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About: Amplitude is a(n) research topic. Over the lifetime, 46213 publication(s) have been published within this topic receiving 733850 citation(s). more


Journal ArticleDOI: 10.1109/PROC.1963.1664
E.T. Jaynes1, F.W. CummingsInstitutions (1)
01 Jan 1963-
Abstract: This paper has two purposes: 1) to clarify the relationship between the quantum theory of radiation, where the electromagnetic field-expansion coefficients satisfy commutation relations, and the semiclassical theory, where the electromagnetic field is considered as a definite function of time rather than as an operator; and 2) to apply some of the results in a study of amplitude and frequency stability in a molecular beam maser. In 1), it is shown that the semiclassical theory, when extended te take into account both the effect of the field on the molecules and the effect of the molecules on the field, reproduces almost quantitatively the same laws of energy exchange and coherence properties as the quantized field theory, even in the limit of one or a few quanta in the field mode. In particular, the semiclassical theory is shown to lead to a prediction of spontaneous emission, with the same decay rate as given by quantum electrodynamics, described by the Einstein A coefficients. In 2), the semiclassical theory is applied to the molecular beam maser. Equilibrium amplitude and frequency of oscillation are obtained for an arbitrary velocity distribution of focused molecules, generalizing the results obtained previously by Gordon, Zeiger, and Townes for a singel-velocity beam, and by Lamb and Helmer for a Maxwellian beam. A somewhat surprising result is obtained; which is that the measurable properties of the maser, such as starting current, effective molecular Q, etc., depend mostly on the slowest 5 to 10 per cent of the molecules. Next we calculate the effect of amplitude and frequency of oscillation, of small systematic perturbations. We obtain a prediction that stability can be improved by adjusting the system so that the molecules emit all their energy h Ω to the field, then reabsorb part of it, before leaving the cavity. In general, the most stable operation is obtained when the molecules are in the process of absorbing energy from the radiation as they leave the cavity, most unstable when they are still emitting energy at that time. Finally, we consider the response of an oscillating maser to randomly time-varying perturbations. Graphs are given showing predicted response to a small superimposed signal of a frequency near the oscillation frequency. The existence of "noise enhancing" and "noise quieting" modes of operation found here is a general property of any oscillating system in which amplitude is limited by nonlinearity. more

Topics: Semiclassical physics (59%), Quantum (55%), Electromagnetic field (55%) more

3,567 Citations

Journal ArticleDOI: 10.1190/1.1442147
01 Apr 1986-Geophysics
Abstract: I present a finite-difference method for modeling P-SV wave propagation in heterogeneous media This is an extension of the method I previously proposed for modeling SH-wave propagation by using velocity and stress in a discrete grid The two components of the velocity cannot be defined at the same node for a complete staggered grid: the stability condition and the P-wave phase velocity dispersion curve do not depend on the Poisson's ratio, while the S-wave phase velocity dispersion curve behavior is rather insensitive to the Poisson's ratio Therefore, the same code used for elastic media can be used for liquid media, where S-wave velocity goes to zero, and no special treatment is needed for a liquid-solid interface Typical physical phenomena arising with P-SV modeling, such as surface waves, are in agreement with analytical results The weathered-layer and corner-edge models show in seismograms the same converted phases obtained by previous authors This method gives stable results for step discontinuities, as shown for a liquid layer above an elastic half-space The head wave preserves the correct amplitude Finally, the corner-edge model illustrates a more complex geometry for the liquid-solid interface As the Poisson's ratio v increases from 025 to 05, the shear converted phases are removed from seismograms and from the time section of the wave field more

Topics: Phase velocity (64%), Wave propagation (64%), Group velocity (64%) more

2,365 Citations

Journal ArticleDOI: 10.1086/186504
George F. Smoot1, Charles L. Bennett2, A. Kogut2, Edward L. Wright3  +24 moreInstitutions (3)
Abstract: Results of the first year of data from the differential microwave radiometers on the Cosmic Background Explorer are presented. Statistically significant structure that is well described as scale-invariant fluctuations with a Gaussian distribution is shown. The rms sky variation, smoothed to a total 10-deg FWHM Gaussian, is 30 +/-5 micro-K for Galactic latitude greater than 20-deg data with the dipole anisotropy removed. The rms cosmic quadrupole amplitude is 13 +/-4 micro-K. The angular autocorrelation of the signal in each radiometer channel and cross-correlation between channels are consistent and give a primordial fluctuation power-law spectrum with index of 1.1 +/-0.5, and an rms-quadrupole-normalized amplitude of 16 +/-4 micro-K. These features are in accord with the Harrison-Zel'dovich spectrum predicted by models of inflationary cosmology. more

Topics: Radiometer (57%), Dipole anisotropy (56%), Very Small Array (53%) more

2,122 Citations

Journal ArticleDOI: 10.1002/J.1538-7305.1968.TB00069.X
Abstract: The statistical characteristics of the fields and signals in the reception of radio frequencies by a moving vehicle are deduced from a scattering propagation model. The model assumes that the field incident on the receiver antenna is composed of randomly phased azimuthal plane waves of arbitrary azimuth angles. Amplitude and phase distributions and spatial correlations of fields and signals are deduced, and a simple direct relationship is established between the signal amplitude spectrum and the product of the incident plane waves' angular distribution and the azimuthal antenna gain. The coherence of two mobile-radio signals of different frequencies is shown to depend on the statistical distribution of the relative time delays in the arrival of the component waves, and the coherent bandwidth is shown to be the inverse of the spread in time delays. Wherever possible theoretical predictions are compared with the experimental results. There is sufficient agreement to indicate the validity of the approach. Agreement improves if allowance is made for the nonstationary character of mobile-radio signals. more

Topics: Plane wave (54%), Azimuth (54%), Radio frequency (53%) more

2,042 Citations

Journal ArticleDOI: 10.1017/S0022112071001745
Abstract: Past evidence suggests that a large-scale orderly pattern may exist in the noiseproducing region of a jet. Using several methods to visualize the flow of round subsonic jets, we watched the evolution of orderly flow with advancing Reynolds number. As the Reynolds number increases from order 102 to 103, the instability of the jet evolves from a sinusoid to a helix, and finally to a train of axisymmetric waves. At a Reynolds number around 104, the boundary layer of the jet is thin, and two kinds of axisymmetric structure can be discerned: surface ripples on the jet column, thoroughly studied by previous workers, and a more tenuous train of large-scale vortex puffs. The surface ripples scale on the boundary-layer thickness and shorten as the Reynolds number increases toward 105. The structure of the puffs, by contrast, remains much the same: they form at an average Strouhal number of about 0·3 based on frequency, exit speed, and diameter.To isolate the large-scale pattern at Reynolds numbers around 105, we destroyed the surface ripples by tripping the boundary layer inside the nozzle. We imposed a periodic surging of controllable frequency and amplitude at the jet exit, and studied the response downstream by hot-wire anemometry and schlieren photography. The forcing generates a fundamental wave, whose phase velocity accords with the linear theory of temporally growing instabilities. The fundamental grows in amplitude downstream until non-linearity generates a harmonic. The harmonic retards the growth of the fundamental, and the two attain saturation intensities roughly independent of forcing amplitude. The saturation amplitude depends on the Strouhal number of the imposed surging and reaches a maximum at a Strouhal number of 0·30. A root-mean-square sinusoidal surging only 2% of the mean exit speed brings the preferred mode to saturation four diameters downstream from the nozzle, at which point the entrained volume flow has increased 32% over the unforced case. When forced at a Strouhal number of 0·60, the jet seems to act as a compound amplifier, forming a violent 0·30 subharmonic and suffering a large increase of spreading angle. We conclude with the conjecture that the preferred mode having a Strouhal number of 0·30 is in some sense the most dispersive wave on a jet column, the wave least capable of generating a harmonic, and therefore the wave most capable of reaching a large amplitude before saturating. more

Topics: Strouhal number (67%), Jet (fluid) (59%), Reynolds number (56%) more

2,012 Citations

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Padma Kant Shukla

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