Frequency Oscillation Modes Research Articles

The Canonical Bicoherence—Part II: QPC Test and Its Application in Geomagnetic Data

In a companion paper [ldquoThe canonical bicoherence-Part I: Definition, multitaper estimation, and statistics,rdquo IEEE transactions on signal processing, vol. 57, no. 4, April 2009], we defined the canonical bicoherence (CBC), proposed its multitaper estimates, showed its feasibility to detect quadratic phase coupling (QPC) for multivariate random processes, and discussed its statistical properties. In this part, the canonical biphase (CBP) is defined, and a two-step QPC test is developed using the first canonical bicoherence and the first canonical biphase at prescribed significance levels. Detection probabilities of this test are given by Monte Carlo simulations. The canonical bicoherence is applied to analyze the possibility of quadratic phase couplings in the Earth's magnetic field. The results of simulations show that lower-frequency <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> -modes of the Sun may interact nonlinearly, producing intermodulation components at the sum and/or difference of fundamental frequency modes of oscillations.

Aerodynamic and Acoustic Effects of Abrupt Frequency Changes in Excised Larynges

To determine the aerodynamic and acoustic effects due to a sudden change from chest to falsetto register or vice versa. It was hypothesized that the continuous change in subglottal pressure and flow rate alone (pressure-flow sweep [PFS]) can trigger a mode change in the canine larynx. Ten canine larynges were each mounted over a tapered tube that supplied pressurized, heated, and humidified air. Glottographic signals were recorded during each PFS experiment, during which airflow was increased in a gradual manner for a period of 20-30 s. Abrupt changes in fundamental frequency (F(0)) and mode of vibration occurred during the PFS in the passive larynx without any change in adduction or elongation. The lower frequency mode of oscillation of the vocal folds, perceptually identified as the chest register, had relatively large amplitude oscillation, significant vocal fold contact, a rich spectral content, and a relatively loud audio signal. The higher frequency mode of oscillation, perceptually identified as falsetto, had little or no vocal fold contact and a dominant first partial. Relatively abrupt F(0) changes also occurred for gradual adduction changes, with the chest register corresponding to greater adduction, falsetto to less adduction.

Nonlinear corrections to the oscillation mode frequencies of an ideal liquid charged jet

An analytical asymptotic expression is derived for the time evolution of an ideal incompressible conducting liquid jet with a uniformly charged surface that moves with a constant velocity along the symmetry axis of an undisturbed cylindrical surface. The expression is obtained in the third order of smallness in jet oscillation amplitude under the conditions when the initial deformation of the equilibrium jet surface is specified by one (axisymmetric or nonaxisymmetric) mode. Analytical expressions are also found for the positions of internal nonlinear degenerate three-and four-mode resonances, which are typical of nonlinear corrections to the equilibrium shape of the jet, liquid velocity field potential in the jet, and electrostatic field near the jet, and also for a nonlinear frequency correction. It is established that the nonlinear oscillations of the jet take place about a surface depending on the type of initial (generally asymmetric) deformation rather than about the equilibrium cylindrical shape.

GOLF-NG spectrometer, a space prototype for studying the dynamics of the deep solar interior

The GOLF-NG (Global Oscillations at Low Frequency New Generation) instrument is devoted to the search for solar gravity and acoustic modes, and also chromospheric modes from space. This instrument which is a successor to GOLF/SOHO will contribute to improve our knowledge of the dynamics of the solar radiative zone. It is a 15 points resonant scattering spectrometer, working on the D1 sodium line. A ground-based prototype is under construction to validate the difficult issues. It will be installed at the Teide Observatory, on Tenerife in 2006 to analyse the separation of the effects of the magnetic turbulence of the line from the solar oscillations. We are prepared to put a space version of this instrument including a capability of identification of the modes, in orbit during the next decade. This instrument should be included in the ILWS program as it offers a key to the improvement of our knowledge of the solar core in combination with observations from SDO and PICARD. We hope to determine the core rotation and magnetic field, through precise measurements of oscillation mode frequency splittings. Understanding the magnetic field of the radiative zone is important for progress in the study of solar activity sources, an important player for the long-term Sun–Earth relationship.

Asteroseismic tests of element diffusion in solar type stars

Following the success of helioseismology, asteroseismology is now becoming a fundamental tool for penetrating the secrets of the internal structure of stars. In preparation of this new era in stellar physics, we study the effects of element diffusion on the computed frequencies of stellar oscillation modes for main-sequence solar-type stars. As the observed stars will be constrained by their atmospheric parameters, stellar models were computed with different physical inputs (whether including element diffusion or not) and iterated in order to fit the same observables (effective temperature, luminosity, surface chemical composition). The theoretical oscillation frequencies of these models were derived and compared. The results show that diffusion alters the internal structure of the models and their oscillation frequencies in a significant way. Although observational uncertainties in stellar external parameters are still important, comparisons between oscillation frequencies observed with the future space mission COROT and theoretically computed ones might provide evidence for diffusion processes in solar type stars.

Elastic stars in general relativity: III. Stiff ultrarigid exact solutions

We present an equation of state for elastic matter which allows for purely longitudinal elastic waves in all propagation directions, not just principal directions. The speed of these waves is equal to the speed of light whereas the transversal type speeds are also very high, comparable to but always strictly less than that of light. Clearly such an equation of state does not give a reasonable matter description for the crust of a neutron star, but it does provide a nice causal toy model for an extremely rigid phase in a neutron star core, should such a phase exist. Another reason for focusing on this particular equation of state is simply that it leads to a very simple recipe for finding stationary rigid motion exact solutions to the Einstein equations. In fact, we show that a very large class of stationary spacetimes with constant Ricci scalar can be interpreted as rigid motion solutions with this matter source. We use the recipe to derive a static spherically symmetric exact solution with constant energy density, regular centre and finite radius, having a nontrivial parameter that can be varied to yield a mass–radius curve from which stability can be read off. It turns out that the solution is stable down to a tenuity R/M slightly less than 3. The result of this static approach to stability is confirmed by a numerical determination of the fundamental radial oscillation mode frequency. We also present another solution with outwards decreasing energy density. Unfortunately, this solution only has a trivial scaling parameter and is found to be unstable.

Drop fall-off from the vibrating ceiling

This work investigates a scheme to rapidly remove liquid drops from a ceiling by vibrating the solid surface. We show that there exist resonant frequencies at which the minimum vibration amplitudes inducing a fall-off of the pendant drops are remarkably less than the detaching amplitudes at neighboring frequencies. These frequencies are shown to correspond to the resonance frequencies of different drop oscillation modes.

Parametric instabilities in magnetized bi-ion and dusty plasmas

The excitation of low frequency modes of oscillations in a magnetized bi-ion or dusty plasma with parametric pumping of the magnetic field is analysed. The equation of motion governing the perturbed plasma is derived and parametrically excited transverse modes propagating along the magnetic field are found. With multiple ion species or charged dust present, a number of different circularly polarized modes can be excited. The stability of these modes is investigated as a function of the plasma parameters. The modulational instabilities of large amplitude normal modes, modified by the extra ion species or dust and propagating along the magnetic field, are also investigated.

Parametric instabilities of Alfvén waves in a dusty plasma

The excitation of low frequency modes of oscillations in a magnetized dusty plasma with parametric pumping of the magnetic field is analyzed. The dust is taken to be stationary, but acts as a sink for negative charge: The absence of a proportion of the electrons in the overall neutral plasma modifies the dispersion properties of the pump and excited waves. The pump is a magnetoacoustic wave modified by the dust, and the excited waves are modifications of Alfvén waves due to the dust and due to ion cyclotron effects. The equation of motion governing the perturbed plasma is derived and pump wave fields are found. The stability of the pump to modes propagating parallel to the magnetic field is investigated as a function of the plasma parameters. It is found that pairs of slow and fast parallel propagating modes are parametrically excited. The growth rates of the various interactions are calculated, and it is shown that the growth rates of slow–fast and fast–fast mode interactions can be maximized by varying the proportion of negative charge on the dust.

Two‐dimensional Modeling of the Solar Oscillation \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage[OT2,OT1]{fontenc} \newcommand\cyr{ \renewcommand\rmdefault{wncyr} \renewcommand\sfdefault{wncyss} \renewcommand\encodingdefault{OT2} \normalfont \selectfont} \DeclareTextFontCommand{\textcyr}{\cyr} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} \landscape $l- \nu $ \end{document} Power Spectrum

We describe an algorithm which can accurately model the spatial-temporal l-ν solar oscillation power spectrum over large ranges in frequency (ν) and degree (l). We show how modeling in two dimensions provides a better representation of the observed spectrum than can be obtained with traditional one-dimensional approaches. The gain comes from using more of the observed signal to constrain the model and improved descriptions of the solar background spectrum and the signal leakage between different spatial scales. We discuss the level of systematic error that can be expected in the solar oscillation mode frequency data published to date.

Perturbative analysis of two-temperature radiative shocks with multiple cooling processes

The structure of the hot downstream region below a radiative accretion shock, such as that of an accreting compact object, may oscillate due to a global thermal instability. The oscillatory behaviour depends on the functional forms of the cooling processes, the energy exchanges of electrons and ions in the shock-heated matter, and the boundary conditions. We analyse the stability of a shock with unequal electron and ion temperatures, where the cooling consists of thermal bremsstrahlung radiation which promotes instability, plus a competing process which tends to stabilize the shock. The effect of transverse perturbations is considered also. As an illustration, we study the special case in which the stabilizing cooling process is of order 3/20 in density and 5/2 in temperature, which is an approximation for the effects of cyclotron cooling in magnetic cataclysmic variables. We vary the efficiency of the second cooling process, the strength of the electron-ion exchange and the ratio of electron and ion pressures at the shock, to examine particular effects on the stability properties and frequencies of oscillation modes.

Oscillatory instability of radiative shocks with multiple cooling processes

The stand-off shock formed in the accretion flow on to a stationary wall, such as the surface of a white dwarf, may be thermally unstable, depending on the cooling processes which dominate the post-shock flow. Some processes lead to instability, while others tend to stabilize the shock. We consider competition between the destabilizing influence of thermal bremsstrahlung cooling, and a stabilizing process which is a power law in density and temperature. Cyclotron cooling and processes which are of order 1, 3/2 and 2 in density are considered. The relative efficiency and power-law indices of the second mechanism are varied, and particular effects on the stability properties and frequencies of oscillation modes are examined.

An investigation into solar wind plasma periodicities

Plasma and magnetic field data from the IMP 8 Earth‐orbiting spacecraft and plasma data from the Voyager 2 spacecraft are analyzed to determine their frequency spectra. The resulting spectra are compared with solar oscillation mode frequencies which recent papers (particularly Thomson et al. [1995]) report are present in solar wind data. The frequency spectra of the plasma and magnetic field data sets are characterized by a diverse set of strong peaks, many of which are stronger than those occurring at frequencies associated with solar oscillatory modes. The frequencies of these peaks are not consistent between data sets, making it unlikely that they represent solar oscillation modes. Although the analysis technique used, the Lomb‐Scargle method, does not permit accurate assignment of statistical uncertainties, it is clear that solar oscillatory frequencies are not the major contributors to the frequency spectra of these data.

Comments on the effect of an acoustic field on the shape oscillations of levitated drops and bubbles

Acoustic levitation has been used as a method for measuring the frequency and dissipative properties of shape oscillation modes of drops and bubbles [P. L. Marston and R. E. Apfel, J. Acoust. Soc. Am. 67, 27–37 (1980); T. J. Asaki et al., J. Acoust. Soc. Am. 93, 706–713 (1993)]. One of the problems in the interpretation of such measurements is the effect of the levitating field. Some of the relevant issues for slightly deformed drops or bubbles, where the equilibrium shape is spheroidal and R is the radius of the sphere of the same volume, are examined. The interaction of shape oscillations with the external acoustic flow is approximated for a spheroid at the velocity antinode of a standing wave in the long‐wavelength limit (kR→0) with the result that the effective restoring force for the quadrupole mode is increased. The curvature of the effective potential well is increased. The analysis makes use of the known solution for the potential flow past an incompressible spheroid in the kR→0 limit. [Work supported by ONR.]

Frequencies of solar oscillations

Solar oscillations have been observed at three different spatial scales at Big Bear Solar Observatory during 1986-1987 and, using three data sets, a new and more accurate table of solar oscillation frequencies has been compiled. The oscillations, which are presented as functions of radial order n and spherical harmonic degree l, are averages over azimuthal order and therefore approximate the normal mode frequencies of a nonrotating, spherically symmetric sun, near solar minimum. The table contains frequencies for most of the solar p and f modes with l between 0 and 1860, n between 0 and 26, and oscillation mode frequencies between 1.0 and 5.3.

Dynamic performance of a radial weak power system with multiple static VAr compensators

The authors describe the dynamic performance of a radial weak, heavily shunt-compensated power system, with three static VAr (volt-ampere reactive) compensators (SVCs) of relatively large rating installed at short distances from one another. Dynamic interactions between the SVC control systems and between them and the network are analyzed by using eigenvalues and frequency-response techniques. Some noteworthy effects concerning the SVCs' regulator stability that can arise in such systems are described. These effects, revealed in the eigenvalue analysis, were confirmed in TNA simulations. A brief description of the mathematical formulation and the complete system data is also included. Among other results, it is shown that the operation of SVCs with low values of ESCR can exhibit oscillation mode frequencies above 5 Hz, depending substantially on SVC regulator gain. In such cases, the representation of both network dynamics and thyristor time delay is crucial in the analysis if the SVC regulator stability limits. >

Oscillation characteristics of Raman regime free electron laser.

Fundamental free electron laser experiments with helical wiggler of 2 cm pitc have been done by using high current, low energy electron beam pulse power machine, Reiden III (0.6MeV/40kA/1kA/150ns) at Institute of Laser Engineering, Osaka University. Oscillation frequency variations in one electron shot were measured, and the frequencies can be explained by the theory of Raman regime free electron laser. In the calculation, we considered the beam velocity variation due to beam potential drop and wiggler field gradient in beam cross-section. Frequency spectra of two oscillation frequency modes shifting closely in each other, were obseved simultaneously by slimming the drift tube and decreasing the beam energy. In this case, the frequency spread effect by the beam cross-section appears widely and the measuring frequency spreads were distributed in the region predicted by the theory. Spatial growth rate was obtained as 1 dB/cm with saturation level of 250 kW and spectral peak at 58 GHz.

High frequency oscillations in a bounded thermally produced plasma

Measurements are reported of a high frequency mode of oscillation of a current carrying, bounded, thermally produced plasma. The oscillation occurs at approximately a third of the electron plasma frequency. A linear theory is presented, which predicts an instability at this frequency. The electron and ion velocity distribution functions used in this theory are determined by the self-consistent d.c. potential distribution. An interesting feature is that the electron velocity distribution function is a discontinuous Maxwellian. The calculated frequency of the instability and its variation as a function of the plasma density agree very well with the experimental observations.

Non-linear analysis of vibrations of irregular plates

A numerical perturbation method is used to investigate the forced vibrations of irregular plates. Non-linear terms associated with the midplane stretching are retained in the analysis. The numerical part of the method involves the use of linear, finite element techniques to determine the free oscillation mode shapes and frequencies and to obtain the linear midplane stress resultants caused by the midplane stretching. Representing the solution as an expansion in terms of these linear mode shapes, we use these modes and the resultants to determine the equations governing the time-dependent coefficients of this expansion. These equations are solved by using the method of multiple scales. Specific solutions are given for the main-resonant vibrations of an elliptical plate in the presence of internal resonances. The results indicate that modes other than the driven mode can be drawn into the steady state response. In some cases, one or more of these other modes may dominate the response. Though the excitation is composed of a single harmonic, the response may not be periodic. Moreover, the particular types of responses that can occur are highly dependent on the mode being excited and are sensitive to small geometrical changes.

Static and dynamic behaviour of complex domain walls

It was previously shown that the application of high-amplitude high-frequency drive fields to epitaxial garnet films affects the properties of the walls to give increased hysteresis, and peculiar modes of oscillation in low frequency test fields. Microscopic observations can also be made to show the behaviour of the walls in the high frequency fields themselves for direct correlation with measurements of magnetization amplitude and phase versus drive field amplitude. A rapidly progressive and irregular pinning of the walls is observed in a critical field region. The low frequency observations do not indicate corresponding high frequency modes of oscillation but are relevant to the interpretation of the results in terms of cumulative Bloch line formation.