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NASA NTRS1994

A brief survey of constrained mechanics and variational problems in terms of differential forms

There has been considerable interest recently in constrained mechanics and variational problems. This is in part due to applied interests (such as 'non-holonomic mechanics in robotics') and in other part due to the fact that several schools of 'pure' mathematics have found that this classical subject is of importance for what they are trying to do. I have made various attempts at developing these subjects since my Lincoln lab days of the late 1950's. In this Chapter, I will sketch a Unified point of view, using Cartan's approach with differential forms. This has the advantage from the C-O-R viewpoint being developed in this Volume that the extension from 'smooth' to 'generalized' data is very systematic and algebraic. (I will only deal with the 'smooth' point of view in this Chapter; I will develop the 'generalized function' material at a later point.) The material presented briefly here about Variational Calculus and Constrained Mechanics can be found in more detail in my books, 'Differential Geometry and the Calculus of Variations', 'Lie Algebras and Quantum Mechanics', and 'Geometry, Physics and Systems'.

Hermann, Robert↗

NASA NTRS1982

Influence of fluids on the abrasion of silicon by diamond

Silicon wafers ((100)-p-type) were abraded at room temperature in acetone, absolute ethanol and water by a pyramid diamond and the resulting groove depth was measured as a function of normal force on the diamond and the absorbed fluids, while all other experimental conditions were held constant. The groove depth rates are in the ratio of 1:2:3 for water, absolute ethanol, and acetone, respectively, for a constant normal force. The groove depth rate is lower when the normal force is decreased. The silicon abraded in the presence of water was chipped as expected for a classical brittle material while the surfaces abraded in the other two fluids showed ductile ploughing as the main mechanism for silicon removal.

Danyluk, S.↗

NASA NTRS1990

A mechanical model for elastic fiber microbuckling

A two-dimensional mechanical model is presented to predict the compressive strength of unidirectional fiber composites using technical beam theory and classical elasticity. First, a single fiber resting on a matrix half-plane is considered. Next, a more elaborate analysis of a uniformly laminated, unidirectional fiber composite half-plane is presented. The model configuration incorporates a free edge which introduces a buckling mode that originates at the free edge and decays into the interior of the half-plane. It is demonstrated that for composites of low volume fraction (less than 0.3), this decay mode furnishes values of buckling strain that are below the values predicted by the Rosen (1965) model. At a higher volume fraction the buckling mode corresponds to a half-wavelength that is in violation of the usual assumptions of beam theory. Causes for deviations of the model prediction from existing experimental results are discussed.

Waas, A. M.↗

NASA NTRS1990

A Mechanical Model for Elastic Fiber Microbuckling

A two-dimensional mechanical model is presented to predict the compressive strength of unidirectional fiber composites using technical beam theory and classical elasticity. First, a single fiber resting on a matrix half-plane is considered. Next, a more elaborate analysis of a uniformly laminated, unidirectional fiber composite half-plane is presented. The model configuration incorporates a free edge which introduces a buckling mode that originates at the free edge and decays into the inferior of the half-plane. It is demonstrated that for composites of low volume fraction (less than 0.3), this decay mode furnishes values of buckling strain that are below the values predicted by the Rosen (1965) model. At a higher volume fraction the buckling mode corresponds to a half wavelength that is in violation of the usual assumptions of beam theory. Causes for deviations of the model prediction froi?i existing experimental results are discussed.

Waas, M. A.↗

NASA NTRS2015

On the Comparison of the Long Penetration Mode (LPM) Supersonic Counterflowing Jet to the Supersonic Screech Jet

The authors provide a brief overview of the classic tonal screech noise problem created by underexpanded supersonic jets, briefly describing the fluid dynamic-acoustics feedback mechanism that has been long established as the basis for this well-known aeroacoustics problem. This is followed by a description of the Long Penetration Mode (LPM) supersonic underexpanded counterflowing jet phenomenon which has been demonstrated in several wind tunnel tests and modeled in several computational fluid dynamics (CFD) simulations. The authors provide evidence from test and CFD analysis of LPM that indicates that acoustics feedback and fluid interaction seen in LPM are analogous to the aeroacoustics interactions seen in screech jets. Finally, the authors propose applying certain methodologies to LPM which have been developed and successfully demonstrated in the study of screech jets and mechanically induced excitation in fluid oscillators for decades. The authors conclude that the large body of work done on jet screech, other aeroacoustic phenomena, and fluid oscillators can have direct application to the study and applications of LPM counterflowing supersonic cold flow jets.

Farr, Rebecca A.↗

NASA NTRS2014

Binary Orbits as the Driver of Gamma-Ray Emission and Mass Ejection in Classical Novae

Classical novae are the most common astrophysical thermonuclear explosions, occurring on the surfaces of white dwarf stars accreting gas from companions in binary star systems. Novae typically expel about 10 (sup -4) solar masses of material at velocities exceeding 1,000 kilometers per second.However, the mechanism of mass ejection in novae is poorly understood, and could be dominated by the impulsive flash of thermonuclear energy, prolonged optically thick winds or binary interaction with the nova envelope. Classical novae are now routinely detected at giga-electronvolt gamma-ray wavelengths, suggesting that relativistic particles are accelerated by strong shocks in the ejecta. Here we report high-resolution radio imaging of the gamma-ray-emitting nova V959 Mon. We find that its ejecta were shaped by the motion of the binary system: some gas was expelled rapidly along the poles as a wind from the white dwarf, while denser material drifted out along the equatorial plane, propelled by orbital motion..At the interface between the equatorial and polar regions, we observe synchrotron emission indicative of shocks and relativistic particle acceleration, thereby pinpointing the location of gamma-ray production. Binary shaping of the nova ejecta and associated internal shocks are expected to be widespread among novae, explaining why many novae are gamma-ray emitters.

binary orbits as the driver of gamma-ray↗

NASA NTRS1971

Analytic expression for the energy-transfer rate from photoelectrons to thermal-electrons.

An analytic form is given for the energy-transfer rate from photoelectrons to thermal electrons. The expression fits the classical formulation of Itakawa and Aono (1966) at low energies and gives a smooth transition to fit the quantum mechanical equation of Schunk and Hays (1971) at higher energies. The corresponding loss function or stopping power has a form that is convenient in auroral and dayglow calculations.

Swartz, W. E.↗

NASA NTRS1972

Energy straggling and radiation reaction for magnetic bremsstrahlung.

Using the method of quantum electrodynamics, the energy distribution of particles and emitted photons is calculated for the case when increases in the average energy of the photon emitted by synchrotron radiation to values appreciable compared to the energy of the particle give rise to particle energy straggling and radiation spectrum broadening. The classical radiative reaction effects which may be tested in this type of experiment are outlined, and a detailed quantum mechanical calculation is presented. The significance of energy straggling in astrophysics is discussed briefly.

Shen, C. S.↗

NASA NTRS1973

Transient analysis of phase-locked tracking systems in the presence of noise.

This paper is concerned with the problem of obtaining time-dependent solutions to a class of Fokker-Planck equations that arise in the analysis and synthesis of a variety of first-order synchronization systems employing the phase-lock principle. These include the classical sinusoidal phase-locked loop, squaring and Costas loops, data-aided loops, hybrid loops, various symbol synchronizer mechanizations, and tunnel-diode oscillators. By analyzing the spectral properties of the associated time-dependent Fokker-Planck boundary value problem, eigenfunction expansions of the reduced modulo-2-pi phase-error-transition probability-density function are developed for a class of first-order synchronization systems.

La Frieda, J. R.↗

NASA NTRS1981

Radiation force on a relativistic plasma and the Eddington limit

Calculations of the radiation force due to Thomson scattering on a relativistic plasma are presented and discussed in relation to certain astronomical objects which operate within a few orders of magnitude of their Eddington luminosity. The radiation force on a hot isotropic plasma is shown to exceed that on a cold plasma by a factor depending on the electron Lorentz factor, which can be substantial in a relativistic plasma. In such a plasma, radiative bulk acceleration is found to occur through the anisotropic loss of internal energy during the Thomson scattering, resulting in an effect termed a Compton rocket. The Compton rocket is shown to be a relevant acceleration mechanism in situations where a relativistic electron plasma lies in the vicinity of a luminous source operating near the classical Eddington limit, including compact galactic X-ray sources and objects associated with active galactic nuclei (quasars, blazars, and Seyfert nuclei).

Odell, S. L.↗

NASA NTRS1981

Ball bearing lubrication: The elastohydrodynamics of elliptical contacts

The history of ball bearings is examined, taking into account rollers and the wheel in the early civilizations, the development of early forms of rolling-element bearings in the classical civilizations, the Middle Ages, the Industrial Revolution, the emergence of the precision ball bearing, scientific studies of contact mechanics and rolling friction, and the past fifty years. An introduction to ball bearings is presented, and aspects of ball bearing mechanics are explored. Basic characteristics of lubrication are considered along with lubrication equations, the lubrication of rigid ellipsoidal solids, and elastohydrodynamic lubrication theory. Attention is given to the theoretical results for fully flooded elliptical hydrodynamic contacts, the theoretical results for starved elliptical contacts, experimental investigations, the elastohydrodynamics of elliptical contacts for materials of low elastic modulus, the film thickness for different regimes of fluid-film lubrication, and applications.

Hamrock, B. J.↗

NASA NTRS1991

Simulation of transient flow in a shock tunnel and a high Mach number nozzle

A finite volume Navier-Stokes code was used to simulate the shock reflection and nozzle starting processes in an axisymmetric shock tube and a high Mach number nozzle. The simulated nozzle starting processes were found to match the classical quasi-1-D theory and some features of the experimental measurements. The shock reflection simulation illustrated a new mechanism for the driver gas contamination of the stagnated test gas.

Jacobs, P. A.↗

NASA NTRS1993

Influence of local fiber undulations on the global buckling behavior of filament-wound cylinders

The predicted compressive stiffness and buckling strength of filament-wound cylinders using classical lamination theory is significantly higher than those observed experimentally. This discrepancy is partially influenced by the variation of mechanical properties in the region of fiber undulations. These regions are localized geometric defects intrinsic to the filament-winding, weaving, and braiding processes. In the present work, the average mechanical properties of the fiber undulation region are quantified using modified models of woven-fabric composites to account for the 3-dimensional effects. The mechanical properties thus determined can be incorporated as local element properties into global finite-element models. Preliminary results from large-displacement analyses of filament-wound cylinders are relatively more accurate when fiber undulations are accounted for.

Jensen, D. W.↗

NASA NTRS2013

Ultimate Limits to Resource Efficiency in Photonic Communication

We review resource-efficiency metrics for transferring classical information with photon, present an overview of the ultimate limits to photon and dimensional efficiency permitted by quantum mechanics, as well as that acheived with structured transmitter-receiver pairs.

background noise↗

NASA NTRS1983

Space radiation interaction mechanisms in materials

Models of charged-particle impact under conditions typical of the space environment are reported, with a focus on impact excitation and nuclear reactions, especially for heavy ions. Impact excitation is studied by using a global model for electronic excitation based on formal relations through the classical dielectric function to derive an approximation related to the local plasma (electron density distribution) within the atoms and molecules; and corrections to the model resulting from the nonfluid nature of this plasma are discussed. Nuclear reactions are studied by reducing quantum-mechanical treatment of this general N-body problem to an equivalent two-body problem that is solvable, and by comparing the results with experimental data. The equations for heavy-charged-particle transport are derived and solution techniques demonstrated. Finally, these methods of analysis are applied to study the change in the electrical properties of a GaAs semiconductor for photovoltaic applications; proton damage to GaAs crystals is found to arise from stable replacement defects and to be nonannealable, in contrast to electron-induced damage.

Wilson, J. W.↗

NASA NTRS1986

Dissipative tides - Application to Venus' lower atmosphere

A linearized planetary scale wave model is used to investigate the effects of thermal and mechanical damping on atmospheric tides. When the damping rate is comparable to the frequency of solar diurnal forcing the circulation consists of three parts: a classical vertically propagating 'atmospheric tide' in the upper atmosphere, a simple thermally direct subsolar-to-antisolar circulation or 'Halley cell' in most of the lower atmosphere, and finally, a reversed 'anti-Halley cell' near the surface. The near-surface circulation produces horizontal divergence near the subsolar point. While tides are a frequently encountered phenomenon (Venus, earth, and Mars), there is so far no observational evidence of a Halley circulation in any planetary atmosphere. A subsolar-antisolar circulation might be possible in Venus' slowly rotating lower atmosphere if the mechanical dissipation time scale is of the order of or less than a Venusian day. Such a circulation could be a factor in maintaining the superrotation of Venus' upper atmosphere.

Covey, Curt↗

NASA NTRS1985

Efficacy of phosphatidylcholine in the modulation of motion sickness susceptibility

This study evaluated the efficacy of pharmacological doses of phosphatidylcholine (lecithin) in the modulation of motion sickness induced by exposure to coriolis stimulation in a rotating chair. Subjects received daily dietary supplements of 25 grams of lecithin (90 percent phosphatidylcholine) and were tested for their susceptibility to motion sickness after 4 h, 2 d, and 21 d. A small but statistically significant increase in susceptibility (+15 percent) was noted 4 h after supplemental phosphatidylcholine, with four of nine subjects demonstrating a marked increase in susceptibility. This finding was attributed to choline's stimulatory action on cholinergic systems, an action which opposes that of the classical antimotion sickness drug scopolamine. Chronic lecithin loading revealed a trend towards reduced susceptibility, possibly indicating the occurrence of adaptive mechanisms such as receptor down-regulation. Withdrawal from lecithin loading, perhaps coupled with anticholinergic treatment, might prove to be a potent prophylactic regimen and ought to be tested.

Kohl, R. L.↗

NASA NTRS1987

Monocrystalline silicon gradiometer for gravity experiments in space

A very important research effort has been made in the last decade in the field of high precision measurement with laser instrumentation. The development of a space borne gradiometer operating at a high sensitivity level using laser measurement of the distance between proof mass over a short base line of order one meter is discussed. Two aspects of laser technology make it a promising tool for gradiometry measurements: quantum limited accuracy and absolute distance measurements. The quantum limit associated with laser instrumentation was formulated. The relevant quantum and classical sources of errors in laser measurements were reviewed and corresponding laser performance requirements for gradient measurements were evaluated. Some mechanical quality factor measurements were made on simple resonant monocrystalline silicon suspensions. It was discovered that the use of zero derivative restoring forces to position the gradiometer test masses will dramatically reduce the gradiometer temperature control requirements. A laser beam side injection scheme was discovered which permits rejection of common mode accelerations. These concepts are briefly discussed.

Richard, Jean-Paul↗