Finite Frequency Effects Research Articles

With a pinch of dissipation all operators can be inverted

With domination of computation over analysis, issues of convergence and uniqueness have largely given way in the engineering/physics literature to issues of numerical stability. A common cause is sometimes the genesis of a lack of convergence or of uniqueness when seeking an analytical prediction, and of a numerical instability when seeking a numerical prediction. If the underlying cause is the same, the actions prompted are sometimes quite different. The introduction of dissipation is widely accepted as a ‘‘tool’’ for ‘‘regularizing’’ numerical codes, by virtue of incorporating a truer physics into the model. Three experiment scenarios are described for which the introduction of dissipation also serves to ‘‘mask’’ errors in the development behind the code, thereby precluding the prediction of significant physical effects. Two of the scenarios are drawn from the published literature—the errors in modeling arise in including finite frequency effects in the scattering by a rough surface, and in including inclusion/inclusion interaction in estimates of the settling rate for nondilute fluid suspensions. The third scenario has not been discussed in the published literature—the modeling error applies to the generalization of a nonreflecting boundary condition at an interior plane of an unbounded range-independent full space, to now model the reflection that obtains at a plane interface connecting two, dissimilar range-independent half-spaces.

Effect of imposed superflow on the superfluid dissipation in the vicinity of the Kosterlitz–Thouless transition

We have developed a new technique for probing the Kosterlitz–Thouless transition in thin helium films. A single quartz crystal microbalance is operated at two different harmonic frequencies simultaneously. We observe the well-known dissipation peak in the vicinity of the superfluid transition, presumably associated with vortex–antivortex pairs having a size comparable to the vortex diffusion length. The dissipation peak is monitored at both harmonic frequencies and the relative displacement of the peaks associated with finite frequency effects is seen. We find, surprisingly, that driving one of the resonant modes of the crystal affects the magnitude of the dissipation peak observed using the second mode. This possibly reflects an alteration of the vortex pair distribution associated with the induced flow.

SMALL SCALE ALFVÉNIC STRUCTURE IN THE AURORA

This paper presents a comprehensive review of dispersive Alfven waves in space and laboratory plasmas. We start with linear properties of Alfven waves and show how the inclusion of ion gyroradius, parallel electron inertia, and finite frequency effects modify the Alfven wave properties. Detailed discussions of inertial and kinetic Alfven waves and their polarizations as well as their relations to drift Alfven waves are presented. Up to date observations of waves and field parameters deduced from the measurements by Freja, Fast, and other spacecraft are summarized. We also present laboratory measurements of dispersive Alfven waves, that are of most interest to auroral physics. Electron acceleration by Alfven waves and possible connections of dispersive Alfven waves with ionospheric-magnetospheric resonator and global field-line resonances are also reviewed. Theoretical efforts are directed on studies of Alfven resonance cones, generation of dispersive Alfven waves, as well their nonlinear interactions with the background plasma and self-interaction. Such topics as the dispersive Alfven wave ponderomotive force, density cavitation, wave modulation/filamentation, and Alfven wave self-focusing are reviewed. The nonlinear dispersive Alfven wave studies also include the formation of vortices and their dynamics as well as chaos in Alfven wave turbulence. Finally, we present a rigorous evaluation of theoretical and experimental investigations and point out applications and future perspectives of auroral Alfven wave physics.

Testing plausible upper‐mantle compositions using fine‐scale models of the 410‐km discontinuity

We constructed models of the 410‐km discontinuity, in which the shape and width of the velocity and density increase were constrained by mineral physics data on the α‐β transition in (Mg,Fe)2SiO4. The transition was represented as cubic functions of depth, and its width was estimated to range between 8–24 km. Reflection coefficients were calculated for these models for competing estimates of the percentage of olivine in the mantle, using synthetic seismograms that include the finite‐frequency effects of the distributed transition. Comparing the synthetic reflectivities with the average reflectivity observed in previous analyses of ScS reverberations, we conclude that the mantle composition is close to that of pyrolite (55 vol. % olivine). Furthermore, much of the range of reflectivity can be explained by temperature variation in a pyrolite mantle. An olivine‐poor composition (35 vol. % olivine) marginally satisfies the seismic data only if the transition thickness averages less than 10 km.

Validity of surface-wave ray theory on a laterally heterogeneous earth

SUMMARY A necessary and sufficient condition for the validity of surface-wave ray theory is S/m << 1, where S is the root-mean-square degree of the phase-velocity perturbation 6c, and 1 is the degree of the equivalent mode ,,Sl or ,,T. This condition, which is independent of the number of orbits, is obtained by consideration of the Fresnel area along the surface-wave ray path between the source and receiver. We assess the accuracy of surface-wave ray theory by comparing the phase, arrival angle and amplitude anomalies obtained using the JWKB approximation with the corresponding quantities measured using 'ground-truth' synthetic coupled-mode seismograms on models of varying roughness. The JWKB results agree well with the coupled-mode results for model S12-WM13; on a contrived model with slightly rougher variations, however, the agreement deteriorates as the condition S/@ << 1 is less well satisfied. The misfit of the ray approximation, which is dependent upon the quantity S/@, can be attributed to diffraction and other finite-frequency effects within the Fresnel area along the ray path; these effects are ignored by the JWKB theory but are fully accounted for by the coupled-mode summation. The wavefront smoothing produced by this Fresnel-area averaging limits the resolution of surface-wave inversion studies based upon the JWKB approximation.

Formalism for traveltime inversion with finite frequency effects

SUMMARY A simple modification of the waveform inversion formula, based on the normal mode perturbation theory, is shown to lead to a formula for traveltime anomalies. The kernel which is derived can be used for traveltime inversion with automatic inclusion of finite frequency effects. Inversion for Earth structure with such kernels will lead to better resolution estimates than ray-theoretical traveltime inversion. Examples of kernels for transverse component seismograms are shown for direct S waves, ScS, Love waves and diffracted S waves. A measure of finite frequency effects is also proposed by comparing our formula with the one from ray theory. A quantity which should be 1 in the case of ray theory is computed for the finite frequency kernels and is shown to have deviations up to about 30 per cent from 1. Therefore, the use of ray theory for long-period body waves applies incorrect weight along a ray path and may introduce a small bias to an earth model.

Cosmic-ray transport and acceleration

view Abstract Citations (32) References (37) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Cosmic-Ray Transport and Acceleration Schlickeiser, Reinhard Abstract We review the transport and acceleration of cosmic rays concentrating on the origin of galactic cosmic rays. Quasi-linear theory for the acceleration rates and propagation parameters of charged test particles combined with the plasma wave viewpoint of modeling weak cosmic electromagnetic turbulence provides a qualitatively and quantitatively correct description of key observations. Incoporating finite frequency effects, dispersion, and damping of the plasma waves are essential in overcoming classical discrepancies with observations as the Kfit - Kql discrepancy of solar particle events. We show that the diffusion-convection transport equation in its general form contains spatial convection and diffusion terms as well as momentum convection and diffusion terms. In particular, the latter momentum diffusion term plays a decisive role in the acceleration of cosmic rays at super-Alfvenic supernova shock fronts, and in the acceleration of ultra-high-energy cosmic rays by distributed acceleration in our own galaxy. Publication: The Astrophysical Journal Supplement Series Pub Date: February 1994 DOI: 10.1086/191927 Bibcode: 1994ApJS...90..929S Keywords: Galactic Cosmic Rays; Mathematical Models; Particle Acceleration; Transport Theory; Wave-Particle Interactions; Electromagnetic Fields; Fokker-Planck Equation; Fourier Transformation; Magnetohydrodynamic Turbulence; Shock Fronts; Wave Scattering; Astrophysics; ACCELERATION OF PARTICLES; CONVECTION; DIFFUSION; ISM: COSMIC RAYS; SHOCK WAVES full text sources ADS |

Time-harmonic impedance tomography using the T-matrix method

A time-harmonic formulation for the electrical impedance tomography (EIT) inverse problem accounting for electrodynamic effects is derived. This work abandons the standard electrostatic impedance model for a full-wave T-matrix model. The advantage of this method is an accurate physical model that includes finite frequency effects, such as diffusion phenomena, and electrode contact impedance effects. This model offers the potential for increased resolution and larger invertible contrast objects than other methods when used on experimental data, because it may represent a more realistic physical model. Also, an accurate gradient matrix is used in the Newton iterative method so the image reconstruction converges in a few iterations. These advantages are realized with no increase in the computational complexity of this algorithm, compared to the static finite element model. A calibration technique is suggested for measurement systems, to test the validity of a theoretical model that includes electrode contact impedance effects.

Cosmic-Ray Transport and Acceleration

AbstractWe review the transport and acceleration of cosmic rays concentrating on the origin of galactic cosmic rays. Quasi-linear theory for the acceleration rates and propagation parameters of charged test particles combined with the plasma wave viewpoint of modeling weak cosmic electromagnetic turbulence provides a qualitatively and quantitatively correct description of key observations. Incorporating finite frequency effects, dispersion, and damping of the plasma waves are essential in overcoming classical discrepancies with observations as the Kfit - Kql discrepancy of solar particle events. We show that the diffusion-convection transport equation in its general form contains spatial convection and diffusion terms as well as momentum convection and diffusion terms. In particular, the latter momentum diffusion term plays a decisive role in the acceleration of cosmic rays at super-Alfvénic supernova shock fronts, and in the acceleration of ultra-high-energy cosmic rays by distributed acceleration in our own galaxy.Subject headings: acceleration of particles — convection — cosmic rays — diffusion — shock waves

Two-band model for halogen-bridged mixed-valence transition-metal complexes. II. Electron-electron correlations and quantum phonons.

We study the effects of electron-electron interactions in halogen-bridged mixed-valence transition-metal linear-chain complexes ({ital MX} chains) applying a simple 3/4-filled two-band discrete tight-binding (extended) Peierls-Hubbard model with both on-site and intersite electron-phonon couplings. We employ a variety of methods: perturbation theory, Hartree-Fock approximation, and exact diagonalization in the limit of classical adiabatic phonons, and a variational approach allowing for a finite phonon frequency, i.e., quantum phonons and isotope effect. This variety of methods has proved necessary to obtain a complete picture, due to the structural richness of this model. We investigate the competition between the electron-electron and electron-phonon interactions in a wide range of parameter regimes for both ground and excited states. We focus on values relevant to the {ital MX} chains, probing the experimental variation as {ital X} and {ital M} are varied among {ital X}=Cl, Br, and I and {ital M}=Pt, Pd, and Ni (spanning electron-phonon-interaction-dominated to electron-electron-interaction-dominated materials).

Nonlinear surface Alfvén waves

The problem of nonlinear surface Alfvén waves propagating on an interface between a plasma and a vacuum is discussed, with dispersion provided by the finite-frequency effect, i.e. the finite ratio of the frequency to the ion-cyclotron frequency. A set of simplified nonlinear wave equations is derived using the method of stretched co-ordinates, and another approach uses the generation of a second-harmonic wave and its interaction with the first harmonic to obtain a nonlinear dispersion relation. A nonlinear Schrödinger equation is then derived, and soliton solutions found that propagate as solitary pulses in directions close to parallel and antiparallel to the background magnetic field.

Direct excitation of the torsional Alfven wave in a Tokamak scrape-off plasma by a Faraday shielded antenna

An experimental study of the direct excitation of the torsional Alfven wave in the scrape-off plasma by an antenna designed for Alfven wave heating experiments in the TORTUS Tokamak is described. The antenna incorporated a Faraday shield, and was printed in the plane perpendicular to the toroidal direction, in order to minimize such direct excitation. Wave magnetic field measurements nevertheless indicated strong direct torsional Alfven wave excitation by antenna elements perpendicular to the Tokamak magnetic field lines due to finite frequency effects. The torsional Alfven wave was measured to propagate essentially parallel to the magnetic field lines, except at frequencies close to the ion cyclotron frequency. The excitation efficiency was found to increase with frequency (up to the ion cyclotron frequency) and electron density. The relevance of these results to the Alfven wave heating scheme is discussed.

Parametric instabilities of circularly polarized Alfvén waves including dispersion

A class of parametric instabilities of large‐amplitude, circularly polarized Alfvén waves is considered in which finite frequency (dispersive) effects are included. The dispersion equation governing the instabilities is a sixth‐order polynomial which is solved numerically. As a function of K ≡ k/k0 (k0 and k are the wave number of the “pump” wave and unstable sound wave, respectively), there are three regions of instability: A modulation instability at K &lt; 1, a decay instability at K &gt; 1, and a relatively weak and narrow instability at K ≃ 1. As a function of β ≡ cs²/υA² (where cs and υA are the sound and Alfvén speeds, respectively), the modulational instability occurs when β &lt; 1 (&gt; 1) for left‐hand (right‐hand) pump waves, in agreement with the previous results of Sakai and Sonnerup (1983). For β ≤ 1, dispersive effects tend to enhance the decay instability for right‐hand waves and to reduce it for left‐hand waves. For β ≥ 1 this tendency is reversed. For right‐hand waves the decay instability is dominant for β ≤ 1, while the modulational instability dominates for sufficiently high β. The growth rate of the decay instability of left‐hand waves is greater than the modulational instability at all values of β. Applications to large‐amplitude waves observed in the solar wind, in computer simulations, and in the vicinity of planetary and interplanetary collisionless shocks are discussed.

Elastic surface waves in rare-earth compounds; exact treatment of finite frequency effects

Elastic surface waves in rare-earth compounds; exact treatment of finite frequency effects

Elastic surface waves in rare-earth compounds; Exact treatment of finite frequency effects

We present an application of the surface Green function matching method to the study of elastic surface waves in rare-earth compounds. The boundary conditions are treated exactly and this allows for an exact treatment of finite frequency effects recently pointed out.

The quantised Hall effect in strong magnetic fields

The Hall conductance is expressed in terms of classical drift trajectories in the high-H limit. The connection of sigma xy with the properties of edge states is established, which explains the quantisation of sigma xy. The quantisation is shown to be exact in the infinite system at zero temperature. The finite frequency effects are also discussed and the AC response is related to the geometrical characteristics of the equipotential lines of the external potential.

Higher Frequency Spectrum of a Diffuse Linear Pinch with Multiple Ion Species

A cold plasma model which takes into account finite ion cyclotron frequency effects and multiple ion species has been developed for wave propagation in arbitrary magnetic field geometries. This model has been used to derive an elegant system of normal mode equations for a 10w-fJ diffuse linear pinch. From a soluble model, general features of the spectrum are discussed up to and including the ion cyclotron range of frequencies. It is indicated that in the vicinity of the ion-ion hybrid cutoff frequency, there could exist global eigenmodes which might be useful for supplementary heating of diffuse linear pinches.

Surface and discrete Alfven waves in a current carrying plasma

MHD surface waves propagating on the interface between a constant density current-free plasma and a vacuum have recently been shown to be strongly affected by finite frequency effects, i.e. the inclusion of the Hall term in the Ohm's Law. Two distinct modes exist, depending on the sign of m, the azimuthal mode number in cylindrical geometry. The authors incorporate the effects of an axial plasma current and investigate the dispersion relation of the resulting modes of a plasma cylinder of uniform density with variable vacuum width. For wave frequency omega << Omega i (the ion-cyclotron frequency) the current introduces an asymmetry in the dispersion relation with respect to the sign of k, the axial wavenumber. An unstable branch also appears, related to the external kink mode. They also find eigenmodes of the discrete Alfven wave (DAW), both stable and unstable. However, the existence of these modes depends strongly on the shear of the magnetic field. At frequency omega approximately= Omega i, the surface wave is not much affected by the current; however, the DAW modes, or ion-cyclotron waves, are eliminated below a limiting frequency due to the effects of the current.

Finite-frequency effects for elastic waves in rare-earth compounds

In rare-earth compounds, the deformation caused by an elastic wave interacts with the crystalline-electric-field- (CEF-) split energy levels of the incomplete $4f$ shell of the rare-earth ions. This magnetoelastic interaction is temperature dependent due to the different thermal population of the CEF levels at different temperatures and leads to a number of interesting effects. One type of effect is found in the zero-frequency limit of the elastic waves. Here we deal with effects that occur only at finite frequencies. We find interesting results in the presence of a magnetic field. In particular, for some geometries we find (1) nonreciprocal Rayleigh-wave propagation, i.e., $\ensuremath{\omega}(\stackrel{\ensuremath{\rightarrow}}{k})\ensuremath{\ne}\ensuremath{\omega}(\ensuremath{-}\stackrel{\ensuremath{\rightarrow}}{k})$, where $\ensuremath{\omega}$ and $\stackrel{\ensuremath{\rightarrow}}{k}$ are the frequency and wave vector of the Rayleigh wave, (2) a mixing of bulk-longitudinal and bulk-transverse waves, and (3) the existence of a pure shear polarized surface wave.

Linear theory of disordered fibre-reinforced composites

A theory is presented for obtaining the effective elastic Green function G(k) of well-bonded fibre-reinforced materials at low volume-fractions of fibre in the presence of disorder. The centre of mass positions of the fibres are taken to be random. The theory is applied to the case where the alignment is also random, and comment is made on its suitability for less totally disordered geometries. The shear stress at the fibre-matrix interface is also calculated, and effective elastic moduli obtained by taking the low k limit. Finite frequency effects are considered; the damping of long wavelength acoustic modes by disorder is calculated. Results are given for general length distribution, Young modulus and number density of fibres in a matrix of arbitrary bulk and shear moduli. The fibre radius is taken to be small compared with the fibre length. In a limiting case, that of high overlap of fibres and high values of Young modulus for the fibres in an incompressible matrix, the results for the composite Young modulus and interface shear stress obtained by a full Green function treatment take forms similar to those first derived heuristically by shear-lag analysis (H. L. Cox, Br. J. appl. Phys. 3, 72 (1952)). The increment in shear modulus of an incompressible elastic medium when inflexible, inextensible random-flight wires or fibres are embedded in it is also calculated.