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Results for “Dispersion relations”

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.

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At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
NASA NTRS1977

Assessment of Relative Velocity as Independent Variable for Space Shuttle First Stage Guidance Attitude Command Tables

The selection of relative velocity as the independent variable for the space shuttle first stage guidance attitude command tables was assessed to support the first stage guidance point design. The criterion for selecting the independent variable for first stage open loop guidance is to reduce or minimize performance dispersions, primarily those affecting structural loads. The products of angle of attack and angle of sideslip times dynamic pressure are used as load indicators, and minimizing their dispersions will indicate a minimum loads dispersion. Relative velocity is shown to be an acceptable steering independent variable.

Kimbrough, M.↗
NASA NTRS1990

Vibration and wave propagation characteristics of multisegmented elastic beams

Closed form analytical solutions are derived for the vibration and wave propagation of multisegmented elastic beams. Each segment is modeled as a Timoshenko beam with possible inclusion of material viscosity, elastic foundation and axial forces. Solutions are obtained by using transfer matrix methods. According to these methods formal solutions are first constructed which relate the deflection, slope, moment and shear force of one end of the individual segment to those of the other. By satisfying appropriate continuity conditions at segment junctions, a global 4x4 matrix results which relates the deflection, slope, moment and shear force of one end of the beam to those of the other. If any boundary conditions are subsequently invoked on the ends of the beam one gets the appropriate characteristic equation for the natural frequencies. Furthermore, by invoking appropriate periodicity conditions the dispersion relation for a periodic system is obtained. A variety of numerical examples are included.

Nayfeh, Adnan H.↗
NASA NTRS2010

Dissipation of Turbulence in the Solar Wind

I will describe the first three-dimensional (3-D) dispersion relations and wavenumber spectra of magnetic turbulence in the solar wind at sub-proton scales. The analysis takes advantage of the short separations of the Cluster spacecraft (d/sim approx.200 km) to apply the {it k}-filtering technique to the frequency range where the transition to sub-proton scales occurs. The dispersion diagrams show unambiguously that the cascade is carried by highly oblique Kinetic Alfven Wave with \omega\leq 0.1\omega_{ci} in the plasma rest frame down to k_\perp\rho_i \sim 2. The wavenumber spectra in the direction perpendicular to the mean magnetic field consists of two ranges of scales separated by a breakpoint in the interval [0.4,1] k_\perp \rho_i. Above the breakpoint, the spectra follow the Kolmogorov scaling k_\perp^{-1.7}, consistent with existing theoretical predictions. Below the breakpoint, the spectra steepen to \sim k_\perp^{-4.5}. We conjecture that the turbulence undergoes a {\it transition-range}, where part of energy is dissipated into proton heating via Landau damping, and the remaining energy cascades down to electron scales where electron Landau damping may predominate.

Goldstein, Melvyn L.↗
NASA NTRS1986

On the applicability of relativistic dispersion to auroral zone electron distributions

An examination is made to identify appropriate times to include weakly relativistic wave dispersion in calculations of auroral zone electron distributions. Two dispersion relations are examined. First, solutions are found for a ring distribution of particles around a cold ambient plasma. The solutions are found only for modes near the electron gyrofrequency. A trapped mode which is decoupled from the freely propagating R-X mode of cold plasmas is found to be the most unstable mode. Wave dispersion is examined with a spherically symmetric Dory-Guest-Harris (DGH) distribution, which describes a shell distribution that has a peak momentum larger than the thermal spread. The trapped mode is again found to be the most unstable. The analysis indicates it is beneficial to include relativistic effects whenever calculating auroral plasma distributions, and that a simple model will have sufficient accuracy.

Strangeway, R. J.↗
NASA NTRS1986

Electron-cyclotron maser instability in relativistic plasmas

The electron-cyclotron maser instability is studied for the case of an anisotropic electron velocity distribution in the regime where the relativistic corrections to the wave dispersion are significant. Solution of the linear dispersion relation reveals that when the plasma frequency-gyrofrequency ratio is less than v(te)/c, the instability is localized just below k(perpendicular)c/Omega(e) = 1. The growth rate is then strongly peaked for emission at 90 deg to the magnetic field and is considerably larger than would be the case if the cold-plasma dispersion theory were valid. These features are confirmed by EM particle simulations.

Pritchett, P. L.↗
NASA NTRS1987

Distributed feedback modes in a partially filled ring cavity

The threshold longitudinal modes of a structure composed of a ring cavity partially filled with a distributed feedback (DFB) medium have been studied. An eigenvalue equation and dispersion relation for the propagation constant, threshold gain, and mode location are derived and numerically solved for a number of cases. It is shown that the incommensurate nature of the unfilled ring cavity eigenfrequencies and DFB eigenfrequencies can lead to an enhancement of the frequency selectivity of the distributed feedback laser. The analysis is extended to consider finite linewidth and dispersion.

Rabinovich, William S.↗
NASA NTRS2016

On Electron-Scale Whistler Turbulence in the Solar Wind

For the first time, the dispersion relation for turbulence magnetic field fluctuations in the solar wind is determined directly on small scales of the order of the electron inertial length, using four-point magnetometer observations from the Magnetospheric Multiscale mission. The data are analyzed using the high-resolution adaptive wave telescope technique. Small-scale solar wind turbulence is primarily composed of highly obliquely propagating waves, with dispersion consistent with that of the whistler mode.

Narita, Y.↗
NASA NTRS1994

Theoretical studies of the solar atmosphere and interstellar pickup ions

Solar atmosphere research activities are summarized. Specific topics addressed include: (1) coronal mass ejections and related phenomena; (2) parametric instabilities of Alfven waves; (3) pickup ions in the solar wind; and (4) cosmic rays in the outer heliosphere. Also included is a list of publications covering the following topics: catastrophic evolution of a force-free flux rope; maximum energy release in flux-rope models of eruptive flares; sheet approximations in models of eruptive flares; material ejection, motions of loops and ribbons of two-ribbon flares; dispersion relations for parametric instabilities of parallel-propagating; parametric instabilities of parallel-propagating Alfven waves; beat, modulation, and decay instabilities of a circularly-polarized Alfven wave; effects of time-dependent photoionization on interstellar pickup helium; observation of waves generated by the solar wind pickup of interstellar hydrogen ions; ion thermalization and wave excitation downstream of the quasi-perpendicular bowshock; ion cyclotron instability and the inverse correlation between proton anisotrophy and proton beta; and effects of cosmic rays and interstellar gas on the dynamics of a wind.

Source record↗
NASA NTRS2019

Tests of General Relativity With the Binary Black Hole Signals from the LIGO-Virgo Catalog GWTC-1

The detection of gravitational waves by Advanced LIGO and Advanced Virgo provides an opportunity to test general relativity in a regime that is inaccessible to traditional astronomical observations and laboratory tests. We present four tests of the consistency of the data with binary black hole gravitational waveforms predicted by general relativity. One test subtracts the best-fit waveform from the data and checks the consistency of the residual with detector noise. The second test checks the consistency of the low- and high-frequency parts of the observed signals. The third test checks that phenomenological deviations introduced in the waveform model (including in the post-Newtonian coefficients) are consistent with 0. The fourth test constrains modifications to the propagation of gravitational waves due to a modified dispersion relation, including that from a massive graviton. We present results both for individual events and also results obtained by combining together particularly strong events from the first and second observing runs of Advanced LIGO and Advanced Virgo, as collected in the catalog GWTC-1. We do not find any inconsistency of the data with the predictions of general relativity and improve our previously presented combined constraints by factors of 1.1 to 2.5. In particular, we bound the mass of the graviton to be 𝑚𝑔≤4.7×10 −23 eV/𝑐 2 (90% credible level), an improvement of a factor of 1.6 over our previously presented results. Additionally, we check that the four gravitational-wave events published for the first time in GWTC-1 do not lead to stronger constraints on alternative polarizations than those published previously.

B P Abbott↗
NASA NTRS1991

ULF waves upstream of the Venus bow shock - Properties of one-hertz waves

Pioneer Venus Orbiter data are used here to study the properties of a class of ULF upstream waves with relatively high observed frequencies. These waves show significant similarity to 'one-Hz' waves identified at earth in the ISEE 1 and 2 observations and the whistler waves identified earlier by IMP 6 observations. The waves appear almost immediately after the spacecraft crosses the magnetic field tangent line to the bow shock surface into the region of connected field lines. The wave amplitude decreases with distance from the shock measured along the magnetic field line. Group velocities calculated using the cold plasma dispersion relation indicate that the waves have sufficient upstream velocities to propagate form the shock into the solar wind. The totality of observations seem best explained by a source of right-handed whistler mode waves at the bow shock.

Orlowski, D. S.↗
NASA NTRS1993

Resonant behavior of MHD waves on magnetic flux tubes. IV - Total resonant absorption and MHD radiating eigenmodes

Resonant absorption of MHD waves on a nonuniform flux tube is investigated as a driven problem for a 1D cylindrical equilibrium. The variation of the fractional absorption is studied as a function of the frequency and its relation to the eigenvalue problem of the MHD radiating eigenmodes of the nonuniform flux tube is established. The optimal frequencies producing maximal fractional absorption are determined and the condition for total absorption is obtained. This condition defines an impedance matching and is fulfilled for an equilibrium that is fine tuned with respect to the incoming wave. The variation of the spatial wave solutions with respect to the frequency is explained as due to the variation of the real and imaginary parts of the dispersion relation of the MHD radiating eigenmodes with respect to the real driving frequency.

Goossens, Marcel↗
NASA NTRS1985

Resistive wave dissipation on magnetic inhomogeneities Normal modes and phase mixing

Numerical solutions of the linearized, resistive MHD equations indicate the presence of two characteristic forms of wave decay on magnetic inhomogeneities. Solutions for relatively long-wavelength disturbances and large values of the resistivity have the behavior of decaying normal modes. In the opposite limits, phase mixing becomes important, with the eventual build-up of large spatial gradients in which the resistive terms dominate. This composite behavior is shown to be conceptually consistent with analytic results, which predict that the complete solution consists of the sum of collective and noncollective contributions. The numerical simulations go beyond analytic theory by defining where each contribution prevails and computing wave decay when phase mixing is effective. The dispersion relation in the normal-mode regime is also determined analytically, with some approximations, and is in good agreement with the numerical solution. The decay time of the normal modes varies with Lundquist number at S1/6, while the phase-mixed decay time scales as S1/3.

Steinolfson, R. S.↗
NASA NTRS1995

Rectangular Waveguides with Two Conventional and Two Superconducting Walls

The propagation properties of transverse electric TE(sup pm) modes and their dispersion relations in rectangular waveguides with two conventional and two superconducting walls, derived by using the Meissner boundary conditions on the superconducting walls, are presented. In addition to recovering some previously known results, some novel results have been obtained: the cut-off wavelength of the dominant TE(sup 10) mode is greater than that of the conventional TE(sub 10) mode, and the tangential electric field and normal magnetic field for the dominant mode TE(sup 10) exist on the superconducting surfaces. Expressions for electromagnetic components, surface currents, attenuation coefficient, maximum transmitted power, dispersion and wave impedance are also presented.

Yalamanchili, Raj↗
NASA NTRS1990

Identification of structural-borne noise components by the use of time-frequency filtering

In this paper it is shown that a time-frequency analysis of a structural impulse response may be used to identify the wave types carrying significant energy through a structure. The identification of various wave types is possible since each is characterized by its own dispersion relation, with the result that each wave type may be associated with characteristic features in the time-frequency domain representation of an impulse response. In the work described here, the Wigner Distribution has been used to obtain appropriate time-frequency representations of impulse responses. Practical aspects of the calculation of the Wigner Distribution are discussed briefly and examples of its application to the analysis of structural impulse responses are given. Additionally, filtering techniques are described that can be used both to detect the presence of and to quantify the energy carried by both nondispersive and dispersive waves.

Wahl, T. J.↗
NASA NTRS1995

Non-parabolic hydrodynamic formulations for the simulation of inhomogeneous semiconductor devices

Hydrodynamic models are becoming prevalent design tools for small scale devices and other devices in which high energy effects can dominate transport. Most current hydrodynamic models use a parabolic band approximation to obtain fairly simple conservation equations. Interest in accounting for band structure effects in hydrodynamic device simulation has begun to grow since parabolic models can not fully describe the transport in state of the art devices due to the distribution populating non-parabolic states within the band. This paper presents two different non-parabolic formulations of the hydrodynamic model suitable for the simulation of inhomogeneous semiconductor devices. The first formulation uses the Kane dispersion relationship (hk)(exp 2)/2m = W(1 + alpha(W)). The second formulation makes use of a power law ((hk)(exp 2)/2m = xW(sup y)) for the dispersion relation. Hydrodynamic models which use the first formulation rely on the binomial expansion to obtain moment equations with closed form coefficients. This limits the energy range over which the model is valid. The power law formulation readily produces closed form coefficients similar to those obtained using the parabolic band approximation. However, the fitting parameters (x,y) are only valid over a limited energy range. The physical significance of the band non-parabolicity is discussed as well as the advantages/disadvantages and approximations of the two non-parabolic models. A companion paper describes device simulations based on the three dispersion relationships: parabolic, Kane dispersion, and power low dispersion.

Smith, Arlynn W.↗
NASA NTRS1996

Non-Parabolic Hydrodynamic Formulations for the Simulation of Inhomogeneous Semiconductor Devices

Hydrodynamic models are becoming prevalent design tools for small scale devices and other devices in which high energy effects can dominate transport. Most current hydrodynamic models use a parabolic band approximation to obtain fairly simple conservation equations. Interest in accounting for band structure effects in hydrodynamic device simulation has begun to grow since parabolic models cannot fully describe the transport in state of the art devices due to the distribution populating non-parabolic states within the band. This paper presents two different non-parabolic formulations or the hydrodynamic model suitable for the simulation of inhomogeneous semiconductor devices. The first formulation uses the Kane dispersion relationship ((hk)(exp 2)/2m = W(1 + alphaW). The second formulation makes use of a power law ((hk)(exp 2)/2m = xW(exp y)) for the dispersion relation. Hydrodynamic models which use the first formulation rely on the binomial expansion to obtain moment equations with closed form coefficients. This limits the energy range over which the model is valid. The power law formulation readily produces closed form coefficients similar to those obtained using the parabolic band approximation. However, the fitting parameters (x,y) are only valid over a limited energy range. The physical significance of the band non-parabolicity is discussed as well as the advantages/disadvantages and approximations of the two non-parabolic models. A companion paper describes device simulations based on the three dispersion relationships; parabolic, Kane dispersion and power law dispersion.

Smith, A. W.↗