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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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Various distinctions are discussed which can be made regarding evaluation of mathematical expressions: regular evaluation vs. infinite evaluation vs. finite evaluation, regular variables vs. mathematical variables vs. shadow variables vs. labels, simplification vs. evaluation vs. solution of equations. The unsatisfactory state of evaluation strategies in symbolic systems is due to insufficient use of such distinctions in the past.
Tomas Garza relates how the Research Center for Applied Mathematics Systems and Services in Mexico became the Research Institute for Applied Mathematics and Systems and what the type of work performed is.
Tensor calculus is applied to the formulation of mathematical models of diverse phenomena. Aeronautics, fluid dynamics, and cosmology are among the areas of application. The feasibility of combining tensor methods and computer capability to formulate problems is demonstrated. The techniques described are an attempt to simplify the formulation of mathematical models by reducing the modeling process to a series of routine operations, which can be performed either manually or by computer.
The capability for predicting the performance of thermal energy storage (RES) subsystems and components using PCM's based on mathematical and physical models is developed. Mathematical models of the dynamic thermal behavior of (TES) subsystems using PCM's based on solutions of the moving boundary thermal conduction problem and on heat and mass transfer engineering correlations are also discussed.
A mathematical model package for thermal pollution analyses and prediction is presented. These models, intended as user's manuals, are three dimensional and time dependent using the primitive equation approach. Although they have sufficient generality for application at sites with diverse topographical features; they also present specific instructions regarding data preparation for program execution and sample problems. The mathematical formulation of these models is presented including assumptions, approximations, governing equations, boundary and initial conditions, numerical method of solution, and same results.
An approach was developed to aid in the integration of many of the biomedical findings of space flight, using systems analysis. The mathematical tools used in accomplishing this task include an automated data base, a biostatistical and data analysis system, and a wide variety of mathematical simulation models of physiological systems. A keystone of this effort was the evaluation of physiological hypotheses using the simulation models and the prediction of the consequences of these hypotheses on many physiological quantities, some of which were not amenable to direct measurement. This approach led to improvements in the model, refinements of the hypotheses, a tentative integrated hypothesis for adaptation to weightlessness, and specific recommendations for new flight experiments.
Some theoretical questions involved in the mathematical modeling of the kinetics of complex chemical process are discussed. The analysis is carried out for the homogeneous oxidation of ethylbenzene in the liquid phase. Particular attention is given to the determination of the general characteristics of chemical systems from an analysis of mathematical models developed on the basis of linear algebra.
A mathematical synthesization approach for rapidly modeling and analyzing complex structures comprised of hundreds or thousands of repeating individual structural members, interconnecting hardware, and other components was described. The techniques are applicable to any structure with repeating structural members. The capabilities are embodied within the Interactive Design and Evaluation of Advanced Spacecraft (IDEAS) computer-aided design system. IDEAS has a full range of integrated spacecraft modeling, design, analysis, performance, and cost estimating capabilities which include about 40 technical program and executive, data base, and file management systems. With IDEAS, a single user at an interactive terminal can create, design, analyze, and conduct parametric studies of Earth orbiting spacecraft in a timely, cost-efficient manner. The system is particularly useful in the conceptual design phases of advanced space missions when a multiplicity of concepts must be evaluated. The IDEAS interactive finite-element modeling capabilities are discussed. The mathematical synthesization programs were structured not only to provide a detailed finite-element model of the structure but also to automatically perform the many auxiliary computations needed to analyze the spacecraft in its orbital operational environment.
The CARE-III mathematical model and code verification performed by Boeing Computer Services were documented. The mathematical model was verified for permanent and intermittent faults. The transient fault model was not addressed. The code verification was performed on CARE-III, Version 3. A CARE III Version 4, which corrects deficiencies identified in Version 3, is being developed.
The optical characteristics of a paraboloidal solar concentrator are analyzed using the intercept factor curve (a format for image data) to describe the results of a mathematical model and to represent reduced data from experimental testing. This procedure makes it possible not only to test an assembled concentrator, but also to evaluate single optical panels or to conduct non-solar tests of an assembled concentrator. The use of three-dimensional ray tracing computer programs to calculate the mathematical model is described. These ray tracing programs can include any type of optical configuration from simple paraboloids to array of spherical facets and can be adapted to microcomputers or larger computers, which can graphically display real-time comparison of calculated and measured data.
Methods are investigated for formally specifying and verifying the correctness of mathematical software (software which uses floating point numbers and arithmetic). Previous work in the field was reviewed. A new model of floating point arithmetic called the asymptotic paradigm was developed and formalized. Two different conceptual approaches to program verification, the classical Verification Condition approach and the more recently developed Programming Logic approach, were adapted to use the asymptotic paradigm. These approaches were then used to verify several programs; the programs chosen were simplified versions of actual mathematical software.
An approximate mathematical formulation for scheduling of future space missions is proposed. The objective is to schedule the flights to efficiently use the available ground resources, to minimize the inventory level of ground resources needed and to minimize the overlapping or conflicting periods during which the same types of resources are used by the various flights. The development of the mathematical formulation of the problem considers the presence of a large number of sequencing and resource constraints: (1) the order in which the flights are to be launched is predetermined; and (2) some types of resources are to be used only by certain flights. A linear objective function based on cost considerations is constructed and this function is minimized subject to the various constraints.
A major challenge to the structural dynamicist is to validate mathematical models of large space structures which cannot be ground tested because of its size and/or flexibility. The paper presents a Multiple Boundary Condition Test (MBCT) approach which allows a systematic validation of the mathematical model by performing a number of ground tests on a large structure with variable boundary conditions. A numerical simulation is presented which illustrates the validity of the MBCT including some of the potential limitations.
Error analysis increases precision of navigation. Report presents improved mathematical models of analysis of Doppler measurements and measurement errors of spacecraft navigation. To take advantage of potential navigational accuracy of Doppler measurements, precise equations relate measured cycle count to position and velocity. Drifts and random variations in transmitter and receiver oscillator frequencies taken into account. Mathematical models also adapted to aircraft navigation, radar, sonar, lidar, and interferometry.
A collection of mathematical problems related to NASA space science projects is presented. In developing the examples and problems, attention was given to preserving the authenticity and significance of the original setting while keeping the level of mathematics within the secondary school curriculum. Computation and measurement, algebra, geometry, probability and statistics, exponential and logarithmic functions, trigonometry, matrix algebra, conic sections, and calculus are among the areas addressed.
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.