Showing papers on "Amplitude published in 1993"

Energy separation in signal modulations with application to speech analysis

Abstract: An efficient solution to the fundamental problem of estimating the time-varying amplitude envelope and instantaneous frequency of a real-valued signal that has both an AM and FM structure is provided. Nonlinear combinations of instantaneous signal outputs from the energy operator are used to separate its output energy product into its AM and FM components. The theoretical analysis is done first for continuous-time signals. Then several efficient algorithms are developed and compared for estimating the amplitude envelope and instantaneous frequency of discrete-time AM-FM signals. These energy separation algorithms are used to search for modulations in speech resonances, which are modeled using AM-FM signals to account for time-varying amplitude envelopes and instantaneous frequencies. The experimental results provide evidence that bandpass-filtered speech signals around speech formants contain amplitude and frequency modulations within a pitch period. >

On amplitude and frequency demodulation using energy operators

Abstract: It is shown that the nonlinear energy-tracking signal operator Psi (x)=(dx/dt)/sup 2/-xd/sup 2/x/dt/sup 2/ and its discrete-time counterpart can estimate the AM and FM modulating signals. Specifically, Psi can approximately estimate the amplitude envelope of AM signals and the instantaneous frequency of FM signals. Bounds are derived for the approximation errors, which are negligible under general realistic conditions. These results, coupled with the simplicity of Psi , establish the usefulness of the energy operator for AM and FM signal demodulation. These ideas are then extended to a more general class of signals that are sine waves with a time-varying amplitude and frequency and thus contain both an AM and an FM component; for such signals it is shown that Psi can approximately track the product of their amplitude envelope and their instantaneous frequency. The theoretical analysis is done for both continuous- and discrete-time signals. >

Measurements of the primary instabilities of film flows

Abstract: We present novel measurements of the primary instabilities of thin liquid films flowing down an incline. A fluorescence imaging method allows accurate measurements of film thickness h(x, y, t) in real time with a sensitivity of several microns, and laser beam deflection yields local measurements with a sensitivity of less than one micron. We locate the instability with good accuracy despite the fact that it occurs (asymptotically) at zero wavenumber, and determine the critical Reynolds number R, for the onset of waves as a function of angle ,8. The measurements of R,(/3) are found to be in good agreement with calculations, as are the growth rates and wave velocities. We show experimentally that the initial instability is convective and that the waves are noisesustained. This means that the waveform and its amplitude are strongly affected by external noise at the source. We investigate the role of noise by varying the level of periodic external forcing. The nonlinear evolution of the waves depends strongly on the initial wavenumber (or the frequency f). A new phase boundary e(R) is measured, which separates the regimes of saturated finite amplitude waves (at high f) from multipeaked solitary waves (at low f). This boundary probably corresponds approximately to the sign reversal of the third Landau coefficient in weakly nonlinear theory. Finally, we show that periodic waves are unstable over a wide frequency band with respect to a convective subharmonic instability. This instability leads to disordered two-dimensional waves.

3-D analytic signal in the interpretation of total magnetic field data at low magnetic latitudes

Abstract: The interpretation of magnetic field data at low magnetic latitudes is difficult because the vector nature of the magnetic field increases the complexity of anomalies from magnetic rocks. The most obvious approach to this problem is to reduce the data to the magnetic pole (RTP), where the presumably vertical magnetisation vector will simplify observed anomalies. However, RTP requires special treatment of north-south features in data observed in low magnetic latitudes due to high amplitude corrections of such features. Furthermore, RTP requires the assumption of induced magnetisation with the result that anomalies from remanently and anisotropically magnetised bodies can be severely disturbed. The amplitude of the 3-D analytic signal of the total magnetic field produces maxima over magnetic contacts regardless of the direction of magnetisation. The absence of magnetisation direction in the shape of analytic signal anomalies is a particularly attractive characteristic for the interpretation of magnetic field data near the magnetic equator. Although the amplitude of the analytic signal is dependent on magneti­sation strength and the direction of geological strike with respect to the magnetisation vector, this dependency is easier to deal with in the interpretation of analytic signal amplitude than in the original total field data or pole-reduced magnetic field. It is also straightforward to determine the depth to sources from the distance between inflection points of analytic signal anomalies.

Habitat‐induced degradation of sound signals: Quantifying the effects of communication sounds and bird location on blur ratio, excess attenuation, and signal‐to‐noise ratio in blackbird song

Abstract: The habitat‐induced degradation of the full song of the blackbird (Turdus merula) was quantified by measuring excess attenuation, reduction of the signal‐to‐noise ratio, and blur ratio, the latter measure representing the degree of blurring of amplitude and frequency patterns over time. All three measures were calculated from changes of the amplitude functions (i.e., envelopes) of the degraded songs using a new technique which allowed a compensation for the contribution of the background noise to the amplitude values. Representative songs were broadcast in a deciduous forest without leaves and rerecorded. Speakers and microphones were placed at typical blackbird emitter and receiver positions. Analyses showed that the three degradation measures were mutually correlated, and that they varied with log distance. Their variation suggests that the broadcast song could be detected across more than four, and discriminated across more than two territories. The song’s high‐pitched twitter sounds were degraded more rapidly than its low‐pitched motif sounds. Motif sounds with a constant frequency projected best. The effect of microphone height was pronounced, especially on motif sounds, whereas the effect of speaker height was negligible. Degradation was inversely proportional to microphone height. Changing the reception site from a low to a high position reduced the degradation by the same amount as by approaching the sound source across one‐half or one‐whole territory. This suggests that the main reason for a male to sing from a high perch is to improve the singer’s ability to hear responses to its songs, rather than to maximize the transmission distance. The difference in degradation between low and high microphone heights may explain why females, which tend to perch on low brush, disregard certain degradable components of the song.

Manipulation of free shear flows using piezoelectric actuators

Abstract: An air jet emanating from a square conduit having an equivalent diameter of 4.34 cm and a centreline velocity of 4 m/s is forced using four resonantly driven piezoelectric actuators placed along the sides of the square exit. Excitation is effected via amplitude modulation of the resonant carrier waveform. The flow is normally receptive to time–harmonic excitation at the modulating frequency but not at the resonant frequency of the actuators. When the excitation amplitude is high enough, the excitation waveform is demodulated by a nonlinear process that is connected with the formation and coalescence of nominally spanwise vortices in the forced segments of the jet shear layer. As a result, the modulating and carrier wave trains undergo spatial amplification and attenuation, respectively, downstream of the exit plane. Strong instabilities of the jet column are excited when the jet is forced at phase relationships between actuators that correspond (to lowest order) to the azimuthal modes m = 0, ±1, ±2, and −1 of an axisymmetric flow. The streamwise velocity component is measured phase locked to the modulating signal in planes normal to the mean flow. Resonantly driving the actuators with different carrier amplitudes results in a distorted mean flow having a featureless spectrum that can be tailored to provide favourable conditions for the introduction and propagation of desirable low-frequency disturbances.

Spectral Estimates of Gravity Wave Energy and Momentum Fluxes. Part I: Energy Dissipation, Acceleration, and Constraints

Abstract: The spectral characteristics of atmospheric gravity wave motions are remarkably uniform in frequency and wavenumber despite widely disparate sources, filtering environments, and altitudes of observation. This permits a convenient and useful means of describing mean spectral parameters, including energy density, anisotropy, energy and momentum fluxes, and wave influences on their environment. The purpose here is to provide a general formulation of the mean energy spectrum as well as estimates of the wave energy and momentum fluxes and the flux divergences expressed as the energy dissipation rate and the induced accelerations in the lower and middle atmosphere. These results show spectral observations to be consistent with independent estimates of energy dissipation rates and to suggest a high degree of anisotropy of the gravity wave field under conditions of strong wave filtering by large-scale, low-frequency motions. In two companion papers, these results are employed to construct a parameterizat...

Gravitational wave tails and binary star systems

Abstract: Gravitational wave tails are produced by back-scattering of the outgoing gravitational radiation (emitted by an isolated system) off the curved spacetime associated with the total mass of the system. This paper investigates the spectral (or Fourier) decomposition of gravitational wave tails at large distances from the system, at the 1.5 post-Newtonian order in the wave field. It is shown that the effects of wave tails are (i) to increase the amplitude of the Fourier components of the (linear) waves by a factor linearly depending on the frequency, and (ii) to add to the phase of the waves a supplementary phase depending on the frequency as omega ln omega . The latter frequency-dependent phase introduces a new effect which should be observable in any radiation containing more than one frequency, for instance in the radiation emitted by a binary star system orbiting a Keplerian ellipse with non-zero eccentricity, or in the radiation emitted by an inspiralling (compact) binary star system. We propose in this paper to include the tail-induced effects (i) and (ii) in the matched filters of the future data analysis of inspiralling compact binary signals in laser interferometer gravity-wave detectors (at least in future, very sensitive, such detectors). In, this way, the filters will be highly correlated with the actual signal, and in particular will remain, as the frequency of the signal increases, in accurate phase with it. The contribution of the wave tail in the total gravitational energy emitted by a binary system is also calculated, and a numerical application to the binary pulsar PSR 1913+16 is presented. We find that the tail-induced relative correction in the orbital PTh of the pulsar is equal to +1.65*10-7 (too small to be observed).

Frequency selective harmonic coding

Abstract: The present invention relates to a method of encoding speech comprised of processing the speech by harmonic coding to provide, a fundamental frequency signal, and a set of optimal harmonic amplitudes, processing the harmonic amplitudes, and the fundamental frequency signal to select a reduced number of bands, and to provide for the reduced number of bands a voiced and unvoiced decision signal, an optimal subset of magnitudes and a signal indicating the positions of the reduced number of bands, whereby the speech signal may be encoded and transmitted as the pitch signal and the signals provided for the reduced number of bands with a bandwidth that is a fraction of the bandwidth of the speech.

X-ray variability of active galactic nuclei : a universal power spectrum with luminosity-dependent amplitude

Abstract: We present power-law model fits to the power spectra of 12 high-quality long look observations of AGNs from the EXOSAT data base. The AGNs concerned differ in X-ray luminosity L x over a range 10 4 . The results are consistent with all objects having a power spectrum index equal to the mean value α=1.55. There is no correlation with L x , suggesting that the power spectrum has little curvature over many decades of frequency. The mean slope is inconsistent with both standard shot-noise processes and traditional 1/f noise but close to the prediction of simple rotating hot spot models. The power spectrum amplitude shows large object-to-object scatter but varies systematically as L x -0.5 . This is inconsistent with any fixed-shape shot-noise model

Optical control of molecular dynamics: Molecular cannons, reflectrons, and wave‐packet focusers

Abstract: We consider the control of molecular dynamics using tailored light fields, based on a phase space theory of control [Y. J. Yan et al., J. Phys. Chem. 97, 2320 (1993)]. This theory enables us to calculate, in the weak field (one‐photon) limit, the globally optimal light field that produces the best overlap for a given phase space target. We present as an illustrative example the use of quantum control to overcome the natural tendency of quantum wave packets to delocalize on excited state potential energy curves. Three cases are studied: (i) a ‘‘molecular cannon’’ in which we focus an outgoing continuum wave packet of I2 in both position and momentum, (ii) a ‘‘reflectron’’ in which we focus an incoming bound wave packet of I2, and (iii) the focusing of a bound wave packet of Na2 at a turning point on the excited state potential using multiple light pulses to create a localized wave packet with zero momentum. For each case, we compute the globally optimal light field and also how well the wave packet produced by this light field achieves the desired target. These globally optimal fields are quite simple and robust. While our theory provides the globally optimal light field in the linear, weak field regime, experiment can in reality only provide a restricted universe of possible light fields. We therefore also consider the control of molecular quantum dynamics using light fields restricted to a parametrized functional form which spans a set of fields that can be experimentally realized. We fit the globally optimal electric field with a functional form consisting of a superposition of subpulses with variable parameters of amplitude, center time, center frequency, temporal width, relative phase, and linear and quadratic chirp. The best fit light fields produce excellent quantum control and are within the range of experimental possibility. We discuss relevant experiments such as ultrafast spectroscopy and ultrafast electron and x‐ray diffraction which can in principle detect these focused wave packets.

Gravity waves generated by a tropical cyclone during the STEP tropical field program: A case study

Abstract: Overflights of a tropical cyclone during the Australian winter monsoon field experiment of the Stratosphere-Troposphere Exchange Project (STEP) show the presence of two mesoscale phenomena: a vertically propagating gravity wave with a horizontal wavelength of about 110 km and a feature with a horizontal scale comparable to that of the cyclone's entire cloud shield. The larger feature is fairly steady, though its physical interpretation is ambiguous. The 110-km gravity wave is transient, having maximum amplitude early in the flight and decreasing in amplitude thereafter. Its scale is comparable to that of 100-to 150-km-diameter cells of low satellite brightness temperatures within the overall cyclone cloud shield; these cells have lifetimes of 4.5 to 6 hrs. These cells correspond to regions of enhanced convection, higher cloud altitude, and upwardly displaced potential temperature surfaces. The temporal and spatial distribution of meteorological variables associated with the 110-km gravity wave can be simulated by a slowly moving transient forcing at the anvil top having an amplitude of 400-600 m, a lifetime of 4.5-6 hrs, and a size comparable to the cells of low brightness temperature.

A Technique for Predicting the Amplitude of the Solar Cycle

Abstract: Predictions of the amplitude of the last three solar cycles have demonstrated the value and accuracy of the group of prediction methods known as the ‘precursor’ techniques. These are based on a correlation between cycle amplitude and phenomena observed on the Sun, or originating from the Sun, during the declining phase of the cycle or at solar minimum. In many cases, precursor predictions make use of the long record of geomagnetic disturbance indices, assuming that these indices are indicative of solar phenomena such as the occurrence of coronal holes. This paper describes a precursor technique for predicting the amplitude of the solar cycle using geomagnetic indices. The technique is accurate — it would have predicted each of the last 11 cycles with a typical error of less than 20 in sunspot number. It has also advantage that a prediction of the lower limit of the amplitude can be made throughout the declining phase, this limit building to a final value at the onset of the new cycle.

On the nonlinear dynamics of free bars in straight channels

Abstract: A simple morphological model is considered which describes the interaction between a unidirectional flow and an erodible bed in a straight channel. For sufficiently large values of the width-depth ratio of the channel the basic state, i.e. a uniform current over a flat bottom, is unstable. At near-critical conditions growing perturbations are confined to a narrow spectrum and the bed profile has an alternate bar structure propagating in the downstream direction. The timescale associated with the amplitude growth is large compared to the characteristic period of the bars. Based on these observations a weakly nonlinear analysis is presented which results in a GinzburgLandau equation. It describes the nonlinear evolution of the envelope amplitude of the group of marginally unstable alternate bars. Asymptotic results of its coefficients are presented as perturbation series in the small drag coefficient of the channel. In contrast to the Landau equation, described by Colombini et al. (1987), this amplitude equation also allows for spatial modulations due to the dispersive properties of the wave packet. It is demonstrated rigorously that the periodic bar pattern can become unstable through this effect, provided the bed is dune covered, and for realistic values of the other physical parameters. Otherwise, it is found that the periodic bar pattern found by Colombini et al. (1987) is stable. Assuming periodic behaviour of the envelope wave in a frame moving with the group velocity, simulations of the dynamics of the Ginzburg-Landau equation using spectral models are carried out, and it is shown that quasi-periodic behaviour of the bar pattern appears.

Azimuthal shear wave velocity anisotropy in the Basin and Range Province using moho Ps converted phases

Abstract: An eight-station large aperture seismometer array was deployed in the Basin and Range province of west-central Nevada for the 1988–1989 Program for Array Seismic Studies of the Continental Lithosphere (PASSCAL) Passive-source seismic experiment. During the 10 months of data collection a total of 100 teleseismic events were recorded (Δ > 30°). Source-equalized P wave receiver functions show waveform variations in timing, amplitude, and polarity in the Moho Ps phase that is diagnostic of shear wave velocity anisotropy. Information regarding the crustal anisotropic component can be recovered through the Ps phase since it is generated at the Moho and is sensitive to shear wave splitting in the crust only. We utilize single-event, stacked, and array-beam-formed receiver functions to minimize the influence of structural variations and scattering on the observed converted phases. Analysis of shear wave splitting of the Ps conversion from the crust-mantle boundary indicates a fast azimuth of anisotropy oriented approximately NW-SE with observed time delays of 0.20 s. This strongly suggests coherent crustal anisotropy with a fast direction perpendicular to the strike of fault block mountain ranges. This fabric is most likely due to the preferred crystallographic orientation of seismically anisotropic minerals in the middle to lower crust rather than the distribution of Basin and Range upper crustal fracture systems.

Amplitude Expansions for Instabilities in Populations of Globally-Coupled Oscillators

Abstract: We analyze the nonlinear dynamics near the incoherent state in a mean-field model of coupled oscillators. The population is described by a Fokker-Planck equation for the distribution of phases, and we apply center-manifold reduction to obtain the amplitude equations for steady-state and Hopf bifurcation from the equilibrium state with a uniform phase distribution. When the population is described by a native frequency distribution that is reflection-symmetric about zero, the problem has circular symmetry. In the limit of zero extrinsic noise, although the critical eigenvalues are embedded in the continuous spectrum, the nonlinear coefficients in the amplitude equation remain finite in contrast to the singular behavior found in similar instabilities described by the Vlasov-Poisson equation. For a bimodal reflection-symmetric distribution, both types of bifurcation are possible and they coincide at a codimension-two Takens Bogdanov point. The steady-state bifurcation may be supercritical or subcritical and produces a time-independent synchronized state. The Hopf bifurcation produces both supercritical stable standing waves and supercritical unstable travelling waves. Previous work on the Hopf bifurcation in a bimodal population by Bonilla, Neu, and Spigler and Okuda and Kuramoto predicted stable travelling waves and stable standing waves, respectively. A comparison to these previous calculations shows that the prediction of stable travelling waves results from a failure to include all unstable modes.

An experimental and analytical study of autoparametric resonance in a 3DOF model of cable-stayed-beam

Abstract: Autoparametric interaction and the associated phenomenon of amplitude saturation are experimentally observed in a physical model of cable-and-beam structure In this system, the horizontal beam is fixed at one end and supported at the other end by an inclined taut cable The longitudinal axes of beam and cable are in a vertical plane Three natural frequencies of the system are approximately of the ratio 1:1:2 This is a combination of two conditions that are very likely to occur in relatively long-span, multi-stay-cable bridges, namely, 1:1 tuning and 1:2 superharmonic tuning While the beam is vertically excited with sufficiently large force near a primary resonance, the cable vibrates horizontally at half of excitation frequency The beam also vibrates horizontally at half-frequency, as well as vertically As the vertical excitation on the bean is further increased in amplitude, the vertical vibration amplitude gets saturated instead of increasing proportionately A 3DOF analytical model of the structure is also derived, where the finite motion of the cable introduces geometric nonlinearities in quadratic and cubic forms The system parameters having been carefully measured from the experimental model, steady-state solutions of the coupled nonlinear equations of motion are obtained, by the perturbation method of multiple time scales Agreement between experimental observation and analytical prediction is very good, both qualitatively and quantitatively Very good agreement is found also in the case of horizontal excitation of the beam, where effects of linear and nonlinear interaction are apparent

Wind stress, bed roughness and sediment suspension on the inner shelf during an extreme storm event

Abstract: Instrumented bottom boundary layer tripods were deployed on the inner shelf at depths of 13 and 8 m off the U.S. Army Corps of Engineers Field Research Facility at Duck, NC, U.S.A., over a 2-week period that included the severe and prolonged “Halloween Storm” of late October 1991. The storm persisted for 5 days and generated waves with heights and periods of up to 6 m and 22 s. Although the instrumentation was destroyed, current profile and suspended sediment concentration profile data were recovered from the 13 m site. Mean currents attained speeds of nearly 0.5 m s −1 at 0.29 m above the bed and were directed about 10° offshore from shore-parallel. These strong currents are shown to be wind driven and result in predictions of a wind-drag coefficient, C a = 4.7 × 10 −3 . The currents were recorded simultaneously with root-mean-square (rms) wave orbital velocity amplitudes in the 0.6–1.0 m s −1 range. During the peak of the storm suspended sediment concentrations exceeded 1 kg m −3 throughout the lower 1 m of the water column. Analysis of current profiles, accounting for the presence of waves, is performed to obtain an equivalent bottom roughness, k n , of approximately 15 times the median sediment diameter, i.e. k n ⋍ 15 d 50 . Analysis of the suspended sediment concentration profiles, using the experimentally obtained hydrodynamic characteristics, results in a value of 4 × 10 −4 for the resuspension parameter, γ 0 , with the reference concentration taken 7 d 50 above the bed. From the severity of the storm condition it is inferred that our estimates of k n and γ 0 correspond to sheet flow conditions.

Linear and nonlinear ac response in the superconducting mixed state

Abstract: The response of the vortex system in the mixed state of type-II superconductors to ac fields is discussed from a unique macroscopic point of view. Linear and nonlinear response are derived as two opposite limits of the same diffusionlike equation for magnetic flux. ac susceptibility experiments carried out in the limit of strong nonlinearity are entirely equivalent to magnetic-relaxation or field-ramp experiments. The magnitude and frequency dependence of the nonlinearity threshold, or amplitude of the ac field where one crosses from essentially linear to strongly nonlinear response, are found and discussed for both the vortex-liquid and vortex-glass states.

Observations of nonlinear elastic wave behavior in sandstone

Abstract: An experimental investigation of nonlinear elastic wave behavior was conducted using a 2‐m‐long cylindrical rod of Berea sandstone in order to study the strong elastic nonlinearity that is characteristic of microcracked materials. Measurements of the displacement field at distance x from the source show rich harmonic content with harmonic amplitudes depending on x, source frequency, and source amplitude. The amplitude of the 2ω harmonic is found to grow linearly with x and as the square of both the source frequency ω and the source amplitude U. This behavior is in agreement with the predictions of nonlinear elasticity theory for a system with cubic anharmonicity. From the measured amplitude of the 2ω harmonic the parameter ‖β‖, a measure of the strength of the cubic anharmonicity, is found to be of order 104 (7.0×103±25%). This value is orders of magnitude greater than that found in ordinary uncracked materials. These results suggest that wave distortion effects due to nonlinear elasticity can be large in seismic wave propagation and significantly influence the relationship of seismic signal to seismic source.

Effects of local variations in skull and scalp thickness on EEG's and MEG's

Abstract: The results of a computer modeling study are reported They indicate that local variations in skull and scalp thickness have effects on electroencephalograms (EEGs) and magnetoencephalograms (MEGs) which range from a simple intuitive effect to complex effects which depend on such factors as source depth and orientation, the geometry of the variation in skull and scalp thickness, etc These results also indicate that local variations in skull and scalp thickness cause EEG localization errors which are generally much less than 1 cm and MEG localization errors which are even smaller These results also indicate that multichannel and single-channel MEG measurements will produce localization errors of approximately the same amplitude when there is a bump on the external surface of the head but that multichannel measurements will produce significantly smaller localization errors than single-channel measurements when a depression is present in that surface >

Chronocyclic tomography for measuring the amplitude and phase structure of optical pulses

Abstract: We describe a new method—chronocyclic tomography—for determining the amplitude and phase structure of a short optical pulse. The technique is based on measurements of the energy spectrum of the pulse after it has passed through a time–frequency-domain imaging system. Tomographic inversion of these measured spectra yields the time–frequency Wigner distribution of the pulse, which uniquely determines the amplitude and phase structure.

Stormtime transport of ring current and radiation belt ions

Abstract: This is an investigation of stormtime particle transport that leads to formation of the ring current. Our method is to trace the guiding-center motion of representative ions (having selected first adiabatic invariants mu) in response to model substorm-associated impulses in the convection electric field. We compare our simulation results qualitatively with existing analytically tractable idealizations of particle transport (direct convective access and radial diffusion) in order to assess the limits of validity of these approximations. For mu approximately less than 10 MeV/G (E approximately less than 10 keV at L equivalent to 3) the ion drift period on the final (ring-current) drift shell of interest (L equivalent to 3) exceeds the duration of the main phase of our model storm, and we find that the transport of ions to this drift shell is appropriately idealized as direct convective access, typically from open drift paths. Ion transport to a final closed drift path from an open (plasma-sheet) drift trajectory is possible for those portions of that drift path that lie outside the mean stormtime separatrix between closed and open drift trajectories, For mu approximately 10-25 MeV/G (110 keV approximately less than E approximately less than 280 keV at L equivalent to 3) the drift period at L equivalent to 3 is comparable to the postulated 3-hr duration of the storm, and the mode of transport is transitional between direct convective access and transport that resembles radial diffusion. (This particle population is transitional between the ring current and radiation belt). For mu approximately greater than 25 MeV/G (radiation-belt ions having E approximately greater than 280 keV at L equivalent to 3) the ion drift period is considerably shorter than the main phase of a typical storm, and ions gain access to the ring-current region essentially via radial diffusion. By computing the mean and mean-square cumulative changes in 1/L among (in this case) 12 representative ions equally spaced in drift time around the steady-state drift shell of interest (L equivalent to 3), we have estimated (from both our forward and our time-reversed simulations) the time-integrated radial-diffusion coefficients D(sup sim)(sub LL) for particles having selected values of mu approximately greater than 15 MeV/G. The results agree surprisingly well with the predictions (D(sup ql)(sub LL)) of quasilinear radial diffusion theory, despite the rather brief duration (approximately 3 hrs) of our model storm and despite the extreme variability (with frequency) of the spectral-density function that characterizes the applied electric field during our model storm. As expected, the values of D(sup sim)(sub LL) deduced (respectively) from our forward and time-reversed simulations agree even better with each other and with D(sup sim)(sub LL) when the impulse amplitudes which characterize the individual substorms of our model storm are systematically reduced.

Role of pumping statistics and dynamics of atomic polarization in quantum fluctuations of laser sources

Abstract: We solve the problem of a laser with variable pumping statistics for any relative magnitude of the atomic- and cavity-decay constants, and obtain a different regime of sub-Poissonian light generation. We show that, even for Poissonian pumping, the noise in the amplitude quadrature outside the cavity can be reduced up to 50% below the shot-noise level when the polarization but not the populations can be adiabatically eliminated. Maximum noise reduction in this case is obtained when the lower level decays much faster than the upper one and occurs at a frequency given by the geometrical mean of the decay rates of the field and the lower-level population. Furthermore, the full consideration of atomic memory effects leads to a generalization of previous results on regularly pumped lasers. We find that, for regular pumping, maximum amplitude-noise reduction (up to complete quieting) still occurs at zero frequency in all cases. However, a long-living polarizaton leads to an increase in amplitude noise and may even eliminate the dip at zero frequency, at the same time leading to a significant quenching of the laser linewidth in the bad-cavity limit.

Seismic Attenuation By Scattering: Theory and Numerical Results

Abstract: SUMMARY Estimates of seismic wave attenuation are strongly affected by scattering. Scattering is an important effect caused by interaction of seismic wavefields with inhomogeneities of hydrocarbon reservoirs, Earth's crust and mantle. In order to study the contribution of scattering to apparent attenuation we consider plane-wave propagation in acoustic 2-D and 3-D inhomogeneous media. Different attenuation estimates result depending on what wavefield function is being averaged during corresponding processing. By wave-theoretical analysis and high-order finite difference modelling in two dimensions we show that scattering attenuation estimates derived from the mean of amplitude spectra and from the mean logarithm of amplitude spectra depend on travel distance. For not too long travel distances, where the coherent part of the wavefield dominates, we give an analytical description of these estimates. In 2-D and 3-D the relations are established between the autocorrelation functions of velocity fluctuations of a random medium and the autocorrelation functions of amplitude and phase fluctuations on a receiver line perpendicular to the general propagation direction of an originally plane wave. For long distances, where the wavefield fluctuates strongly, we show that both mean logarithm of amplitude and logarithm of mean amplitude tend to constants. They differ approximately by a factor two in both scattering regimes. the scattering attenuation coefficient of the meanfield is not dependent on travel distance. We compared our theoretical results with numerical calculations and found excellent agreements. the concept presented clarifies the nature of seismic Q estimations in the presence of scattering and can help to yield statistical earth models from seismic data.