Search NASA⌕ Search

SEARCH · Search NASA

Results for “MATHEMATICS - BOUNDARY VALUES”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Investigation of a Diagnostic for Perturbation Theory: Comparison to the T(sub 1) Diagnostic of Coupled-Cluster Theory

A diagnostic for perturbation theory calculations, S(sub 2), is defined and numerical results are compared to the established T(sub 1) diagnostic from coupled-cluster theory. S(sub 2) is the lowest order non-zero contribution to a perturbation expansion of T(sub 1). S(sub 2) is a reasonable estimate of the importance of non-dynamical electron correlation, although not as reliable as T(sub 1). S(sub 2) values less than or equal to 0.012 suggest that low orders of perturbation theory should yield reasonable results; S(sub 2) values between 0.012-0.015 suggest that caution is required in interpreting results from low orders of perturbation theory; S(sub 2) values greater than or equal to 0.015 indicate that low orders of perturbation theory are not reliable for accurate results. Although not required mathematically, S(sub 2) is always less than T(sub 1) for the examples studied here.

Lee, Timothy J.↗
NASA NTRS2002

Complex Refractive Index of Ammonium Nitrate in the 2-20 micron Spectral Range

Using high resolution Fourier Transform Infrared Spectroscopy (FTIR) absorbance/transmittance spectral data for ammonium sulfate (AMS), calcium carbonate (CAC) and ammonium nitrate (AMN), comparisons were made with previously published complex refractive indices data for AMS and CAC to infer experimental parameters to determine the imaginary refractive index for AMN in the infrared wavelength range from 2 to 20 microns. Kramers-Kronig mathematical relations were applied to calculate the real refractive index for the three compositions. Excellent agreement for AMS and CAC with the published values was found, validating the complex refractive indices obtained for AMN. Backscatter calculations using a lognormal size distribution for AMS, AMN, and CAC aerosols were performed to show differences in their backscattered spectra.

Jarzembski, Maurice A.↗
NASA NTRS2004

Force Density Function Relationships in 2-D Granular Media

An integral transform relationship is developed to convert between two important probability density functions (distributions) used in the study of contact forces in granular physics. Developing this transform has now made it possible to compare and relate various theoretical approaches with one another and with the experimental data despite the fact that one may predict the Cartesian probability density and another the force magnitude probability density. Also, the transforms identify which functional forms are relevant to describe the probability density observed in nature, and so the modified Bessel function of the second kind has been identified as the relevant form for the Cartesian probability density corresponding to exponential forms in the force magnitude distribution. Furthermore, it is shown that this transform pair supplies a sufficient mathematical framework to describe the evolution of the force magnitude distribution under shearing. Apart from the choice of several coefficients, whose evolution of values must be explained in the physics, this framework successfully reproduces the features of the distribution that are taken to be an indicator of jamming and unjamming in a granular packing. Key words. Granular Physics, Probability Density Functions, Fourier Transforms

Youngquist, Robert C.↗
NASA NTRS1974

Hydrostatics and steady dynamics of spatially varying electromechanical flow structures

The hydrostatic and steady laminar hydrodynamic equilibria of spatially varying electromechanical flow structures are investigated. Under certain conditions the relationship between the dielectric height of rise and the applied voltage is found to be double valued. It is found that one of the two equilibrium values is always unstable. This gives rise to the experimentally observed spontaneous rise of the fluid to the top of the structure, once a certain critical voltage is reached. Starting above this critical voltage with the structure completely filled and decreasing the applied voltage toward the critical value results in pinch-in failure at an intermediate point along the structure and trapping of dielectric fluid at the top. The simple mathematical model developed predicts all these phenomena, without recourse to tedious point-by-point surface force equilibrium determination. Experiments are reported which verify the results for the hydrostatic case.

Jones, T. B.↗
NASA NTRS1986

Integrated analysis tools for trade studies of spacecraft controller and sensor locations

The present investigation was conducted with the aim to evaluate the practicality and difficulties of modern control design methods for large space structure controls. The evaluation is used as a basis for the identification of useful computer-based analysis tools which would provide insight into control characteristics of a spacecraft concept. A description is presented of the wrap-rib antenna and its packaging concept. Attention is given to active control requirements, a mathematical model of structural dynamics, aspects of sensor and actuator location, the analysis approach, controllability, observability, the concept of balanced realization, transmission zeros, singular value plots, analysis results, model reduction, and an interactive computer program. It is pointed out that the application of selected control analysis tools to the wrap-rib antenna demonstrates several capabilities which can be useful during conceptual design.

Rowell, L. F.↗
NASA NTRS1988

Optimal placement of tuning masses for vibration reduction in helicopter rotor blades

Methods are presented for the reduction of helicopter rotor blade vibration through a formal mathematical optimization technique determination of optimum tuning mass sizes and locations; these are used as design variables that are systematically changed to achieve low values of shear without large mass penalty. Matrix expressions are obtained for the modal shaping parameter and modal shear amplitude that are required for FEM structural analysis of the blade as well as the optimization formulation. Sensitivity derivatives are also obtained. Three different optimization strategies are developed and tested.

Pritchard, Jocelyn I.↗
NASA NTRS1990

Quantifying fault recovery in multiprocessor systems

Various aspects of reliable computing are formalized and quantified with emphasis on efficient fault recovery. The mathematical model which proves to be most appropriate is provided by the theory of graphs. New measures for fault recovery are developed and the value of elements of the fault recovery vector are observed to depend not only on the computation graph H and the architecture graph G, but also on the specific location of a fault. In the examples, a hypercube is chosen as a representative of parallel computer architecture, and a pipeline as a typical configuration for program execution. Dependability qualities of such a system is defined with or without a fault. These qualities are determined by the resiliency triple defined by three parameters: multiplicity, robustness, and configurability. Parameters for measuring the recovery effectiveness are also introduced in terms of distance, time, and the number of new, used, and moved nodes and edges.

Malek, Miroslaw↗
NASA NTRS1994

Pdf modeling for premixed turbulent combustion based on the properties of iso-concentration surfaces

In premixed turbulent flames the presence of intense mixing zones located in front of and behind the flame surface leads to a requirement to study the behavior of iso-concentration surfaces defined for all values of the progress variable (equal to unity in burnt gases and to zero in fresh mixtures). To support this study, some theoretical and mathematical tools devoted to level surfaces are first developed. Then a database of direct numerical simulations of turbulent premixed flames is generated and used to investigate the internal structure of the flame brush, and a new pdf model based on the properties of iso-surfaces is proposed.

Vervisch, L.↗
NASA NTRS2003

Theory of Collective Intelligence

In this chapter an analysis of the behavior of an arbitrary (perhaps massive) collective of computational processes in terms of an associated "world" utility function is presented We concentrate on the situation where each process in the collective can be viewed as though it were striving to maximize its own private utility function. For such situations the central design issue is how to initialize/update the collective's structure, and in particular the private utility functions, so as to induce the overall collective to behave in a way that has large values of the world utility. Traditional "team game" approaches to this problem simply set each private utility function equal to the world utility function. The "Collective Intelligence" (COIN) framework is a semi-formal set of heuristics that recently have been used to construct private utility. functions that in many experiments have resulted in world utility values up to orders of magnitude superior to that ensuing from use of the team game utility. In this paper we introduce a formal mathematics for analyzing and designing collectives. We also use this mathematics to suggest new private utilities that should outperform the COIN heuristics in certain kinds of domains. In accompanying work we use that mathematics to explain previous experimental results concerning the superiority of COIN heuristics. In that accompanying work we also use the mathematics to make numerical predictions, some of which we then test. In this way these two papers establish the study of collectives as a proper science, involving theory, explanation of old experiments, prediction concerning new experiments, and engineering insights.

Nash equilibrium↗
NASA NTRS2007

Tachometers Derived From a Brushless DC Motor

The upper part of the figure illustrates the major functional blocks of a direction-sensitive analog tachometer circuit based on the use of an unexcited two-phase brushless dc motor as a rotation transducer. The primary advantages of this circuit over many older tachometer circuits include the following: Its output inherently varies linearly with the rate of rotation of the shaft. Unlike some tachometer circuits that rely on differentiation of voltages with respect to time, this circuit relies on integration, which results in signals that are less noisy. There is no need for an additional shaft-angle sensor, nor is there any need to supply electrical excitation to a shaft-angle sensor. There is no need for mechanical brushes (which tend to act as sources of electrical noise). The underlying concept and electrical design are relatively simple. This circuit processes the back-electromagnetic force (back-emf) outputs of the two motor phases into a voltage directly proportional to the instantaneous rate (sign magnitude) of rotation of the shaft. The processing in this circuit effects a straightforward combination of mathematical operations leading to a final operation based on the well-known trigonometric identity (sin x)2 + (cos x)2 = 1 for any value of x. The principle of operation of this circuit is closely related to that of the tachometer circuit described in Tachometer Derived From Brushless Shaft-Angle Resolver (MFS-28845), NASA Tech Briefs, Vol. 19, No. 3 (March 1995), page 39. However, the present circuit is simpler in some respects because there is no need for sinusoidal excitation of shaftangle- resolver windings.

Howard, David E.↗
NASA NTRS1979

NASA Tech Briefs, Summer 1979

Topics include: NASA TU Services: Technology Utilization services that can assist you in learning about and applying NASA technology; New Product Ideas: A summary of selected innovations of value to manufacturers for the development of neW products; Electronic Components and Circuits; Electronic Systems; Physical Sciences; Materials; Life Sciences; Mechanics; Machinery; Fabrication Technology; Mathematics and Information Sciences.

Source record↗
NASA NTRS1979

NASA Tech Briefs, Fall 1979

Topics include: NASA TU Services: Technology Utilization services that can assist you in learning about and applying NASA technology; New Product Ideas: A summary of selected innovations of value to manufacturers for the development of new products; Electronic Components and Circuits; Electronic Systems; Physical Sciences; Materials; Life Sciences; Mechanics; Machinery; Fabrication Technology; Mathematics and Information Sciences.

Source record↗
NASA NTRS1976

NASA Tech Briefs, Fall 1976

Topics include: NASA TU Services: Technology Utilization services that can assist you in learning about and applying NASA technology; New Product Ideas: A summary of seloc.ted Innovations of value to manufacturers for the development of new products; Electronic Components and Circuits; Electronic Systems; Physical Sciences; Materials; Life Sciences; Mechanics; Machinery; Fabrication Technology; Mathematics and Information Sciences.

Source record↗
NASA NTRS1977

NASA Tech Briefs, Spring 1977

Topics: NASA TU Services: Technology Utilization services that can assist you in learning about and applying NASA technology; New Product Ideas: A summary of sel~ted innovations of value to manufacturers for the development of new products; Electronic Components and Circuits; Electronic Systems; Physical Sciences; Materials; Life Sciences; Mechanics; Machinery; Fabrication Technology; Mathematics and Information Sciences.

Source record↗
NASA NTRS1977

NASA Tech Briefs, Winter 1977

Topics include: NASA TU Services: Technology Utilization services that can assist you in learning about and applying NASA technology; New Product Ideas: A summary of selected innovations of value to manufacturers for the development of new products; Electronic Components and Circuits; Electronic Systems; Physical Sciences; Materials; Life Sciences; Mechanics; Machinery; Fabrication Technology; Mathematics and Information Sciences.

Source record↗
NASA NTRS1977

NASA Tech Briefs, Summer 1977

Topics: NASA TU Services: Technology Utilization services that can assist you in learning about and applying NASA technology; New Product Ideas: A summary of selected Innovations of value to manufacturers for the development of new products; Electronic Components and Circuits; Electronic Systems; Physical Sciences; Materials; Life Sciences; Mechanics; Machinery; Fabrication Technology; Mathematics and Information Sciences.

Source record↗
NASA NTRS1978

NASA Tech Briefs, Spring 1978

Topics covered include: NASA TU Services: Technology Utilization services that can assist you in learning about and applying NASA technology; New Product Ideas: A summary of selected innovations of value to manufacturers for the development of new products; Electronic Components and Circuits; Electronic Systems; Physical Sciences; Materials; Life Sciences; Mechanics; Machinery; Fabrication Technology; Mathematics and Information Sciences.

Source record↗
NASA NTRS1977

NASA Tech Briefs, Fall 1977

Topics include: NASA TU Services: Technology Utilization services that can assist you in learning about and applying NASA technology; New Product Ideas: A summary of selected Innovations of value to manufacturers for the development of new products; Electronic Components and Circuits; Electronic Systems; Physical Sciences; Materials; Life Sciences; Mechanics; Machinery; Fabrication Technology; Mathematics and Information Sciences.

Source record↗