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Research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis, and computer science during the period October 1, 1986 through March 31, 1987 is summarized.
This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis, and computer science during the period April l, 1988 through September 30, 1988.
Research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis, and computer science during the period October 1, 1988 through March 31, 1989 is summarized.
Research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis, and computer science is summarized.
The individual software processes used in the flight computers on-board the Advanced Transport Operating System (ATOPS) aircraft have many common functional elements. A library of commonly used software modules was created for general uses among the processes. The library includes modules for mathematical computations, data formatting, system database interfacing, and condition handling. The modules available in the library and their associated calling requirements are described.
Several computer programs which are available through the NASA Technology Utilization Program are outlined. Presented are: (1) Computer operational programs which can be applied to resolve procedural problems swiftly and accurately. (2) Mathematical applications for the resolution of problems encountered in numerous industries. Although the functions which these programs perform are not new and similar programs are available in many large computer center libraries, this collection may be of use to centers with limited systems libraries and for instructional purposes for new computer operators.
Big Bang Nucleosynthesis (BBN), the process of creation of lightest elements in the early universe, is a highly robust, precise, and ultimately successful theory that forms one of the three pillars of the standard hot-Big-Bang cosmological model. Existing theoretical treatments of BBN and the associated computer codes are accurate and flexible, but are typically highly technical and opaque, and not suitable for pedagogical understanding of the BBN. Here we present BBN-simple - a from-scratch numerical calculation of the lightest element abundances pitched at an advanced undergraduate or beginning graduate level. We review the physics of the early universe relevant for BBN, provide information about the reaction rates, and discuss computational-mathematics background that is essential in setting up a BBN calculation. Here, we calculate the abundances of the principal nuclear species in a standard cosmological model, and find a reasonably good agreement with public precision-level BBN codes.
Mathematical computation of classical trajectories of gas molecules near crystalline solid
Discussing problems in design and implementation of practical batch processing systems for performing symbolic mathematical computation
A mathematical computation based on the t-matrix approach shows that a system of strongly interacting baryons under sufficiently high pressure (approximately 10 to the 30th power atm) and densities greater than 10 to the 15th power g/cu cm minimizes the energy by arranging the constituents in a lattice structure rather than in a fluid phase. The solution is given assuming an optimum spin arrangement, although all other possible arrangements would also satisfy the conditions for crystallization to occur.
The necessary elements to perform global inventories of agriculture, forestry, and range resources are being brought together through the use of satellites, sensors, computers, mathematics, and phenomenology. Results of ERTS-1 applications in these areas, as well as soil mapping, are described.
A preliminary evaluation of the on-orbit induced environment from identified major sources of contamination for the STS shuttle orbiter is presented. A contamination computer mathematical model is discussed that was used to develop the description and predictions of the induced environment along with the extent and physical makeup of the molecular induced environment from these sources. The predicted induced molecular environment from each source is evaluated against current Space Shuttle Program on-orbit contamination control criteria. The flash evaporator vents and the VCS 25-lb thrust engines are shown to significantly exceed applicable contamination control criteria and were the subject of extensive evaluation. Preliminary conclusions concerning the contaminant potential of these sources along with recommendations for various measures of contamination control regarding the shuttle orbiter design and operational activities are made.
A model being developed, permits the understanding and prediction of passenger discomfort in a multifactor environment with particular emphasis upon combined noise and vibration. The model has general applicability to diverse transportation systems and provides a means of developing ride quality design criteria as well as a diagnostic tool for identifying the vibration and/or noise stimuli causing discomfort. Presented are: (1) a review of the basic theoretical and mathematical computations associated with the model, (2) a discussion of methodological and criteria investigations for both the vertical and roll axes of vibration, (3) a description of within-axis masking of discomfort responses for the vertical axis, thereby allowing prediction of the total discomfort due to any random vertical vibration, (4) a discussion of initial data on between-axis masking, and (5) discussion of a study directed towards extension of the vibration model to the more general case of predicting ride quality in the combined noise and vibration environments.
An active optical technique (differential absorption lidar (DIAL)) for detecting, ranging, and quantifying the concentration of anhydrous HCl contained in the ground cloud emitted by solid rocket motors (SRM) is evaluated. Results are presented of an experiment in which absorption coefficients of HCl were measured for several deuterium fluoride (DF) laser transitions demonstrating for the first time that a close overlap exists between the 2-1 P(3) vibrational transition of the DF laser and the 1-0 P(6) absorption line of HCl, with an absorption coefficient of 5.64 (atm-cm) to the -1 power. These measurements show that the DF laser can be an appropriate radiation source for detecting HCl in a DIAL technique. Development of a mathematical computer model to predict the sensitivity of DIAL for detecting anhydrous HCl in the ground cloud is outlined, and results that assume a commercially available DF laser as the radiation source are presented.
The MACSYMA program for symbolic and algebraic manipulation enables exact, symbolic mathematical computations to be performed on a computer. This program is rather large, and various approaches to the hardware and software problems are examined.
The effects on handling qualities of elastic modes interaction with the rigid body dynamics of a large flexible aircraft are studied by a mathematical computer simulation. An analytical method to predict the pilot ratings when there is a severe modes interactions is developed. This is done by extending the optimal control model of the human pilot response to include the mode decomposition mechanism into the model. The handling qualities are determined for a longitudinal tracking task using a large flexible aircraft with parametric variations in the undamped natural frequencies of the two lowest frequency, symmetric elastic modes made to induce varying amounts of mode interaction.
The paper discusses an SAR problem based on actual requirements set forth by NASA for a spaceborne application. The requirements for high resolution and high quality necessitate a data sampling rate of 7.5 MHz. For each data value 1,025 4-bit complex multiply + add operations are needed, which is equivalent to 7.7 GHz complex multiply + add operation rate. Since this rate is much too high for general purpose systems, a special-purpose device was sought. This paper discusses two architectures based on parallel operation of 1,025 identical cells, each of which is capable of performing arithmetic, storage, and several control operations. The operation rate in each device is only 7.5 MHz, which is quite manageable, especially with the help of a substantial degree of pipelining. A computational-mathematical analysis is used as a primary tool for evaluating the design and some of its tradeoffs. Two different approaches are discussed and compared; both are based on having 1,025 identical cells working in parallel, but differ in their dual approaches to the flow of data.
A tentative mathematical computer model of the microfissuring process during electron beam welding of Inconel 718 has been constructed. Predictions of the model are compatible with microfissuring tests on eight 0.25-in. thick test plates. The model takes into account weld power and speed, weld loss (efficiency), parameters and material characteristics. Besides the usual material characteristics (thermal and strength properties), a temperature and grain size dependent critical fracture strain is required by the model. The model is based upon fundamental physical theory (i.e., it is not a mere data interpolation system), and can be extended to other metals by suitable parameter changes.