Showing papers on "Amplitude published in 1991"

The determination of the seismic quality factor q from vsp data: a comparison of different computational methods1

Abstract: Ten methods for the computation of attenuation have been investigated, namely: amplitude decay, analytical signal, wavelet modelling, phase modelling, frequency modelling, rise-time, pulse amplitude, matching technique, spectral modelling and spectral ratio. In particular, we have studied the reliability of each of these methods in estimating correct values of Q using three synthetic VSP seismograms for plane P-waves with different noise contents. The investigations proved that no single method is generally superior. Rather, some methods are more suitable than others in specific situations depending on recording, noise or geology. The analytical signal method has been demonstrated to be superior if true amplitude recordings are available. Otherwise spectral modelling or, in the ‘ noise-free’ case the spectral ratio method, is optimal. Finally, two field VSPs in sediments are investigated. Only in the case of the highest quality VSP can significant information be deduced from the computed attenuation.

Estimation and classification of polynomial-phase signals

Abstract: The measurement of the parameters of complex signals with constant amplitude and polynomial phase, measured in additive noise, is considered. A novel new integral transform that is adapted for signals of this type is introduced. This transform is used to derive estimation and classification algorithms that are simple to implement and that exhibit good performance. The algorithms are extended to constant amplitude and continuous nonpolynomial phase signals. >

A measurement of the mass fluctuation spectrum from the cluster X-ray temperature function

Abstract: A statistically complete sample of galaxy clusters is presented which also has complete X-ray temperature information. Using this sample, the cluster bolometric luminosity and temperature functions are derived. The temperature function constrains the shape and amplitude of the mass fluctuation power spectrum. For a power law, i.e., with the fluctuation power spectrum proportional to k exp n, n = {minus}(1.7 + 0.65, {minus} 0.35), and an amplitude is obtained which implies that the rms value of {delta}{minus}M/M is 0.59 + or {minus} 0.02 on a scale of 8/h Mpc at the present epoch. 31 refs.

The Cramer-Rao lower bound for signals with constant amplitude and polynomial phase

Abstract: The authors derive the Cramer-Rao lower bound (CRLB) for complex signals with constant amplitude and polynomial phase, measured in additive Gaussian white noise. The exact bound requires numerical inversion of an ill-conditioned matrix, while its O(N/sup -1/) approximation is free of matrix inversion. The approximation is tested for several typical parameter values and is found to be excellent in most cases. The formulas derived are of practical value in several radar applications, such as electronic intelligence systems (ELINT) for special pulse-compression radars, and motion estimation from Doppler measurements. Consequently, it is of interest to analyze the best possible performance of potential estimators of the phase coefficients, as a function of signal parameters, the signal-to-noise ratio, the sampling rate, and the number of measurements. This analysis is carried out. >

The Density Perturbation in the Chaotic Inflation with Non-Minimal Coupling

Abstract: We formulate a method to rigorously evaluate the density perturbation amplitude in inflation models with non-canonical gravity. As a specific example but which contains essential features of non-canonical models, the density perturbation in the λφ^4 chaotic inflation model with non-minimal coupling ξRφ^2 is carefully investigated in terms of the Hamiltonian formalism for constrained systems. We utilize a particular conformal transformation under which the original system with a non-minimally coupled scalar field is transformed into one with a minimal coupling and derive a reduced Hamiltonian for scalar-type perturbations (which describe density perturbations) in which only the dynamical degrees of freedom are contained. We then evaluate the amplitude of density perturbations arising from vacuum fluctuations of the system. We find the amplitude in the conformally transformed metric exactly agrees with that in the original metric. Thus the result obtained in the previous papers by a rather crude approach is confirmed in a more rigorous manner; i.e., the constraint on λ is weakened if ξ is large.

Microtransport induced by ultrasonic Lamb waves

Abstract: We have observed pumping of water induced by 4.7 MHz ultrasonic Lamb waves traveling in a 4‐μm‐thick composite membrane of silicon nitride and piezoelectric zinc oxide. The observed pumping speed is proportional to the square of the wave amplitude; the speed was 100 μm/s for a rf drive voltage of 8 V and a 6.5 nm wave amplitude. A nonlinear model based on acoustic streaming theory predicts velocities in good agreement with experiment.

Arbitrary-amplitude electron-acoustic solitons in a two-electron-component plasma

Abstract: Motivated by plasma and wave measurements in the cusp auroral region, we have investigated electron-acoustic solitons in a plasma consisting of fluid ions, a cool fluid electron and a hot Boltzmann electron component. A recently described method of integrating the full nonlinear fluid equations as an initial-value problem is used to construct electron-acoustic solitons of arbitrary amplitude. Using the reductive perturbation technique, a Korteweg-de Vries equation, which includes the effects of finite cool-electron and ion temperatures, is derived, and results are compared with the full theory. Both theories admit rarefactive soliton solutions only. The solitons are found to propagate at speeds greater than the electron sound speed (e0c/e0e)½υe, and their profiles are independent of ion parameters. It is found that the KdV theory is not a good approximation for intermediate-strength solitons. Nor does it exhibit the fact that the cool- to hot-electron temperature ratio restricts the parameter range over which electron-acoustic solitons may exist, as found in the arbitrary-amplitude calculations.

Experimental and theoretical investigation of large-amplitude oscillations of liquid droplets

Abstract: Finite-amplitude, axially symmetric oscillations of small (0.2 mm) liquid droplets in a gaseous environment are studied, both experimentally and theoretically. When the amplitude of natural oscillations of the fundamental mode exceeds approximately 10% of the droplet radius, typical nonlinear effects like the dependence of the oscillation frequency on the amplitude, the asymmetry of the oscillation amplitude, and the interaction between modes are observed. As the amplitude decreases due to viscous damping, the oscillation frequency and the amplitude decay factor reach their asymptotical values predicted by linear theory. The initial behaviour of the droplet is described quite satisfactorily by a proposed nonlinear inviscid theoretical model.

Square patterns and secondary instabilities in driven capillary waves

Abstract: Amplitude equations (including nonlinear damping terms) are derived which describe the evolution of patterns in large-aspect-ratio driven capillary wave experiments. For drive strength just above threshold, a reduction of the number of marginal modes (from travelling capillary waves to standing waves) leads to simpler amplitude equations, which have a Lyapunov functional. This functional determines the wavenumber and symmetry (square) of the most stable uniform state. The original amplitude equations, however, have a secondary instability to transverse amplitude modulation (TAM), which is not present in the standing-wave equations. The TAM instability announces the restoration of the full set of marginal modes.

Controlling chaos in spin-wave instabilities

Abstract: A microwave-pumped spin-wave-instability experiment is used to demonstrate that chaos can be controlled by a small periodic perturbation of an available system parameter, as recently proposed by Ott, Grebogi, and Yorke The experiment is performed in an yttrium-iron-garnet sphere in the subsidiary-resonance configuration with a small modulation in the applied magnetic field Observation of the Fourier spectrum of the low-frequency auto-oscillations and measurment of the attractor dimension and metric entropy demonstrate clearly that the chaotic attractor becomes periodic when the modulation frequency and amplitude are carefully chosen

Electron Image Plane Off-axis Holography of Atomic Structures

Abstract: Fundamentally, Transmission Electron Microscopy is wave optics, i.e. the object structure is encoded in the amplitude and phase of the emergent electron wave, which is then transferred into the image wave by the subsequent lenses. In conventional microscopy, only the intensity, i.e. amplitude squared, is recorded, whereas the phase is lost. This gives rise to severe loss of information about the object structure. Therefore, electron holography, which furnishes amplitude and phase separately, offers the only path to a complete understanding of the object structure including atomic positions and species, as well as intrinsic electric and magnetic fields. By means of an electron biprism the image wave is superimposed on a coherent plane reference wave giving rise to an interference pattern called a “hologram”. The position of the electron biprism in the optical path has to be optimized with respect to both intended lateral resolution and field of view. By means of light optical or numerical image processing, the amplitude and phase of the image wave are reconstructed from the hologram. For interpretation of the image wave in terms of the object, one has to understand in detail not only the interaction with the object but also the transfer of the object wave into the image wave. The conversion of amplitude and phase of the object wave into amplitude and phase of the image wave by means of lenses is described; the aberrations of these lenses affect this process and holography allows us to correct these aberrations during the reconstruction of the wave from the recorded hologram. Performance, as measured by achievable resolution and field of view, is finally limited by the degree of lateral coherence, i.e., by the brightness of the electron source.

Amplitude model for the effects of mutations and temperature on period and phase resetting of the Neurospora circadian oscillator.

Abstract: This paper analyzes published and unpublished data on phase resetting of the circadian oscillator in the fungus Neurospora crassa and demonstrates a correlation between period and resetting behavior in several mutants with altered periods: As the period increases, the apparent sensitivity to resetting by light and by cycloheximide decreases. Sensitivity to resetting by temperature pulses may also decrease. We suggest that these mutations affect the amplitude of the oscillator and that a change in amplitude is responsible for the observed changes in both period and resetting by several stimuli. As a secondary hypothesis, we propose that temperature compensation of period in Neurospora can be explained by changes in amplitude: As temperature increases, the compensation mechanism may increase the amplitude of the oscillator to maintain a constant period. A number of testable predictions arising from these two hypotheses are discussed. To demonstrate these hypotheses, a mathematical model of a time-delay oscillator is presented in which both period and amplitude can be increased by a change in a single parameter. The model exhibits the predicted resetting behavior: With a standard perturbation, a smaller amplitude produces type 0 resetting and a larger amplitude produces type 1 resetting. Correlations between period, amplitude, and resetting can also be demonstrated in other types of oscillators. Examples of correlated changes in period and resetting behavior in Drosophila and hamsters raise the possibility that amplitude changes are a general phenomenon in circadian oscillators.

Growth of alternate bars in unsteady flow

Abstract: A theoretical model is formulated to investigate the development of the amplitude of alternate bars in unsteady flows The problem is tackled by means of a weakly nonlinear analysis developed in a neighborhood of the threshold conditions for bar formation Bar response to unsteady flow is found to depend on a parameter that is a measure of the ratio between the time scale of the basic flow and the time scale of bar growth The present theory shows that if is O(1), as often occurs in nature, flow unsteadiness affects the instantaneous growth rate and phase of bar perturbations and controls the final amplitude reached by the bed configuration A procedure for determining the final amplitude for a given flood event is proposed Flume experiments were performed to test the main theoretical results The bed response to unsteady flow was measured for different values of the period of the flood The observed temporal behavior of the bar amplitude proves to be strongly affected by the unsteady character of the flow for of O(1), as predicted by the theory

Response of the shear layers separating from a circular cylinder to small-amplitude rotational oscillations

Abstract: The frequency response of the shear layers separating from a circular cylinder subject to small-amplitude rotational oscillations has been investigated experimentally in water for the Reynolds number (Re) range 250 to 1200. A hot-film anemometer was placed in the separated shear layers from 1 to 1.5 diameters downstream of the cylinder, and connected to a lock-in analyser. by referencing the lock-in analyser to the cylinder oscillations, the amplitude and phase of the response to different frequency oscillations were measured directly. It is shown that rotational oscillations corresponding to cylinder peripheral speeds between 0.5 and 3% of the free stream can be used to influence the primary (Karman) mode of vortex generation. For Re greater than ≈ 500, such oscillations can also force the shear-layer vortices associated with the instability of the separating shear layers. Corresponding to the primary and shear-layer modes are two distinct peaks in response amplitude versus frequency curves, and two very different phase versus frequency curves. The response of the shear layers (and near wake) in the range of Karman frequency suggests qualitative similarities with the response of an oscillator near resonance. Forced oscillations in the higher-frequency shear-layer mode range are simply convected by the shear layers. Close to the cylinder, the shear-layer response is shown to be comparable to that of generic free shear layers studied by others.

The minimum multimodal radiation efficiency of baffled finite beams

Abstract: A technique for deriving the optimal surface velocity distribution on the surface of a finite baffled beam has been developed. The optimal velocity distribution minimizes the radiation efficiency of the beam for a specified maximum permissible mode and frequency. A modal expansion of the surface velocity in terms of unknown modal amplitude coefficients, the Rayleigh integral, and a far‐field intensity integration are employed to obtain a quadratic expression for the radiation efficiency of the beam. Application of a suitable constraint to avoid trivial solutions leads to an eigenvalue problem identical in form to the Rayleigh quotient employed in dynamic mechanical systems. The eigenvector of modal amplitude coefficients corresponding to the lowest eigenvalue yields the minimum radiation efficiency, while the eigenvalue itself is the actual value of the minimum radiation efficiency. Near and below coincidence, the optimal eigenvector of modal amplitude coefficients yields a radiation efficiency significantly less than the radiation efficiency of any single modal component acting alone. Simply supported and clamped–clamped boundary conditions are considered, and numerical examples are presented for each.

Calibration of a magnetic direction finding network using measured triggered lightning return stroke peak currents

Abstract: Peak currents from 18 triggered lightning return strokes lowering negative charge have been measured at the NASA Kennedy Space Center, Florida. These strokes are correlated with simultaneous measurements by six Lightning Location and Protection (LLP) Inc. wideband magnetic direction finders (DFs) in Georgia and Florida operating at high gain from 1985 through 1988. The following have been determined: (1) The normalized signal strength amplitudes, in LLP units, can be used to estimate the peak current in lightning return strokes by the relation, I(kA) = 2.3+0.19(Normalized Amplitude), where the amplitude is range-normalized to 100 km. An approximation of the form, I(kA) = 0. 2(Normalized Amplitude) is also valid, introducing errors of typically less than 6 %. (2) Range-normalized signal strength amplitudes, in LLP units, for individual DFs have been examined as a function of the measured return stroke peak currents. It is found that a DFs normalized amplitude has a higher correlation with peak currents, the further the DF site is from the triggered lightning. The correlation coefficients range from 0.53 to 0.93, At a DF site the standard deviation of the normalized amplitudes from the best fit line to the measured peak currents are independent of the DF site's distance from the triggered lightning, averaging 28 LLP units, which corresponds to 6 kA. (3) Signal strength amplitudes, which are proportional to the peak magnetic radiation fields, have been examined for seven triggered lightning return strokes. The signal strength amplitudes decay with distance, D, as D−1.13. (4) An evaluation of the error in the mean range-normalized signal strength amplitude caused by lightning location errors reveals that the mean amplitude is typically in error by less than 2% from the value calculated using the exact location of the triggered flash.

Guiding-center soliton in fibers with periodically varying dispersion.

Abstract: The guiding-center (or the averaged) amplitude υ(T, Z) of the optical soliton is derived in the presence of periodic amplification and periodic variation of the fiber dispersion. It is also shown that υ(T, Z) permits a solitary-wave solution to all orders of Za/Z0. This result further confirms the stability of optical solitons in fibers under periodic perturbations.

On the evolution of a wave packet in a laminar boundary layer

Abstract: The transition process of a small-amplitude wave packet, generated by a controlled short-duration air pulse, to the formation of a turbulent spot is traced experimentally in a laminar boundary layer. The vertical and spanwise structures of the flow field are mapped at several downstream locations. The measurements, which include all three velocity components, show three stages of transition. In the first stage, the wave packet can be treated as a superposition of two- and three-dimensional waves according to linear stability theory, and most of the energy is centred around a mode corresponding to the most amplified wave. In the second stage, most of the energy is transferred to oblique waves which are centred around a wave having half the frequency of the most amplified linear mode. During this stage, the amplitude of the wave packet increases from 0.5 % to 5 % of the free-stream velocity. In the final stage, a turbulent spot develops and the amplitude of the disturbance increases to 27 % of the free-stream velocity.Theoretical aspects of the various stages are considered. The amplitude and phase distributions of various modes of all three velocity components are compared with the solutions provided by linear stability theory. The agreement between the theoretical and measured distributions is very good during the first two stages of transition. Based on linear stability theory, it is shown that the two-dimensional mode of the streamwise velocity component is not necessarily the most energetic wave. While linear stability theory fails to predict the generation of the oblique waves in the second stage of transition, it is demonstrated that this stage appears to be governed by Craik-type subharmonic resonances.

Amplitude and phase recording of ultrashort pulses

Abstract: The performance of a new method of measuring the amplitude and phase of ultrashort pulses is evaluated with simulated and real data.

Phase‐shifting electron holography by beam tilting

Abstract: A phase‐shifting method to directly measure the amplitude and phase distribution of specimen in an electron holographic microscope without the introduction of large number of carrier fringes is proposed. The initial phase of electron holograms is shifted by tilting the incident electron beam with a digital voltage/current supply. Several holograms of a specimen with properly different phase shifts are recorded digitally and used to calculate the amplitude and phase distributions of the specimen. Experimental result of observing the phase distribution of a cubic MgO crystal is shown.

Calibrating lasers for optical recording using a maximal readback signal amplitude as a criterion

Abstract: A magnetooptic recorder uses a magnetooptic disk for any predetermined number of radially inward tracks which are designated as calibration tracks. One of the calibration tracks is selected as a laser calibration track. The selected track is high powered erased and a test pattern is written on the track. A test pattern is repeated at diverse levels of laser recording power. A test pattern preferably includes or is limited to the highest frequency to be recorded in the ensuing data recordings. The recorded test pattern is read back with the readback signal amplitude being envelope indicated and detected. A table of signal envelope values is created in a digital computer. The values then are fit to a curve using second order polynomial curve fitting techniques. The maximal readback signal amplitude is then selected from the curve corresponding to laser write power used to obtain that maximum signal amplitude and is then selected as a criteria for indicating the laser write power as well as the erase write power.

Filament formation in semiconductor laser gain regions

Abstract: We have linearized the equations for propagation of the beam of light in a semiconductor optical amplifier about an operating point and have derived the rate of growth of small sinusoidal perturbations of the phase and modulus of the complex field amplitude. The perturbations grow if the spatial frequency is below a critical value that depends on the intensity of the field at the operating point. For spatial frequencies above the critical value, the perturbations die out. The critical spatial frequency decreases as the intensity increases above a certain value. In other words, the tendency to filament becomes weaker as the intensity increases above a certain value. Computer‐generated solutions of the propagation and gain equations are included to illustrate the growth of filaments as the plane‐wave intensity changes in an amplifier.

Instantaneous frequency and amplitude at the envelope peak of a constant-phase wavelet

Abstract: Robertson and Nogami (1984) have shown that the instantaneous frequency at the peak of a zero‐phase Ricker wavelet is exactly equal to that wavelet’s average Fourier spectral frequency weighted by its amplitude spectrum. Bodine (1986) gave an example which shows this is also true for constant‐phase bandpass wavelets. Here I prove that this holds for any constant‐phase wavelet. I then develop an equation expressing this quantity as a function of propagation time through an attenuating medium. A corresponding equation is derived for the amplitude of the envelope peak. Taken together, these may aid in the analysis of seismic data as suggested by Robertson and Nogami (1984), Bodine (1986), and Robertson and Fisher (1988).

Chaos and mixing in a geostrophic flow

Abstract: Experiments on Rossby waves on an azimuthal jet in a rapidly rotating annular tank reveal a striking barrier to mixing across the jet. A model based on the experiments assumes a two‐dimensional incompressible flow described by a time‐dependent streamfunction consisting of azimuthally propagating waves on a narrow jet. When there is only one wave, all Lagrangian particle trajectories are closed in the appropriate reference frame. When two independent waves are present, some trajectories are chaotic, and the size of the chaotic sea grows as the amplitude of the second wave is increased; however, at least one barrier to global transport—an invariant surface—prohibits trajectories from crossing the jet. The addition of a third wave is found to break the barrier only if the wave amplitudes exceed the width of the jet. In the experiment, the wave amplitude is typically about one‐half the jet width, and the barrier to mixing persists even at the highest accessible Reynolds numbers.