Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “dispersion relation”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

New results on the generation of broadband electrostatic waves in the magnetotail

The theory of the generation of broadband electrostatic noise (BEN) in the magnetotail is extended through numerical solution of the dispersion relation under conditions that exist in the plasma sheet boundary layer. It is found that the low-frequency portion of the spectrum has a broad angular spectrum but a fairly sharp peak near 75 deg with respect to the magnetic field, while the high-frequency portion has a narrower angular spectrum that is strongly concentrated along the magnetic field line. These results are in excellent agreement with observations of the broadband wave spectrum and a recent measurement of the propagation direction. The effect of a second cold component of electrons is analyzed, and it is found that it can increase the upper cutoff frequency of BEN to the observed value at about the plasma frequency.

Grabbe, C. L.↗
NASA NTRS1985

Structure variation of the index of refraction of GaAs-AlAs superlattices and multiple quantum wells

A detailed calculation of the index refraction of various GaAs-AlAs superlattices is presented for the first time. The calculation is performed by using a hybrid approach which combines the k-p method with the pseudopotential technique. Appropriate quantization conditions account for the influence of the superstructures on the electronic properties of the systems. The results of the model are in very good agreement with the experimental data. In comparison with the index of refraction of the corresponding AlGaAs alloy, characterized by the same average mole fraction of Al, the results indicate that the superlattice index of refraction values attain maxima at the various quantized transition energies. For certain structures the difference can be as large as 2 percent. These results suggest that the waveguiding and dispersion relation properties of optoelectronic devices can be tailored to design for specific optical application by an appropriate choice of the superlattice structure parameters.

Kahen, K. B.↗
NASA NTRS1986

Stress waves in transversely isotropic media: The homogeneous problem

The homogeneous problem of stress wave propagation in unbounded transversely isotropic media is analyzed. By adopting plane wave solutions, the conditions for the existence of the solution are established in terms of phase velocities and directions of particle displacements. Dispersion relations and group velocities are derived from the phase velocity expressions. The deviation angles (e.g., angles between the normals to the adopted plane waves and the actual directions of their propagation) are numerically determined for a specific fiber-glass epoxy composite. A graphical method is introduced for the construction of the wave surfaces using magnitudes of phase velocities and deviation angles. The results for the case of isotropic media are shown to be contained in the solutions for the transversely isotropic media.

Marques, E. R. C.↗
NASA NTRS1985

Fundamental and harmonic electron cyclotron maser emission

The plasma conditions and features of the energetic electron distribution in electron cyclotron maser emission for which growth in a particular mode is favored when the ratio of the plasma frequency omega(p) to the electron cyclotron frequency Omega(e) is greater than about 0.3 are determined. It is shown that growth at the fundamental is suppressed as omega(p)/Omega(e) increases and emission at harmonics of Omega(e) dominates. Growth at harmonics of Omega(e) is not restricted to the O and X modes, but can also occur for the Z mode. Whether or not growth in a particular mode dominates depends both on omega(p)/Omega(e) and on the form of the distribution. If the density of the energetic electrons is sufficiently large, the dispersion relations of the O and X modes are modified so that the group velocities of the growing O and X mode waves can be comparable to that of the growing Z mode waves.

Winglee, R. M.↗
NASA NTRS1985

Upconversion of lower-hybrid waves by gyrating ion beams in a plasma

A gyrating ion beam, with ring shape distribution in velocity space, supports negative energy modes near the harmonics of beam gyrofrequency. An investigation of the nonlinear interaction of high-frequency lower-hybrid waves with the negative energy beam cyclotron mode is made. A nonlinear dispersion relation is derived for the coupled modes. It is shown that a gyrating ion beam frequency upconverts the lower-hybrid waves separated by harmonics of the beam gyrofrequency. This process of upconversion may thus provide a tool for the diagnostics of the gyrating ion beams. The process may also be important in the saturation of lower-hybrid waves observed in the auroral zone S3-3 satellite data.

Sharma, O. P.↗
NASA NTRS1985

Effect of a fibril magnetic field on solar p-modes

The dispersion relation is obtained for acoustic plane waves that scatter coherently from an ensemble of parallel magnetic flux tubes when the wave vector is perpendicular to the flux-tube axis. When the magnetic flux tubes are distributed uniformly and possess radii that are small compared with the wavelength, the frequency can be calculated exactly. The waves are damped slightly due to a loss of coherence and are shifted downward or upward in frequency relative to a medium devoid of magnetic fibrils, depending primarily on whether the flux tubes are more or less dense than their surroundings. It is suggested that the influence of the fibril magnetic fields observed at the solar surface cannot be ignored in the interpretation of high-1 surface p-mode data.

Bogdan, T. J.↗
NASA NTRS1985

Propagation and stability of wavelike solutions of finite difference equations with variable coefficients

The propagation and dissipation of wavelike solutions to finite difference equations is analyzed on the basis of an asymptotic approach in which a wave solution is expressed as a product of a complex amplitude and an oscillatory phase function whose frequency and wavenumber may also be complex. An asymptotic expansion leads to a local dispersion relation for wavenumber and frequency; the first-order terms produce an equation for the amplitude in which the local group velocity appears as the convection velocity of the amplitude. Equations for the motion of wavepackets and their interaction at boundaries are derived, and a global stability analysis is carried out.

Giles, M. B.↗
NASA NTRS1986

Spray atomization and combustion

New theoretical and experimental methods for studying sprays are reviewed. Common methods to analyze dilute sprays are described and used to interpret recent measurements of the structure of dilute sprays and related dispersed turbulent jets. Particle-laden jets, nonevaporating, evaporating, and combusting sprays, and noncondensing and condensing bubbly jets are examined and used to initially evaluate current analytical methods for a wide range of conditions. Dense sprays are briefly discussed.

Faeth, G. M.↗
NASA NTRS1986

Turbulent motion in galactic H II regions

An investigation of radial velocities across the face of NGC 1499, NGC 7000, and S252 reveals that the fine-scale (turbulent) motions are well ordered from the limit of spatial resolution to the full size of the nebulae. As in higher spatial resolution studies of S142 and M17, analysis of the dispersion relation reveals that there is agreement with Kolmogorov theory (1941). However, study of the structure function reveals the same result as found by Roy and Joncas (1985), that the structure function increases with separation much more slowly than theoretically expected, calling into question the application of Kolmogorov theory. The Roy-Joncas result that the fine-scale motion seems to begin at about the sonic velocity are confirmed. It is shown that a condition exists of near equipartition of energies between fine-scale mass motion and thermal gas motion, which raises the question of a possible link.

Odell, C. R.↗
NASA NTRS1985

Raman scattering from phonons and magnons in magnetic semiconductors, MnTe

Comparisons are made between theoretical and experimental data on laser Raman scattering by phonons and two-magnons in antiferromagnetic and paramagnetic phases of MnTe. The study was performed specifically to characterize the magnetic exchange coupling constants of the Mn ions in the samples. Crystal MnTe samples were bombarded with an Ar ion laser beam to obtain spectrometer and photon counter data. One E(2g) phonon with a room temperature energy of 178/cm and a two-magnon peak of 360/cm were observed in the Raman spectrum. A spin wave dispersion relation is presented for the spectrum. Finally, a Monte Carlo technique was used to calculate the two-magnon joint density of states that best fits the experimental data.

Mobasser, S. R.↗
NASA NTRS1986

Variation of refractive index in strained In(x)Ga(1-x)As-GaAs heterostructures

In(x)Ga(1-x)As-GaAs heterostructures and strained-layer superlattices can be used as optical waveguides. For such applications it is important to know explicitly the refractive index variation with mismatch strain and with alloying in the ternary layer. Starting from the Kramers-Kronig integral dispersion relations, a model has been developed from which the refractive index change in the ternary layer of In(x)Ga(1-x)As-GaAs heterojunctions can be calculated. The results are presented and discussed. The expected changes in a superlattice have been qualitatively predicted.

Das, U.↗
NASA NTRS1986

Desingularization of periodic vortex sheet roll-up

An analytical approach is used in an attempt to model the evolution of a vortex sheet past the critical time by means of a desingularization method. Evolution of the sheet, which is embedded in a two-dimensional flow, is described by approximating the total circulation between a fixed material point and an imaginary point on the curve of the flow. A linear dispersion relation is defined which shows that the short wavelength modes of the sheet are not unstable and therefore do adversely effect the computations as artifacts of round-off errors. The desingularization approach is demonstrated to converge beyond the critical time for the vortex sheet. Application of the technique for the study of the vortex sheet shed from an elliptically loaded wing is indicated.

Krasny, R.↗
NASA NTRS1987

Remarks on the stability analysis of reactive flows

A simple model of compressible reacting flow is studied. First, a dispersion relation is derived for the linearized problem making a distinction between frozen and equilibrium sound speed. Second, the stability of the Von Neumann-Richtmyer scheme applied to this model is studied. A natural generalization of the C.F.L. condition is found.

Scheurer, B.↗
NASA NTRS1987

Hamiltonian theory of nonlinear waves in planetary rings

The derivation of a Hamiltonian field theory for nonlinear density waves in Saturn's rings is discussed. Starting with a Hamiltonian for a discrete system of gravitating streamlines, an averaged Hamiltonian is obtained by successive applications of Lie transforms. The transformation may be carried out to any desired order in q, where q is the nonlinearity parameter defined in the work of Shu, et al (1985) and Borderies et al (1985). Subsequent application of the Wentzel-Kramer-Brillouin Method approximation yields an asymptotic field Hamiltonian. Both the nonlinear dispersion relation and the wave action transport equation are easily derived from the corresponding Lagrangian by the standard variational principle.

Stewart, G. R.↗
NASA NTRS1986

Oscillations of a viscous compound drop

The effect of viscosity on normal mode oscillations of a compound drop is determined for a range of values of the viscosity, and the effect of a host medium is considered. The general form of the dispersion relation is derived, and numerical values are obtained for the case of an annular liquid region composed of silicon oil and with the core and host regions taken to be air. Results indicate that the sloshing mode of the compound drop is more damped than the bubble mode.

Lyell, M. J.↗
NASA NTRS1986

Discrete Dirac equation on a finite half-integer lattice

The formulation of the Dirac equation on a discrete lattice with half-integer spacing and periodic boundary conditions is investigated analytically. The importance of lattice formulations for problems in field theory and quantum mechanics is explained; the concept of half-integer Fourier representation is introduced; the discrete Dirac equation for the two-dimensional case is derived; dispersion relations for the four-dimensional case are developed; and the spinor formulation for the Dirac fields on the half-integer lattice and the discrete time variable for the four-dimensional time-dependent Dirac equation are obtained. It is argued that the half-integer lattice, because it takes the Dirac Lagrangian into account, is more than a mere relabeling of the integer lattice and may have fundamental physical meaning (e.g., for the statistics of fermions). It is noted that the present formulation does not lead to species doubling, except in the continuum limit.

Smalley, L. L.↗
NASA NTRS1986

Nonlinear density waves in planetary rings

The steady-state structure of planetary rings in the presence of density waves at the Lindblad resonances of a satellite is indicated. The study is based on the dispersion relation and damping rate for nonlinear density waves, derived by Shu et al. (1985) and by Borderies, Goldreich, and Tremaine (1985). It is shown that strong density waves lead to an enhancement of the background surface density in the wave zone.

Borderies, Nicole↗
NASA NTRS1986

On the structure of artificially generated water wave trains

The structure of an artificially generated sinusoidal water wave train of fixed frequency under the influence of wind is analyzed. Artificially generated waves of 1 Hz are studied at seven wind speeds in the range of 140-400 cm/s. It is observed that the water wave train deformed by wind consists of two components at both the fundamental mode and the harmonics. The amplitude and phase of the wave components are derived, and the dispersion relation and component phase speeds are examined. The data reveal that the amplitude of the forced and free-traveling second harmonics correlate with previous theories, and that the deviation of the measured phase speed from the linear theory is caused by the nonlinearity of the primary wave, the interaction between short gravity waves and the primary wave, and the advection effects of wind drift.

Papadimitrakis, Yiannis A.↗