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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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The project initiated a study of a mathematical model of a tunable Ti:sapphire solid-state laser. A general mathematical model was developed for the purpose of identifying design parameters which will optimize the system, and serve as a useful predictor of the system's behavior.
The BVI impulsive content of a rotor acoustic signal is shown to appear in the mid-frequency range of the power spectrum, between the fifth and thirtieth harmonics of the blade passage frequency, concentrated at the harmonics of the blade passage frequency. These harmonics exhibit a humped or scalloped shape in this mid-frequency spectral region. Increased energy at the harmonics of the shaft frequency appears when the BVI impulsive content demonstrates unsteadiness and blade-to-blade differences in the time domain. A mathematical model of a generalized BVI acoustic signal and its power spectrum shows that the power spectrum is scalloped and filtered by a comb function. The spectrum amplitude is defined by the impulse amplitude and emission time. The scalloping of the spectrum is related to the emission time of the impulse itself, and the spacing of the comb function is related to the repetition time (period) of the impulse. The decay rate of the spectral humps is governed by the inverse of frequency squared. The mathematical model validates the characteristics observed in the data and verify that these characteristics are due to blade-vortex interaction activity.
The reader is informed of what was done for the mathematical modeling of the dc-ac inverter for the Space Shuttle. The mathematical modeling of the dc-ac inverter is an essential element in the modeling of the electrical power distribution system of the Space Shuttle. The electrical power distribution system which is present on the Space Shuttle is made up to 3 strings each having a fuel cell which provides dc to those systems which require dc, and the inverters which convert the dc to ac for those elements which require ac. The inverters are units which are 2 wire structures for the main dc inputs and 2 wire structures for the ac output. When 3 are connected together a 4 wire wye connection results on the ac side. The method of modeling is performed by using a Least Squares curve fitting method. A computer program is presented for implementation of the model along with graphs and tables to demonstrate the accuracy of the model.
The rudiments of a mathematical formalism for handling operational, physiological, and psychological concepts are developed for use by the man-machine system design engineer. The formalism provides a framework for developing a structured, systematic approach to the interface design problem, using existing mathematical tools, and simplifying the problem of telling a machine how to measure and use performance.
A previously formulated mathematical model, describing how observers reconstruct three-dimensional spatial layouts from perspective projections, has been extended to more complex situations. The model assumes that the observer has a priori knowledge of certain characteristics of the viewed objects, like size, shape, or parallelism or perpendicularity of lines or planes. These assumptions are used in a three-dimensional process to reconstruct a spatial layout that `best matches' the perceived lines of sight to the object coordinates. Sources of errors and biases in this process are specified and their effects on model outputs are discussed. An experiment, in which eight subjects judged the relative direction of one object with respect to another, has been conducted to validate the model. The model has been found to generally reproduce the systematic trends of the experimental results and also has provided an analytical explanation for them. The mathematical model is expected to be a useful tool in analyzing and developing pictorial perspective flight displays.
A methodology is described for automatic mathematical modeling and generating simulation models. The major objective was to create a user friendly environment for engineers to design, maintain, and verify their models; to automatically convert the mathematical models into conventional code for computation; and finally, to document the model automatically.
Ada packages implementing selected mathematical functions for the support of scientific and engineering applications were written. The packages provide the Ada programmer with the mathematical function support found in the languages Pascal and FORTRAN as well as an extended precision arithmetic and a complete complex arithmetic. The algorithms used are fully described and analyzed. Implementation assumes that the Ada type FLOAT objects fully conform to the IEEE 754-1985 standard for single binary floating-point arithmetic, and that INTEGER objects are 32-bit entities. Codes for the Ada packages are included as appendixes.
The dynamic properties and the mathematical model for the adaptive control of the robotic system presently under investigation at Robotic Application and Development Laboratory at Kennedy Space Center are discussed. NASA is currently investigating the use of robotic manipulators for mating and demating of fuel lines to the Space Shuttle Vehicle prior to launch. The Robotic system used as a testbed for this purpose is an ASEA IRB-90 industrial robot with adaptive control capabilities. The system was tested and it's performance with respect to stability was improved by using an analogue force controller. The objective of this research project is to determine the mathematical model of the system operating under force feedback control with varying dynamic internal perturbation in order to provide continuous stable operation under variable load conditions. A series of lumped parameter models are developed. The models include some effects of robot structural dynamics, sensor compliance, and workpiece dynamics.
During the last several years, solid state lasers were developed that have the potential for meeting rigorous performance requirements for space-based remote sensing of the atmosphere. In order to design a stable and efficient laser and to understand the effect on laser output of changes in the physical and design parameters, an understanding of the development of the dynamical processes of the laser is necessary. Typically, the dynamical processes in a laser system are investigated via rate equations describing the evolution of the occupancy in the electronic levels and of the photon density in the laser cavity. There are two approaches to this type of study. Most often, for the sake of simplicity, the spatial variations of the dynamic variables in the laser system are disregarded and the mathematical model consists of a system of first order nonlinear ordinary differential equations (ODE). The second approach is to take into account both spatial and temporal variations in the dynamic variables in the laser cavity. The resulting model consists of a first order semilinear system of partial differential equations (PDE). The model which was studied was studied was generic in the sense that it was a four-level laser system, but the parameters used in the numerical study were specific to Titanium-doped sapphire. For simplicity, a constant, spatially uniform pumping scheme was considered. In addition, a simplification of the model was made so that it treats a single lasing wavelength with a narrow bandwidth. The purpose was to investigate both versions of the mathematical model and to determine whether the numerical solutions are similar both qualitatively and quantitatively. The systems of ordinary differential equations were solved numerically using a Runge-Kutta-Fehlberg algorithm which was very efficient for typical values of the physical parameters. A numerical scheme, based on the Modified Euler method, for computing solutions to the system of partial differential equations was developed and implemented. The PDE model was solved numerically at the expense of greatly increased computer time.
The mathematical optimization of vertical-junction photovoltaic converters for use with diode laser arrays supplying powers up to 1 MW is discussed. Photovoltaic parameters were optimized using a mathematical model. The optimized converters have 500 single junctions connected in series. The efficiency varies from 41 percent for a 0.73-micron diode laser to 46 percent for a 0.83-micron diode laser. The optimum width of the single-junction converter is small, 3.0 microns, in order for the p-n junction to be within a diffusion length of the light-generated carriers. Another critical parameter is the series resistance; the optimum value of 0.001 ohms should be achievable. Another critical parameter is the donor carrier concentration, for which an optimum value of 5 x 10 to the 15th carriers/cu cm has been chosen.
Research conducted at the Institute in Science and Engineering in applied mathematics, numerical analysis, and computer science is summarized. The Institute conducts unclassified basic research in applied mathematics in order to extend and improve problem solving capabilities in science and engineering, particularly in aeronautics and space.
The practices of researchers in many fields who use qualitative reasoning are summarized and explained. The goal is to gain an understanding of the formal assumptions and mechanisms that underlie this kind of analysis. The explanations given are based on standard mathematical formalisms, particularly on ordinal properties, continuous differentiable functions, and the mathematics of nonlinear dynamic systems.
A mathematical basis for the optimal design of adaptive trusses to be used in supporting precision equipment is provided. The general theory of adaptive structures is introduced, and the global optimization problem of placing a limited number, q, of actuators, so as to maximally achieve precision control and provide prestress, is stated. Two serialized optimization problems, namely, optimal actuator placement for prestress and optimal actuator placement for precision control, are addressed. In the case of prestressing, the computation of a 'desired' prestress is discussed, the interaction between actuators and redundants in conveying the prestress is shown in its mathematical form, and a methodology for arriving at the optimal placement of actuators and additional redundants is discussed. With regard to precision control, an optimal placement scheme (for q actuators) for maximum 'authority' over the precision points is suggested. The results of the two serialized optimization problems are combined to give a suboptimal solution to the global optimization problem. A method for improving this suboptimal actuator placement scheme by iteration is presented.
A physical model of the Porous Ceramic Tube Plant Nutrification System (PCTPNS) was developed through microscopic observations of the tube surface under various operational conditions. In addition, a mathematical model of this system was developed which incorporated the effects of the applied suction pressure, surface tension, and gravitational forces as well as the porosity and physical dimensions of the tubes. The flow of liquid through the PCTPNS was thus characterized for non-biological situations. One of the key factors in the verification of these models is the accurate and rapid measurement of the 'wetness' or holding capacity of the ceramic tubes. This study evaluated a thermistor based moisture sensor device and recommendations for future research on alternative sensing devices are proposed. In addition, extensions of the physical and mathematical models to include the effects of plant physiology and growth are also discussed for future research.
The mathematical relations between the measured velocity fields for the same compressor rotor flow field resolved by two fringe type laser anemometers at different observational locations are developed in this report. The relations allow the two sets of velocity measurements to be combined to produce a total velocity vector field for the compressor rotor. This report presents the derivation of the mathematical relations, beginning with the specification of the coordinate systems and the velocity projections in those coordinate systems. The vector projections are then transformed into a common coordinate system. The transformed vector coordinates are then combined to determine the total velocity vector. A numerical example showing the solution procedure is included.
The validation of the results of physically-based mathematical models against experimental results was discussed. Systematic techniques are used for: (1) isolating subsets of the simulator mathematical model and comparing the response of each subset to its experimental response for the same input conditions; (2) evaluating the response error to determine whether it is the result of incorrect parameter values, incorrect structure of the model subset, or unmodeled external effects of cross coupling; and (3) modifying and upgrading the model and its parameter values to determine the most physically appropriate combination of changes.
The goal of the mathematical and statistical analysis component of RICIS is to research, develop, and evaluate mathematical and statistical techniques for aerospace technology applications. Specific research areas of interest include modeling, simulation, experiment design, reliability assessment, and numerical analysis.
Various attempts have been made to construct a rigorous mathematical theory of optimization for size, shape, and topology (i.e. layout) of an elastic structure. If these are represented by a finite number of parametric functions, as Armand described, it is possible to construct an existence theory of the optimum design using compactness argument in a finite dimensional design space or a closed admissible set of a finite dimensional design space. However, if the admissible design set is a subset of non-reflexive Banach space such as L(sup infinity)(Omega), construction of the existence theory of the optimum design becomes suddenly difficult and requires to extend (i.e. generalize) the design problem to much more wider class of design that is compatible to mechanics of structures in the sense of variational principle. Starting from the study by Cheng and Olhoff, Lurie, Cherkaev, and Fedorov introduced a new concept of convergence of design variables in a generalized sense and construct the 'G-Closure' theory of an extended (relaxed) optimum design problem. A similar attempt, but independent in large extent, can also be found in Kohn and Strang in which the shape and topology optimization problem is relaxed to allow to use of perforated composites rather than restricting it to usual solid structures. An identical idea is also stated in Murat and Tartar using the notion of the homogenization theory. That is, introducing possibility of micro-scale perforation together with the theory of homogenization, the optimum design problem is relaxed to construct its mathematical theory. It is also noted that this type of relaxed design problem is perfectly matched to the variational principle in structural mechanics.