Showing papers on "Amplitude published in 1977"
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TL;DR: An integral equation for the t-channel partial wave amplitudes in the investigation of the multi-Regge form of the 2..-->..2+n amplitude was derived in this article.
Abstract: An integral equation is derived for the t-channel partial wave amplitudes in the investigation of the multi-Regge form of the 2..-->..2+n amplitude. For a t-channel state with isospin T=1 the solution of this equation is a Regge pole. The analytic properties of the isospin T=0, 2 partial wave amplitudes are investigated near the threshold for the production of two or three particles. It is shown that in the j-plane there are moving poles and cuts. For the T=0 vacuum channel it was found that the partial wave amplitude has a fixed square-root type branch point to the right of j=1.
838 citations
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TL;DR: Single fusimotor fibres were stimulated repetitively to test their action on the responsiveness of muscle spindle primary endings in the cat soleus to sinusoidal stretching of both large and small amplitude.
Abstract: 1. Single fusimotor fibres were stimulated repetitively to test their action on the responsiveness of muscle spindle primary endings in the cat soleus to sinusoidal stretching of both large and small amplitude. Frequencies of 0.06-4 Hz were used at amplitudes from 10 mum to 3 mm.2. The response was assessed by fitting a sinusoid to the cycle histogram of the afferent firing throughout the course of the cycle; this linear approximation measures the fundamental of the response and ignores any harmonics. The sine was allowed to project to negative values and any empty bins in the histogram were ignored when fitting.3. With small amplitudes of stretching the histograms were reasonably sinusoidal, but with large amplitudes they showed appreciable distortion of the wave form for the passive ending and during dynamic fusimotor stimulation. Non-linearity of response manifested itself also, with increasing amplitude of stretching, by an increase in the phase advance of the response, by increasing r.m.s. deviation of the histogram points from the fitted sine and (for dynamic stimulation) by an increase in the mean value of the fitted sine.4. With increasing amplitude the response modulation ceased to increase proportionately with the stimulus, so that the sensitivity of the ending to a large stretch (defined as afferent modulation/stretch amplitude) was appreciably less than for a small stretch. This effect was most pronounced for the passive ending.5. Whatever the amplitude of movement the modulation during static stimulation was less than that for the passive or during dynamic stimulation. For small amplitudes the response during dynamic stimulation was less than that of the passive, but for large amplitudes the response during dynamic stimulation was always the greater. At some intermediate cross-over amplitude the two responses were the same size, though still differing slightly in other respects. The value of the cross-over amplitude was usually about 200 mum at 1 Hz, and increased on lowering the frequency. Thus dynamic fusimotor action does not uniformly produce either an increase or a decrease in the sensitivity of the ending in relation to the passive.6. Bode plots, for each amplitude, of sensitivity and phase against frequency suggested that(a) under all conditions the ending is relatively insensitive to frequency in the range studied, for the slope of the log-log sensitivity lines was only 0.15-0.2 (3.5-6 db/decade);(b) the mechanism which makes for non-linearity is not particularly frequency sensitive;(c) static fusimotor stimulation does not change the frequency sensitivity of the ending;(d) dynamic fusimotor stimulation very slightly increases the frequency sensitivity of the ending for large amplitudes.In reaching these conclusions more attention was paid to the slope of the sensitivity lines than to the values of phase.7. It appears that the major effect of fusimotor action, whether static or dynamic, is to regulate the sensitivity of the primary ending to stretching for all amplitudes of movement (i.e. gain) rather than to control the relative values of its sensitivity to length and to velocity (i.e. crudely, the damping in a feed-back loop).
214 citations
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TL;DR: In this article, the authors measured the shear-stress variation along and the velocity profiles above a solid wavy wall bounding a turbulent flow for three waves with height-to-length ratios of 2a/λ = 0·0312 and 0·05.
Abstract: Measurements of the shear-stress variation along and the velocity profiles above a solid wavy wall bounding a turbulent flow are presented for waves with height-to-length ratios of 2a/λ = 0·0312 and 0·05. These are compared with previous measurements of the wall shear stress reported by Thorsness (1975) and by Morrisroe (1970) for 2a/λ = 0·012. The investigation covered a range of conditions from those for which a linear behaviour is observed to those for which a separated flow is just being initiated.Pressure measurements indicate a linear response in that the spatial variation is described quite well by a single harmonic with a wavelength equal to that of the surface. However, the variation of τw for waves with 2a/λ = 0·0312 and 0·05 can be more rapid on the leeward side of the wave. The degree of departure from a sinusoidal variation increases with increasing wave height and fluid velocity and, from the results reported in this paper, it is suggested that nonlinear behaviour will become evident when au*/v [ges ] 27.Many aspects of the flow for all three waves are described by a solution of the linear momentum equations previously presented by Thorsness (1975) and by Thorsness & Hanratty (1977). These include the phase and amplitude of the pressure profile and the first harmonic of the shear-stress profile and the velocity field outside the viscous wall region.These results suggest that up to separation the flow is approximated quite well by linear theory. Nonlinearities affect the flow only in a region very close to the wave surface and are manifested by the appearance of higher harmonics in the variation of τw.
188 citations
01 Oct 1977
TL;DR: In this article, the amplitude ratio is computed by integrating the spatial amplification rate of the parallel flow theory along a ray, and the dispersion relation is most directly obtained with the temporal theory, but only after the direction of the group velocity is known.
Abstract: Linear stability theory is used in computing the amplitude ratio for other than two-dimensional instability waves The wave motion is obtained from the ray equations of kinematic wave theory, and the amplitude ratio by simply integrating the spatial amplification rate of the parallel flow theory along a ray Both the temporal and spatial theories are examined for two- and three-dimensional incompressible and two-dimensional compressible boundary layers The dispersion relation is most directly obtained with the temporal theory, but the magnitude and direction of the group velocity have to be computed to give the spatial amplification rate, and then only approximately The spatial theory gives the spatial amplification rate directly, but only after the direction of the group velocity is known Transition prediction methods, divided into amplitude-density and amplitude methods, are discussed
178 citations
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TL;DR: The real part of the proton proton elastic scattering amplitude has been determined from its interference with the Coulomb amplitude at total centre-of-mass energies up to 62 GeV as discussed by the authors.
172 citations
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TL;DR: In this paper, an analogue of the Boussinesq equation is presented which is exact for ion-sound (s) waves in the linear limit and which is correct in the sense of the Cauchy problem.
156 citations
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TL;DR: In this paper, a least squares method is proposed to invert Rayleigh and Love wave observations in source mechanism studies, where the inversion scheme converges to a unique solution independent of the orientation of the initial trial source.
Abstract: A least squares method is proposed to invert Rayleigh and Love wave observations in source mechanism studies. When complex spectra is available the inversion scheme is linear and it is carried out in a single step. When only amplitude spectra is available the inversion scheme may be linearized and it converges to a unique solution independent of the orientation of the initial trial source. Source depth is found by minimizing errors in repeated application of the method at different trial depths. Application to real data requires a careful weighting of observations when the path structure is not well-known. The source representation in term of seismic moment tensor components allows for a simple analysis of the surface wave data resolving power. Complex spectra of Rayleigh waves render a unique solution, but complex spectra of Love waves admit infinite solutions. If a double-couple source is assumed, the Love wave data may have either one or three equally satisfactory solutions. When only absolute values of surface wave spectra are available, any solution may be rotated 180° in azimuth and/or all the source tensor components may be changed in sign.
128 citations
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TL;DR: In this paper, the authors show that for the frequency band over which incident waves are large enough to break a universal saturation form for the vertical run-up spectrum, a limiting amplitude for standing waves formed by reflection at the shoreline is related to a critical parameter ∆cs by a = ∈csgβ2/(2πƒ)2.
Abstract: Time series of shoreline run-up on two natural beaches have been measured by using a time-lapse camera. Spectra of these time series and two other run-up spectra measured by Suhayda (1972) suggest that for the frequency band over which incident waves are large enough to break a universal ‘saturation’ form for the vertical run-up spectrum occurs, with energy density E(ƒ) = [∈ˆcsgβ2/(2πƒ)2]2, where g is the gravitational acceleration, β is the beach slope, and ƒ is the frequency (in hertz). Parameter ∈ˆcs(Δƒ)½ is a universal nondimensional constant, found to have a value of about 1, where Δƒ is the bandwidth over which incident waves are large enough to break in the surf zone. This result is discussed in relation to previous laboratory experiments and theories, based on monochromatic waves, which suggest the existence of a limiting amplitude for standing waves formed by reflection at the shoreline. This limiting amplitude is related to a critical parameter ∈cs by a = ∈csgβ2/(2πƒ)2. A possible interpretation of ∈ˆcs(Δƒ)½ in terms of ∈cs is given based on percentage exceedances of the critical downslope acceleration gβ2. In this interpretation we have assumed a Gaussian distribution for run-up acceleration. This assumption cannot be tested directly, but the observed distribution functions for run-up elevation suggest that it may need to be modified. Departures from the universal spectrum athigher and lower frequencies are briefly discussed.
115 citations
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TL;DR: In this article, a frequency-dependent full wave theory is successfully employed to synthesize long-period seismograms of the core phases SmKS (m= 1, 2, …) in the distance range 100°-125°.
Abstract: Summary. A frequency-dependent full wave theory is successfully employed to synthesize long-period seismograms of the core phases SmKS (m= 1, 2, …) in the distance range 100°–125°. Body-wave displacements are calculated by numerically integrating in the complex ray parameter plane. Langer's method is employed to obtain a uniformly asymptotic approximation to the vertical wave functions. Plane-wave reflection and transmission coefficients are adequately corrected for the effect of the curvature at the core -mantle discontinuity by the use of generalized cosines. Results are presented in the time domain, after a numerical Fourier (inverse) transform.
The computed seismograms exhibit many non-ray effects that the SmKS incur upon interacting with the core- -mantle boundary. For SKS, the amplitude, group delay and phase delay are very strong functions of frequency at less than 0.5 Hz, both because of the frequency dependence of the reflection/transmission coefficients at the core—mantle boundary, and because of the presence of diffracted energy, called SP(diff)KS, perturbing the waveform. The diffracted energy of the type that perturbs SKS may also interact with shear waves to give rise to a precursor to the body-wave ScS, called SP(diff)S. The major complication in synthesizing the portion of the seismogram containing SmKS for m≥ 2 is that the arrival time of each successively higher order reflection is within the waveform of previous lower order reflections. It is found that a summation of body-wave displacements from S2KS to S15KS gives an adequate seismogram in the distance range 100°–125°. Each individual reflection has an amplitude spectrum, group delay and phase delay which are strongly frequency-dependent at less than 0.2 Hz. It is shown that arrival times for SmKS, m≥ 2, cannot be picked accurately by conventional methods. Furthermore, neglecting the frequency-dependence of reflection/transmission coefficients can significantly distort the interpretation of amplitude and phase data.
The seismograms generated by this method agree so remarkably well with observed records that the synthetic waveforms provide a powerful test of the validity of particular earth models. In particular, we find that the waveforms of SmKS are exceedingly sensitive to velocity gradients of the upper 200-km of the outer core, and indications are that the velocities in the outer 200-km of the core are higher, but the velocity gradient is lower, than that predicted by Hales & Roberts or earth model 1066B. The pulse widths of SmKS are also used to determine some fault parameters.
104 citations
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TL;DR: In this article, the linear stability of an internal gravity wave of arbitrary amplitude in an unbounded stratified inviscid Boussinesq fluid is considered mathematically and the instability is governed by a Floquet system and treated by a generalization of the method of normal modes.
Abstract: The linear stability of an internal gravity wave of arbitrary amplitude in an unbounded stratified inviscid Boussinesq fluid is considered mathematically. The instability is shown to be governed by a Floquet system and treated by a generalization of the method of normal modes. Some properties of the Floquet system, and in particular those of its parametric instability, are analysed. The parametric instability is related to the theory of resonant wave interactions; and the surface of marginal stability in the control space of the amplitude and wavenumbers is shown to be describable by the catastrophe theory of Thom. Finally some results of numerical calculations of the marginal surface are shown. The main physical conclusion is to confirm that the internal gravity wave is unstable always, even when its amplitude is small and so its local Richardson number is large everywhere for all time. It is suggested, by various illustrations and arguments, that the methods developed in this paper are applicable to the instability of many symmetric nonlinear waves.
102 citations
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TL;DR: Improved numerical solutions have been found for the two‐dimensional cochlear model proposed by Lesser and Berkley using the Green’s‐function method, which has proven to be stable, accurate, and faster than several other numerical solution techniques that have been tried.
Abstract: Many theories have been developed in past years which have attempted to model the function of the human cochlea. With the recent availability of the physical measurements of Rhode [J. Acoust. Soc. Am. 49, 1218 (1971)], these theories now appear to be inadequate. In this paper, improved numerical solutions have been found for the two‐dimensional cochlear model proposed by Lesser and Berkley [J. Fluid Mech. 51,497 (1970)], using the Green’s‐function method as first suggested by Cox and Lien [(1973) unpublished]. The Green’s‐function method is used to derive an integral equation which may then be solved numerically. This procedure has proven to be stable, accurate, and faster than several other numerical solution techniques that have been tried. With an appropriate selection of the assumed membrane dissipation, the results are seen to agree within a few decibels of the Mossbauer measurements of Rhode, including the sharp change in slope observed in his amplitude ratio measurements just above the best frequency. This plateau occurs at a level which is 58 dB lower in amplitude than the amplitude at the best frequency.
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TL;DR: A new method for real-time detection and measurement of small vibrations, based on phase modulation in time-average electronic speckle pattern interferometry, is described, which can study the deformation of the object in slow motion.
Abstract: We describe a new method for real-time detection and measurement of small vibrations, based on phase modulation in time-average electronic speckle pattern interferometry. The modulation frequency is shifted relative to the vibration frequency, which makes the intensity of the reconstructed image vary at the difference frequency. The amplitude detection limits are about 20 A by visual observation and 0.1 A by photoelectric measurement using a lockin technique. No auxiliary system for fringe stabilization is required. At higher amplitude levels we can study the deformation of the object in slow motion. Measurements on different objects, including human ear preparation, are presented.
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TL;DR: In this article, the authors used elliptical hysteresis loops in basalt and granite samples subjected to sinusoidal strains of order 10−6 and this is strong evidence that attenuation does become a linear phenomenon at low strain amplitudes.
Abstract: LINEAR theories of attenuation of acoustic or seismic waves in media, such as rocks, which are characterised by constant or nearly constant Q factors (fractional energy loss per cycle equals 2π/Q) imply velocity dispersion and, therefore, frequency dependence of elasticity The effect is small, corresponding to a change of order 1 % over the period range of seismological interest (1 s to 1 h), and is consequently difficult to observe However, it leads to an internal inconsistency in the development of earth models by inversion of free oscillation data and to discrepancies between these models and body wave data1–3 It is a matter of considerable geophysical interest to resolve the problem Validity of the linearity assumption has been questioned4 but we are now observing elliptical hysteresis loops in basalt and granite samples subjected to sinusoidal strains of order 10−6 and this is strong evidence that attenuation does become a linear phenomenon at low strain amplitudes But whether or not perfect linearity applies, a direct demonstration of body wave dispersion is the most satisfying indication that earth model studies need revision
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TL;DR: In this article, the authors present a scheme of analysis of their differential equations which yields simple analytic formulae characterizing: (a) the domain in parameter space of local asymptotic stability of the steady state solution, (b) the amplitude, period, and waveform of limit cycle oscillations, (c) the direction of bifurcation of small amplitude periodic solutions, (d) the existence of large amplitude stable periodic solutions simultaneously with a locally stable constant solution, and (e) the threshold of excitation and transient response to perturbations from a
Abstract: On the basis of their thorough investigation of the mechanism of the malonic acid–bromate–cerium reaction, Field and Noyes have proposed a simple model for the sustained oscillations observed in this system. In this paper, I present a scheme of analysis of their differential equations which yields simple analytic formulae characterizing: (a) the domain in parameter space of local asymptotic stability of the steady state solution, (b) the amplitude, period, and waveform of limit cycle oscillations, (c) the direction of bifurcation of small amplitude periodic solutions, (d) the existence of large amplitude stable periodic solutions simultaneously with a locally stable constant solution, (e) the threshold of excitation and transient response to perturbations from a globally, asymptotically stable solution, and (f) the spatial and temporal development of the concentrations of key intermediates in periodic traveling waves (plane, axisymmetric, and rotating‐spiral waves). These formulae facilitate the choice of parameter values to give reasonable agreement between model calculations and observed oscillations.
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TL;DR: The amplitude of Pc 3,4 magnetic pulsations at Calgary is shown to increase as the solar wind velocity increases as discussed by the authors, which can be understood in terms of the Kelvin-Helmholtz instability at the magnetopause boundary.
Abstract: The amplitude of Pc 3,4 magnetic pulsations at Calgary is shown to increase as the solar wind velocity increases The pulsation amplitude dependence on solar wind velocity can be understood in terms of the Kelvin-Helmholtz instability at the magnetopause boundary
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TL;DR: In this paper, the analysis of Lin is extended to investigate the nonlinear stability of a liquid film with respect to three-dimensional side-band disturbances, and it is shown that the supercritically stable, finite amplitude, long monochromatic wave is stable to 3D sideband disturbances under modal interaction if the bandwidth is less in magnitude than e.
Abstract: The analysis of Lin is extended to investigate the nonlinear stability of a liquid film with respect to three‐dimensional side‐band disturbances. Near the upper branch of the linear‐stability curve where the amplification ci is O (e2), e being proportional to the ratio of the amplitude to the film thickness, the nonlinear evolution of initially infinitestimal three‐dimensional disturbances of a finite band width is shown to obey the nonlinear Schrodinger equation. Near the lower branch of the neutral curve, the nonlinear evolution is stronger. An equation is derived which describes this strong nonlinear development of relatively long three‐dimensional waves. It is shown that the supercritically stable, finite amplitude, long monochromatic wave is stable to three‐dimensional side‐band disturbances under modal interaction if the bandwidth is less in magnitude than e.
01 Aug 1977
TL;DR: In this article, a relatively short cylindrical antenna with continuously tapered resistive loading has been studied for the purpose of picosecond pulse measurements, and the experimental results indicate excellent linear amplitude and phase response over the frequency range.
Abstract: A relatively short cylindrical antenna with continuously tapered resistive loading has been studied for the purpose of picosecond pulse measurements. The antenna considered is a nonconducting cylinder with continuously deposited varying-conductivity resistive loading. The current distributions on the antenna were numerically calculated using the method of moments. Using these current distributions, other quantities such as input admittance, near-field and farfield radiation patterns, and radiation efficiency, were also numerically calculated and compared with the results using the Wu-King's approximate current distribution. Agreement is relatively good except at high frequencies kh > \pi/2 where the method of moments appears to give better results. To verify the theoretical results, several resistively loaded antennas were fabricated, and their picosecond pulse receiving characteristics were analyzed for the frequency range between 5 kHz and 5 GHz. The experimental results indicate excellent linear amplitude and phase response over the frequency range. This provides the unique capability of this antenna to measure fast time-varying electromagnetic fields with minimal pulse-shape distortion due to nonlinear amplitude or phase characteristics.
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TL;DR: In this article, Coupled partial differential equations for the amplitude of the electric field in a general two-dimensional volume hologram were derived for dielectric and absorption gratings.
Abstract: Coupled partial differential equations are derived for the amplitude of the electric field in a general two‐dimensional volume hologram. Nonuniform amplitude distributions, nonplanar wave fronts, losses, and non‐Bragg incidence are considered both for dielectric and absorption gratings. The formulation is in holographic terminology but the equations are valid for weakly modulated Bragg devices in general.
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TL;DR: In the cat's retina the sinewave light flicker response nonlinearity of Hm-type horizontal cells was analyzed and it appeared that some filtering preceded the amplitude compression stage.
Abstract: In the cat's retina we analyzed the sinewave light flicker response nonlinearity of Hm-type horizontal cells. (For a description of the three types of dynamic responses of cat retinal H-units see Foerster et al., 1977). For equal decreases in the Hm-response amplitude an increase in stimulus frequency had a much stronger linearizing effect than a decrease in stimulus area. Thus the distortion is not simply proportional to response amplitude. Both Hm- and Hn-units had frequency dependent nonlinear area-response functions. The receptive field of Hm-units increased dramatically with stimulus frequency, e.g. from 1 ° at 1 Hz to 8 ° or more at 44 Hz. Intensity transfer data could be described by the function Lb· (ob+Lb)−1 with b ≈ 1 for Hm-units and b ≈ 0.5 for Hn-units. Distortion values predicted from intensity transfer data were too high. It was also found that higher harmonics were attenuated more than the first harmonic at increasing frequencies. Therefore it appeared that some filtering preceded the amplitude compression stage.
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TL;DR: In this paper, a general theory of finite amplitude envelope Langmuir solitons is presented, and a comparison with beam-plasma experiments suggests identification of the observed localized structures with these solITons.
Abstract: A general theory of finite amplitude envelope Langmuir solitons is presented. Comparison with recent beam‐plasma experiments suggests identification of the observed localized structures with these solitons.
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TL;DR: In this paper, the square root energy ratios and pulse shapes for P, SV and SH waves transmitted through a layer of orthorhombic olivine between two isotropic half-spaces are presented.
Abstract: Summary. The square-root energy ratios and pulse shapes are presented for P, SV and SH waves transmitted through a layer of orthorhombic olivine between two isotropic half-spaces. Off incident planes of symmetry, incident P waves generate two small amplitude SH waves (one from each interface), whose amplitudes decrease slowly with increasing period. Incident SV (orSH) waves can generate large amplitude SH (or SV) waves which decrease rapidly with increasing period. For incident S waves, many pulses not present in isotropic models are generated, often of large relative amplitude, with many of the transmitted S pulses showing evidence of double arrivals, either in the form of S-wave splitting, or a modification of the shape of the input waveform.
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TL;DR: Data transmission with combined amplitude and phase modulation is considered with signal design carried out in a four-dimensional space of two amplitude and two phase variables and quaternions are used to represent signal vectors.
Abstract: Data transmission with combined amplitude and phase modulation is considered with signal design carried out in a four-dimensional space of two amplitude and two phase variables. The energy for each signal is fixed. Quaternions are used to represent signal vectors and an algebra for quaternions is introduced which allows distance between signal vectors and equivalence between signal codes to be defined. It is also used to characterize the structure of codes. Code construction is based on regular four-dimensional polytopes and particular interest is focused on group codes with 8, 24, 48 and 120 elements. Two classes of phase modulated signals have interest as reference codes. Code evaluation is carried out by calculation of the distance distribution and the error probability assuming opitmum coherent detection. The group codes are found to be between 1.3 and 3.4 dB better than the best phase modulated codes. By using a suitable representation for a signal code it may be realized by using a few amplitude and several phase values.
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TL;DR: In this article, a study of surface waves in a uniform channel is described, where the waves are generated by a plane flap executing torsional oscillations about a vertical axis at a frequency near a cut-off value for a wave mode.
Abstract: This paper describes a study of surface waves in a uniform channel, where the waves are generated by a plane flap executing torsional oscillations about a vertical axis at a frequency near a cut-off value for a wave mode. Experiments indicate that, near a cut-off frequency, the wave response is relatively large, and indeed linear inviscid theory suggests that the wave amplitudes are infinitely large at the cut-off frequency itself. Here we present theories for the modification of this result by making allowance (separately) for nonlinear terms in the surface boundary condition and for viscous dissipation. In order to estimate the effectiveness of the wavemaker in forcing the motions, a separate calculation was made to apportion the driving condition into a part driving a parasitic non-propagating field and a part forcing the wave modes. Also described in the paper are experiments in which the wave response has been measured in a similar situation to that modelled by the analytic work, and one of the main purposes of this study is to try to ascertain how well the theoretical model describes the experimental situation. An important feature to emerge from the comparison is that, even though the observed wave amplitudes were rather large and the temporal decay rate of standing waves corresponding to the cut-off mode was quite small, the dissipative effect played a crucial role in determining the structure of the response. Because of this the theoretical response was determined by numerical computation. Some of the results show a similarity with the response of a nonlinear spring, but there are significant differences. The results indicate that the model gave a good qualitative description of the experiments, and accordingly our main conclusions to the study are: (i) the multiple-scale calculation, by which the nonlinear effects were estimated, appears to have given useful results in this particular case; (ii) the way in which the dissipative effects were modelled appears to have been satisfactory; (iii) the method of estimating the effective driving condition at the wavemaker seems to have worked very well.
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TL;DR: In this paper, the authors constructed numerically representing pure gravitational radiation with no sources of wormholes, under the conditions of time symmetry, axisymmetry, vacuum, and no rotation.
Abstract: Initial data were constructed numerically representing pure gravitational radiation with no sources of wormholes, under the conditions of time symmetry, axisymmetry, vacuum, and no rotation. The constraints were solved by making a conformal transformation on a base metric and solving the scale equation for the conformal factor. The initial data contains a black hole if the amplitude of the waves is sufficiently strong. The locations of apparent horizons were found for several such amplitudes. At a critical amplitude the throat pinches off and the geometry becomes singular.
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TL;DR: In this paper, the effect of a finite bandwidth driver or of turbulence on the parametric instability is considered, and exact equations are obtained for special values of the group velocity of the fluctuations V0, with bandwidth modeled by a Kubo-Anderson process.
Abstract: The effect of a finite bandwidth driver or of turbulence on the parametric instability is considered. First, exact equations are obtained for special values of the group velocity of the fluctuations V0, with bandwidth modeled by a Kubo–Anderson process. Next, a method which enables one to deal with the space‐time problem for arbitrary V0 is given. For the averaged amplitudes it reduces to the Bourret approximation and for the correlation function it gives the kinetic equation for random phase waves. Convective and absolute instability thresholds are given. It is found that for absolute instabilities the threshold obtained from the averaged intensities is lower than the one obtained from the averaged amplitudes.
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TL;DR: The phase and amplitude of the annual, semiannual, and quasi-biennial oscillations to total ozone data for the Northern Hemisphere in the period 1957-1972 and for Northern Hemisphere ozonesonde data for variable periods from 1962-1974 have been plotted as functions of latitude, longitude, and altitude.
Abstract: The phase and amplitude of the annual, semiannual, and quasi-biennial oscillations to total ozone data for the Northern Hemisphere in the period 1957-1972 and for Northern Hemisphere ozonesonde data for variable periods from 1962-1974 have been plotted as functions of latitude, longitude, and altitude. The largest annual wave amplitude in total ozone occurs over eastern Siberia. In total ozone, the region of maximum quasi-biennial oscillation (QBO) coincides with that of the annual wave. The major feature of the QBO in the vertical distribution is the maximum amplitude in the arctic just above the tropopause. As for the semiannual wave, the maximum in total ozone lies in the arctic, displaced slightly to the Siberian side. In the vertical, its maximum amplitude is near 18 km. The phase appears to progress poleward, with maxima at high latitudes occurring in March-April.
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TL;DR: In this article, a model of two photon absorption in a cavity with an external driving field is presented, where phase and amplitude fluctuations in the driving field are taken into account to model a partially coherent multimode source.
Abstract: A model of two photon absorption in a cavity with an external driving field is presented. Phase and amplitude fluctuations in the driving field are taken into account to model a partially coherent multimode source. The photon statistics of the light in the cavity are investigated through a calculation of the second-order correlation function of the light field in the steady state. For a coherent driving field the field inside the cavity will exhibit photon antibunching for low intensities. As the fluctuations in the driving field are increased the photon antibunching is lost. For a particular coherent field, g(2)(0) is reduced with increasing laser intensity. This reduction with laser intensity is slower with increasing laser amplitude fluctuations. This could provide a possible explanation for the recent experimental observations of Kransinski and Dinev (1976).
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TL;DR: In this article, the propagation of the fundamental and harmonically generated longitudinal elastic waves is treated by means of an asymptotic iterative procedure directly in the governing nonlinear differential equation.
Abstract: The propagation of the fundamental and harmonically generated longitudinal elastic waves is treated by means of an asymptotic iterative procedure directly in the governing nonlinear differential equation. Explicit results are obtained for the steady‐state, spatial growth of the second and third harmonic and the depletion of the input wave. As expected, the analysis indicates that the amplitude of the Nth harmonic depends on all the elastic constants up to order N+1. However, the forms for the amplitudes obtained in the asymptotic solution reveal that, for the known range of ratios of elastic constants of successively increasing order and propagation distances commonly encountered in harmonic generation experiments, only the quadratic nonlinearity, which depends on the second‐ and third‐order elastic constants, is required to accurately account for the experimental results. In addition, the amplitude dependence of the phase velocity of the fundamental longitudinal wave is determined.
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TL;DR: In this article, a model for the large scale coherent structure of subsonic and supersonic axisymmetric jets is developed for a time-averaged component, a periodic wave-like component and a random small scale component.
01 Jan 1977
TL;DR: In this article, the Magnus approximation is applied to derive the transition amplitude and the cross section for $K$-shell ionization of atoms by heavy-ion impact, where the target electron is described by a hydrogenic wave function and the projectile as a point charge moving along a straight-line trajectory.
Abstract: The Magnus approximation (or sudden approximation) is applied to derive the transition amplitude and the cross section for $K$-shell ionization of atoms by heavy-ion impact. The target electron is described by a hydrogenic wave function and the projectile as a point charge moving along a straight-line trajectory. The transition amplitude for each partial wave of the ejected electron is expressed as an infinite (but rapidly converging) sum over hypergeometric functions. To obtain the total cross section, only integrals over impact parameter and the final electron momentum have to be evaluated numerically. The approach, because it is nonperturbative, should be particularly useful for treating collisions of light atoms with much heavier projectile ions. It also allows the study of the impact-parameter dependence of the ionization process. The connection with the Glauber approximation is pointed out.