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NASA NTRS1995

Galactic oscillator symmetry

Riemann ellipsoids model rotating galaxies when the galactic velocity field is a linear function of the Cartesian coordinates of the galactic masses. In nuclear physics, the kinetic energy in the linear velocity field approximation is known as the collective kinetic energy. But, the linear approximation neglects intrinsic degrees of freedom associated with nonlinear velocity fields. To remove this limitation, the theory of symplectic dynamical symmetry is developed for classical systems. A classical phase space for a self-gravitating symplectic system is a co-adjoint orbit of the noncompact group SP(3,R). The degenerate co-adjoint orbit is the 12 dimensional homogeneous space Sp(3,R)/U(3), where the maximal compact subgroup U(3) is the symmetry group of the harmonic oscillator. The Hamiltonian equations of motion on each orbit form a Lax system X = (X,F), where X and F are elements of the symplectic Lie algebra. The elements of the matrix X are the generators of the symplectic Lie algebra, viz., the one-body collective quadratic functions of the positions and momenta of the galactic masses. The matrix F is composed from the self-gravitating potential energy, the angular velocity, and the hydostatic pressure. Solutions to the hamiltonian dynamical system on Sp(3,R)/U(3) are given by symplectic isospectral deformations. The Casimirs of Sp(3,R), equal to the traces of powers of X, are conserved quantities.

Rosensteel, George↗

NASA NTRS1992

Analysis of delamination related fracture processes in composites

An anisotropic thin walled closed section beam theory was developed based on an asymptotical analysis of the shell energy functional. The displacement field is not assumed a priori and emerges as a result of the analysis. In addition to the classical out-of-plane torsional warping, two new contributions are identified namely, axial strain and bending warping. A comparison of the derived governing equations confirms the theory developed by Reissner and Tsai. Also, explicit closed form expressions for the beam stiffness coefficients, the stress and displacement fields are provided. The predictions of the present theory were validated by comparison with finite element simulation, other closed form analyses and test data.

Armanios, Erian A.↗

NASA NTRS1985

Electrical measurements in the atmosphere and the Ionosphere over an active thunderstorm. II - Direct current electric fields and conductivity

On August 9, 1981, a series of three rockets was launched over an air mass thunderstorm off the eastern seaboard of Virginia while simultaneous stratospheric and ground-based electric field measurements were made. The conductivity was substantially lower at most altitudes than the conductivity profiles used by theoretical models. Direct current electric fields over 80 mV/m were measured as far away as 96 km from the storm in the stratosphere at 23 km altitude. No dc electric fields above 75 km altitude could be identified with the thunderstorm, in agreement with theory. However, vertical current densities over 120 pA/sq m were seen well above the classical 'electrosphere' (at 50 or 60 km). Frequent dc shifts in the electric field following lightning transients were seen by both balloon and rocket payloads. These dc shifts are clearly identifiable with either cloud-to-ground (increases) or intercloud (decreases) lightning flashes.

Holzworth, R. H.↗

NASA NTRS1990

The computation of induced drag with nonplanar and deformed wakes

The classical calculation of inviscid drag, based on far field flow properties, is re-examined with particular attention to the nonlinear effects of wake roll-up. Based on a detailed look at nonlinear, inviscid flow theory, the paper concludes that many of the classical, linear results are more general than might have been expected. Departures from the linear theory are identified and design implications are discussed. Results include the following: wake deformation has little effect on the induced drag of a single element wing, but introduces first order corrections to the induced drag of a multi-element lifting system. Far field Trefftz-plane analysis may be used to estimate the induced drag of lifting systems, even when wake roll-up is considered, but numerical difficulties arise. The implications of several other approximations made in lifting line theory are evaluated by comparison with more refined analyses.

Kroo, Ilan↗

NASA NTRS1999

Mid-Field Sonic Boom Extrapolation Methodology

In the design cycle of low-boom airplanes, sonic boom prediction must be accurate and efficient. The classical linear method, Whitham's F-function theory, has been widely applied to predict sonic boom signatures. However, linear theory fails to capture the nonlinear effects created by large civil transport. Computational fluid dynamics (CFD) has been used successfully to predict sonic boom signals at the near and mid fields. Nevertheless, it is computationally expansive in airplane design runs. In the present study, the method of characteristics is used to predict sonic boom signals in an efficient fashion. The governing equations are the axisymmetric Euler's equations with constant enthalpy. Since the method solves Euler's equations, it captures more nonlinear effects than the classical Whitham's F-function technique. Furthermore, the method of characteristics is an efficient marching scheme for initial value problems. In this study, we will first review the current CFD extrapolation technique and the work previously done in sonic boom extrapolation. Then, we will introduce the governing equations and the method of characteristics. Finally, we will show that the present method yields the same accurate results as previous CFD techniques, but with higher efficiency.

Cheung, Samson↗

NASA NTRS1973

Mie scattering of the interplanetary magnetic field by the whole moon

It is known from the Apollo magnetometer experiments that significant electromagnetic induction takes place in the lunar interior. This induction is excited by fluctuations of the interplanetary magnetic field and is detected by the induced fields on the surface of the moon. These results are reviewed briefly and the formal properties of the theory are discussed. It is shown that the mathematical treatment parallels that for classical electromagnetic scattering. Further the wavelength spectrum of the fluctuations of the interplanetary magnetic field include scales consistent with the radius of the moon. The consequence is that the moon is excited in several modes. Quadrupole and possibly octupole magnetic multipoles are found in the data. The electric type radiation corresponding to transverse magnetic excitation appears suppressed and far below the detection threshold of the magnetometers.

Sonett, C. P.↗

NASA NTRS1973

The relativistic dynamics of a point charge in the field of a plane electromagnetic wave traveling in the direction of a uniform static magnetic field

The motion of a charged particle in electromagnetic fields of various geometric configurations and arising from a variety of sources is of intrinsic interest in electromagnetic theory. The particular configuration consisting of a plane wave propagating in the presence of a static uniform magnetic field whose direction is parallel to the wave normal is examined. The analysis presented here is treated within the context of classical electromagnetic theory. A numerical solution - at least to the approximate Lorentz-Dirac equation - is obtained.

Mitchell, T. P.↗

NASA NTRS1988

Gauged Q-balls

Classical non-topological soliton configurations are considered within the theory of a complex scalar field with a gauged U symmetry. Their existence and stability against dispersion are demonstrated and some of their properties are investigated analytically and numerically. The soliton configuration is such that inside the soliton the local U symmetry is broken, the gauge field becomes massive and for a range of values of the coupling constants the soliton becomes a superconductor pushing the charge to the surface. Furthermore, because of the repulsive Coulomb force, there is a maximum size for these objects, making impossible the existence of Q-matter in bulk form. Also briefly discussed are solitons with fermions in a U gauge theory.

Lee, Kimyeong↗

NASA NTRS1990

Geostrophic adjustment in a baroclinic atmosphere

The classical geostrophic adjustment problem is reexamined in a baroclinically unstable atmosphere. After the geostrophic balance is disturbed by either adding mass or momentum to the atmosphere, the resulting evolution of the mass and momentum fields is found by using Laplace and Fourier transforms. In general, the results from classical geostrophic theory hold in the baroclinically unstable atmosphere. Although the most unstable modes eventually dominate, in certain situations the perturbations may actually decay before they begin to grow. This may be a key mechanism which explains a portion of the spinup problem commonly encountered in numerical models.

Duffy, Dean G.↗

NASA NTRS1990

Extensional reactivation of an abandoned thrust - A bound on shallowing in the brittle regime

Shallow dip angles (not greater than 45 deg) suggested by field observations of continental extensional faults are not predicted by classical isotropic Mohr-Coulomb-Anderson theory. Earthquake data indicate that normal faults exist in the upper crust with dip angles commonly as shallow as 30 deg. One explanation of the apparent conflict between theory and structural/seismic observations is that intrinsically weak, shallow-dipping pre-existing faults are preferentially reactivated. An analytical treatment clarifies the roles of geometry, intact/preexisting fault strengths and fluid pore pressures. Frictional strength ratios of 3 or greater could account for extremely shallow normal faults (dips 10-20 deg) without consideration of pore pressures in excess of the least principal stress or of principal stress systems rotated away from the gravity vector. Moderate reduction in friction (3/4) with respect to wall rock can reduce the dip to 30 deg and can account for shallow normal-slip earthquakes.

Ivins, E. R.↗

NASA NTRS2016

Grain-Scale Supercharging and Breakdown on Airless Regoliths

Interactions of the solar wind and emitted photoelectrons with airless bodies have been studied extensively. However, the details of how charged particles interact with the regolith at the scale of a single grain have remained largely uncharacterized. Recent efforts have focused upon determining total surface charge under photoemission and solar wind bombardment and the associated electric field and potential. In this work, theory and simulations are used to show that grain-grain charge differences can exceed classical sheath predictions by several orders of magnitude, sometimes reaching dielectric breakdown levels. Temperature-dependent electrical conductivity works against supercharging by allowing current to leak through individual grains; the balance between internal conduction and surface charging controls the maximum possible grain-to-grain electric field. Understanding the finer details of regolith grain charging, conductive equilibrium, and dielectric breakdown will improve future numerical studies of space weathering and dust levitation on airless bodies.

airless↗

NASA NTRS2017

Non-Classical Stress Concentration Behavior in a Radically Stretched Hyperelastic Sheet Containing a Circular Hole

Non-classical stress concentration behavior in a stretched circular hyperelastic sheet (outer radius b = 10 in., thickness t = 0.0625 in.) containing a central hole (radius a = 0.5 in.) was analyzed. The hyperelastic sheet was subjected to different levels of remote radial stretchings. Nastran large-strain large-deformation analysis and the Blatz-Ko large deformation theory were used to calculate the equal-biaxial stress concentration factors K. The results show that the values of K calculated from the Blatz-Ko theory and Nastran are extremely close. Unlike the classical linear elasticity theory, which gives the constant K = 2 for the equal-biaxial stress field, the hyperelastic K values were found to increase with increased stretching and can exceed the value K = 6 at a remote radial extension ratio of 2.35. The present K-values compare fairly well with the K-values obtained by previous works. The effect of the hole-size on K-values was investigated. The values of K start to decrease from a hole radius a = 0.125 in. down to K = 1 (no stress concentration) as a shrinks to a = 0 in. (no hole). Also, the newly introduced stretch and strain magnification factors {K(sub λ),K(sub ε) } are also material- and deformation-dependent, and can increase from linear levels of {1.0, 4.0} and reaching {3.07, 4.61}, respectively at a remote radial extension ratio of 2.35.

stress concentration↗

NASA NTRS2001

Semi-Classical Models for Virtual Antiparticle Pairs

Virtual particle-antiparticle pairs of massive elementary particle& are predicted in Quantum Field Theory (QFT) to appear from the vacuum and annihilate each other again within their Heisenberg lifetimes h/4mc(exp 2). In this work, semiclassical models of this process - for the cases of massive leptons, quarks, and the massive weak bosons W and Z - are constructed. It is shown that the dynamical lifetime of the particle- antiparticle system in each case equals the Heisenberg lifetime to good approximation, and obeys appropriate quantization conditions on the field fluctuation action. In other words, the dynamical lifetime of the semiclassical model agrees with QED and QCD to good approximation. But the formula for the dynamical lifetime in each model includes the force strength coupling constant (e in the lepton case, alpha(sup s) (q(exp 2)) in the quark cases), while the Heisenberg lifetime formula does not. Observing the agreement of the Heisenberg and dynamical lifetimes, we may derive the QED and QCD coupling constants in terms of h, c, and numerical factors only.

Batchelor, David↗

NASA NTRS1974

Do massive Brans-Dicke theories of gravitation imitate Brans-Dicke theories with nonzero divergence of energy-momentum tensor

Acharya and Hogan (1973) have introduced a massive scalar field into the usual Brans-Dicke (1961) theory of gravitation. Formally they obtain certain field equations. The assumption of a nonzero divergence for T mu nu (or equivalently the introduction of sources) formally imitates a massive Brans-Dicke and satisfies the condition of Acharya and Hogan that the theory be indistinguishable with the classical test of the Einstein theory. Although it was shown elsewhere that the modified Brans-Dicke theory agrees with the classical test under certain conditions, there were no specified limits on omega, a similar circumstance discovered by Acharya and Hogan for the massive scalar field.

Smalley, L. L.↗

NASA NTRS2011

Phase-Sensitive Coherence and the Classical-Quantum Boundary in Ghost Imaging

The theory of partial coherence has a long and storied history in classical statistical optics. the vast majority of this work addresses fields that are statistically stationary in time, hence their complex envelopes only have phase-insensitive correlations. The quantum optics of squeezed-state generation, however, depends on nonlinear interactions producing baseband field operators with phase-insensitive and phase-sensitive correlations. Utilizing quantum light to enhance imaging has been a topic of considerable current interest, much of it involving biphotons, i.e., streams of entangled-photon pairs. Biphotons have been employed for quantum versions of optical coherence tomography, ghost imaging, holography, and lithography. However, their seemingly quantum features have been mimicked with classical-sate light, questioning wherein lies the classical-quantum boundary. We have shown, for the case of Gaussian-state light, that this boundary is intimately connected to the theory of phase-sensitive partial coherence. Here we present that theory, contrasting it with the familiar case of phase-insensitive partial coherence, and use it to elucidate the classical-quantum boundary of ghost imaging. We show, both theoretically and experimentally, that classical phase-sensitive light produces ghost imaging most closely mimicking those obtained in biphotons, and we derived the spatial resolution, image contrast, and signal-to-noise ratio of a standoff-sensing ghost imager, taking into account target-induced speckle.

coherence theory↗

NASA NTRS1984

Magnetic field observations at the dayside magnetopause: ISEE-1 and -2 contributions during the IMS

Dayside magnetopause macroscopic characteristics such as velocities and thicknesses of the boundary and internal magnetic field structure of the current layer were studied by ISEE-1 and 2. The ISEE results suggest that the magnetopause is much thicker than previously thought. A current sheet thicker than several proton gyroradii rules out classical kinetic theories of a magnetopause current layer of the order of the ion gyroradius. Such a thick boundary may explain the failure of theories which predict a unique polarization for the field rotation inside the current sheet.

Berchem, J.↗

NASA NTRS1974

Coherent propagation of charged-particle bunches in random magnetic fields

When the distribution function for energetic particles moving in interplanetary space is expressed in terms of eigenfunctions of an operator which describes pitch-angle scattering by random magnetic fields, the familiar phenomenon of diffusion is the dominant solution of the transport equations provided that the spectrum of magnetic fluctuations is not too steep. However, if the power-versus-wavenumber spectrum of the random fields has a spectral index greater than 2, the dominant solution of the same equations is a qualitatively different mode of transport in which density inhomogeneities propagate coherently along the guiding field with a characteristic velocity equal to half the particle speed. The present work, which extends classical transport theory to give a detailed treatment of the new mode, presents explicit formulae which describe the spatial and temporal structure of the coherent disturbance. It is shown that this disturbance evolves asymptotically into a moving Gaussian pulse whose width increases with time.

Earl, J. A.↗

NASA NTRS1994

An estimate of the momentum deposition in the lower thermosphere by the observed diurnal tide

This paper reports a calculation of the acceleration of the zonal mean flow induced by dissipating tides in the equatorial lower thermosphere. Estimates of the gravest symmetric gravitiational Hough mode (1,1) of the migrating diurnal tide are obtained from monthly composites of global winds observed by the Upper Atmosphere Research Satellite (UARS) High Resolution Doppler Imager (HRDI). Using the principles of classical tidal theory, the tidal momentum flux divergence is computed for a series of monthly mean (1,1) fields from January 1992 to May 1993. The contribution to the mean flow by the leading mode of the migrating tide ranges between -5 and -20 (easterly) m/s/day in the equatorial lower thermosphere. A semiannual variation is noted in the tidal amplitudes and the inferred tidal accelerations. These variations are consistent with observed trends in the zonal mean flow of the lower thermosphere.

Lieberman, Ruth S.↗