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NASA NTRS2001

Radiometry Measurements of Mars at 1064 nm Using the Mars Orbiter Laser Altimeter

Measurements by the Mars Orbiter Laser Altimeter (MOLA) on board the Mars Global Surveyor (MGS) may be used to provides a radiometric measurement of Mars in addition to the topographic measurement. We will describe the principle of operation, a mathematical model, and the receiver calibration in this presentation. MOLA was designed primarily to measure Mars topography, surface roughness end the bidirectional reflectance to the laser beam. To achieve the highest sensitivity the receiver detection threshold is dynamically adjusted to be as low as possible while keeping a predetermined false alarm rate. The average false alarm rate 29 monitored in real time on board MOLA via a noise counter, whose output is fed to the threshold control loop. The false alarm rate at a given threshold is a function of the detector output noise which is the sum of the photo detector, shot noise due to the background light seen by the detector and the dark noise. A mathematical model has been developed that can be used to numerically solve for the optical background power given the MOLA threshold setting and the average noise count. The radiance of Mars can then be determined by dividing the optical power by the solid angle subtended by the MOLA receiver, the receiver optical band-width, end the Mars surface area within the receiver field of view. The phase angle which is the sun-Mars-MOLA angle is available from the MGS database. MOLA also measures simultaneously the bidirectional reflectance of Mars vie its 106-lum loser beam at nadir with nearly zero phase angle. The optical bandwidth of the MOLA receiver is 2um full width at half maximum (FWHM) and centered at 106-lum. The receiver field of view is 0.95mrad FWHM. The nominated spacecraft altitude is 100km and the ground track speed is about 3km/s. Under normal operation, the noise counter are read and the threshold levels are updated at 1Hz. The receiver sensitivity is limited by the detector dark noise to about 0.1nW, which corresponds to less than 2% the maximum radiance during daytime from the brightest area on Mars. The results from the mathematical model agree well with the prelaunch measurements at several calibrated optical power levels. The radiance of sunlit Mars estimated with this technique correlates well with the measurement from the MGS. Thermal Emission Spectrometer (TES) and the Hubble Space Telescope at similar wavelength.

Sun, Xiao-Li↗

NASA NTRS1995

Scientific Visualization and Computational Science: Natural Partners

Scientific visualization is developing rapidly, stimulated by computational science, which is gaining acceptance as a third alternative to theory and experiment. Computational science is based on numerical simulations of mathematical models derived from theory. But each individual simulation is like a hypothetical experiment; initial conditions are specified, and the result is a record of the observed conditions. Experiments can be simulated for situations that can not really be created or controlled. Results impossible to measure can be computed.. Even for observable values, computed samples are typically much denser. Numerical simulations also extend scientific exploration where the mathematics is analytically intractable. Numerical simulations are used to study phenomena from subatomic to intergalactic scales and from abstract mathematical structures to pragmatic engineering of everyday objects. But computational science methods would be almost useless without visualization. The obvious reason is that the huge amounts of data produced require the high bandwidth of the human visual system, and interactivity adds to the power. Visualization systems also provide a single context for all the activities involved from debugging the simulations, to exploring the data, to communicating the results. Most of the presentations today have their roots in image processing, where the fundamental task is: Given an image, extract information about the scene. Visualization has developed from computer graphics, and the inverse task: Given a scene description, make an image. Visualization extends the graphics paradigm by expanding the possible input. The goal is still to produce images; the difficulty is that the input is not a scene description displayable by standard graphics methods. Visualization techniques must either transform the data into a scene description or extend graphics techniques to display this odd input. Computational science is a fertile field for visualization research because the results vary so widely and include things that have no known appearance. The amount of data creates additional challenges for both hardware and software systems. Evaluations of visualization should ultimately reflect the insight gained into the scientific phenomena. So making good visualizations requires consideration of characteristics of the user and the purpose of the visualization. Knowledge about human perception and graphic design is also relevant. It is this breadth of knowledge that stimulates proposals for multidisciplinary visualization teams and intelligent visualization assistant software. Visualization is an immature field, but computational science is stimulating research on a broad front.

Uselton, Samuel P.↗

NASA NTRS2002

Evaluating the Effectiveness of the 1999-2000 NASA CONNECT Program

NASA CONNECT is a standards-based, integrated mathematics, science, and technology series of 30-minute instructional distance learning (satellite and television) programs for students in grades 6-8. Each of the five programs in the 1999-2000 NASA CONNECT series included a lesson, an educator guide, a student activity or experiment, and a web-based component. In March 2000, a mail (self-reported) survey (booklet) was sent to a randomly selected sample of 1,000 NASA CONNECT registrants. A total of 336 surveys (269 usable) were received by the established cut-off date. Most survey questions employed a 5-point Likert-type response scale. Survey topics included (1) instructional technology and teaching, (2) instructional programming and technology in the classroom, (3) the NASA CONNECT program, (4) classroom use of computer technology, and (5) demographics. About 73% of the respondents were female, about 92% identified "classroom teacher" as their present professional duty, about 90% worked in a public school, and about 62% held a master's degree or master's equivalency. Regarding NASA CONNECT, respondents reported that (1) they used the five programs in the 1999-2000 NASA CONNECT series; (2) the stated objectives for each program were met (4.54); (3) the programs were aligned with the national mathematics, science, and technology standards (4.57); (4) program content was developmentally appropriate for grade level (4.17); and (5) the programs in the 1999-2000 NASA CONNECT series enhanced/enriched the teaching of mathematics, science, and technology (4.51).

Pinelli, Thomas E.↗

NASA NTRS2002

CaTs Lab (CHAOS and Thermal Sciences Laboratory)

The CHAOS and Thermal Sciences Laboratory (CaTs) at James Madison University evolved into a noteworthy effort to increase minority representation in the sciences and mathematics. Serving ten students and faculty directly, and nearly 50 students indirectly, CaTs, through recruitment efforts, workshops, mentoring programs, tutorial services and research and computational laboratories, fulfilled its intent to initiate an academically enriched research program aimed at strengthening the academic and self-actualization skills of undergraduate students with potential to pursue doctoral study in the sciences. The stated goal of the program was to increase by 5% the number of enrolled mathematics and science students into the program. Success far exceeded the program goals by producing 100% graduation rate of all supported recipients during its tenure, with 30% of the students subsequently in pursuit of graduate degrees. Student retention in the program exceeded 90% and faculty participation exceeded the three members involved in mentoring and tutoring, gaining multi-disciplinary support. Aggressive marketing of the program resulted in several paid summer internships and commitments from NASA and an ongoing relationship with CHROME, a nationally recognized organization which focuses on developing minority students in the sciences and mathematics. Success of the program was only limited by the limited fiscal resources at NASA which resulted in phasing out of the program.

Teate, Anthony A.↗

NASA NTRS2002

Implementing a Workforce Development Pipeline

Through science, technology, mathematics, and engineering, our nation continues to lead the world in the development and utilization of new technologies. Whether related to our health, to the environment, or to our production of material goods, science, mathematics, engineering, and technology are integral and essential parts of daily life for virtually everyone in the United States and around the globe. However, the understanding of science, mathematics, engineering, and technology by most Americans is inadequate for full participation in this increasingly technological world. This reflects the level of education in these areas most Americans have received. To have a competent workforce for the future, we must assist education in developing students for future jobs.

Billy Hix↗

NASA NTRS2002

An Introduction to Tensors for Students of Physics and Engineering

Tensor analysis is the type of subject that can make even the best of students shudder. My own post-graduate instructor in the subject took away much of the fear by speaking of an implicit rhythm in the peculiar notation traditionally used, and helped us to see how this rhythm plays its way throughout the various formalisms. Prior to taking that class, I had spent many years "playing" on my own with tensors. I found the going to be tremendously difficult but was able, over time, to back out some physical and geometrical considerations that helped to make the subject a little more transparent. Today, it is sometimes hard not to think in terms of tensors and their associated concepts. This article, prompted and greatly enhanced by Marlos Jacob, whom I've met only by e-mail, is an attempt to record those early notions concerning tensors. It is intended to serve as a bridge from the point where most undergraduate students "leave off" in their studies of mathematics to the place where most texts on tensor analysis begin. A basic knowledge of vectors, matrices, and physics is assumed. A semi-intuitive approach to those notions underlying tensor analysis is given via scalars, vectors, dyads, triads, and higher vector products. The reader must be prepared to do some mathematics and to think. For those students who wish to go beyond this humble start, I can only recommend my professor's wisdom: find the rhythm in the mathematics and you will fare pretty well.

Kolecki, Joseph C.↗

NASA NTRS2002

Evaluating the Effectiveness of the 2000-2001 NASA "Why?" Files Program

NASA 'Why?' Files, a research and standards-based, Emmy-award winning series of 60-minute instructional programs for grades 3-5, introduces students to NASA; integrates mathematics, science, and technology by using Problem-Based Learning (PBL), scientific inquiry, and the scientific method; and motivates students to become critical thinkers and active problem solvers. All four 2000-2001 NASA 'Why?' Files programs include an instructional broadcast, a lesson guide, an interactive web site, plus numerous instructional resources. In March 2001, 1,000 randomly selected program registrants participated in a survey. Of these surveys, 185 (154 usable) met the established cut-off date. Respondents reported that (1) they used the four programs in the 2000-2001 NASA 'Why?' Files series; (2) series goals and objectives were met; (3) programs met national mathematics, science, and technology standards; (4) program content was developmentally appropriate for grade level; and (5) programs enhanced/enriched the teaching of mathematics, science, and technology.

Pinelli, Thomas E.↗

NASA NTRS2002

Evaluating the Effectiveness of the 2001-2002 NASA CONNECT(tm) Program

NASA CONNECT(tm) is a research and standards-based, integrated mathematics, science, and technology series of 30-minute instructional distance learning (television and web-based) programs for students in grades 6-8. Respondents who evaluated the programs in the 2001-2002 NASA CONNECT(tm) series reported that (1) they used the programs in the series; (2) the goals and objectives for the series were met; (3) the programs were aligned with the national mathematics, science, and technology standards; (4) the program content was developmentally appropriate for grade level; and (5) the programs in the series enhanced and enriched the teaching of mathematics, science, and technology.

Pinelli, Thomas E.↗

NASA NTRS2002

NASA Langley/CNU Distance Learning Programs

NASA Langley Research Center and Christopher Newport University (CNU) provide, free to the public, distance learning programs that focus on math, science, and/or technology over a spectrum of education levels from K-adult. The effort started in 1997, and we currently have a suite of five distance-learning programs. We have around 450,000 registered educators and 12.5 million registered students in 60 countries. Partners and affiliates include the American Institute of Aeronautics and Astronautics (AIAA), the Aerospace Education Coordinating Committee (AECC), the Alliance for Community Media, the National Educational Telecommunications Association, Public Broadcasting System (PBS) affiliates, the NASA Learning Technologies Channel, the National Council of Teachers of Mathematics (NCTM), the Council of the Great City Schools, Hampton City Public Schools, Sea World Adventure Parks, Busch Gardens, ePALS.com, and Riverdeep. Our mission is based on the "Horizon of Learning," a vision for inspiring learning across a continuum of educational experiences. The programs form a continuum of educational experiences for elementary youth through adult learners. The strategic plan for the programs will evolve to reflect evolving national educational needs, changes within NASA, and emerging system initiatives. Plans for each program component include goals, objectives, learning outcomes, and rely on sound business models. It is well documented that if technology is used properly it can be a powerful partner in education. Our programs employ both advances in information technology and in effective pedagogy to produce a broad range of materials to complement and enhance other educational efforts. Collectively, the goals of the five programs are to increase educational excellence; enhance and enrich the teaching of mathematics, science, and technology; increase scientific and technological literacy; and communicate the results of NASA discovery, exploration, innovation and research. All pre-college distance learning programs support the national mathematics, science, and technology standards; support K-12 systemic change; involve educators in their development, implementation, and evaluation; and are based on alliances and partnerships. In addition the programs seek to invoke a sense of geographic, ethnic and cultural diversity by featuring schools from all over the U.S.; schools from urban, suburban, and rural areas; public, private, and religious schools; and schools with large populations of African-American, Asian and Hispanic students.

Caton, Randall↗

NASA NTRS2003

Quantifying Astronaut Tasks: Robotic Technology and Future Space Suit Design

The primary aim of this research effort was to advance the current understanding of astronauts' capabilities and limitations in space-suited EVA by developing models of the constitutive and compatibility relations of a space suit, based on experimental data gained from human test subjects as well as a 12 degree-of-freedom human-sized robot, and utilizing these fundamental relations to estimate a human factors performance metric for space suited EVA work. The three specific objectives are to: 1) Compile a detailed database of torques required to bend the joints of a space suit, using realistic, multi- joint human motions. 2) Develop a mathematical model of the constitutive relations between space suit joint torques and joint angular positions, based on experimental data and compare other investigators' physics-based models to experimental data. 3) Estimate the work envelope of a space suited astronaut, using the constitutive and compatibility relations of the space suit. The body of work that makes up this report includes experimentation, empirical and physics-based modeling, and model applications. A detailed space suit joint torque-angle database was compiled with a novel experimental approach that used space-suited human test subjects to generate realistic, multi-joint motions and an instrumented robot to measure the torques required to accomplish these motions in a space suit. Based on the experimental data, a mathematical model is developed to predict joint torque from the joint angle history. Two physics-based models of pressurized fabric cylinder bending are compared to experimental data, yielding design insights. The mathematical model is applied to EVA operations in an inverse kinematic analysis coupled to the space suit model to calculate the volume in which space-suited astronauts can work with their hands, demonstrating that operational human factors metrics can be predicted from fundamental space suit information.

Newman, Dava↗

NASA NTRS2004

Evaluating the Effectiveness of the 2002-2003 NASA CONNECT(TM) Program

NASA CONNECT is a research-, inquiry-, and standards-based, integrated mathematics, science, and technology series of 30-minute instructional distance learning (television and web-based) programs for students in grades 6 8. Respondents who evaluated the programs in the 2002 2003 NASA CONNECT series reported that (1) they used the programs in the series; (2) the goals and objectives for the series were met; (3) the programs were aligned with the national mathematics, science, and technology standards; (4) the program content was developmentally appropriate for grade level; and (5) the programs in the series enhanced and enriched the teaching of mathematics, science, and technology.

Pinelli, Thomas E.↗

NASA NTRS2004

Evaluating the Effectiveness of the 2002-2003 NASA SCIence Files(TM) Program

NASA SCIence Files (tm) is a research-, inquiry-, and standards-based, integrated mathematics, science, and technology series of 60-minute instructional distance learning (television and web-based) programs for students in grades 3-5. Respondents who evaluated the programs in the 2002-2003 NASA SCIence Files (tm) series reported that (1) they used the programs in the series; (2) the goals and objectives for the series were met; (3) the programs were aligned with the national mathematics, science, and technology standards; (4) the program content was developmentally appropriate for grade level; and (5) the programs in the series enhanced and enriched the teaching of mathematics, science, and technology.

Pinelli, Thomas E.↗

NASA NTRS2004

Theory, Modeling, Software and Hardware Development for Analytical and Computational Materials Science

The focus of this Cooperative Agreement between the Computational Materials Laboratory (CML) of the Processing Science and Technology Branch of the NASA Glenn Research Center (GRC) and the Department of Theoretical and Applied Mathematics at The University of Akron was in the areas of system development of the CML workstation environment, modeling of microgravity and earth-based material processing systems, and joint activities in laboratory projects. These efforts complement each other as the majority of the modeling work involves numerical computations to support laboratory investigations. Coordination and interaction between the modelers, system analysts, and laboratory personnel are essential toward providing the most effective simulations and communication of the simulation results. Toward these means, The University of Akron personnel involved in the agreement worked at the Applied Mathematics Research Laboratory (AMRL) in the Department of Theoretical and Applied Mathematics while maintaining a close relationship with the personnel of the Computational Materials Laboratory at GRC. Network communication between both sites has been established. A summary of the projects we undertook during the time period 9/1/03 - 6/30/04 is included.

Young, Gerald W.↗

NASA NTRS1994

Physiological time-series analysis: what does regularity quantify?

Approximate entropy (ApEn) is a recently developed statistic quantifying regularity and complexity that appears to have potential application to a wide variety of physiological and clinical time-series data. The focus here is to provide a better understanding of ApEn to facilitate its proper utilization, application, and interpretation. After giving the formal mathematical description of ApEn, we provide a multistep description of the algorithm as applied to two contrasting clinical heart rate data sets. We discuss algorithm implementation and interpretation and introduce a general mathematical hypothesis of the dynamics of a wide class of diseases, indicating the utility of ApEn to test this hypothesis. We indicate the relationship of ApEn to variability measures, the Fourier spectrum, and algorithms motivated by study of chaotic dynamics. We discuss further mathematical properties of ApEn, including the choice of input parameters, statistical issues, and modeling considerations, and we conclude with a section on caveats to ensure correct ApEn utilization.

NASA Discipline Cardiopulmonary↗

NASA NTRS2005

Project LAUNCH: Bringing Space into Math and Science Classrooms

Project LAUNCH is a K-12 teacher professional development program, which has been created in collaboration between the Whitaker Center for Science, Mathematics and Technology Education at Florida Gulf Coast University (FGCU), and the Florida Space Research Institute (FSRI). Utilizing Space as the overarching theme it is designed to improve mathematics and science teaching, using inquiry based, hands-on teaching practices, which are aligned with Florida s Sunshine State Standards. Many students are excited about space exploration and it provides a great venue to get them involved in science and mathematics. The scope of Project LAUNCH however goes beyond just providing competency in the subject area, as pedagogy is also an intricate part of the project. Participants were introduced to the Conceptual Change Model (CCM) [1] as a framework to model good teaching practices. As the CCM closely follows what scientists call the scientific process, this teaching method is also useful to actively engage institute participants ,as well as their students, in real science. Project LAUNCH specifically targets teachers in low performing, high socioeconomic schools, where the need for skilled teachers is most critical.

Fauerbach, M.↗

NASA NTRS2005

A Theoretical Investigation of Oxidation Efficiency of a Volatile Removal Assembly Reactor Under Microgravity Conditions

Volatile Removal Assembly (VRA) is a subsystem of the Closed Environment Life Support System (CELSS) installed in the International Space Station. It is used for removing contaminants (volatile organics) in the wastewater produced by the space station crews. The major contaminants are formic acid, ethanol, and propylene glycol. The VRA contains a slim packbed reactor (3.5 cm diameter and four 28 cm long tubes in series) to perform catalyst oxidation of wastewater at elevated pressure and temperature under microgravity conditions. In the reactor, the contaminants are burned with oxygen gas (O2) to form water and carbon dioxide (CO2) that dissolves in the water stream. Optimal design of the reactor requires a thorough understanding about how the reactor performs under microgravity conditions. The objective of this study was to develop a mathematical model to interpret experimental data obtained from normal and microgravity conditions, and to predict the performance of VRA reactor under microgravity conditions. Catalyst oxidation kinetics and the total oxygen-water contact area control the efficiency of catalyst oxidation for mass transfer, which depends on oxygen gas holdup and distribution in the reactor. The process involves bubbly flow in porous media with chemical reactions in microgravity environment. This presents a unique problem in fluid dynamics that has not been studied. Guo et al. (2004) developed a mathematical model that predicts oxygen holdup in the VRA reactor. No mathematical model has been found in the literature that can be used to predict the efficiency of catalyst oxidation under microgravity conditions.

Guo, Boyun↗

NASA NTRS2005

Safety Verification of the Small Aircraft Transportation System Concept of Operations

A critical factor in the adoption of any new aeronautical technology or concept of operation is safety. Traditionally, safety is accomplished through a rigorous process that involves human factors, low and high fidelity simulations, and flight experiments. As this process is usually performed on final products or functional prototypes, concept modifications resulting from this process are very expensive to implement. This paper describe an approach to system safety that can take place at early stages of a concept design. It is based on a set of mathematical techniques and tools known as formal methods. In contrast to testing and simulation, formal methods provide the capability of exhaustive state exploration analysis. We present the safety analysis and verification performed for the Small Aircraft Transportation System (SATS) Concept of Operations (ConOps). The concept of operations is modeled using discrete and hybrid mathematical models. These models are then analyzed using formal methods. The objective of the analysis is to show, in a mathematical framework, that the concept of operation complies with a set of safety requirements. It is also shown that the ConOps has some desirable characteristic such as liveness and absence of dead-lock. The analysis and verification is performed in the Prototype Verification System (PVS), which is a computer based specification language and a theorem proving assistant.

Carreno, Victor↗

NASA NTRS1949

Lame's Wave Functions of the Ellipsoid of Revolution

It has recently Miss Gertrude Blanch that errors exist in been brought to the attention of the NACA by of the Bureau of Standards, Department of Commerce the tabulated values appearing in tables 11 to 17 of TM 1224. Miss Blanch notes that C. J. Bouwkamp~ from whom Meixner obtained the values presented, subsequently corrected them in tables. appearing in the Journal of Mathematics and Physics, vol. XXVI, no. 2, JULY 1947, pp. 88-91. In spite of the difference in symbols and notation in the two papers, reprints of tables I to IX included in the July 1947 issue of the Journal of Mathematics and Physics are attached for the use of those interested in receiving them. The NACA wishes to express its appreciation to the Journal of Mathematics and Physics for permitting these tables to be reproduced for this purpose.

Meixner, J.↗