A new formalism for the effect of lateral heterogeneity on normal modes and surface waves--I: isotropic perturbations, perturbations of interfaces and gravitational perturbations

We studied the quasi-normal modes (QNM) of electromagnetic and gravitational perturbations of a Schwarzschild black hole in an asymptotically anti-de Sitter (AdS) spacetime, extending previous works1,2 on the subject. Some of the electromagnetic modes do not oscillate, they only decay, since they have pure imaginary frequencies. The gravitational modes show peculiar features: the odd and even gravitational perturbations no longer have the same characteristic quasinormal frequencies. There is a special mode for odd perturbations whose behavior differs completely from the usual one in scalar1 and electromagnetic perturbation in an AdS spacetime, but has a similar behavior to the Schwarzschild black hole3 in an asymptotically flat spacetime: the imaginary part of the frequency goes as [Formula: see text], where r+ is the horizon radius. We also investigated the small black hole limit showing that the imaginary part of the frequency goes as [Formula: see text]. These results are important to the AdS/CFT4 conjecture since according to it the QNMs describe the approach to equilibrium in the conformal field theory. For other geometries see5,6.

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Stability and dynamics of rotating dielectrophoretic equilibria

Journal of Fluid Mechanics ◽

10.1017/s0022112069002564 ◽

1969 ◽

Vol 38 (4) ◽

pp. 721-742 ◽

Cited By ~ 5

Author(s):

R. T. Calvert ◽

J. R. Melcher

Keyword(s):

Electric Field ◽

Surface Waves ◽

Field Intensity ◽

Electric Field Intensity ◽

Normal Modes ◽

Liquid Interfaces ◽

Field Gradients ◽

Orientation System ◽

Strong Gradient

In the design of dielectrophoretic liquid orientation and expulsion systems for zero-gravity environments, maximum electromechanical effect of an imposed electric field is obtained by concentrating the field gradients in the neighbourhood of liquid interfaces. In typical configurations, the electric field gradient plays the role of an electromechanical wall, with a stiffness and inertia represented dynamically by electrohydrodynamic surface waves. As an orientation system rotates, the liquid motions are characterized by these waves as they couple to inertial bulk oscillations and centrifugal surface waves resulting from the rotation. A study is made of configurations typified by an equilibrium in which a circular cylindrical column of inviscid liquid undergoes rigid body rotation. The equilibrium is made possible, even though the cylindrical interface is bounded from outside only by its vapour, because the interface is stressed by an essentially tangential axial electric field intensity, with a strong gradient in the radial direction. Dispersion equations are developed for the electrohydrodynamic centrifugal waves of small amplitude. Conditions for incipience of instability and the frequencies of normal modes of oscillation are given. Experimental observations, which demonstrate the destabilizing influence of the rotation and the effect of rotation and electric field intensity on the normal mode frequencies, are in satisfactory agreement with the theory.

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MHD surface waves in high- and low-beta plasmas. Part 1. Normal-mode solutions

Journal of Plasma Physics ◽

10.1017/s0022377800014197 ◽

1989 ◽

Vol 42 (1) ◽

pp. 75-89 ◽

Cited By ~ 5

Author(s):

Z. E. Musielak ◽

S. T. Suess

Keyword(s):

Magnetic Field ◽

Surface Waves ◽

Normal Mode ◽

General Structure ◽

Normal Modes ◽

Resonant Absorption ◽

Normal Surface ◽

Phase Mixing ◽

Cold Plasmas ◽

The Waves

Since the first paper by Barston (1964) on electrostatic oscillations in inhomogeneous cold plasmas, it has been commonly accepted that all finite layers with a continuous profile in pressure, density and magnetic field cannot support normal surface waves but instead the waves always decay through phase mixing (also called resonant absorption). Here we reanalyse the problem by studying a compressible current sheet of a general structure with rotation of the magnetic field included. We find that all inhomogeneous layers considered in the high-β plasma limit do not support normal modes. However, in the limit of a low-β plasma there are some cases when normal-mode solutions are recovered. The latter means that the process of resonant absorption is not common for all inhomogeneous layers.

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Split free oscillation amplitudes for the 1960 Chilean and 1964 Alaskan earthquakes

Bulletin of the Seismological Society of America ◽

10.1785/bssa0670030651 ◽

1977 ◽

Vol 67 (3) ◽

pp. 651-660 ◽

Cited By ~ 3

Author(s):

Robert J. Geller ◽

Seth Stein

Keyword(s):

Surface Waves ◽

Volume Change ◽

Free Oscillation ◽

Additional Data ◽

Normal Modes ◽

Source Mechanisms ◽

Split Mode ◽

Theoretical Results

abstract Splitting of the Earth's normal modes was observed for both the 1960 Chilean and 1964 Alaskan earthquakes. The strong peaks in the observed spectrum of each split multiplet correspond to singlets with much higher amplitudes than the others. Using theoretical results we have derived elsewhere (Stein and Geller, 1977a), we are able to predict this pattern. We show that the source mechanisms inferred for these earthquakes from surface waves are consistent with the observed pattern of relative spectral amplitudes of the split modes. However other mechanisms, such as a slow isotropic volume change, are also consistent with the split-mode amplitudes and are excluded only by additional data.

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Normal modes of continental surface waves

Bulletin of the Seismological Society of America ◽

10.1785/bssa0480010033 ◽

1958 ◽

Vol 48 (1) ◽

pp. 33-49 ◽

Cited By ~ 2

Author(s):

Jack Oliver ◽

Maurice Ewing

Keyword(s):

Surface Waves ◽

Normal Modes ◽

Wave Dispersion ◽

Low Velocity ◽

Surface Wave Dispersion ◽

Mode Dispersion ◽

Seismic Surface Waves ◽

Low Velocity Layer ◽

Rayleigh Mode ◽

Velocity Layer

Abstract When the path between epicenter and station traverses only continental structure, the dispersion of the entire train of directly arriving seismic surface waves can be explained as the result of normal mode propagation in a crust-mantle system in which the velocity increases in some manner with depth within the crust. At least four modes, the Rayleigh mode, Sezawa's M2 mode, and the first two Love waves, may appear prominently on the seismogram. The characteristics of the higher-mode dispersion curves permit the explanation of the Lg phase of Press and Ewing, B䳨's Lg1 and Lg2, and, in some cases, Caloi's Sa without recourse to a low-velocity layer in the crust or mantle. Speculation on changes in these curves for less simplified models indicates that the remaining cases of Sa as well as Leet's C or coupled wave may be explained by classical theory. The occurrence of the higher-mode waves is widespread; they are found on the four continents for which data are available. Higher-mode data, particularly when combined with information from the fundamental modes, make surface-wave dispersion, previously a useful tool, a much more potent method for the study of crustal structure.

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