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NASA NTRS1989

A modified equivalent-width technique for diode-laser line strength measurements

A modified equivalent-width method is introduced that improves the accuracy of spectral line strength measurements using diode lasers. This method differs from the standard method in that no attempt is made to calculate the true equivalent width in order to determine the line strength. Instead, the line strength is derived directly from a measurement of the area under the line close to the line center and ignore the normal correction terms. Tests with actual spectra and simulations indicate that this method is accurate to better than 1 percent with lines broadened by up to 50 percent by the laser instrument function.

Strow, L. Larrabee↗

NASA NTRS1990

Global transport calculations with an equivalent barotropic system

Transport properties of the two-dimensional equations governing equivalent barotropic motion are investigated on the sphere. This system has ingredients such as forcing, equivalent depth, and thermal dissipation explicitly represented, and takes into account compression effects associated with vertical motion along isentropic surfaces. Horizontal transport properties of this system are investigated under adiabatic and diabatic conditions for different forms of dissipation, and over a range of resolutions. It is shown that forcing represetative of time-mean and amplified conditions at 10 mb leads to the behavior typical of observations at this level. The displacement of the polar night vortex and its distortion into a comma shape are evident, as is irreversible mixing under sufficiently strong forcing amplitude. It is shown that thermal dissipation influences the behavior significantly by inhibiting the amplification of unstable eddies and thereby the horizontal stirring of air.

Salby, Murry L.↗

NASA NTRS1989

Equilibrium polymerization on the equivalent-neighbor lattice

The equilibrium polymerization problem is solved exactly on the equivalent-neighbor lattice. The Flory-Huggins (Flory, 1986) entropy of mixing is exact for this lattice. The discrete version of the n-vector model is verified when n approaches 0 is equivalent to the equal reactivity polymerization process in the whole parameter space, including the polymerized phase. The polymerization processes for polymers satisfying the Schulz (1939) distribution exhibit nonuniversal critical behavior. A close analogy is found between the polymerization problem of index the Schulz r and the Bose-Einstein ideal gas in d = -2r dimensions, with the critical polymerization corresponding to the Bose-Einstein condensation.

Kaufman, Miron↗

NASA NTRS1990

The equivalence between dislocation pile-ups and cracks

Cracks and dislocation pile-ups are equivalent to each other. In this paper, the physical equivalence between cracks and pile-ups is delineated, and the relationshps between crack-extension force, force on the leading dislocation, stress-intensity factor, and dislocation density are reviewed and summarized. These relations make it possible to extend quantitatively the recent advances in the concepts and practices of fracture mechanics to the studies of microfractures and microplastic deformations.

Liu, H. W.↗

NASA NTRS1990

Secular Change in Equivalent Width of C 5380, 1978-1990

The equivalent width of the high excitation photospheric line of C 5380A has been measured 3 to 4 times monthly in the solar irradiance spectrum since 1978. C 5380 behaves differently than other spectral lines in that it is unmodulated by the activity cycle, yet has increased in strength by 0.081 plus or minus .008 mA in 12 years. Nominal equivalent width is 22.25 mA. Implied is a temperature increase of 4.6 K which is an order of magnitude greater than constraints allowed by Active Cavity Radiometer Irradiance Monitor (ACRIM) results.

Livingston, William C.↗

NASA NTRS1993

Recent developments in equivalent plate modeling for wing shape optimization

A new technique for structural modeling of airplane wings is presented taking transverse shear effects into account. The kinematic assumptions of first order shear deformation plate theory in combination with numerical analysis based on simple polynomials which define geometry, construction and displacement approximations lead to analytical expressions for elements of the stiffness and mass matrices and load vector. Contributions from the cover skins, spar and rib caps and spar and rib webs are included as well as concentrated springs and concentrated masses. Limitations of current equivalent plate wing modeling techniques based on classical plate theory are discussed, and the improved accuracy of the new equivalent plate technique is demonstrated through comparison to finite element analysis and test results. Analytical derivatives of stiffness, mass and load terms with respect to wing shape lead to analytic sensitivities of displacements, stresses and natural modes with respect to planform shape and depth distribution. This makes the new capability an effective structural tool for wing shape optimization.

Livne, Eli↗

NASA NTRS1993

Dark matter and the equivalence principle

A survey is presented of the current understanding of dark matter invoked by astrophysical theory and cosmology. Einstein's equivalence principle asserts that local measurements cannot distinguish a system at rest in a gravitational field from one that is in uniform acceleration in empty space. Recent test-methods for the equivalence principle are presently discussed as bases for testing of dark matter scenarios involving the long-range forces between either baryonic or nonbaryonic dark matter and ordinary matter.

Frieman, Joshua A.↗

NASA NTRS1940

Stress distribution in and equivalent width of flanges of wide, thin-wall steel beams

The use of different forms of wide-flange, thin-wall steel beams is becoming increasingly widespread. Part of the information necessary for a national design of such members is the knowledge of the stress distribution in and the equivalent width of the flanges of such beams. This problem is analyzed in this paper on the basis of the theory of plane stress. As a result, tables and curves are given from which the equivalent width of any given beam can be read directly for use in practical design. An investigation is given of the limitations of this analysis due to the fact that extremely wide and thin flanges tend to curve out of their plane toward the neutral axis. A summary of test data confirms very satisfactorily the analytical results.

BEAMS, BOX-STRESSES↗

NASA NTRS1954

The flow past a straight and a swept-wing-body combination and their equivalent bodies of revolution at Mach numbers near 1.0

Tests utilizing the Schlieren method of flow photography have been conducted to provide a comparison of the complete flow fields past a straight and a swept-wing-body combination and the flow fields past their equivalent bodies of revolution at Mach numbers around 1.0. The results indicated that the shock growth and positions on the wing-body combinations were closely reproduced in the flow past the equivalent body.

Lindsey, Walter F↗

NASA NTRS1992

A linear spectral matching technique for retrieving equivalent water thickness and biochemical constituents of green vegetation

Over the last decade, technological advances in airborne imaging spectrometers, having spectral resolution comparable with laboratory spectrometers, have made it possible to estimate biochemical constituents of vegetation canopies. Wessman estimated lignin concentration from data acquired with NASA's Airborne Imaging Spectrometer (AIS) over Blackhawk Island in Wisconsin. A stepwise linear regression technique was used to determine the single spectral channel or channels in the AIS data that best correlated with measured lignin contents using chemical methods. The regression technique does not take advantage of the spectral shape of the lignin reflectance feature as a diagnostic tool nor the increased discrimination among other leaf components with overlapping spectral features. A nonlinear least squares spectral matching technique was recently reported for deriving both the equivalent water thicknesses of surface vegetation and the amounts of water vapor in the atmosphere from contiguous spectra measured with the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS). The same technique was applied to a laboratory reflectance spectrum of fresh, green leaves. The result demonstrates that the fresh leaf spectrum in the 1.0-2.5 microns region consists of spectral components of dry leaves and the spectral component of liquid water. A linear least squares spectral matching technique for retrieving equivalent water thickness and biochemical components of green vegetation is described.

Gao, Bo-Cai↗

NASA NTRS1993

Size distributions and aerodynamic equivalence of metal chondrules and silicate chondrules in Acfer 059

The CR2 chondrite Acfer 059 is unusual in that the original droplet shapes of metal chondrules are well preserved. We determined separate size distributions for metal chondrules and silicate chondrules; the two types are well sorted and have similar size distributions about their respective mean diameters of 0.74 mm and 1.44 mm. These mean values are aerodynamically equivalent for the contrasting densities, as shown by calculated terminal settling velocities in a model solar nebula. Aerodynamic equivalence and similarity of size distributions suggest that metal and silicate fractions experienced the same sorting process before they were accreted onto the parent body. These characteristics, together with depletion of iron in Acfer 059 and essentially all other chondrites relative to primitive CI compositions, strongly suggest that sorting in the solar nebula involved a radial aerodynamic component and that sorting and siderophile depletion in chondrites are closely related.

Skinner, William R.↗

NASA NTRS1994

Modelling of Surfaces. Part 1: Monatomic Metallic Surfaces Using Equivalent Crystal Theory

We present a detailed description of equivalent crystal theory focusing on its application to the study of surface structure. While the emphasis is in the structure of the algorithm and its computational aspects, we also present a comprehensive discussion on the calculation of surface energies of metallic systems with equivalent crystal theory and other approaches. Our results are compared to experiment and other semiempirical as well as first-principles calculations for a variety of fcc and bcc metals.

Bozzolo, Guillermo↗

NASA NTRS1994

Satellite Test of the Equivalence Principle (STEP)

This grant provided support for the STEP (Satellite Test of the Equivalence Principle) program between October 1991 and September 1993. STEP, previously supported by NASA under Grant NAG8-837 'A Satellite Test of the Equivalence Principle,' was selected by the European Space Agency for a Phase A study as a candidate for ESA's next medium size mission (M2). STEP was conceived as a joint NASA/ESA mission with equal participation by both agencies. ESA's contribution to the program would be the spacecraft; NASA would provide the launcher and half of the instrument, while the other half of the instrument would be provided by various European agencies. STEP was in competition with three other programs, INTEGRAL, PRISMA, and MARSNET. The final selection of a single mission for M2 took place in April 1993. STEP was not selected for M2 but made a very close second. The program is continuing in modified form.

Worden, Paul↗

NASA NTRS1959

A Numerical Method for Calculating the Wave Drag of a Configuration from the Second Derivative of the Area Distribution of a Series of Equivalent Bodies of Revolution

A method based on linearized and slender-body theories, which is easily adapted to electronic-machine computing equipment, is developed for calculating the zero-lift wave drag of single- and multiple-component configurations from a knowledge of the second derivative of the area distribution of a series of equivalent bodies of revolution. The accuracy and computational time required of the method to calculate zero-lift wave drag is evaluated relative to another numerical method which employs the Tchebichef form of harmonic analysis of the area distribution of a series of equivalent bodies of revolution. The results of the evaluation indicate that the total zero-lift wave drag of a multiple-component configuration can generally be calculated most accurately as the sum of the zero-lift wave drag of each component alone plus the zero-lift interference wave drag between all pairs of components. The accuracy and computational time required of both methods to calculate total zero-lift wave drag at supersonic Mach numbers is comparable for airplane-type configurations. For systems of bodies of revolution both methods yield similar results with comparable accuracy; however, the present method only requires up to 60 percent of the computing time required of the harmonic-analysis method for two bodies of revolution and less time for a larger number of bodies.

Levy, Lionel L., Jr.↗

NASA NTRS1994

Analytic Sensitivities for Shape Optimization in Equivalent Plate Structural Wing Models

Equivalent plate modeling techniques based on Ritz analysis with simple polynomials prove to be efficient tools for structural modeling of wings in the preliminary design stage. Accuracy problems are encountered, however, when these models are used to obtain finite difference behavior sensitivities with respect to planform shape. The accuracy problems are associated with the poor numerical conditioning of static and eigenvalue equations. As higher-order polynomials are being used to Improve the analysis itself, the more sensitive is the finite difference derivative to the step size used. This article describes a formulation of wing equivalent plate modeling in which it is simple to obtain analytic, explicit expressions for stiffness and mass matrix elements without the need to perform numerical integration. This formulation leads naturally to analytic expressions for the derivatives of displacements, stresses, and natural frequencies with respect to shape design variables. This article examines the accuracy of finite difference derivatives compared with the analytic derivatives, and shows that In some cases it is impossible to obtain any information of value by finite differences. Analytic sensitivities, in this case, are still sufficiently accurate for design optimization.

Livne, Eli↗

NASA NTRS1996

Gravitational Redshift in a Local Freely Falling Frame: A Proposed New Null Test of the Equivalence Principle

We consider the gravitational redshift effect measured by an observer in a local freely failing frame (LFFF) in the gravitational field of a massive body. For purely metric theories of gravity, the metric in a LFFF is expected to differ from that of flat spacetime by only "tidal" terms of order (GM/c(exp 2)R)(r'/R )(exp 2), where R is the distance of the observer from the massive body, and r' is the coordinate separation relative to the origin of the LFFF. A simple derivation shows that a violation of the equivalence principle for certain types of "clocks" could lead to a larger apparent redshift effect of order (1 - alpha)(G M/c(exp 2)R)(r'/R), where alpha parametrizes the violation (alpha = 1 for purely metric theories, such as general relativity). Therefore, redshift experiments in a LFFF with separated clocks can provide a new null test of the equivalence principle. With presently available technology, it is possible to reach an accuracy of 0.01% in the gravitational field of the Sun using an atomic clock orbiting the Earth. A 1% test in the gravitational field of the galaxy would be possible if an atomic frequency standard were flown on a space mission to the outer solar system.

Krisher, Timothy P.↗

NASA NTRS2001

Equivalent-Continuum Modeling of Nano-Structured Materials

A method has been developed for modeling structure-property relationships of nano-structured materials. This method serves as a link between computational chemistry and solid mechanics by substituting discrete molecular structures with an equivalent-continuum model. It has been shown that this substitution may be accomplished by equating the vibrational potential energy of a nano-structured material with the strain energy of representative truss and continuum models. As an important example with direct application to the development and characterization of single-walled carbon nanotubes, the model has been applied to determine the effective continuum geometry of a graphene sheet. A representative volume element of the equivalent-continuum model has been developed with an effective thickness. This effective thickness has been shown to be similar to, but slightly smaller than, the interatomic spacing of graphite.

Odegard, Gregory M.↗

NASA NTRS2001

Scattering by Randomly Oriented Thin Ice Disks with Moderate Equivalent-Sphere Size Parameters

We use the T-matrix method to compute the scattering matrix for randomly oriented circular ice cylinders with diameter-to-length ratios 1 and 20 and surface-equivalent-sphere size parameters up to 12. We show that wavelength-sized, sharp-edged ice plates with extreme diameter-to-length ratios possess the same scattering properties as smooth plate-like spheroids: their phase functions are similar to those of surface-equivalent compact particles, whereas all other elements of the scattering matrix are typical of Rayleigh scattering.

Zakharova, Nadia T.↗