to the two-dimensional nonlinear multisignal helix traveling-wave amplifier analysis program TWA3. The algorithms were used to optimize the computed RF efficiency of a TWT by determining the phase velocity profile of the slow-wave circuit. The mathematical theory and computational details of the DSSA algorithms will be presented and results will be compared to those obtained with a SA algorithm.

Wilson, Jeffrey D.↗

NASA NTRS1963

Mathematical Optimization Techniques

The papers collected in this volume were presented at the Symposium on Mathematical Optimization Techniques held in the Santa Monica Civic Auditorium, Santa Monica, California, on October 18-20, 1960. The objective of the symposium was to bring together, for the purpose of mutual education, mathematicians, scientists, and engineers interested in modern optimization techniques. Some 250 persons attended. The techniques discussed included recent developments in linear, integer, convex, and dynamic programming as well as the variational processes surrounding optimal guidance, flight trajectories, statistical decisions, structural configurations, and adaptive control systems. The symposium was sponsored jointly by the University of California, with assistance from the National Science Foundation, the Office of Naval Research, the National Aeronautics and Space Administration, and The RAND Corporation, through Air Force Project RAND.

Bellman, R.↗

NASA NTRS1990

Robustness, generality and efficiency of optimization algorithms in practical applications

The theoretical foundations of two approaches, sequential quadratic programming (SQP) and optimality criteria (OC), are analyzed and compared, with emphasis on the critical importance of parameters such as accuracy, generality, robustness, efficiency, and ease of use in large scale structural optimization. A simplified fighter wing and active control of space structures are considered with other example problems. When applied to general system identification problems, the OC methods are shown to lose simplicity and demonstrate lack of generality, accuracy and robustness. It is concluded that the SQP method with a potential constraint strategy is a better choice as compared to the currently prevalent mathematical programming and OC approaches.

Thanedar, P. B.↗

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 NTRS1984

Mathematical modeling of fluid-electrolyte alterations during weightlessness

Fluid electrolyte metabolism and renal endocrine control as it pertains to adaptation to weightlessness were studied. The mathematical models that have been particularly useful are discussed. However, the focus of the report is on the physiological meaning of the computer studies. A discussion of the major ground based analogs of weightlessness are included; for example, head down tilt, water immersion, and bed rest, and a comparison of findings. Several important zero g phenomena are described, including acute fluid volume regulation, blood volume regulation, circulatory changes, longer term fluid electrolyte adaptations, hormonal regulation, and body composition changes. Hypotheses are offered to explain the major findings in each area and these are integrated into a larger hypothesis of space flight adaptation. A conceptual foundation for fluid electrolyte metabolism, blood volume regulation, and cardiovascular regulation is reported.

Leonard, J. I.↗

NASA NTRS2005

A Fundamental Mathematical Model of a Microbial Predenitrification System

Space flight beyond Low Earth Orbit requires sophisticated systems to support all aspects of the mission (life support, real-time communications, etc.). A common concern that cuts across all these systems is the selection of information technology (IT) methodology, software and hardware architectures to provide robust monitoring, diagnosis, and control support. Another dimension of the problem space is that different systems must be integrated seamlessly so that communication speed and data handling appear as a continuum (un-interrupted). One such team investigating this problem is the Advanced Integration Matrix (AIM) team whose role is to define the critical requirements expected of software and hardware to support an integrated approach to the command and control of Advanced Life Support (ALS) for future long-duration human space missions, including permanent human presence on the Moon and Mars. A goal of the AIM team is to set the foundation for testing criteria that will assist in specifying tasks, control schemes and test scenarios to validate and verify systems capabilities. This project is to contribute to the goals of the AIM team by assisting with controls planning for ALS. Control for ALS is an enormous problem it involves air revitalization, water recovery, food production, solids processing and crew. In more general terms, these systems can be characterized as involving both continuous and discrete processes, dynamic interactions among the sub-systems, nonlinear behavior due to the complex operations, and a large number of multivariable interactions due to the dimension of the state space. It is imperative that a baseline approach from which to measure performance is established especially when the expectation for the control system is complete autonomous control.

Hoo, Karlene A.↗

NASA NTRS1994

Databases post-processing in Tensoral

The Center for Turbulent Research (CTR) post-processing effort aims to make turbulence simulations and data more readily and usefully available to the research and industrial communities. The Tensoral language, introduced in this document and currently existing in prototype form, is the foundation of this effort. Tensoral provides a convenient and powerful protocol to connect users who wish to analyze fluids databases with the authors who generate them. In this document we introduce Tensoral and its prototype implementation in the form of a user's guide. This guide focuses on use of Tensoral for post-processing turbulence databases. The corresponding document - the Tensoral 'author's guide' - which focuses on how authors can make databases available to users via the Tensoral system - is currently unwritten. Section 1 of this user's guide defines Tensoral's basic notions: we explain the class of problems at hand and how Tensoral abstracts them. Section 2 defines Tensoral syntax for mathematical expressions. Section 3 shows how these expressions make up Tensoral statements. Section 4 shows how Tensoral statements and expressions are embedded into other computer languages (such as C or Vectoral) to make Tensoral programs. We conclude with a complete example program.

Dresselhaus, Eliot↗

NASA NTRS1996

Mechanical Response of Elastomers to Magnetic Fields

Elastomeric materials represent an important class of engineering materials, which are widely used to make components of structures, machinery, and devices for vibration and noise control. Elastomeric material possessing conductive or magnetic properties have been widely used in applications such as conductive and magnetic tapes, sensors, flexible permanent magnets, etc. Our interest in these materials has focussed on understanding and controlling the magnitude and directionality of their response to applied magnetic fields. The effect of magnetic fields on the mechanical properties of these materials has not been the subject of many published studies. Our interest and expertise in controllable fluids have given us the foundation to make a transition to controllable elastomers. Controllable elastomers are materials that exhibit a change in mechanical properties upon application of an external stimuli, in this case a magnetic field. Controllable elastomers promise to have more functionality than conventional elastomers and therefore could share the broad industrial application base with conventional elastomers. As such, these materials represent an attractive class of smart materials, and may well be a link that brings the applications of modern control technologies, intelligent structures and smart materials to a very broad industrial area. This presentation will cover our research work in the area of controllable elastomers at the Thomas Lord Research Center. More specifically, the presentation will discuss the control of mechanical properties and mathematical modeling of the new materials prepared in our laboratories along with experiments to achieve adaptive vibration control using the new materials.

Munoz, B. C.↗

NASA NTRSDate not supplied

Towards Sheaf Theoretic Analyses for Delay Tolerant Networking

The goal of Delay Tolerant Networking (DTN) is to take a collection of heterogeneous, disparate connections between satellites, space assets, ground stations, and ground infrastructure and bring it together into a cohesive, functioning overlay network. Depending on the systems being considered, one can find links with a one-way light time exceeding minutes (and hours),periodic links which can sometimes be predicted by orbital mechanics, and restrictions based on the variety of capabilities built into these systems. These characteristics preclude traditional network models and routing techniques and have classically led to either rigid routing tables or purely probabilistic models. As the deeper underlying structures remain unknown, development of more DTN-optimized algorithms has lacked the necessary foundation. In a continuation of previous work, the goal of this paper is to identify and study these fundamental structures that exist in delay tolerant networks (DTN), with a focus on space networks. The current routing methodology has been to use contact graph routing (CGR) algorithms. CGR models a series of known contacts as a static graph. For CGR to work, this graph must be globally consistent and must have an accurate picture of the network. Because this is a globally controlled structure, there is little room for flexibility in the event of changes to the network which would naturally occur as the network grows. As a response to the desire for flexibility as the network changes, we introduced the mathematical structure known as sheaves to DTNs last year. The tag-line for sheaves is that they are a mathematically precise way of gluing local data together into unique global data. Thus, sheaves lend extra power to traditional models(and routing algorithms) by taking additional information and merging it, in as consistent a manner as possible, with the representation itself. The clearest example of how Earth-bound networks exhibit behavior that is “sheafy” is link state routers, which build a local-to-global picture of their network by gluing local information together into a global network, exactly as a sheaf would do. For routing within delay tolerant networks to truly exploit this structure, a deeper structure than a graph is required. In this paper, we develop sheaves that can work over directed graphs such as temporal flow networks, we construct a sheaf representation for Dijkstra’s algorithm, and we outline a construction for routing sheaves capable of modeling multicast scenarios. Finally, there is a section of future work suggesting follow-on research.

Robert Short↗

NASA NTRS2021

Generation-based Evolutionary Tool for the Optimization of Constellations (GenETOC)

With the rapid growth in the capabilities of smaller satellites, satellite architectures that replace a single, extremely capable spacecraft with multiple, cheaper ones are gaining in popularity. Unfortunately, the orbit design process for constellations can be significantly more involved, especiallywhen the relative placement of the individual spacecraft within the constellation is not constrained by mission and/or science objectives. Optimizing a satellite constellation in the presence of multiple, competing objectives is a highly complex problem to which many traditional mathematical optimization methods cannot be applied and few tools exist to help mission designers search for promising candidate mission designs. The Generation-based Evolutionary Tool for the Optimization of Constellations (GenETOC) has been created to search for near-optimal constellation design options. GenETOC combines a modified version of the Non-dominated Sorting Genetic Algorithm II (NSGA II) with STK Components libraries (a 3rdparty .NET package created by Analytical Graphics Inc.) to create a framework that enables a mission designer to generate a simulation that models the design problem and obtain a family of potential, near-optimal solutions that can be investigated more in detail. GenETOC was developed in C# using the .NET framework with Windows Presentation Foundation (WPF) serving as the framework from which to create the graphical user interface (GUI). GenETOC user inputs can be categorized into three major data components: definition of the problem (areas of interest, satellite decision parameters, and sensor configurations), definition of performance objectives, and specification of the genetic algorithm (GA) parameters. In the problem definition component, the user is prompted to define the areas of interest against which the performance metrics will be computed, define the sensor parameters and attach them to specific spacecraft, select which satellite orbital parameters will be added to the decision space of the GA, and specify the range of desired values for each optimization parameter. For performance objectives, the user is presented with a list of available coverage and revisit performance based calculation options from which two metrics are chosen to serve as the objective functions that the GA will use to evaluate solutions during the optimization process. Finally, the definition of the GA parameters provides user control over the number of generations (number of optimization iterations), the population size (number of candidate constellations created in each generation), and the adaptive mutation and crossover threshold values (control parameters for how frequently each process occurs during the optimization). GenETOC has been extensively tested to verify the individual components of the optimization process. The GA has been tested against a suite of GA test problems to confirm convergence to the known two and three-dimensional Pareto fronts. The coverage and revisit performance metrics obtained in GenETOC are compared with STK desktop scenarios, confirming the constellations are being appropriately modeled within GenETOC simulations. A walkthrough of a simple, example problem is provided to illustrate the workings of GenETOC and to demonstrate the output available to the mission designer.

mission design↗

NASA NTRS2010

When Black Holes Collide

Among the fascinating phenomena predicted by General Relativity, Einstein's theory of gravity, black holes and gravitational waves, are particularly important in astronomy. Though once viewed as a mathematical oddity, black holes are now recognized as the central engines of many of astronomy's most energetic cataclysms. Gravitational waves, though weakly interacting with ordinary matter, may be observed with new gravitational wave telescopes, opening a new window to the universe. These observations promise a direct view of the strong gravitational dynamics involving dense, often dark objects, such as black holes. The most powerful of these events may be merger of two colliding black holes. Though dark, these mergers may briefly release more energy that all the stars in the visible universe, in gravitational waves. General relativity makes precise predictions for the gravitational-wave signatures of these events, predictions which we can now calculate with the aid of supercomputer simulations. These results provide a foundation for interpreting expect observations in the emerging field of gravitational wave astronomy.

Baker, John↗

NASA NTRS2014

ARES Biennial Report 2012 Final

Since the return of the first lunar samples, what is now the Astromaterials Research and Exploration Science (ARES) Directorate has had curatorial responsibility for all NASA-held extraterrestrial materials. Originating during the Apollo Program (1960s), this capability at Johnson Space Center (JSC) included scientists who were responsible for the science planning and training of astronauts for lunar surface activities as well as experts in the analysis and preservation of the precious returned samples. Today, ARES conducts research in basic and applied space and planetary science, and its scientific staff represents a broad diversity of expertise in the physical sciences (physics, chemistry, geology, astronomy), mathematics, and engineering organized into three offices (figure 1): Astromaterials Research (KR), Astromaterials Acquisition and Curation (KT), and Human Exploration Science (KX). Scientists within the Astromaterials Acquisition and Curation Office preserve, protect, document, and distribute samples of the current astromaterials collections. Since the return of the first lunar samples, ARES has been assigned curatorial responsibility for all NASA-held extraterrestrial materials (Apollo lunar samples, Antarctic meteorites - some of which have been confirmed to have originated on the Moon and on Mars - cosmic dust, solar wind samples, comet and interstellar dust particles, and space-exposed hardware). The responsibilities of curation consist not only of the longterm care of the samples, but also the support and planning for future sample collection missions and research and technology to enable new sample types. Curation provides the foundation for research into the samples. The Lunar Sample Facility and other curation clean rooms, the data center, laboratories, and associated instrumentation are unique NASA resources that, together with our staff's fundamental understanding of the entire collection, provide a service to the external research community, which relies on access to the samples. The curation efforts are greatly enhanced by a strong group of planetary scientists who conduct peerreviewed astromaterials research. Astromaterials Research Office scientists conduct peer-reviewed research as Principal or Co-Investigators in planetary science (e. g., cosmochemistry, origins of solar systems, Mars fundamental research, planetary geology and geophysics) and participate as Co-Investigators or Participating Scientists in many of NASA's robotic planetary missions. Since the last report, ARES has achieved several noteworthy milestones, some of which are documented in detail in the sections that follow. Within the Human Exploration Science Office, ARES is a world leader in orbital debris research, modeling and monitoring the debris environment, designing debris shielding, and developing policy to control and mitigate the orbital debris population. ARES has aggressively pursued refinements in knowledge of the debris environment and the hazard it presents to spacecraft. Additionally, the ARES Image Science and Analysis Group has been recognized as world class as a result of the high quality of near-real-time analysis of ascent and on-orbit inspection imagery to identify debris shedding, anomalies, and associated potential damage during Space Shuttle missions. ARES Earth scientists manage and continuously update the database of astronaut photography that is predominantly from Shuttle and ISS missions, but also includes the results of 40 years of human spaceflight. The Crew Earth Observations Web site (http://eol.jsc.nasa.gov/Education/ESS/crew.htm) continues to receive several million hits per month. ARES scientists are also influencing decisions in the development of the next generation of human and robotic spacecraft and missions through laboratory tests on the optical qualities of materials for windows, micrometeoroid/orbital debris shielding technology, and analog activities to assess surface science operations. ARES serves as host to numerous students and visiting scientists as part of the services provided to the research community and conducts a robust education and outreach program. ARES scientists are recognized nationally and internationally by virtue of their success in publishing in peer-reviewed journals and winning competitive research proposals. ARES scientists have won every major award presented by the Meteoritical Society, including the Leonard Medal, the most prestigious award in planetary science and cosmochemistry; the Barringer Medal, recognizing outstanding work in the field of impact cratering; the Nier Prize for outstanding research by a young scientist; and several recipients of the Nininger Meteorite Award. One of our scientists received the Department of Defense (DoD) Joint Meritorious Civilian Service Award (the highest civilian honor given by the DoD). ARES has established numerous partnerships with other NASA Centers, universities, and national laboratories. ARES scientists serve as journal editors, members of advisory panels and review committees, and society officers, and several scientists have been elected as Fellows in their professional societies. This biennial report summarizes a subset of the accomplishments made by each of the ARES offices and highlights participation in ongoing human and robotic missions, development of new missions, and planning for future human and robotic exploration of the solar system beyond low Earth orbit.

Stansbery, Eileen↗