Showing papers on "Amplitude published in 1972"

Delay Doppler characteristics of multipath propagation at 910 MHz in a suburban mobile radio environment

Abstract: Statistical descriptions of the time delays and Doppler shifts associated with multipath propagation in a suburban mobile radio environment obtained from bandpass impulse response measurements are presented. The measuring equipment which has 0.1 \mu s resolution in time delay and a data output bandwidth of less than 5 kHz is also described. For the first time small scale statistics of the multipath propagation for vehicle travel distances on the order of 30 m along streets are presented in the following forms: 1) average power-delay profiles made up of over 200 individual profiles, 2) cumulative distributions of signal amplitude at fixed delays, and 3) radio frequency Doppler spectra at fixed delays. Delay spreads for typical suburban streets are on the order of 0.25 \mu s. Extreme cases have paths with significant amplitudes at excess delays of 5 to 7 \mu s and the square root of the second central moment delay spreads up to about 2 \mu s. Often the signal at fixed delays has a Rayleigh distributed amplitude but large departures from the Rayleigh distribution also occur. RF Doppler spectra at fixed delays indicate that some of the multipath is from one relatively discrete scattering center while at other delays several scattering centers distributed widely in angle are involved. The observed RF Doppler spectra are consistent with the cumulative amplitude distributions at the same delays.

Nonlinear Development of Electromagnetic Instabilities in Anisotropic Plasmas

Abstract: Theory and simulation experiment are presented for a wide variety of transverse electromagnetic instabilities in plasmas with different sources and degrees of anisotropy. In each of the electron bi‐Maxwellian, electron‐pinch, and ion‐pinch experiments, the bulk response of the system during the initial stages of instability is in good agreement with the predictions of quasilinear theory. Furthermore, the two independent energy constants which derive from the fully nonlinear Vlasov‐Maxwell equations are found to remain constant to very good accuracy, even when the magnetic field energy reaches a substantial fraction of the total system energy. In each simulation experiment it is found that the magnetic energy saturates once the magnetic bounce frequency has increased to a value comparable to the linear growth rate prior to saturation, i.e., when ω¯B∼γ¯k. It is concluded that amplitude limitation for Weibel instabilities is a result of magnetic trapping for a broad range of system parameters. In many experi...

Seismic Rays and Ray Intensities in Inhomogeneous Anisotropic Media

Abstract: Summary A ray series expansion for seismic body waves propagating in inhomogeneous anisotropic media is studied. Methods for calculation of rays and amplitude coefficients of the ray series are suggested. A seismic ray is described by a system of ordinary differential equations of first order which can be solved by standard numerical techniques. Another system of ordinary differential equations can be used to compute amplitude coefficients. The method may be applied to general anisotropic media in which the elastic parameters are arbitrary continuous functions of all three co-ordinates.

A ninth-order solution for the solitary wave

Abstract: Several solutions for the solitary wave have been attempted since the work of Boussinesq in 1871. Of the approximate solutions, most have obtained series expansions in terms of wave amplitude, these being taken as far as the third order by Grimshaw (1971). Exact integral equations for the surface profile have been obtained by Milne-Thomson (1964,1968) and Byatt-Smith (1970), and these have been solved numerically. In the present work an exact operator equation is developed for the surface profile of steady water waves. For the case of a solitary wave, a form of solution is assumed and coefficients are obtained numerically by computer to give a ninth-order solution. This gives results which agree closely with exact numerical results for the surface profile, where these are available. The ninth-order solution, together with convergence improvement techniques, is used to obtain an amplitude of 0.85for the solitary wave of greatest height and to obtain refined approximations to physical quantities associated with the solitary wave, including the surface profile, speed of the wave and the drift of fluid particles.

Nonlinear vibration of cylindrical shells

Abstract: The large amplitude vibrations of a thin-walled cylindrical shell are analyzed using the Donnell's shallow-shell equations. A perturbation method is applied to reduce the nonlinear partial differential equations into a system of linear partial differential equations. The simply-supported boundary condition and the circumferential periodicity condition are satisfied. The resulting solution indicates that in addition to the fundamental modes, the response contains asymmetric modes as well as axisymmetric modes with the frequency twice that of the fundamental modes. In the previous investigations in which the Galerkins procedure was applied, only the additional axisymrnetric modes were assumed. Vibrations involving a single driven mode response are investigated. The results indicate that the nonlinearity is either softening or hardening depending on the mode. The vibrations involving both a driven mode and a companion mode are also investigated. The region where the companion mode participates in the vibration is obtained and the effects due to the participation of the companion mode are studied. An experimental investigation is also conducted. The results are generally in agreement with the theory. "Non-stationary4 response is detected at some frequencies for large amplitude response where the amplitude drifts from one value to another. Various nonlinear phenomena are observed and quantitative comparisons with the theoretical results are made.

Analysis and Compensation of Bandpass Nonlinearities for Communications

Abstract: There are many instances in communication systems where bandpass signals are passed through nonlinear devices, such as traveling wave tubes, which exhibit both amplitude and phase nonlinearities. When the input signal is narrow band, the device may be characterized by measurements of its single-carrier amplitude and phase transfer functions. A sufficient model for such a device is a quadrature structure that includes two nonlinearities each of which, acting on its own, would exhibit only amplitude distortion. The outputs of the two halves of this model are linearly independent for arbitrary narrow-band input signals so that their power spectra add. Consequently, almost all previously published results for amplitude nonlinearities can be readily applied to the analysis of the general device. Emphasis is laid on practical procedures for analysis based directly on measured device characteristics rather than analytic approximations and accuracy is checked by comparison of certain intermodulation results with previous results and with measurements. A new result is the performance of an Intelsat IV tube for a large number of independent equal-power-density signals. A heuristically optimal saturating nonlinearity is introduced and analyzed and two methods of compensating an arbitrary saturating device to obtain this optimal characteristic are presented. Two methods of inverting the Chebyshev transform are used in this paper and the choice of basis functions for obtaining series representations of the measured device characteristics is discussed.

Peristaltic motion of a non-Newtonian fluid

Abstract: To understand theoretically the flow properties of physiological fluids, we have considered as a model the peristaltic motion of a power law fluid in a tube, with a sinusoidal wave of small amplitude travelling down its wall. The solution for the stream function is obtained as a power series in terms of the amplitude of the wave. The stream function and the velocity components are evaluated by solving numerically two point boundary value problems with a singular point at the origin. The influence of the applied pressure gradient along with non-Newtonian parameters on the streamlines and velocity profiles are discussed in detail.

Magnitude from short-period P-wave data

Abstract: An empirical surface-focus amplitude-distance curve, based on approximately 2400 short-period P -wave amplitudes from 43 large explosions at 19 different sites, and a corresponding curve based on geometrical spreading in the Herrin earth model are developed. The relative amplitude differences are inverted to obtain the Q structure of the mantle. Theoretical, deep-focus, amplitude-distance curves incorporating geometric spreading and attenuation are developed. Corresponding distance and depth amplitude-correction P factors are given for computing magnitude ( mp ). The correction factors are evaluated and are shown to provide a significantly improved basis for computing magnitude relative to the presently used Q factors which yield mb . Values of mp were normalized to be equal on the average to values of mb for a surface source; differences in attenuation factors generally make mb larger than mp for deep earthquakes.

A nonlinear instability burst in plane parallel flow

Abstract: An infinitesimal centre disturbance is imposed on a fully Ldveloped plane Poiseuille flow at a Reynolds number R slightly greater than the critical value Rc for instability. After a long time, t, the disturbance consists of a modulated wave whose amplitude A is a slowly varying function of position and time. In an earlier paper (Stewartson & Stuart 1971) the parabolic differential equation satisfied by A for two-dimensional disturbances was found; the theory is here extended to three dimensions. Although the coefficients of the equation are coinples, a start is made on elucidating the properties of its solutions by assuming that these coefficients are real. It is then found numerically and confirmed analytically that, for a finite value of (R-Rc)t, the amplitude A develops an infinite peak at the wave centre. The possible relevance of this work to the phenomenon of transition is discussed.

The mechanics of an organized wave in turbulent shear flow. Part 2. Experimental results

Abstract: Results on the behaviour of controlled wave disturbances introduced artificially into turbulent channel flow are reported. Weak plane-wave disturbances are introduced by vibrating ribbons near each wall. The amplitude and relative phase of the streamwise component of the induced wave is educed from a hot-wire signal, allowing the wave speed, the attenuation characteristics and the wave shape to be traced downstream. These results form a basis for evaluation of closure models for the dynamical equations describing wave components in shear-flow turbulence.

Further Evidence of Global-Scale 5-Day Pressure Waves

Abstract: Cross spectra between long time series (5–10 years) of pressure data from 27 stations and that from Canton Island show peaks in the coherence squares near 5-day periods. Phase angles indicate that these peaks are manifestations of a westward propagating, zonal wavenumber 1 disturbance. Sea-level pressures and 500-mb heights recorded during the IGY are filtered in time and harmonically analyzed in space revealing the westward propagating 5-day waves. A composite wave based on the IGY sea-level pressure data suggests that the amplitude of the disturbance increases with increasing latitude. The observed characteristics of the 5-day pressure wave are shown to he not inconsistent with those of a planetary wave, or wave mode of the second class, theoretically predicted by Laplace's tidal equations.

Temporal frequency spectra of multifrequency waves in turbulent atmosphere

Abstract: General formulations for temporal frequency spectra of the fluctuations of plane, spherical, and beam waves operating at two frequencies are given based on weak turbulence and frozen-in assumptions. The cross spectra and the coherence are obtained for the amplitude at two frequencies, the phase at two frequencies, and the amplitude at one frequency and the phase at another frequency. The results are examined in detail for plane and spherical waves. For the spectrum of the index of refraction \kappa^{-n} in the inertial subrange, the amplitude spectrum behaves as k^{(5-n)/2} for \omega \rightarrow 0 and k^{2}\omega^{1-n} for \omega \rightarrow \infty . The phase spectrum for \omega\rightarrow 0 and for \omega\rightarrow\infty behaves as k^{2}\omega^{1-n} with different constants. These results agree well with the experimental work of Janes et al. [11] at 9.6 and 34.5 GHz, and explains the ratio of the spectra at two frequencies. Also noted is the experimental slope of -2.6 as and for \omega \rightarrow \infty which may be compared with 1-n = -2.66 using the Kolmogorov spectrum of n = 11/3 . The amplitude and phase coherence are calculated, and the results agree well with the experimental data. This agreement is indicative of the general validity of the theory for frequencies as low as 10\sim30 GHz and the path length as long as 60 km. It is also shown that using the preceding theory, the wind velocity and the structure constant C_{n} can be deduced from the experimental data. Theoretical wind velocity of 15.6 knots obtained from the propagation data compares favorably with the meteorologically measured value of 14 knots, and two values of C_{n} obtained independently from the amplitude and phase measurements closely agree with each other.

Anomalous High‐Frequency Resistivity of a Plasma

Abstract: In one‐ and two‐dimensional computer simulations an anomalous high‐frequency resistivity in a plasma driven by a large electric field oscillating near the electron plasma frequency is investigated. The large field excites the oscillating two‐stream and the ion‐acoustic decay instabilities in agreement with the linear theory. When the ion and electron fluctuations saturate, a strong anomalous heating of the plasma sets in. This strong heating is due to an efficient coupling of the externally imposed large electric field to the plasma by ion fluctuations. The anomalous collision frequency and the saturation fluctuation amplitudes are determined as a function of the external field amplitude and frequency, and the electron‐ion mass ratio. A simple nonlinear theory gives results in reasonable agreement with simulations.

On non-linear theory of instability of a mono-energetic electron beam in plasma"

Abstract: The excitation of a monochromatic plasma wave by a 'cold' electron beam is investigated. The solution obtained describes the transition from the exponential growth of the wave amplitude in the linear stage to the amplitude oscillations associated with trapping of the beam in the potential well created by the wave. The maximum amplitude and its oscillation period are found. Both non-relativistic and relativistic beams are investigated.

Long wave generation on a sloping beach

Abstract: A general solution of the linear long-wave equation is obtained for arbitrary ground motion on a uniformly sloping beach. Numerical results are presented for specific shapes and time histories of ground motion. Near-shore large amplitude waves are also investigated using non-linear theory.

The electromagnetic fields of a subterranean cylindrical inhomogeneity excited by a line source

Abstract: The anomalous fields from a buried cylindrical inhomogeneity in an otherwise uniform half-space are analyzed. The problem is rendered two-dimensional by assuming that the uniform line source of current is parallel to the subsurface cylinder. The multipole scattered field coefficients are obtained from the numerical solution to the associated singular Fredholm integral equation of the second kind. The horizontal magnetic field amplitude, the vertical magnetic field phase, and the amplitude and phase of the ratio of horizontal to vertical magnetic fields are shown to be diagnostic of the location of the inhomogeneity. The results have possible applications to electromagnetic location in mine rescue operations and to geophysical prospecting.

Nonlinear Interaction of a Small Cold Beam and a Plasma. Part II

Abstract: A single‐wave model was previously used to construct a properly scaled universal solution for the initial nonlinear interaction between a small cold beam and a plasma. Two experimentally motivated extensions of the single‐wave model are now related back to this universal solution. The first extension shows that although the universal solution was originally obtained for boundary conditions where the wave grows temporally, it is, with proper scaling, equally valid for the more realistic boundary conditions in which the wave grows spatially from the point where the beam enters the plasma. The second extension concerns the statistical properties of the single‐wave model. The universal solution is generalized so that it depends analytically on the initial phase and amplitude of the single wave, and the ensemble average of this generalized solution is then taken over all possible values of the initial phase and amplitude. This is a straightforward average of the solution over the initial conditions, and it does not rely on the random phase approximation usually invoked in the theory of weak turbulence. The ensemble average corresponds to the typical experimental practice of time averaging the received signal, provided the ergodic theorem applies.

Finite-Amplitude Baroclinic Wave Packets

Abstract: A theory is presented for the propagation of wave packets in a slightly unstable baroclinic shear flow in a quasi-geostrophic two-layer model on the beta plane. The theory for inviscid motions is considered and packet solutions resembling solitary waves are found. It is shown that the propagation speed of the packet, which is a function of its amplitude, exceeds the most naturally defined group velocity. A physical explanation is presented and it is suggested that the enhancement of the signal velocity above the group velocity is a general property of systems possessing linear instability and nonlinear stability.

Microscale pressure fluctuations near waves being generated by the wind

Abstract: Measurements of static pressure and wave height are used to describe the waveinduced pressure field above generating sea waves. A large hump in the pressure spectra is observed at the wave frequencies. The amplitude of this hump increases and the rate of its vertical decay decreases as the mean wind speed increases. The phase difference between the pressure and the waves during active generation is about 135°, pressure lagging the waves, and does not change vertically for measurements at heights greater than the wave crests. In the present data, active wave generation appears to occur only when the wind at a height of 5 metres is greater than or about equal to twice the phase speed of the waves.

Wave Modulations in Anharmonic Lattices

Abstract: Wave modulations in one-dimensional anharmonic lattices are studied by the use of a perturbation method established by Taniuti and Yajima. A system of equations to determine the evolution of the slowly varying parts in the lowest order of an asymptotic expansion is derived. One interesting result is that the nonlinearly modulated wave must be accompanied by the other slowly varying wave which tends to stabilize the modulated one. '§ I. Introduction Many physical properties of real crystals are directly related to nonlinear effects produced by anharmonic forces. It is important to examine the properties of wave propagations in anharmonic lattices in connection with the thermal expan­ sion of lattices/l the non-ergodic character of nonlinear lattices2J,SJ and the nonlinear propagation of heat observed by Narayanamulti and Varma.4l For special problems on harmonic lattices two- or three-dimensional ones have been studied but the problems on anharmonic lattices, even in the one-dimensional case, are complicated to be studied. Under certain conditions, however, real crystals can be approximated by one-dimensional lattice models.5l Thus in this paper we will focus our attention on the wave modulations in one-dimensional . anharmonic monatomic lattices. Recently, Tappert and Varma5l considered this problem in a continuum limit, assuming that the cubic term in the interaction potential is sufficiently small. In 1970 LowelPl also examined this problem according to Whitham's variational me­ thod6l and showed that for frequencies smaller than a certain critical value the uniform wave is unstable against changes in wavenumber and amplitude. However, he did not take an essential feature acting upon the stabilization of the modulated waves into account. Namely he did not adopt correctly the interactions between an envelope wave and the other slowly varying wave accompanied by the envelope one. In this paper, using the perturbation method established by Taniuti and Yajima/l the wave modulations in anharmonic lattices are investigated. We per­ form the perturbation with due regard to the above effect without the continuum approximation for carrier waves, and obtain the following results: The modulated wave must be accompanied by the other slowly varying wave with the same order as the modulated one, and the both are simultaneously determined with a coupled

Acoustic-surface-wave amplitude and phase measurements using laser probes

Abstract: The investigation of acoustic-field distributions on free surfaces is important in several different classes of application. Measurements of the phase of acoustic surface waves using optical probes allow direct measurement of their velocity. A number of different optical-probe types are compared on the basis of sensitivity and stability. The operation and design of an optical heterodyne probe, capable of high-precision phase and group-velocity measurement, is described.

The excitation of resonant triads by single internal waves

Abstract: The stability of progressive internal waves of modes 1 and 3, propagating down a long tank filled with a linearly stratified salt water solution, is studied theoretically and experimentally. Examination of the spectra of the waves shows when a1 > 10−2, where a is the wave amplitude and l is the vertical wavenumber, that single internal waves excite waves of several resonant triads, where the excited waves belong to that set of triads with the largest theoretical growth rates. For example, a wave of mode 3 with a non-dimensional frequency around 0.66 excites waves of the following triads: (5,8,3), (6,9,3), (8,11,3), (9,12,3) and (10,13,3), where the integers are mode numbers. The spontaneous appearance of these naturally excited triads greatly complicates attempts to isolate and study preselected wave interactions. In one case, when waves of mode 1 and 3 with al > 10−2 were generated simultaneously while tuned to the (1,3,4,7) multiple resonance, the fastest growing wave was neither a wave of mode 4 located at the difference frequency nor a wave of mode 7 at the sum frequency, but rather a wave of mode 9 located at a frequency slightly above that of the 4-wave.

Dynamic Characteristics of Retinal Ganglion Cell Responses in Goldfish

Abstract: A cross-correlation technique has been applied to quantify the dependence of the dynamic characteristics of retinal ganglion cell responses in goldfish on intensity, wavelength, spatial configuration, and spot size. Both theoretical and experimental evidence justify the use of the cross-correlation procedure which allows the completion of rather extensive measurements in a relatively short time. The findings indicate the following. (a) The shape of the amplitude characteristics depends on the energy per unit of time (power) falling within the center of a receptive field rather than on the intensity of the stimulus spot. For spot diameters of up to 1 mm, identical amplitude characteristics can be obtained by interchanging area and intensity. Therefore the receptor processes do not contribute to the change in the amplitude characteristics as a function of the power of the stimulus light. (b) For high frequencies the amplitude characteristics obtained as a function of power join together in a common envelope if plotted on an absolute sensitivity scale. For spontaneous ganglion cells this envelope holds over a range of three log units and the shape is identical for central and peripheral processes. (c) The amplitude characteristics of the central and peripheral processes converging to a ganglion cell are identical, irrespective of the sign (on or off) and the spectral coding of the response. Therefore we have no evidence for interneurons in the goldfish retina unique to the periphery of the receptive field.

Formation and Interaction of Ion‐Acoustic Solitary Waves in a Collisionless Warm Plasma

Abstract: The formation and interaction of solitary waves in a warm‐ion, hot isothermal electron plasma have been studied with the Vlasov equation for ions and Boltzmann distribution for electrons. An arbitrary initial potential pulse having a width smaller (or larger) than that of a solitary wave decomposes into one (or several) solitary wave(s) with (or without) ion‐acoustic oscillations behind. In the interaction of two solitary waves, it has been found that: (1) If the initial amplitude ratio is not too large, the two waves exchange their amplitudes and bounce apart; (2) if the initial amplitude ratio is large, the larger wave first absorbs the smaller, subsequently re‐emits it behind. A steady‐state solitary wave solution for the ion fluid equations with a scalar pressure and Boltzmann electrons presents a smaller width and a larger velocity than the solution of the Korteweg‐de Vries equation with the same amplitude. The limiting Mach number is smaller than Sagdeev's value.