Showing papers on "Amplitude published in 1989"

Analysis of an AC-to-DC voltage source converter using PWM with phase and amplitude control

Abstract: A comprehensive analysis is presented of a pulse-width modulated AC-to-DC voltage source converter under phase and amplitude control. A general mathematical model of the converter, which is discontinuous, time-variant, and nonlinear, is first established. To obtain closed-form solutions, the following three techniques are used: Fourier analysis; transformation of reference frame; and small-signal linearization. Three models, namely, a steady-state DC model, a low-frequency small-signal AC model, and a high-frequency model, are consequently developed. Finally, three solution sets, namely, the steady-state solution, various dynamic transfer functions, and the high-frequency harmonic components, are obtained from the three models. The theoretical results were verified experimentally. >

High frequency electrosurgical apparatus for thermal coagulation of biologic tissues

Abstract: A high frequency surgical apparatus for the thermal coagulation of biologic tissues is described, in which for monitoring the fluctuations in amplitude of the high frequency current during each coagulation process a current monitor (25) is provided, which by means of a current-to-voltage coverter generates an electrical voltage proportional to the amplitude fluctuations of the high frequency current, from which voltage, by means of a first detector, a first direct voltage proportional to the amplitude fluctuations is formed and, by means of a second detector acting as a peak value detector, a second direct voltage is formed that rises in proportion to the amplitude of the high frequency current. The first direct voltage (Ua) and the second direct voltage (kUb), which is divided downward by an adjustable factor by means of a voltage divider, are supplied to a voltage comparator, the output signal of which sets a bistable circuit as soon as the first direct voltage (Ua) becomes lower than the downwardly divided second direct voltage (kUb). The output signal of the bistable circuit switches the high frequency current off until the high frequency current is switched back on again by actuation of a manual switch and/or by means of an automatic switch. Instead of or in addition to this current monitor (25), and electric arc monitor (26) for monitoring the generation of anharmonic frequencies of the base frequency of the frequency generator can be connected to the output of the surgical apparatus, the arc monitor including a filter which passes at least one of the anharmonic frequencies, generated by the electric arc, of the base frequency of the high frequency generator. The output signal of the filter is supplied to a voltage comparator, the output signal of which resets a bistable circuit such that its output signal switches off the high frequency current.

Onset of nonlinear saturation for Rayleigh-Taylor growth in the presence of a full spectrum of modes

Abstract: It is generally recognized that a single Rayleigh-Taylor unstable mode grows exponentially, proportional to the initial amplitude, until the amplitude is about (1/10 to (1/5 of the wavelength. The growth then becomes nonlinear, and the mode evolves into spikes and bubbles. This paper considers how this picture of the transition to nonlinearity changes when, instead of there being a single mode, there is a full spectrum of modes. We argue that nonlinear behavior begins whenever the sum of modes over a specified small region of k space becomes comparable to the wavelength. In the case of a single mode, this reduces to the usual comparison of the mode's amplitude with its wavelength \ensuremath{\lambda}. But if the modal amplitudes are smooth functions of k, the modes begin to saturate when their amplitude is comparable to ${\ensuremath{\lambda}}^{2}$/R times a dimensionless scale factor; here, R is the radius in spherical geometry, or the length of the surface in planar geometry. Given this new notion of the amplitude at which nonlinear saturation begins, we construct a simple model to estimate the net perturbation resulting from a broadband initial spectrum. We assume that modes grow exponentially until saturation occurs, and then the growth of the individual modes becomes linear in time. The model predictions in two and three dimensions are compared with Read and Young's experiments [Atomic Weapons Research Establishment Report No. 011/83, Aldermasten, 1983 (unpublished)], and to Youngs's calculations [Physica 12D, 32 (1984)]. The experimental results are used to set the single parameter characterizing the onset of nonlinearity. The model provides a complete description of a weak dependence on initial amplitude. The model can be easily extended to any situation for which one can estimate single-mode growths; results are presented regarding effects on multimode growth of spherical geometry, ablation stabilization, and interface coupling.

Gravitational-wave measurements of the mass and angular momentum of a black hole.

Abstract: A deformed black hole produced in a cataclysmic astrophysical event should undergo damped vibrations which emit gravitational radiation. By fitting the observed gravitational waveform h(t) to the waveform predicted for black-hole vibrations, it should be possible to deduce the hole’s mass M and dimensionless rotation parameter a=(c/G)(angular momentum)/M^2. This paper estimates the accuracy with which M and a can be determined by optimal signal processing of data from laser-interferometer gravitational-wave detectors. It is assumed that the detector noise has a white spectrum and has been made Gaussian by cross correlation of detectors at different sites. Assuming, also, that only the most slowly damped mode (which has spheroidal harmonic indices l=m=2) is significantly excited—as probably will be the case for a hole formed by the coalescence of a neutron-star binary or a black-hole binary—it is found that the one-sigma uncertainties in M and a are ΔM/M≃2.2ρ^-1(1-a)^0.45, Δa≃5.9ρ^-1(1-a)^1.06, where ρ≃hs(πSh)^-1/2 (1-a)^-0.22. Here ρ is the amplitude signal-to-noise ratio at the output of the optimal filter, hs is the wave’s amplitude at the beginning of the vibrations, f is the wave’s frequency (the angular frequency ω divided by 2π), and Sh is the frequency-independent spectral density of the detectors’ noise. These formulas for ΔM and Δa are valid only for ρ≳10. Corrections to these approximate formulas are given in Table II.

Monopole emission of sound by asymmetric bubble oscillations. Part 1. Normal modes

Abstract: On a linearized theory, the pressure field due to bubbles oscillating asymmetrically in a ‘distortion mode’ decays with radial distance r like r−(n+1), where n > 1. Hence these modes have been thought to produce a negligible emission of sound. In this paper it is shown that, on the contrary, in nonlinear theory the distortion modes produce a monopole radiation of sound (n=0) at second order. Its frequency is twice the basic frequency of the distortion mode, and the sound amplitude is proportional to the square of the distortion amplitude. The magnitude of the pressure fluctuations within the bubble is comparable with 1 atmosphere.

Surface wave mode interactions: effects of symmetry and degeneracy

Abstract: Parametrically excited surface wave modes on a fluid layer driven by vertical forcing can interact with each other when more than one spatial mode is excited. We have investigated the dynamics of the interaction of two modes that are degenerate in a square layer, but non-degenerate in a rectangular one. Novel experimental techniques were developed for this purpose, including the real-time measurement of all relevant slowly varying mode amplitudes, investigation of the phase-space structure by means of transient studies starting from a variety of initial conditions, and automated determination of stability boundaries as a function of driving amplitude and frequency. These methods allowed both stable and unstable fixed points (sinks, sources, and saddles) to be determined, and the nature of the bifurcation sequences to be clearly established. In most of the dynamical regimes, multiple attractors and repellers (up to 16) were found, including both pure and mixed modes. We found that the symmetry of the fluid cell has dramatic effects on the dynamics. The fully degenerate case (square cell) yields no time-dependent patterns, and is qualitatively understood in terms of third-order amplitude equations whose basic structure follows from symmetry arguments. In a slightly rectangular cell, where the two modes are separated in frequency by a small amount (about 1%), mode competition produces both periodic and chaotic states organized around unstable pure and mixed-state fixed points.

Propagation properties of dark solitons.

Abstract: We numerically study the initial-value problem of the nonlinear Schrodinger equation in the normal-dispersion regime of an optical fiber. A nonchirped hyperbolic tangent input pulse having arbitrary amplitude is found to evolve into a primary dark soliton having a constant amplitude and speed. The effect of the input amplitude is to alter the pulse width of the primary dark soliton. In addition, a set of secondary dark solitons of smaller amplitude moving away from the primary pulse is also generated. It is also shown that nonlinear dark pulses in optical fibers are more stable than bright pulses with respect to loss and noise.

Comparison of seismic waveform inversion results for the rupture history of a finite fault : Application to the 1986 North Palm Springs, California, earthquake

Abstract: The July 8, 1986, North Palm Springs earthquake is used as a basis for comparison of several different approaches to the solution for the rupture history of a finite fault. The inversion of different waveform data is considered; both teleseismic P waveforms and local strong ground motion records. Linear parametrizations for slip amplitude are compared with nonlinear parametrizations for both slip amplitude and rupture time. Inversions using both synthetic and empirical Green's functions are considered. In general, accurate Green's functions are more readily calculable for the teleseismic problem where simple ray theory and flat-layered velocity structures are usually sufficient. However, uncertainties in the variation in t* with frequency most limit the resolution of teleseismic inversions. A set of empirical Green's functions that are well recorded at teleseismic distances could avoid the uncertainties in attenuation. In the inversion of strong motion data, the accurate calculation of propagation path effects other than attenuation effects is the limiting factor in the resolution of source parameters. The assumption of a laterally homogeneous velocity structure is usually not a good one, and the use of empirical Green's functions is desirable. Considering the parametrization of the problem, any degree of fault rupture complexity can be described in terms of a linear parametrization for slip amplitudes. However, a nonlinear parametrization for rupture times and slip amplitudes can have a distinct advantage over a simple linear one by limiting the number of unknown parameters. Regardless of the choice of data or the type of parametrization, the model or solution will be affected by the choice of minimization norm and the type of stabilization used.

Steady state rocking response of rigid blocks part 1: Analysis

Abstract: The result of a theoretical study on the rocking response of rigid blocks subjected to sinusoidal base motion is presented. The study indicates that, for a given excitation amplitude and frequency, a rigid block can respond in several different ways. Based on analysis, the regions of different classes of steady state symmetric response solutions are mapped on the excitation amplitude-frequency parameter space. The steady state response solutions (both harmonic and subharmonic) are classified into two classes, out-of-phase and in-phase with respect to the excitation. Only out-of-phase solutions are found to be stable. A parametric study shows that steady rocking response amplitude is highly sensitive to the size of the block and the excitation frequency in the low frequency range. It is relatively insensitive to the excitation amplitude and the system's coefficient of restitution of impact. For two blocks of the same aspect ratio and coefficient of restitution subjected to the same excitation, the larger block always responds in smaller amplitude than the smaller block. Computer simulation is carried out to study the stability of the symmetric steady state response solutions obtained from analysis. It is found that as the excitation frequency is decreased beyond the boundary of stable symmetric response, the response becomes unsymmetric where the mean amplitude of oscillation is non-zero. Further decrease in excitation frequency beyond the stable unsymmetric response boundary causes instability in the form of overturning.

Convection driven magnetohydrodynamic dynamos in rotating spherical shells

Abstract: Finite amplitude solutions for magnetohydrodynamic dynamos driven by convection in rotating spherical fluid shells with a radius ratio of ηequals; 0.4 are obtained numerically by the Galerkin method. Solutions which are twice periodic in the azimuth (case m equals; 2) are emphasized, but a few cases with higher azimuthal wavenumber have also been considered. An electrically insulating space outside the fluid shell has been assumed. A comparison of the dynamo solutions of both, dipolar and quadrupolar, symmetries with the corresponding non-magnetic solutions shows a strong increase of the amplitude of convection owing to the release of the rotational constraint by the Lorentz force. In some cases at low Taylor number the amplitude of convection is decreased, however, owing to the competition of the magnetic degree of freedom for the same energy source. The strength of differential rotation is usually reduced by the Lorentz force, especially in the case of quadrupolar dynamos which differ in this r...

Spiral arm amplitude variations and pattern speeds in the grand design galaxies M51, M81, and M100

Abstract: In the modal theory of galactic spiral structure, the amplitude of a prominent two-arm spiral pattern should oscillate slightly with galactocentric distance because of an interference between the outward and inward propagating waves. In the stellar dynamical theory, the spiral arm amplitudes should oscillate because of differential crowding near and between wave-orbit resonances. Two and three cycles of such oscillations have been found in computer-enhanced images at B and I passbands of the grand design galaxies M81 and M100, respectively, and what is probably one cycle of such an amplitude variation in M51. These three galaxies are the most symmetric and global of the two-arm spirals in the near-IR survey of Elmegreen (1981), so the occurrence of such spiral amplitude oscillations could be common among galaxies of this type. The positions of the features discussed are used to suggest possible arm pattern speeds. 23 refs.

Solitary pulses in an amplified nonlinear dispersive medium

Abstract: An analytical solution is obtained for solitary pulse propagation in an amplified nonlinear dispersive system. For a homogeneously broadened gain medium, this solitary pulse has a hyperbolic secant amplitude and a hyperbolic tangent instantaneous frequency variation. The pulse is a gain-guided pulse in either the positive or the negative dispersion regime as well as in the self-focusing or self-defocusing regime. A dark solitary pulse that has a hyperbolic tangent amplitude and a similar instantaneous frequency variation is also obtained.

Neutron Starquake Models for Gamma-Ray Bursts

Abstract: We assess neutron starquake models for γ-ray bursts. The elastic energy the crust can store is sufficient to account for that radiated in a single burst, but it is insufficient to supply the ≳ 10^6 bursts each star produces over its lifetime, and so it must be replenished. Seismic waves are radiated if shear stress is relieved by brittle fracture. However they cannot propagate directly to the surface but are temporarily trapped below a reflecting layer. Between the reflecting layer and the surface the displacement amplitude of the wave is nearly constant and the strain is very small. At low frequencies, ≾ 10^4 Hz, the reflection is associated with an evanescent zone. At high frequencies, ≳ 10^4 Hz, the reflection occurs where the magnetic field stress starts to dominate the crustal rigidity. The shaking of the stellar surface couples the seismic waves to Alfen waves which propagate out into the magnetosphere. At low frequencies, the coupling coefficient, T, is proportional to the square of the magnetic field, B, and increases with the seventh power of the wave frequency, v. At high frequencies, T is proportional to B^(4/7)v^(3/7). Alfven wave luminosities sufficient to power Galactic γ-ray bursts are possible if magnetic fields ≳ 10^(11) G cover at least part of the stellar surface. The conversion of Alfven waves into γ-rays may occur if the waves are charge-starved or if their amplitudes approach that of the background magnetic field.

Lg-wave propagation in heterogeneous media

Abstract: The Lg -wave phase, which is of considerable interest for nuclear discrimination problems, is normally observed after propagation through a few hundred kilometres. This phase is dominantly guided in the crustal waveguide, which is known to be a region with a very significant horizontal variability in properties. The effect of heterogeneous crustal structures on Lg waves has been determined by using a “coupled-mode” technique in which the local seismic wavefield in the real medium is expressed as a horizontally varying combination of the modal eigenfunctions of a stratified reference structure. Departures of the seismic properties in the medium from those of the reference medium lead to coupling between the various amplitude coefficients in the modal expansion. The evolution of these modal weighting factors with horizontal position are described by a coupled set of ordinary differential equations. This approach provides a calculation scheme for studying guided wave propagation over extended distances, at frequencies of 1 Hz and above. The heterogeneity models that have been used are two-dimensional and calculations are carried out for one frequency at a time. A sequence of models with varying levels of heterogeneity have been considered in order to determine the merits and limitations of the computation scheme. The coupled mode technique works well with heterogeneous models in which the local seismic velocities differ from the stratified reference model by up to two per cent and there are no significant distortions of the main discontinuities (e.g., the crust-mantle boundary). The approach can be used for higher levels of heterogeneity and with distorted interfaces but a large number of modes needs to be considered with consequent high computation costs. If the level of heterogeneity is not too large, the interaction between modes can be restricted, rather than extending over the whole mode set, with consequent reduction in computation cost. One of the major effects of crustal heterogeneity is to introduce the possibility of smearing out the main amplitude peak in the Lg wave train over a band of group velocities. As a result, an effective measure of the energy content of the Lg waves will be to consider the integrated amplitude along the trace between group velocities of 3.6 and 3.3 km/sec. The effects of heterogeneity vary between different parts of the Lg wave train and the representation of the wavefield in terms of modal contributions allow a detailed analysis in terms of the group velocity components, which can be illustrated by constructing theoretical seismograms (with a narrow bandwidth in frequency) for the heterogeneous models.

Oscillatory Phase Modulation of Parametrically Forced Surface Waves

Abstract: We present a study of secondary instabilities of parametrically generated standing waves in a horizontal layer of fluid submitted to vertical vibrations. The fluid is contained in a thin annulus, and thus the basic standing wave behaves as a one-dimensional spatial structure. When the driving frequency is increased (respectively, decreased), the system bifurcates abruptly to another standing wave pattern by nucleation (respectively, annihilation) of one wavelength. When the driving amplitude is increased, the standing-wave pattern undergoes various instabilities, and in particular an oscillatory instability that corresponds to a one-dimensional compression mode of the periodic structure. This secondary instability is understood in the framework of the amplitude equation formalism.

Interactions of currents and weakly nonlinear water waves in shallow water

Abstract: Two-dimensional Boussinesq-type depth-averaged equations are derived for describing the interactions of weakly nonlinear shallow-water waves with slowly varying topography and currents. The current velocity varies appreciably within a characteristic wavelength. The effects of vorticity in the current field are considered. The wave field is decomposed into Fourier time harmonics. A set of evolution equations for the wave amplitude functions of different harmonics is derived by adopting the parabolic approximation. Numerical solutions are obtained for shallow-water waves propagating over rip currents on a plane beach and an isolated vortex ring. Numerical results show that the wave diffraction and nonlinearity are important in the examples considered.

The Perturbation Method in Elastic Wave Scattering

Abstract: Methods of theoretical study in seismic wave scattering are reviewed with the emphasis on the perturbation method. Detailed analysis for weak scattering using Born approximation is given. For elastic random media, the mean square amplitudes of scattered waves are derived using a new approach by working directly in the spectrum domain. The conditions for the scalar wave approximation are obtained. The problem of sensitivity of fore- and backscattering to heterogeneities with different scales and properties (velocity or impedance) is discussed.

Ten Years of SS 433 Kinematics

Abstract: Observations of the highly Doppler shifted emission lines in SS 433 have now been obtained over a period of 10 years, and some inferences available from this data base are discussed. The nature of the instability in the 164-day precession clock remains obscure; a conservative conclusion is that the instability amplitude is not increasing. The higher frequency nodding motions of the accretion disk is used to set an upper limit on any change in the orbital period of the binary system to absolute value of P-d at 13 less than 10 to the -6th (2 sigma). This limit, almost a full order of magnitude more stringent than the previously published one, in turn constrains the mass loss rate through the relativistic jets, and the jet kinetic energy. The nature of the substantial residuals remaining in the Doppler shift observations is discussed when the best-fit models for the precission, nodding, and clock noise are removed; no further periodic components are evident. 27 refs.

Correlation with a spatial light modulator having phase and amplitude cross coupling.

Abstract: In correlation filtering a spatial light modulator is traditionally modeled as affecting only the phase or only the amplitude of light. Usually, however, a single operating parameter affects both phase and amplitude. An integral constraint is developed that is a necessary condition for optimizing a correlation filter having single parameter coupling between phase and amplitude. The phase-only filter is shown to be a special case.

Observations and modeling of the backscattering of short tone bursts from a spherical shell: Lamb wave echoes, glory, and axial reverberations

Abstract: Tone bursts having durations of 3 or 4 cycles were incident on an air‐filled stainless steel shell in water. The resulting sequence of echoes included a specular reflection and echoes radiated by Lamb waves on the shell. Echo structure was studied for ka of 24 to 75, where a denotes the outer radius; b/a=0.838, where b denotes the inner radius. The amplitudes of Lamb wave echoes were modeled using an elastic generalization of the geometrical theory of diffraction (GTD) [P. L. Marston, J. Acoust. Soc. Am. 83, 25–37 (1988)]. The required Lamb wave parameters (the phase velocity cl and damping βl ) were found by the Sommerfeld–Watson method; an efficient numerical method for the computation of the required complex root νl is described. The echoes were identified by comparing arrival times with predictions; bursts reflected from a solid tungsten carbide sphere were used for a reference amplitude. Measurements with ka=24 of the largest Lamb wave echo (which was due to a flexural wave) were made at various back...

Time evolution from linear to nonlinear stages in magnetohydrodynamic parametric instabilities

Abstract: The nonlinear evolution of the magnetohydrodynamic (MHD) parametric instability of wave fluctuations propagating along an unperturbed magnetic field is investigated. Both a magnetohydrodynamic perturbation‐theoretical approach and a nonlinear MHD simulation are used. It is shown that high harmonic waves are rapidly excited by wave–wave coupling, and that the wave spectrum evolves from a state containing a small number of degrees of freedom in k space to one which contains a large number of degrees of freedom. It is found that the spectral evolution prior to nonlinear saturation is well described by the perturbation theory. During this stage, the ratio of the growth rate of the nth harmonic wave to the linear growth rate of the fundamental wave is n. The nonlinear saturation stage is characterized by a frequency shift of the fundamental wave that destroys the wave–wave resonance condition which, in turn, causes the wave amplitude to cease its growth.

The Two-Mode Approximation to Nonlinear Acoustics in Combustion Chambers I. Exact Solution for Second Order Acoustics

Abstract: The behavior of unsteady pressure fluctuations in combustion chambers is examined. An approximate method used in the derivation of the amplitude equations is based on the spatial and time domain averaging of the conservation equations, and follows the analytical framework introduced by Culick (1976a,b). The first order perturbation terms retained in the analysis correspond to linear contributions from the combustion processes, gas/particle interactions, mean flow and boundary conditions, as well as second order nonlinear gas dynamics terms. Further simplification of these equations is obtained by an appropriate change of variables. Following this step, the analysis based on two longitudinal modes is reduced to the solution of a three-dimensional system of nonlinear equations. This enables derivation of exact results for the existence, stability and the amplitude of the limit cycle, in the general case of frequency shifted periodic oscillations. Consideration is also given to the transfer of energy within the spectrum of the acoustic modes. In agreement with experimental observations, it is shown analytically that the preferred direction of energy transfer is from the lower to the higher acoustic modes. Validation of the results is accomplished by comparison with numerical results obtained when higher numbers of modes are treated. Finally, it is shown that combustion instabilities can be treated analytically using the center manifold theory.

Effects of two-dimensional topographies using the discrete wavenumber-boundary integral equation method in P-SV cases

Abstract: The effect of topography on surface motion is studied in the case of incident P and SV waves and in presence of an explosive source. The discrete wavenumber‐boundary integral equation method is formulated for this case and is applied to the problem of diffraction of an elastic wave field by a ridge‐shaped topography. The amplitude of the scattered field, which mostly consists of surface P waves and Rayleigh waves, is strongly dependent on the steepness of the topography. The generation of surface waves by an explosion located in the vicinity of the ridge topography is studied and an increase in Rayleigh wave amplitude and a broadening of the Rayleigh pulse when the explosion occurs within the ridge is found.

Nonlinear Faraday resonance in a box with a square base

Abstract: Surface wave motions in a container with a square base, which is subject to a vertical oscillation, are considered when the amplitude of the oscillation is small and the frequency of the oscillation is close to twice the natural frequency of the system. Subcritical wave motions are found for single modes as well as mixed modes. Here, single modes are described by either one of the two horizontal coordinates whereas mixed modes depend on both coordinates. It is found that in some subcritical region a stable single mode and a stable mixed mode coexist, producing complex basins of attraction.