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All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

Uncertainty relations for light waves and the concept of photons

A Lorentz-covariant localization for light waves is presented. The unitary representation for the electromagnetic four-potential is constructed for a monochromatic light wave. A model for covariant superposition is constructed for light waves with different frequencies. It is therefore possible to construct a wave function for light waves carrying a covariant probability interpretation. It is shown that the time-energy uncertainty relation (Delta-t)(Delta-omega) = about 1 for light waves is a Lorentz-invariant relation. The connection between photons and localized light waves is examined critically.

Han, D.↗
NASA NTRS1993

Wavelets and spacetime squeeze

It is shown that the wavelet is the natural language for the Lorentz covariant description of localized light waves. A model for covariant superposition is constructed for light waves with different frequencies. It is therefore possible to construct a wave function for light waves carrying a covariant probability interpretation. It is shown that the time-energy uncertainty relation (Delta(t))(Delta(w)) is approximately 1 for light waves is a Lorentz-invariant relation. The connection between photons and localized light waves is examined critically.

Han, D.↗
NASA NTRS2004

Studying Biological Rhythms of Person's Skin-galvanic Reaction and Dynamics of Light Transmission by Isomeric Substance in Space Flight Conditions

Intensity and amplitude of human functional systems and human most important organs are wavelike, rhythmic by nature. These waves have constant periodicity, phase and amplitude. The mentioned characteristics can vary, however their variations have a pronounced reiteration in the course of time. This indicates a hashing of several wave processes and their interference. Stochastic changes in wave processes characteristics of a human organism are explained either by 'pulsations' associated with hashing (superposition) of several wave processes and their interference, or by single influence of environmental physical factors on a human organism. Human beings have respectively periods of higher and lower efficiency, state of health and so on, depending not only of environmental factors, but also of 'internal' rhythmic factor. Sometimes peaks and falls periodicity of some or other characteristics is broken. Disturbance of steady-state biological rhythms is usually accompanied by reduction of activity steadiness of the most important systems of a human organism. In its turn this has an effect on organism's adaptation to changing living conditions as well as on general condition and efficiency of a human being. The latter factor is very important for space medicine. Biological rhythmology is a special branch of biology and medicine, it studies rhythmic activity mechanisms of organs, their systems, individuals and species. Appropriate researches were also carried out in space medicine.

Glushko, Vladimir↗
NASA NTRS2012

Interpretation of Vector Electric Field Measurements of Bursty Langmuir Waves in the Cusp

An analysis of auroral Langmuir waves in the cusp observed by two high-frequency electric field instruments on the TRICE high-flyer sounding rocket shows many examples of Langmuir wave bursts modulated at approximately 10 kHz. Previous studies have explained these and similar observations as the result of beating between waves with very close frequencies near the Langmuir cutoff, resulting from either wave-wave interactions or independent linear excitations. The unique three-dimensional (3-D) data set provided by the NASA Goddard Space Flight Center TAEFWD instrument shows that up to 25% of waveforms selected from the most intense bursts exhibit anisotropic modulations, i.e., the beat nulls and peaks are not aligned in time across the three perpendicular electric field components. Modulations of this type arise when superposed wave normal modes possess differing polarizations, and simulations using wave modes calculated with the J-WHAMP numerical dispersion code show (1) that waves with differing polarizations can exist in conditions like those observed by TRICE-High and (2) that superpositions of such waves can produce anisotropic modulation. Fourier analysis of the 3-D waveform data suggests that both linear and elliptically polarized waves are present near the Langmuir cutoff at these times. These observations illustrate how 3-D measurements can give valuable insight into the nature of wave interactions in the auroral plasma environment.

Dombrowski, M. P.↗
NASA NTRS1977

The tropospheric-stratospheric polar vortex breakdown of January 1977

An extraordinary warming of the stratosphere in December-January 1976-77 was followed by tropospheric warming in the polar region and cooling in middle latitudes. During January 10-20, the associated polar anticyclone extended from the surface to 10 mb. Antecedents of the polar vortex breakdown are reviewed with the aid of results of zonal-harmonic analyses of planetary waves, for heights of the pressure surfaces (700-10 mb), temperature, and mean stratospheric temperature (the latter determined from satellite radiation measurements). Wave 1 in height and temperature played a dominant role in the stratosphere, attaining amplitudes of 1600 gpm and 25 C, respectively, at 10 mb. On the other hand, superposition of retrogressing wave 1 and quasi-stationary wave 2 in the height of the 300-mb surface, with individual amplitudes exceeding 300 gpm, is judged to have been an important factor in the overall development.

Quiroz, R. S.↗
NASA NTRS1981

Noise shielding by a hot subsonic jet

An analysis is conducted of the shielding of the noise emitted by a high speed round jet by a hot, subsonic, semicircular jet. A plane wave front in the primary jet is resolved into elementary plane waves which undergo multiple reflections at the jet boundaries of the primary and the shielding jets. The jet boundaries are idealized to be vortex sheets. The far field sound is evaluated asymptotically by a superposition of the waves that penetrate the shielding jet. The angular directivities are plotted for several values of jet temperature and velocity to examine the effectiveness of shielding by the semicircular jet layer.

Vijayaraghavan, A.↗
NASA NTRS1989

Advances in understanding the gravity wave spectrum during MAP

Prior to MAP, virtually nothing was known about gravity wave spectra in the atmosphere. The development of observational techniques has played a major role in these studies. Radar and lidar have been particularly important since they can measure atmospheric parameters continuously over large height ranges. Some advances made are: (1) The observed fluctuations and power spectra in the free atmosphere are mostly if not entirely due to a superposition of gravity waves, which can be modeled by the Garrett Munk (GM) model; (2) There is no evidence that 2-D turbulence makes a significant contribution to the observed fluctuations. In any case, the agreement between observations and the GM model shows that the 2DT contribution must be relatively small; (3) Spectra versus vertical wave number are saturated at large wave number, with theory and observations indicating that t approximately equals 3; and (4) Vertical velocity fluctuations and spectra measured near rough terrain are strongly contaminated by mountain waves. But over very flat terrain the spectra are dominated by gravity waves at periods shorter than about 6 hours and apparently by synoptic scale velocities at periods longer than 6 hours. Thus it may be possible to study synoptic scale vertical velocities using radars located in very flat terrain.

Vanzandt, T. E.↗
NASA NTRS1976

Steady incompressible variable thickness shear layer aerodynamics

A shear flow aerodynamic theory for steady incompressible flows is presented for both the lifting and non lifting problems. The slow variation of the boundary layer thickness is considered. The slowly varying behavior is treated by using multitime scales. The analysis begins with the elementary wavy wall problem and, through Fourier superpositions over the wave number space, the shear flow equivalents to the aerodynamic transfer functions of classical potential flow are obtained. The aerodynamic transfer functions provide integral equations which relate the wall pressure and the upwash. Computational results are presented for the pressure distribution, the lift coefficient, and the center of pressure travel along a two dimensional flat plate in a shear flow. The aerodynamic load is decreased by the shear layer, compared to the potential flow. The variable thickness shear layer decreases it less than the uniform thickness shear layer based upon equal maximum shear layer thicknesses.

Chi, M. R.↗
NASA NTRS1978

Integral equation formulation for probe corrected far-field reconstruction from measurements on a cylinder

A method has been developed for far-field evaluation from measurements taken on a cylinder. The antenna and probe fields are represented by superpositions of plane waves, and two integral equations are derived whose functions are the elevation and azimuthal components of the antenna pattern. The known components are the measurements taken by either two probes or a single probe with two geometrical orientations. The convolutional nature of the integral equations makes Fourier analysis techniques applicable to a straightforward solution and an efficient computational procedure. Good agreement has been found between experimental and reconstructed patterns for both nominal and cross polarized field components.

Borgiotti, G. V.↗
NASA NTRS1977

Probe corrected far-field reconstruction from measurements on a cylinder: A novel formulation and efficient algorithm

A novel and numerically efficient method of far field evaluation from measurements taken on a cylinder is based on the representation of both the antenna and the probe fields as superpositions of plane waves. A system of two integral equations are established whose unknown functions are the azimuthal and elevation components of the antenna pattern and whose known terms are the set of measurement data taken with two different probes - the second probe in most practical instances being simply the same probe with a different geometrical orientation. The equations express the known data - for each angular position of the antenna under measurement - as the integrals of the products of the corresponding components of the unknown antenna and known probe patterns multiplied by a phase term. The convolutional nature of the integral equations makes their solutions straight-forward. If, as is virtually always the case, the probe is small or of moderate size so that the axis of rotation of the antenna mount is in the far field of the probe, the intervention of asymptotic techniques makes the solution numerically very efficient. The agreement of calculated and experimental patterns is excellent.

Borgiotti, G. V.↗
NASA NTRS1987

Rigorous approaches to tether dynamics in deployment and retrieval

Dynamics of tethers in a linearized analysis can be considered as the superposition of propagating waves. This approach permits a new way for the analysis of tether behavior during deployment and retrieval, where a tether is composed by a part at rest and a part subjected to propagation phenomena, with the separating section depending on time. The dependence on time of the separating section requires the analysis of the reflection of the waves travelling toward the part at rest. Such a reflection generates a reflected wave, whose characteristics are determined. The propagation phenomena of major interest in a tether are transverse waves and longitudinal waves, all mathematically modelled by the vibrating chord equations, if the tension is considered constant along the tether. An interesting problem also considered is concerned with the dependence of the tether tension from the longitudinal position, due to microgravity, and the influence of this dependence on the propagation waves.

Antona, Ettore↗
NASA NTRS1990

On resonance in linear conservation laws without source terms

A phenomena is described occuring in wave propagation for systems of conservation laws which are not hyperbolic. The nature of the wave propagation for linear systems of conservation laws which are degenerate in the sense that they are not equivalent to diagonal systems is examined. It is concluded that in the degenerate case, 'resonance' occurs, that is, the solutions are combinations of traveling waves and 'resonance waves'. Here resonance means that the solution may become unbounded even if the initial values are bounded. The solutions (waves) can be described as a superposition of 'packets' (groups) of 'resonance waves' traveling with the same speed. These are linear systems with constant coefficients which are self-exciting, which is what one would expect to encounter in nonlinear systems.

Gingold, H.↗
NASA NTRS1994

A new approach to the photon localization problem

Since wavelets form a representation of the Poincare group, it is possible to construct a localized superposition of light waves with different frequencies in a Lorentz-covariant manner. This localized wavelet satisfies a Lorentz-invariant uncertainty relation, and also the Lorentz-invariant Parseval's relation. A quantitative analysis is given for the difference between photons and localized waves. It is then shown that this localized entity corresponds to a relativistic photon with a sharply defined momentum in the non-localization limit. Waves are not particles. It is confirmed that the wave-particle duality is subject to the uncertainty principle.

Han, D.↗
NASA NTRS2003

Effects of a Scanning Reflectarray Antenna on Modulated Data Modeled

The ferroelectric reflectarray is a new type of scanning antenna under development for space and ground communications and radar applications at the NASA Glenn Research Center. The reflectarray offers tremendous cost, gain, and efficiency advantages in comparison to the state-of-the-art phased arrays, but there is an inherent intersymbol interference (ISI) problem with digital communication data streams processed through the array because of the way the reflectarray is operated. This interference stems from the fact that the antenna beam is formed by the superposition of reflected waves from the array elements. The delays from the elements to the observation point of each wave differ. Ferroelectric phase shifters are designed to compensate for the modulo-2p phase differences so that the waves will constructively interfere at the sinusoidal carrier level; however, the delays of the integer-number multiple of the carrier period are not compensated for. This lack of compensation causes ISI in digital modulated signals. ISI has not been a problem with analog modulations and low-rate digital modulations since the distortion (or ISI) introduced is negligible. The problem becomes acute when the data rate gets higher, and the electrical size of the array gets bigger. Moreover, there are intrinsic transient effects associated with the phase shifters and the controller that executes the algorithm to direct the beam. That is, phase shifter updates to redirect the beam may be initiated simultaneously, but nonlinearity will cause different settling times. The ISI problem and other effects ultimately limit the size (gain) and data rate of the reflectarray. An ISI analysis was required to prove or disprove the suitability of the reflectarray antenna for high-rate digitally modulated signals and to give guidance for determining antenna parameters. In this research, the nature of the ISI of the reflectarray has been mathematically modeled.

Romanofsky, Robert R.↗
NASA NTRS1961

A Study of the Free Oscillations of the Earth

Published observations on the toroidal oscillations of the earth are critically reviewed. A supplementary analysis of the record obtained by the Lamont strain seismometer is presented. Eleven toroidal modes are identified, and it is concluded that the periods are known to within 1 per cent. A perturbation scheme involving the ratio of the angular velocity of the earth to the resonant frequency is used in calculating the effects due to the rotation of the earth on the resonant frequency. The free oscillations are viewed as a superposition of traveling waves. In a nonrotating system two traveling waves combine to produce a stationary standing wave. In a rotating system, the rotation distinguishes between waves that travel in the direction of rotation and those that travel in the opposite direction. Rotation removes a degeneracy and results in a splitting of a spectral peak of order l into 2 times l plus 1 peaks. The fractional displacement in frequency for the lowest-order toroidal oscillations is 1/206 and of the same order as the Q of the peak, so that splitting will probably not be observed in the toroidal oscillations. Viewed locally, rotation causes a particle to precess about a direction parallel to the axis of rotation. This precession will cause a variation of amplitude with time if the motion is recorded by an instrument with an anisotropic response function. Care is therefore needed in studying the time decay of a given spectral peak. Rotation also couples the normal coordinates so that a motion that is initially purely horizontal will develop a vertical component. It is expected that vertical seismometers should record particle motion with the toroidal frequencies. The perturbations of the toroidal oscillations due to core-mantle interaction are treated in detail. An exact expression is obtained for the rate of energy dissipated by a finitely conducting plate oscillating across a magnetic field. The energy dissipated at the core-mantle boundary due to viscous and hydromagnetic coupling is shown to be insignificant as compared with the energy dissipated within the mantle. The toroidal magnetic field leaking into the lower mantle combines with the dipole field, resulting in a stress on the mantle, tending to stiffen the lower boundary. The stress is of sufficient magnitude to produce a displacement toward higher frequency in the lower-order toroidal oscillations. Observations on the (sub 0) T (sub 2) oscillations lead to an estimate of the toroidal magnetic field in the lower mantle. A calculation of elastic energy in the low-order oscillations suggests a value of 10 (sup 18) ergs per cycles per hour for the energy density at low frequencies in the Chilean earthquake. Each mode of oscillation has a characteristic radial distribution of elastic energy associated with it. This distribution determines which parts of the earth contribute most heavily in determining a particular resonant frequency. The distribution of energy for the lower 17 modes for a homogeneous and a Gutenberg model earth is calculated. The resonant frequencies for models of the earth based on the Gutenberg and Lehmann distribution of elastic properties are presented. It is shown that the Gutenberg model earth fits the observations more closely than the Lehmann model and that a slight alteration of the Gutenberg model gives a significantly better fit to the observations. The alteration involves a lower shear-wave velocity in the lower mantle while the Gutenberg velocity distribution is maintained in the upper mantle. Various studies of the earth's oscillations coupled with surface-wave investigations substantiate Gutenberg's hypothesis of a layer of low velocity in the upper mantle. The physical conditions required for the formation of a region of low velocity are examined in detail. The results confirm Birch's earlier statement that a temperature gradient in excess of 6 degrees to 7 degrees per kilometer is needed to produce a decrease in velocity. The low-velocity layer does not require that the temperature approach or exceed the melting temperature. If tile upper mantle is homogeneous, the region of lower velocity should commence at the base of the crust and extend to 150 kilometers under the oceans and about 100 kilometers under continental regions. The distribution of thermal conductivity and radioactivity consistent with the low-velocity layer is also considered.

MacDonald, Gordon J. F.↗
NASA NTRS1995

Energy spectrum transfer equations of solar wind turbulence

The recent studies of transfer equations for solar wind magnetohydrodynamic (MHD) turbulence are reviewed with emphasis on the comparison with the statistical observational results. Helios and Voyager missions provide an opportunity to study the the radial evolution of the power spectrum. the cross-helicity the Alfven ratio and the minimum variance direction. Spectrum transfer equations are considered as a tool to explore the nature of this radial evolution of the fluctuations. The transfer equations are derived from incompressible MHD equations. Generally one needs to make assumptions about the nature of the fluctuations and the nature of the turbulent non-linear interactions to obtain numerical results which can be compared with the observations. Some special model results for several simple cases SUCH as for structures or strong mixing. for Alfven waves with weak turbulent interactions. and for a superposition of structures and Alfven waves. are discussed. The difference between the various approaches to derive and handle the transfer equations are also addressed. Finally some theoretical description of the compressible fluctuations are also briefly reviewed.

Tu, C.-Y.↗
NASA NTRS2012

Upper Limits on a Stochastic Gravitational-Wave Background Using LIGO and Virgo Interferometers at 600-1000 Hz

A stochastic background of gravitational waves is expected to arise from a superposition of many incoherent sources of gravitational waves, of either cosmological or astrophysical origin. This background is a target for the current generation of ground-based detectors. In this article we present the first joint search for a stochastic background using data from the LIGO and Virgo interferometers. In a frequency band of 600-1000 Hz, we obtained a 95% upper limit on the amplitude of omega(sub GW)(f) = omega(sub 3) (f/900Hz)3, of omega(sub 3) < 0.33, assuming a value of the Hubble parameter of h(sub 100) = 0.72. These new limits are a factor of seven better than the previous best in this frequency band.

Abadie, J.↗