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

1977 ◽  
Vol 67 (3) ◽  
pp. 651-660 ◽  
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.

Symmetry-breaking bifurcations in resonant surface waves

1989 ◽  
Vol 199 ◽  
pp. 495-518 ◽  
Author(s):  
Z. C. Feng ◽  
P. R. Sethna
Keyword(s):  
Normal Form ◽  
Symmetry Breaking ◽  
Surface Waves ◽  
Bifurcation Analysis ◽  
Internal Resonance ◽  
Travelling Waves ◽  
Chaotic Behaviour ◽  
Derived Set ◽  
Parameter Values ◽  
Theoretical Results

Surface waves in a nearly square container subjected to vertical oscillations are studied. The theoretical results are based on the analysis of a derived set of normal form equations, which represent perturbations of systems with 1:1 internal resonance and with D4 symmetry. Bifurcation analysis of these equations shows that the system is capable of periodic and quasi-periodic standing as well as travelling waves. The analysis also identifies parameter values at which chaotic behaviour is to be expected. The theoretical results are verified with the aid of some experiments.

scholarly journals Stability and dynamics of rotating dielectrophoretic equilibria

1969 ◽  
Vol 38 (4) ◽  
pp. 721-742 ◽  
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.

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

1989 ◽  
Vol 42 (1) ◽  
pp. 75-89 ◽  
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.

scholarly journals The Convergence of the Legendre–Galerkin Spectral Method for Constructing Atmospheric Acoustic Normal Modes

2020 ◽  
Vol 28 (03) ◽  
pp. 2050002
Author(s):  
Richard B. Evans
Keyword(s):  
Legendre Polynomials ◽  
Normal Modes ◽  
Sobolev Norm ◽  
Linear Operators ◽  
Basis Sets ◽  
Spectral Approximation ◽  
Spectral Approximations ◽  
Potential Applications ◽  
Galerkin Spectral Method ◽  
Theoretical Results

The asymptotic rate of convergence of the Legendre–Galerkin spectral approximation to an atmospheric acoustic eigenvalue problem is established, as the dimension of the approximating subspace approaches infinity. Convergence is in the [Formula: see text] Sobolev norm and is based on the existing theory [F. Chatelin, Spectral Approximations of Linear Operators (SIAM, 2011)]. The assumption is made that the eigenvalues are simple. Numerical results that help interpret the theory are presented. Eigenvalues corresponding to acoustic modes with smaller [Formula: see text] norms are especially accurately approximated, even with lower dimensioned basis sets of Legendre polynomials. The deficiencies in the potential applications of the theoretical results are noted in connection with the numerical examples.

scholarly journals Time-domain observation and synthesis of split spheroidal and torsional free oscillations of the 1960 chilean earthquake: Preliminary results

1978 ◽  
Vol 68 (2) ◽  
pp. 325-332 ◽  
Author(s):  
Seth Stein ◽  
Robert J. Geller
Keyword(s):  
Time Domain ◽  
Normal Modes ◽  
Wave Form ◽  
Central Frequency ◽  
Complex Wave ◽  
Location Depth ◽  
The Time Domain ◽  
Theoretical Results ◽  
Good Agreement ◽  
Chilean Earthquake

Abstract The rotationally and elliptically split normal modes of the earth are observed for the 1960 Chilean earthquake by analysis in the time domain. One hundred and fifty hours of the Isabella, California, strain record are narrow band filtered about the central frequency of each split multiplet to isolate the complex wave form resulting from the interference of the different singlets. We compute synthetic seismograms using our previous theoretical results, which show the dependence of the amplitude and phase of the singlets on source location, depth, mechanism, and the position of the receiver. By comparing these synthetics to the filtered record, we conclusively demonstrate the splitting of modes whose splitting had not been definitely resolved: torsional modes (0T3, 0T4) and spheroidal modes (0S4, 0S5). The splitting of 0S2 and 0S3 is reconfirmed. We obtain good agreement between the synthetics and the filtered data for a source mechanism (previously determined from long-period surface waves) of thrust motion on a shallow dipping fault.

Free Oscillations of a Damped Simple Pendulum: An Analog Simulation Experiment

2019 ◽  
Vol 01 (04) ◽  
pp. 1950015 ◽  
Author(s):  
Ivan Skhem Sawkmie ◽  
Mangal C. Mahato
Keyword(s):  
Harmonic Oscillator ◽  
Free Oscillation ◽  
Simulation Experiment ◽  
Free Oscillations ◽  
Analog Simulation ◽  
Simple Pendulum ◽  
Electronic Circuitry ◽  
Undergraduate Laboratory ◽  
Angular Amplitude ◽  
Theoretical Results

The frequency of free oscillation of a damped simple pendulum with large amplitude depends on its amplitude unlike the amplitude-independent frequency of oscillation of a damped simple harmonic oscillator. This aspect is not adequately emphasized in the undergraduate courses due to experimental and theoretical difficulties. We propose an analog simulation experiment to study the free oscillations of a simple pendulum that could be performed in an undergraduate laboratory. The needed sinusoidal potential is obtained approximately by using the available AD534 IC by suitably augmenting the electronic circuitry. To keep the circuit simple enough we restrict the initial angular amplitude of the simple pendulum to a maximum of [Formula: see text]. The results compare well qualitatively with the theoretical results. The small quantitative discrepancy is attributed to the inexact nature of the used “sinusoidal potential”.

WORKING CONDITIONS AS MOTIVATION FOR EMPLOYEES

2018 ◽  
Vol 28 (1) ◽  
pp. 341-344
Author(s):  
Hava Qarri ◽  
Jusuf Fejza
Keyword(s):  
Working Conditions ◽  
Additional Data ◽  
Physical Hazards ◽  
Degree Of Satisfaction ◽  
Psychological Difficulties ◽  
As Stress ◽  
Theoretical Results

Organizations engage their employees to work in extreme working conditions to try to maximize their profits. The term for working conditions refers not only to work with physical hazards, but it also includes psychological difficulties such as stress, overwork, harassment, and so on.Though many studies have been conducted that relate to these issues, sometimes the results of these studies contradict. For this reason, in order to evaluate the working conditions and the degree of satisfaction of the workers in different countries, research has been undertaken in order to collect additional data on this issue.The theoretical results show overall satisfaction with working conditions, with the exception of stress-related conditions. The relevance of the samples tested has no effect on the result. It can be concluded that, overall, the results of the research are correlated with the results of the researches found in the literature.

Normal modes of continental surface waves

1958 ◽  
Vol 48 (1) ◽  
pp. 33-49 ◽  
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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