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NASA NTRS1984

What Would a Dynamo Theorist like to Know About the Dynamics of the Solar Convection Zone?

Observations about the current status of solar dynamo theory are given. The induction equation for magnetic field is solved using assumed velocities and parametric representations of the inductive or diffusive effects of velocities. The equations of motion governing these flow are not solved in parallel. Results from global compressible convection models are discussed. Differential rotation and convection are also investigated.

Gilman, P. A.↗

NASA NTRS1987

Shape design sensitivity analysis and optimization of three dimensional elastic solids using geometric modeling and automatic regridding

An automatic regridding method and a three dimensional shape design parameterization technique were constructed and integrated into a unified theory of shape design sensitivity analysis. An algorithm was developed for general shape design sensitivity analysis of three dimensional eleastic solids. Numerical implementation of this shape design sensitivity analysis method was carried out using the finite element code ANSYS. The unified theory of shape design sensitivity analysis uses the material derivative of continuum mechanics with a design velocity field that represents shape change effects over the structural design. Automatic regridding methods were developed by generating a domain velocity field with boundary displacement method. Shape design parameterization for three dimensional surface design problems was illustrated using a Bezier surface with boundary perturbations that depend linearly on the perturbation of design parameters. A linearization method of optimization, LINRM, was used to obtain optimum shapes. Three examples from different engineering disciplines were investigated to demonstrate the accuracy and versatility of this shape design sensitivity analysis method.

Yao, Tse-Min↗

NASA NTRS1987

Near fields in the vicinity of pulsed electron beams in space

Most measurements of the radio frequency emissions from artificial electron beams in space have been made in close proximity to the beam. This paper presents theory and results for the near-field radiation associated with the operation of a pulsed electron beam, taking into account the effects of the ionospheric plasma. The beam is modeled as an infinite train of square-wave pulses and the radiation is obtained by adding coherently the radiation from each individual electron in the idealized helical trajectory assumed by the beam as it traverses the magnetized plasma. The mathematical solution is obtained by taking the Fourier transform in space and time of Maxwell's equations and the driving modulated beam current, and then taking the inverse transform of the resulting electric field. Typical electric field strengths are presented for a range of modulation frequencies extending from below the ion cyclotron to the electron cyclotron frequency.

Harker, K. J.↗

NASA NTRS1987

A study of the mechanism of internal gravity wave generation by quasigeostrophic meteorological motions

Numerous experiments on the detection of atmospheric waves in the frequency range from acoustic to planetary at meteor heights have revealed that important wave sources are meteorological processes in the troposphere (cyclones, atmospheric fronts, jet streams, etc.). A dynamical theory based on the others work include describing the adaptation of meteorological fields to the geostropic equilibrium state. According to this theory, wave motions appear as a result of constant competition between the maladjustment of the wind and pressure fields due to nonlinear effects and the tendency of the atmosphere to establish a quasi-geostrophic equilibrium of these fields. These meteorological fields are discussed.

Medvedev, A. S.↗

NASA NTRS1990

Direct formulation of a 4-node hybrid shell element with rotational degrees of freedom

A simple 4-node assumed-stress hybrid quadrilateral shell element with rotational or 'drilling' degrees of freedom is formulated. The element formulation is based directly on a 4-node element rather than being derived from an 'internal' 8-node isoparametric element. The formulation is based on the principle of minimum complementary energy. The membrane part of the element has 12 degrees of freedom. The bending part of the element also has 12 degrees of freedom. The bending part of the element uses the Reissner-Mindlin plate theory which takes into account the transverse shear effects. Quadratic variations for both in-plane and out-of-plane displacement fields and linear variations for both in-plane and out-of-plane rotation fields are assumed along the edges of the element. The element passes the patch test, is nearly insensitive to mesh distortion, has no spurious modes, and is invariant with respect to node numbering.

Aminpour, Mohammad A.↗

NASA NTRS2001

Finite Element Analysis of Active and Sensory Thermopiezoelectric Composite Materials

Analytical formulations are developed to account for the coupled mechanical, electrical, and thermal response of piezoelectric composite materials. The coupled response is captured at the material level through the thermopiezoelectric constitutive equations and leads to the inherent capability to model both the sensory and active responses of piezoelectric materials. A layerwise laminate theory is incorporated to provide more accurate analysis of the displacements, strains, stresses, electric fields, and thermal fields through-the-thickness. Thermal effects which arise from coefficient of thermal expansion mismatch, pyroelectric effects, and temperature dependent material properties are explicitly accounted for in the formulation. Corresponding finite element formulations are developed for piezoelectric beam, plate, and shell elements to provide a more generalized capability for the analysis of arbitrary piezoelectric composite structures. The accuracy of the current formulation is verified with comparisons from published experimental data and other analytical models. Additional numerical studies are also conducted to demonstrate additional capabilities of the formulation to represent the sensory and active behaviors. A future plan of experimental studies is provided to characterize the high temperature dynamic response of piezoelectric composite materials.

Lee, Ho-Jun↗

NASA NTRS1978

Moon-magnetosphere interaction and estimates of possible lunar core size

It is shown that estimates of the size of a possible lunar core are negligibly affected by currents due to a directed plasma flux toward the moon. A theory for the compression of an induced lunar dipole by an incoming sub-Alfvenic flux of cold plasma is presented for the time-independent case where the external magnetic field, induced dipole moment, and plasma velocity vector are all aligned, and it is demonstrated that, at very long time periods, effects due to the inertia of an incoming flow of cold plasma can be ignored. A theory for time-dependent fluctuations in a stationary plasma is modified to include the effects of incoming flux.

Goldstein, B. E.↗

NASA NTRS1994

Towards an MHD theory for the standoff distance of Earth's bow shock

An MHD theory is developed for the stand-off distance a(sub s) of the bow shock and the thickness delta(sub ms) of the magnetosheath, using the empirical Spreiter et al. relation delta(sub ms) = kX and the MHD density ratio X across the shock. The theory includes as special cases the well-known gasdynamic theory and associated phenomenological MHD-like models for delta(sub ms) and a(sub s). In general, however, MHD effects produce major differences from previous models, especially at low Alfven (M(sub A)) and sonic (M(sub S)) Mach numbers. The magnetic field orientation, M(sub A), M(sub S) and the ratio of specific heats gamma are all important variables of the theory. Three principal conclusions are reached. First, the gasdynamic and phenomenological models miss important dependances on field orientation and M(sub S) and generally provide poor approximations to the MHD results. Second, changes in field orientation and M(sub S) are predicted to cause factor of approximately 4 changes in delta(sub ms) at low M(sub A). Third, using Spreiter et al.'s value for k in the MHD theory leads to maximum a(sub s) values at low M(sub A) and nominal M(sub S) that are much smaller than observations and MHD simulations require. Resolving this problem requires either the modified Spreiter-like relation and larger k found in recent MHD simulations and/or breakdown in the Spreiter-like relation at very low M(sub A).

Cairns, Iver H.↗

NASA NTRS1999

Radiative Smoothing in Clouds at Transparent and Absorbing Wavelengths

For absorbing and transparent wavelengths, we discuss the effect of horizontal solar radiative fluxes in clouds on the accuracy of a conventional plane-parallel radiative transfer calculations for a single pixel, known as the Independent Pixel Approximation (IPA). We address the question of correlations between horizontal fluxes, IPA accuracies and radiative smoothing. By smoothing we understand a radiative transfer process whereby radiation does not follow the small-scale fluctuations of cloud structure, producing much smoother radiation fields. The scale eta that characterizes this process is called "radiative smoothing scale." We relate radiative smoothing to the photon's horizontal displacement that characterizes a "spot" of reflected light associated with a point source. We generalize the "spot-size" estimate derived for conservative scattering using the diffusion theory to the case of non-conservative scattering. For reflected light, theoretical results are confirmed with numerical simulations. The radiative smoothing scale eta is a critical value where IPA effectively breaks down; for scales smaller than TI, real radiation field are much smoother than their IPA counterparts for the same cloud structure. In addition to the estimate of il for absorbing wavelengths, we show that: (1) with more absorption, the scale break determined by eta in a log-log plot of wavenumber spectra moves towards smaller scales and (2) the smaller eta the flatter the small-scale slope which means less radiative smoothing, thus more accuracy in the IPA reflection.

Marshak, A.↗

NASA NTRS1996

Receiver design, performance analysis, and evaluation for space-borne laser altimeters and space-to-space laser ranging systems

We report here the design and the performance measurements of the breadboard receiver of the Geoscience Laser Altimeter System (GLAS). The measured ranging accuracy was better than 2 cm and 10 cm for 5 ns and 30 ns wide received laser pulses under the expected received signal level, which agreed well with the theoretical analysis. The measured receiver sensitivity or the link margin was also consistent with the theory. The effects of the waveform digitizer sample rate and resolution were also measured.

Davidson, Frederic M.↗

NASA NTRS1992

Steady induction effects in geomagnetism. Part 1A: Steady motional induction of geomagnetic chaos

Geomagnetic effects of magnetic induction by hypothetically steady fluid motion and steady magnetic flux diffusion near the top of Earth's core are investigated using electromagnetic theory, simple magnetic earth models, and numerical experiments with geomagnetic field models. The problem of estimating a steady fluid velocity field near the top of Earth's core which induces the secular variation indicated by broad-scale models of the observed geomagnetic field is examined and solved. In Part 1, the steady surficial core flow estimation problem is solved in the context of the source-free mantle/frozen-flux core model. In the first paper (IA), the theory underlying such estimates is reviewed and some consequences of various kinematic and dynamic flow hypotheses are derived. For a frozen-flux core, fluid downwelling is required to change the mean square normal magnetic flux density averaged over the core-mantle boundary. For surficially geostrophic flow, downwelling implies poleward flow. The solution of the forward steady motional induction problem at the surface of a frozen-flux core is derived and found to be a fine, easily visualized example of deterministic chaos. Geomagnetic effects of statistically steady core surface flow may well dominate secular variation over several decades. Indeed, effects of persistent, if not steady, surficially geostrophic core flow are described which may help explain certain features of the present broad-scale geomagnetic field and perhaps paleomagnetic secular variation.

Voorhies, Coerte V.↗

NASA NTRS1993

An extended UTD analysis for the scattering and diffraction from cubic polynomial strips

Spline and polynomial type surfaces are commonly used in high frequency modeling of complex structures such as aircraft, ships, reflectors, etc. It is therefore of interest to develop an efficient and accurate solution to describe the scattered fields from such surfaces. An extended Uniform Geometrical Theory of Diffraction (UTD) solution for the scattering and diffraction from perfectly conducting cubic polynomial strips is derived and involves the incomplete Airy integrals as canonical functions. This new solution is universal in nature and can be used to effectively describe the scattered fields from flat, strictly concave or convex, and concave convex boundaries containing edges. The classic UTD solution fails to describe the more complicated field behavior associated with higher order phase catastrophes and therefore a new set of uniform reflection and first-order edge diffraction coefficients is derived. Also, an additional diffraction coefficient associated with a zero-curvature (inflection) point is presented. Higher order effects such as double edge diffraction, creeping waves, and whispering gallery modes are not examined. The extended UTD solution is independent of the scatterer size and also provides useful physical insight into the various scattering and diffraction processes. Its accuracy is confirmed via comparison with some reference moment method results.

Constantinides, E. D.↗

NASA NTRS1962

The Response of Ribbed Panels to Reverberant Acoustic Fields

A statistical method for estimating the response of ribbed panels to acoustic excitation is discussed. It is shown that the acceleration spectrum of the vibrational field is related to the pressure spectrum by a coupling factor which is a simple function of the radiation and mechanical resistance of the structure. The radiation resistance of a ribbed panel is studied as a function of frequency. The analysis predicts that ribbing increases the radiation resistance of the panel and hence its coupling to the acoustic field. The effect of various panel-rib boundary conditions is also considered. The results of experiments which were conducted to test the theory are reported. The agreement between theory and experiments is shown to be satisfactory.

BOUNDARY↗

NASA NTRS1978

Transmission of sound through high subsonic flows in non-uniform ducts

The transmission of sound through a near-sonic throat in a variable area duct is studied using the method of matched asymptotic expansions applied to a quasi-one-dimensional model. Nonlinear interactions between the mean flow and the acoustic perturbation in the throat region are shown to cause significant effects on the sound field upstream and downstream of the throat. Numerical results are presented for several special applications of the general nonlinear theory.

Myers, M. K.↗

NASA NTRS1988

Temporal and spatial distribution of stratospheric trace gases over Antarctica in August and September, 1987

There have been a large number of suggestions made concerning the origin of the Antarctic 'ozone hole' since its discovery; these changes include stratospheric chemistry, or changes in the solar input, or combinations of these effects. Supporting or refuting these theories requires a wide variety of data for comparison with the predictions. In Aug. and Sept., 1987, a field observation expedition was made over Antarctica from a base in Punta Arenas, Chile. Two aircraft, an ER-2 with in-situ instruments flew at altitudes up to 18 km measuring ozone, water, ClO, BrO, NO sub x, particles, and meteorological parameters in the ozone layer. A DC-8 flew at altitudes of 10 to 12 km, below the ozone layer, using remote sensing instruments for measuring composition and aerosol content of the ozone layer, as well as in-situ instruments for measuring composition at aircraft altitudes. The obsevation of a number of chemical species and their correlation with each other and with meteorological parameters gives a useful set of data for comparison with various theories.

Coffey, M. T.↗

NASA NTRS1990

Short wavelength striations on expanding plasma clouds

The present evaluation of current understanding of the growth and evolution of less-than-1 ion gyroradius 'flute modes' on a plasma as it expands across and ambient magnetic field notes that the mechanism by which the instability is generated, and its approximate linear theory (encompassing nonlocal, finite-beta, and collisional effects), have reached a satisfactory degree of development. AMPTE Ba releases have been the bases of most of the observational studies. Substantial progress is also noted in the development of a nonlinear mode-coupling theory which can resolve remaining differences between theory and observation.

Winske, D.↗

NASA NTRS1954

Longitudinal Aerodynamic Characteristics to Large Angles of Attack of a Cruciform Missile Configuration at a Mach Number of 2

The lift, pitching-moment, and drag characteristics of a missile configuration having a body of fineness ratio 9.33 and a cruciform triangular wing and tail of aspect ratio 4 were measured at a Mach number of 1.99 and a Reynolds number of 6.0 million, based on the body length. The tests were performed through an angle-of-attack range of -5 deg to 28 deg to investigate the effects on the aerodynamic characteristics of roll angle, wing-tail interdigitation, wing deflection, and interference among the components (body, wing, and tail). Theoretical lift and moment characteristics of the configuration and its components were calculated by the use of existing theoretical methods which have been modified for application to high angles of attack, and these characteristics are compared with experiment. The lift and drag characteristics of all combinations of the body, wing, and tail were independent of roll angle throughout the angle-of-attack range. The pitching-moment characteristics of the body-wing and body-wing- tail combinations, however, were influenced significantly by the roll angle at large angles of attack (greater than 10 deg). A roll from 0 deg (one pair of wing panels horizontal) to 45 deg caused a forward shift in the center of pressure which was of the same magnitude for both of these combinations, indicating that this shift originated from body-wing interference effects. A favorable lift - interference effect (lift of the combination greater than the sum of the lifts of the components) and a rearward shift in the center of pressure from a position corresponding to that for the components occurred at small angles of attack when the body was combined with either the exposed wing or tail surfaces. These lift and center-of-pressure interference effects were gradually reduced to zero as the angle of attack was increased to large values. The effect of wing-tail interference, which influenced primarily the pitching-moment characteristics, is dependent on the distance between the wing trailing vortex wake and the tail surfaces and thus was a function of angle of attack, angle of roll, and wing- tail interdigitation. Although the configuration at zero roll with the wing and tail in line exhibited the least center-of-pressure travel, the configuration with the wing and tail interdigitated had the least change in wing- tail interference over the angle - of-attack range. The lift effectiveness of the variable-incidence wing was reduced by more than 70 percent as a result of an increase in the combined angle of attack and wing incidence from 0 deg to 40 deg center dot The wing- tail interference (effective downwash at the tail) due to wing deflection was nearly zero as a result of a region of negative vorticity shed from the inboard portion of the wing. The lift characteristics of the configuration and its components were satisfactorily predicted by the calculated results, but the pitching moments at large angles of attack were not because of the influence of factors for which no adequate theory is available, such as the variation of the cross flow drag coefficient along the body and the effect of the wing downwash field on the after body loading.

Spahr, J Richard↗

NASA NTRS1966

On a logical basis for division of responsibilities in statistical practice

The purpose of this paper is to explain principles for division of responsibilities between the statistician and the people that he works with, and reasons why this division of responsibilities is important -- that is, how it improves the performance of both statistician and expert in subject-matter. The aim is to find and illustrate principles of practice by which statisticians may make effective use of their knowledge of theory. The specialist in statistical methods may find himself applying the same basic theory in a dozen different fields in a week, rotating through the same projects the next week. Or, he may work day after day primarily in a single substantive field. Either way, he requires rules of practice. A statement of statistical reliability should present any information that might help the reader to form his own opinion concerning the validity of conclusions likely to be drawn from the results. The aim of a statistical report is to protect the client from seeing merely what he would like to see; to protect him from losses that could come from misuse of results. A further aim is to forestall unwarranted claims of accuracy that the client's public might otherwise accept.

Deming, W. Edwards↗