Showing papers on "Amplitude published in 1988"

Laser wakefield acceleration and relativistic optical guiding

Abstract: An electron acceleration method is investigated which employs a short (τL ∼2πωω−1p ∼1 ps), high‐power (P≥1015 W), single frequency laser pulse to generate large amplitude (E≥1 GeV/m) plasma waves (wakefields). At sufficiently high laser powers [P≥17(ω/ωp )2 GW], relativistic optical guiding may be used to prevent the pulse from diffracting within the plasma.

Spectral wave attenuation by bottom friction: theory

Abstract: Based on the linearized form of the boundary layer equations and a simple eddy viscosity formulation of shear stress, the turbulent bottom boundary layer flow is obtained for a wave motion specified by its directional spectrum. Closure is obtained by requiring the solution to reduce, in the limit, to that of a simple harmonic wave. The resulting dissipation is obtained in spectral form with a single friction factor determined from knowledge of the bottom roughness and an equivalent monochromatic wave having the same root-mean-square near-bottom orbital velocity and excursion amplitude as the specified wave spectrum. The total spectral dissipation rate is obtained by integration and compared with the average dissipation obtained from a model considering the statistics of individual waves defined by their maximum orbital velocity and zero-crossing period. The agreement between the two different evaluations of total spectral dissipation supports the validity of the spectral dissipation model.

Resonance of a fluid-driven crack: Radiation properties and implications for the source of long-period events and harmonic tremor

Abstract: A dynamic source model is presented, in which a three-dimensional crack containing a viscous compressible fluid is excited into resonance by an impulsive pressure transient applied over a small area ΔS of the crack surface. The crack excitation depends critically on two dimensionless parameters called the crack stiffness, C = (b/μ)(L/d), and viscous damping loss, F = (12ηL)/(ρƒd2α), where b is the bulk modulus, η is the viscosity, ρƒ is the density of the fluid, μ is the rigidity, α is the compressional velocity of the solid, L is the crack length, and d is the crack thickness. The first parameter characterizes the ability of the crack to vibrate and shapes the spectral signature of the source, and the second quantifies the effect of fluid viscosity on the duration of resonance. Resonance is sustained by a very slow wave trapped in the fluid-filled crack. This guided wave, called the crack wave, is similar to the tube wave propagating in a fluid-filled borehole; it is inversely dispersive, showing a phase velocity that decreases with increasing wavelength, and its wave speed is always lower than the acoustic velocity of the fluid, decreasing rapidly as the crack stiffness increases. The source spectrum shows many sharp peaks characterizing the individual modes of vibration of the crack; the variation of spectral shape, both in the number and width of peaks, is surprisingly complex, reflecting the interference between the lateral and longitudinal modes of resonance, as well as nodes for these modes. The far-field spectrum is marked by narrow-band dominant and subdominant peaks that reflect the interaction of the various source modes. The frequency of the dominant spectral peak radiated by the source is independent of the radiation direction. The frequency, bandwidth, and spacing of the resonant peaks are strongly dependent on the crack stiffness, larger values of the stiffness factor shifting these peaks to lower frequencies and decreasing their bandwidth. The excitation of a particular mode depends on the position of the trigger and on the extent of the crack surface affected by the pressure transient. Fluid viscosity decreases the amplitudes of the main spectral peaks, smears out the finer structure of the spectrum, and greatly reduces the duration of the radiated signal. The energy loss by radiation is stronger for high frequencies, producing a seismic signature that is marked by a high-frequency content near the onset of the signal and dominated by a longer-period component of much longer duration in the signal coda. Such signature is in harmony with those displayed by long-period events observed on active volcanoes and in hydrofracture experiments. The very low velocity which is possible in a crack with high stiffness (C ≥ 100) also provides an attractive explanation for very long period tremor, such as type 2 tremor at Aso volcano, Japan, without the requirement of an unrealistically large magma container. The standing wave pattern set up on the crack surface by the sustained resonance in the fluid is observable in the near field of the crack, suggesting that the location and extent of the source may be estimated from the mapping of the pattern of nodes and antinodes seen in its vicinity. According to the model, the long-period event and harmonic tremor share the same source but differ in the boundary conditions for fluid flow and in the triggering mechanism setting up the resonance of the source, the former being viewed as the impulse response of the tremor generating system and the latter representing the excitation due to more complex forcing functions.

Stability of solitons in birefringent optical fibers. II. Arbitrary amplitudes

Abstract: Propagation of short pulses in birefringent single-mode fibers is considered. Initial pulses are assumed to be linearly polarized at an arbitrary angle with respect to the polarization axes. The Kerr nonlinearity leads to a substantial interaction between the partial pulses in each of the two polarizations. When the amplitudes of the partial pulses are equal, it is found that above a certain amplitude threshold, whose size increases with birefringence, the two partial pulses lock together and travel as one unit. This unit can be a single soliton or, at higher amplitudes, a breather. At the same time, the central frequencies of both polarizations shift just far enough so that, if a rapid oscillation is ignored, their group velocities become identical. When the initial amplitudes are unequal, it is found as before that above a certain threshold one or more solitons emerge from the initial pulse. However, the breathers that appeared when the amplitudes were equal are unstable; they break up into two distinct solitons moving at different velocities when the amplitudes become slightly unequal. It is further shown that realistic fiber attenuation has little effect on these results. The numerical method used to obtain these results is described in detail.

On vortex formation from a cylinder. part 1: the initial instability

Abstract: Vortex shedding from a circular cylinder is examined over a tenfold range of Reynolds number, 440 ≤ Re ≤ 5040. The shear layer separating from the cylinder shows, to varying degrees, an exponential variation of fluctuating kinetic energy with distance downstream of the cylinder. The characteristics of this unsteady shear layer are interpreted within the context of an absolute instability of the near wake. At the trailing-end of the cylinder, the fluctuation amplitude of the instability correlates well with previously measured values of mean base pressure. Moreover, this amplitude follows the visualized vortex formation length as Reynolds number varies. There is a drastic decrease in this near-wake fluctuation amplitude in the lower range of Reynolds number and a rapid increase at higher Reynolds number. These trends are addressed relative to the present, as well as previous, observations.

Time-domain response of a semi-circular canyon for incident SV, P, and Rayleigh waves calculated by the discrete wavenumber boundary element method

Abstract: The responses of a semi-circular canyon for incident SH, SV, P , and Rayleigh waves in a two-dimensional elastic half-space are investigated in time domain as well as in frequency domain. The author proposes the discrete wavenumber boundary element method, in which the direct boundary element method is used with the discrete wavenumber Green's function. This combination achieves both the efficiency in computation and the flexibility for boundary configurations. First, the validity of the method is confirmed by comparing its results with published ones in frequency domain. Then time histories of seismic motion along the surface in and around the canyon are studied for incident SH, SV, P , and Rayleigh waves with the shape of a Ricker wavelet. In all cases, the diffracted waves called the creeping waves can be seen propagating inside the canyon with P - or S -wave velocity. For SV -wave incidence, Rayleigh waves generated at the edges of the canyon carry a significant portion of energy outward, while for SH -wave incidence the direct and reflected waves play a major role. It should be noted that the amplitude fluctuation in frequency domain does not always mean that in time domain because different arrival time of wavelets results in the fluctuation in spectral amplitude even if each wavelet propagates with the same shape and amplitude.

Reheat buzz: an acoustically coupled combustion instability. Part 1. Experiment

Abstract: Reheat buzz is a combustion instability which occurs in the afterburners of jet aeroengines. Similar oscillations have been observed on a laboratory rig in which a confined flame is stabilized in the wake of a conical gutter. The source of energy for the instability is the unsteady heat release as the flame responds to velocity fluctuations in the approach flow. The amount of energy fed into the instability is determined primarily by the phase relationship between the unsteady heat release rate and pressure fluctuations. Two types of relationship between pressure and heat release have been observed. In the first kind, perturbations in heat release rate convect downstream from the lip of the flame stabilizer at the axial velocity of the cold reactants. In the second type, which occurs downstream of the first, the phase of the heat release rate at the buzz frequency is constant and close to the phase of the unsteady pressure. The characteristics of the resulting instability depend on which of these occupies the larger portion of the duct. Consequently two types of instability exist and the transition between them occurs sharply, with little change in mean flow conditions. The transition is associated with an abrupt change in buzz amplitude and frequency as well as with a change in the shape of the modal distributions.

A numerical model of the combined wave and current bottom boundary layer

Abstract: A numerical model of oscillatory rough-turbulent boundary layer flow, featuring closure via the turbulent energy equation, is used to examine the principal features of wave-current interaction above the seabed. Results are presented from case studies carried out with water depth of 10 m, bed roughness of 0.5 cm and wave period of 8 s. The steady surface current in the absence of waves is nominally 100 cm/s, and waves having near-bottom velocity amplitudes of 50, 100, and 150 cm/s are superimposed on this current at angles ϕ = 0, π/4, and π/2. Velocity, turbulent energy, shear stress, and eddy viscosity distributions are compared for the steady current alone, for waves alone, and for waves superimposed on the current, and the interaction in the wave-current boundary layer is examined. Cycle-averaged vertical profiles of horizontal velocity illustrate the extent to which the mean flow is retarded by wave-current interaction. For the general case in which the waves are superimposed at an arbitrary angle ϕ, the mean current veers to form an angle with the wave direction greater than that of the initial steady current. Finally, the enhancement of the bed shear stress and the increase in oscillatory boundary layer thickness associated with wave-current interaction are both quantified.

Dynamics of phase-locked semiconductor laser arrays

Abstract: Time‐dependent coupled mode theory is used to investigate the stability of phase‐locked semiconductor laser arrays. The output of individual array elements is dynamically unstable and exhibits large amplitude chaotic pulsations. The total output initially exhibits damped relaxation oscillations and then settles down to a quasi‐steady state characterized by small amplitude fluctuations. The theory predicts both the pulsation frequency and the phase lock‐in time of the array.

Fourier transform mechanical spectroscopy of viscoelastic materials with transient structure

Abstract: A new technique is presented to measure the frequency dependent complex modulus simultaneously at several frequencies instead of consecutively as in a frequency sweep. For this purpose, the strain in a dynamical mechanical experiment is prescribed as a superposition of several different modes (three in our case). The resulting stress is decomposed into sinusoidal components, each of them characterized by their frequency, amplitude, and phase shift with respect to the corresponding strain component. Phase shift and amplitude are expressible in a frequency dependent complex modulus. A single experiment gives, therefore, values for the complex modulus at a set of prescribed frequencies. The method was demonstrated on three stable viscoelastic fluids and was applied to determine the instant of sol-gel transition (gel point) of a crosslinking polymer.

Angular dependent post-collision interaction in Auger processes

Abstract: We have reformulated the theory of post-collision interaction (PCI) for Auger-decay following inner-shell photoionisation in order to take the time into account with the Auger-electron need to overtake the slow electron. The energy-shift of the Auger-electron due to PCI is calculated by solving in a reasonable approximation the classical equation of motion for the Auger electron. In contrast to the theory of Russek and Mehlhorn we derive analytical expressions for the transition amplitude, the line shape and the line shift of the Auger-electrons. If in our model the Auger electron and the slow electron are treated uncorrelated in direction our analytical expressions agree well with the numerical results of Russek and Mehlhorn. However if we account for directional electron-electron correlations, we show that deviations from the theory of Russek and Mehlhorn are to be expected. The possibility of detecting these deviations is discussed.

Weak nonlinear electromagnetic waves and low-frequency magnetic-field generation in electron-positron-ion plasmas

Abstract: The weakly nonlinear localization of obliquely modulated high-frequency electromagnetic waves in an electron-positron-ion plasma is considered. It is shown that the amplitude of the wave turns out to be a strongly dependent function of the angle between the slow modulations and the fast spatial variations and that the possibility appears of spontaneous generation of low-frequency magnetic fields. These magnetic fields are also functions of this angle and of the high-frequency wave polarization. The analysis of colinear modulation in electron-positron plasmas shows that some restriction must be made regarding the validity of previous calculations.

Wave-breaking amplitude of relativistic oscillations in a thermal plasma.

Abstract: The maximum amplitude of relativistic plasma oscillations (${\ensuremath{\upsilon}}_{\mathrm{ph}}$ near $c$) is obtained with a combined one-dimensional waterbag and warm-fluid model. The waterbag description is used to obtain expressions for the pressure and internal energy as functions of the proper density. A relativistic Euler's equation that is valid for arbitrarily large amplitudes and an analytic expression for the wave-breaking amplitude in the limit ${\ensuremath{\upsilon}}_{\mathrm{ph}}\ensuremath{\cong}c$ are obtained. Even a small amount of thermal energy can significantly reduce the maximum plasma-wave amplitude relative to the cold wave-breaking value. The significance of the results for recent accelerator schemes is discussed.

Observations of 20-Day Period Meridional Current Oscillations in the Upper Ocean along the Pacific Equator

Abstract: Prominent oscillations of the meridional current, with a mean period of approximately 20 days, have been observed in the upper ocean over several years from May 1979 to October 1985 using moored current measurements along the Pacific equator at 95°, 110°, 124°,140°W and 152°W, as well as off (but near) the equator at 110° and 140°W. The fluctuations are relatively narrowband (±0.005 cpd) in frequency. A 95% statistically significant peak in power spectra of meridional current occurred at 110°, 124° and 140°W, but not at 95° and 152°W where the spectral peaks were smaller. The dominant wave period decreased by about 4% from 110° to 140°W. Maximum amplitude was measured at 124°W; the amplitude above 80 m was maximum at the equator and decreased poleward from the equator. At 15 m the annual averaged root-mean-square amplitude was about 20.5 cm s−1, and individual peak-to-trough values reached 150 cm s−1. The wave amplitude decreased with depth and the wave was essentially confined to the upper 80 m....

Small-scale structure in the lithosphere and asthenosphere deduced from arrival time and amplitude fluctuations at NORSAR

Abstract: We analyze the pattern of phase and amplitude variations of seismic waves across the NORSAR array on a statistical basis in order to determine the statistical distribution of heterogeneities under NORSAR. Important observables that have been analyzed in the past are the phase (or travel time) and log amplitude variances and the transverse coherence functions (TCFs) of phase and amplitude fluctuations. We propose and develop the theory and methods of using other observables to reduce the degree of nouniqueness and increase the spatial resolution of the analysis. Most important are the angular coherence functions (ACFs), which characterize quantitatively the change in the pattern of fluctuations across the array from one incoming angle (or beam) to another and which have a different sensitivity to the depth distribution of heterogeneities than the TCFs. A combination of the ACFs and TCFs allows estimation of the power spectra of the P wave speed variations under the array as a function of depth. We use data for phase fluctuations from 104 incident beams and amplitude fluctuations from 185 beams with 2-Hz center frequency at NORSAR to calculate the three ACFs and three TCFs (of phase, log amplitude, and their cross coherence). The measured rms travel time fluctuation is 0.135 s, and the rms log amplitude fluctuation is 0.41. The half-coherence widths of the ACFs are 3° for log amplitude and 9° for phase. The half-coherence widths of the TCFs are 18 km for phase and less than the minimum separation between the elements of the array for log amplitude. In order to account for these features of the data, we adopt a two-overlapping-layer model for lithospheric and asthenospheric heterogeneities underneath NORSAR, with spectra that are band-limited between the wavelengths of 5.5 and 110 km. Our best model has an upper layer with a flat power spectrum extending from the surface to about 200 km, and a lower layer with a K−4 power spectrum extending from 15 to 250 km. The latter spectrum corresponds to an exponential correlation function with scale larger than the observation aperture (110 km). The rms P wave speed variations the in the range 1–4%. The small scale heterogeneities may be attributed to clustered cracks or intrusions; the larger-scale wavespeed heterogeneities are temperature or compositional heterogeneities that may be related to chemical differentiation, or dynamical processes in the boundary layer of mantle convection.

Large‐Scale waveform inversions of surface waves for lateral heterogeneity: 2. Application to surface waves in Europe and the Mediterranean

Abstract: Linear surface wave scattering theory is used to reconstruct the lateral heterogeneity under Europe and the Mediterranean using surface wave data recorded with the Network of Autonomously Recording Seismographs (NARS). The waveform inversion of the phase and the amplitude of the direct surface wave leads to a variance reduction of approximately 40% and results in phase velocity maps in the period ranges 30–40 s, 40–60 s and 60–100 s. A resolution analysis is performed in order to establish the lateral resolution of these inversions. Using the phase velocity perturbations of the three period bands, a two-layer model for the S velocity under Europe and the Mediterranean is constructed. The S′ velocity perturbations in the deepest layer (100–200 km) are much more pronounced than in the top layer (0–100 km), which confirms that the low-velocity zone exhibits pronounced lateral variations. In both layers the S velocity is low under the western Mediterranean, while the S velocity is high under the Scandinavian shield. In the deepest layer a high S velocity region extends from Greece under the Adriatic to northern Italy. Several interesting smaller features, such as the Massif Central, are reconstructed. One of the spectacular features of the reconstructed models is a sharp transition in the layer between 100 and 200 km near the Tornquist-Tesseyre zone. This would indicate that there is a sharp transition at depth between Central Europe and the East European platform. The waveform inversion of the surface wave coda leads to good waveform fits, but the reconstructed models are chaotic. This is due both to a lack of sufficient data for a good imaging of the surface wave energy on the heterogeneities and to an appreciable noise component in the surface wave coda.

Late Pleistocene paleoclimatology of the central equatorial Pacific: Sea surface response to the southeast Trade Winds

Abstract: Proxy indicators of sea surface temperature and equatorial divergence based on radiolarian assemblage data, and of trade wind intensity based on eolian grain size data show similar aspects of variability during the late Pleistocene: All indicators fluctuate at higher frequencies than the 100,000-year glacial-interglacial cycle, display reduced amplitude variations since 300,000 years ago, exhibit a change in the record character at about 300,000 years ago (the mid-Brunhes climatic event), and have higher amplitude variations in sediments 300,000–850,000 years old. Time series analyses were conducted to determine the spectral character of each record (δ18O of planktonic foraminifer, sea surface temperature values, equatorial divergence indicators, and wind intensity indicators) and to quantify interrecord coherence and phase relationships. The record was divided at the 300,000-year clear change in climatic variability (nonstationarity). The δ18O-based time scale is better lower in the core so our spectral analyses concentrated on the interval from 402,000–774,000 years. The δ18O spectra show 100,000- and 41,000-year power in the younger portion, 0–300,000 years, and 100,000-, 41,000- and 23,000-year power in the older interval, all highly coherent and in phase with the SPECMAP average stacked isotope record. Unlike the isotope record the dominant period in both the eolian grain size and equatorial divergence indicators is 31,000 years. This period is also important in the sea surface temperature signal where the dominant spectral peak is 100,000 years. The 31,000-year spectral component is coherent and in phase between the eolian and divergence records, confirming the link between atmospheric and ocean surface circulation for the first time in the paleoclimate record. Since the 31,000-year power appears in independent data sets within this core and also appears in other equatorial records [J. Imbrie personal communication, 1987], we assume it to be real and representative of both a nonlinear response to orbital forcing, possibly a combination of orbital tilt and eccentricity, and some resonance phenomenon required to amplify the response at this period so that it appears as a dominant frequency component. The mid-Brunhes climatic event is an important aspect of these records, but its cause remains unknown.

The turbulent layer in the water at an air—water interface

Abstract: The velocity fields beneath an air—water interface have been determined in a laboratory facility for the cases of wind-generated waves, with wind speeds ranging from 1.5 to 13.1 m/s, and of wind-ruffled mechanically generated waves of about 22 mm amplitude and 1 Hz frequency, with wind speeds ranging from 1.7 to 6.2 m/s. The velocity was measured in a fixed frame of reference with a two-component, laser-Doppler anemometer. It was possible to determine the lengthscales and evaluate the behaviour of the mean, wave-related and turbulent components of the flows. The waves affect the mean flows, even though the profiles remain essentially logarithmic and the wave field conforms generally with the results of linear theory. In the wind-wave cases the turbulent quantities behave similarly to those in flows over flat plates. They have different trends in the mechanical-wave cases, suggesting a coupling between waves and turbulence. Finally, measured values of the mean wave-induced shear stress were negative, leading to an energy transfer from the waves to the mean flow.

L2 amplitude density method for multichannel inelastic and rearrangement collisions

Abstract: A new method for quantum mechanical calculations of cross sections for molecular energy transfer and chemical reactions is presented, and it is applied to inelastic and reactive collisions of I, H, and D with H2. The method involves the expansion in a square‐integrable basis set of the amplitude density due to the difference between the true interaction potential and a distortion potential and the solution of a large set of coupled equations for the basis function coefficients. The transition probabilities, which correspond to integrals over the amplitude density, are related straightforwardly to these coefficients.

Trapping of Low-Level Internal Gravity Waves

Abstract: The characteristics of internal gravity waves propagating on a layer of high stratification near the ground with a deeper, weakly stratified layer above are examined with the aid of a nonhydrostatic numerical model. Simulations are performed of a density current propagating into an environment with a typically observed thermodynamic structure and with no shear. These simulations indicate that the amplitude of the disturbance that forms ahead of the density current is limited considerably by the upward propagation of energy in the upper layer. To explain the large amplitude of observed gravity waves there must exist some additional mechanism, besides the weak stratification in the upper layer, to trap energy at low levels. A thorough examination of several observed gravity wave events suggested three commonly occurring mechanisms. The first mechanism, explored in a previous paper, occurs when winds in the upper layer oppose the wave motion. This reduces the Scorer parameter l2 = N2/(U − c)2 − U″/(...

Subharmonic resonance, pairing and shredding in the mixing layer

Abstract: An instability-wave analysis is presented to describe the spatial evolution of a fundamental mode and its subharmonic on an inviscid parallel mixing layer. It incorporates explicitly the weakly nonlinear interaction between the two modes. The computational finding that the development of the subharmonic, leading eventually to pairing or shredding, crucially depends on its phase relation with the fundamental is fully confirmed. Furthermore it is shown that a critical fundamental amplitude has to be reached before the (spatial) subharmonic becomes phase locked with the fundamental and exhibits a modified growth rate. Then the analysis is exploited to explain the occurrence of amplitude modulations in ‘natural’ mixing layers and to estimate the width of the subharmonic spectral peaks. Also, the case of oblique subharmonic waves is briefly touched upon. In the last part, ways are explored to model non-parallel effects, i.e. to handle the saturation of the rapidly growing subharmonic. Using this wave description, the role of mode interaction in the ‘vortex pairing’ and ‘shredding’ process is assessed.

Large amplitude quasi-stationary MHD modes in JET

Abstract: Oscillating MHD modes in JET are often observed to slow down as they grow and generally stop rotating (lock) when the amplitude exceeds a critical value, then continue to grow to large amplitudes (r/Bθ ~ 1%). The mode can grow early in the current rise or after perturbations, such as a pellet injection or a large sawtooth collapse, and maintain a large amplitude throughout the remainder of the discharge. Such large amplitude quasistationary MHD modes can apparently have profound effects on the plasma, including stopping central ion plasma rotation, reducing the amplitude and changing the shape of sawteeth, flattening the temperature profile around resonant q surfaces and reducing the stored energy. Perhaps most important, large amplitude locked modes are precursors to most disruptions. Some large amplitude modes can be avoided by proper programming of the q evolution. The apparent reasons for the mode locking in a particular location are discussed and a comparison with theory is made.

Rapid movements with reversals in direction. II: Control of movement amplitude and inertial load

Abstract: Transformations of the underlying movement control of rapid sequential (reversal) responses were examined as the movement amplitude (Experiment 1) and moment of inertia (Experiment 2) were altered, with constant movement time. Increases in amplitude and inertia were both met by sharply increased joint torques with a constant temporal structure, suggesting that the alterations may have been governed by a single gain parameter. The durations of various EMG bursts were essentially constant across changes in inertia, supporting a model in which the output of a fixed temporal representation is amplified to alter joint torques. The EMG amplitudes increased greatly with both amplitude and load. However, the fact that the EMG durations increased systematically with increases in distance provided difficulties for this model of amplitude control. The data suggest an economy in motor control in simple agravitational movements, whereby relatively simple transformations of an underlying representation can accomodate large changes in movement amplitude and moment of inertia.