Showing papers on "Amplitude published in 1979"
TL;DR: In this article, the significance of color patterns and their geological interpretation is illustrated by examples of seismic data from three areas in the US and the UK, showing that color patterns can help an interpreter see their interrelationship and spatial changes.
Abstract: The conventional seismic trace can be viewed as the real component of a complex trace which can be uniquely calculated under usual conditions. The complex trace permits the unique separation of envelope amplitude and phase information and the calculation of instantaneous frequency. These and other quantities can be displayed in a color-encoded manner which helps an interpreter see their interrelationship and spatial changes. The significance of color patterns and their geological interpretation is illustrated by examples of seismic data from three areas.
1,290 citations
TL;DR: In this paper, a new equation was derived for large amplitude forced radial oscillations of a bubble in an incident sound field, including the effects of acoustic radiation, as in Keller and Kolodner's equation.
Abstract: A new equation is derived for large amplitude forced radial oscillations of a bubble in an incident sound field. It includes the effects of acoustic radiation, as in Keller and Kolodner’s equation, and the effects of viscosity and surface tension, as in the modified Rayleigh equation due to Plesset, Noltingk and Neppiras, and Poritsky. The free and forced periodic solutions are computed numerically. For large bubbles, such as underwater explosion bubbles, the free oscillations agree with those obtained by Keller and Kolodner. For small bubbles, such as cavitation bubbles, with small or intermediate forcing amplitudes, the results agree with those calculated by Lauterborn from the modified Rayleigh equation of Plesset et al. For large forcing amplitudes that equation yielded unsatisfactory results whereas the new equation yields quite satisfactory ones.
1,027 citations
TL;DR: Individual quantal responses exhibited a smooth shape very similar to that of the average quantal response, which suggests that a single photoisomerization releases many particles of transmitter and that radial diffusion of internal transmitter is not a major source of delay in the light response.
Abstract: 1 A suction electrode was used to record the membrane current of single rod outer segments in pieces of toad retina During dim illumination the membrane current showed pronounced fluctuations 2 Amplitude histograms of responses to dim flashes of fixed intensity exhibited two discrete peaks, one at 0 pA and one near 1 pA, suggesting that the response was quantized By setting a criterion amplitude level, flash responses could be classed as 'failures' (no response) or as 'successes' (at least one quantal event) 3 The variation of fraction of successes with flash intensity was consistent with the hypothesis that each quantal electrical event resulted from a single photoisomerization 4 The quantal event had a mean amplitude of about 1 pA (5% of the standing dark current) and a standard deviation of 02 pA Dispersion in the event amplitude prevented identification of histogram peaks corresponding to two or more photoisomerizations 5 Individual quantal responses exhibited a smooth shape very similar to that of the average quantal response This suggests that a single photoisomerization releases many particles of transmitter and that radial diffusion of internal transmitter is not a major source of delay in the light response 6 The 'quantum efficiency' with which an absorbed photon generated an electrical event was measured as 05 +/- 01 (SE of mean, n = 4) This is slightly lower than the quantum efficiency of photoisomerization obtained previously for rhodopsin in solution 7 At wavelengths between 420 and 700 nm the quantal event was invariant in size, although the cell's sensitivity varied over a range of 10(5) 8 The power spectrum of the fluctuations in dim steady light was predicted by assuming that a random series of quantal events occurred independently 9 In brighter light the fluctuations were faster, and the response to an incremental flash was reduced in size and duration The power spectrum could be predicted by assuming random superposition of events with the shape of the incremental flash response
836 citations
TL;DR: The velocity of shortening at zero load was studied during fused tetanic contractions and single twitches in isolated skeletal muscle fibres of Rana temporaria and the technique used for determination of the speed of unloaded shortening consisted of a series of quick releases of different amplitudes applied at a given instant during activity.
Abstract: 1. The velocity of shortening at zero load was studied during fused tetanic contractions and single twitches in isolated skeletal muscle fibres of Rana temporaria. 2. The technique used for determination of the speed of unloaded shortening consisted of a series of quick releases of different amplitudes applied at a given instant during activity. The time, delta t, needed for the fibre to take up the slack was plotted against the amplitude of release, delta L. The slope of the straight line relating delta t-delta L provided a measure of the velocity of shortening at zero load, V0. 3. V0 was compared with force-velocity data obtained at finite loads (load-clamp recordings). The predicted velocity of shortening at zero load, derived by hyperbolic extrapolation from velocities at low and intermediate loads, was not significantly different from V0. 4. The temperature dependence of isometric force and of shortening velocity was investigated between 2 and 12 degrees C in the same fibres. Q10 was 2.67 +/- 0.07 (S.E. of mean, n = 6) for V0 and 1.24 +/- 0.01 for tetanic force. 5. The velocity of unloaded shortening was determined at different sarcomere lengths in the range 1.4--3.1 microns. V0 was constant between 1.65 microns and approximately 2.7 microns. It decreased below 1.65 microns and increased above 2.7 microns. 6. The decrease in velocity at short sarcomere lengths probably reflects an increase of the passive resistance to shortening. The increase in velocity at long sarcomere lengths can be accounted for by the passive compressive force that is produced by the parallel elastic elements of the prestretched fibre. 7. V0 was determined at the peak of the twitch and during the plateau of the fused tetanus in the same fibre. Whereas the peak twitch force varied between 38 and 85% of the tetanic tension in the different fibres (mean: 71 +/- 5%, n = 8), V0 during the twitch was 99 +/- 2% of the value recorded during the tetanus. Depression of the isometric twitch amplitude to 10% of the control value by dantrolene did not cause any significant reduction of V0.
767 citations
TL;DR: In this paper, the evolution of an axially symmetric vortex is calculated with a quasi-geostrophic, adiabatic, hydrostatic β-plane, two vertical mode model.
Abstract: The evolution of an isolated, axially symmetric vortex is calculated with a quasi-geostrophic, adiabatic, hydrostatic. β-plane, two vertical mode model. The circumstances of greatest interest are those of weak friction and large vortex amplitude (strong nonlinearity). Systematic studies are made of the consequences of varying the frictional coefficient, the vortex amplitude, the vortex radius (relative to the deformation radius), the degree of nonlinear coupling between the two vertical modes and the initial vertical structure of the vortex. Results of note include the following. Within the approximation of a single vertical mode model (i.e., in the absence of modal coupling), a baroclinic vortex has an increased westward and a finite meridional propagation speed when its amplitude is greater than infinitesimal. Both of these speeds, however, are limited by the wave speeds (as determined from infinitesimal amplitude theory) of the weak dispersion field outside the vortex. The vortex amplitude dec...
361 citations
TL;DR: In this paper, it was shown that the quasi-static transient response in the air due to an arbitrary loop situated at the earth's surface can be represented by a downward and outward moving current filament, of diminishing amplitude and having the same shape as the transmitter loop.
Abstract: For a step‐function excitation, it is shown that, to a first‐order approximation, the quasi‐static transient response in the air due to an arbitrary loop situated at the earth’s surface can be represented by a downward and outward moving current filament, of diminishing amplitude and having the same shape as the transmitter loop.
304 citations
TL;DR: In this paper, the average swimming speed and power consumption for planar sinusoidal waves (amplitude α, wave-number k) are computed for a wide range of parameters.
Abstract: Numerical results are presented for planar sinusoidal waves (amplitude α, wave-number k). The average swimming speed and power consumption are computed for a wide range of the parameters. The optimal sine wave for minimizing power consumption is found to be a single wave with amplitude αk ≈ 1. The power consumption is found to be relatively insensitive to changes in the flagellar radius. The optimal flagellar length is found to be in the range L/A = 20–40. The instantaneous force distribution and flow field for a typical organism are presented. The trajectory of the organism through one cycle shows that a wave of constant amplitude may have the appearance of increasing amplitude owing to the yawing motion of the organism.The results are compared with those obtained using resistance coefficients. For organisms with small cell bodies (A/L = 0.05), the average swimming speed predicted by Gray-Hancock coefficients is accurate to within 10%. For large cell bodies (A/L = 0.2), the error in swimming speed is approximately 20%. The relative error in the predicted power consumption is 25–50%. For the coefficients suggested by Lighthill, the power is consistently underestimated. The Gray-Hancock coefficients underestimate the power for small cell bodies and overestimate it for large cell bodies.
224 citations
TL;DR: In this article, the collapse of an isothermal protostellar cloud with pressure, gravity, and rotation included is followed with two independent computer codes, and the collapse is followed through an increase in density of over four orders of magnitude to the point where a binary protostar forms.
Abstract: The collapse of an isothermal protostellar cloud with pressure, gravity, and rotation included is followed with two independent computer codes. For the initial condition, a nonaxisymmetric perturbation of mode m = 2 and 50% amplitude is introduced into a cloud of 1 solar mass with a mean density of 1.44 x 10 to the -17g/cu cm and a uniform angular velocity of 1.6 x 10 to the -12 rad/sec. The collapse is followed through an increase in density of over four orders of magnitude to the point where a binary protostar forms. The agreement between the results of the two calculations is good.
194 citations
TL;DR: In this paper, the authors present a general self-consistent nonlinear theory of the FEL process, which results in a set of coupled differential equations governing the spatial evolution of the amplitudes and wavelength of the radiation and space charge fields.
Abstract: The development of lasers in which the active medium is a relativistic stream of free electrons has recently evoked much interest. The potential advantages of such free-electron lasers include, among other things, continuous frequency tunability, very high operating power, and high efficiency. The free-electron laser (FEL) is characterized by a pump field, for example, a spatially periodic magnetic field which scatters from a relativistic-electron beam. The scattered radiation has a wavelength much smaller than the pump wavelength, depending on the electron-beam energy. The authors present a general self-consistent nonlinear theory of the FEL process. The nonlinear formulation of the temporal steady-state FEL problem results in a set of coupled differential equations governing the spatial evolution of the amplitudes and wavelength of the radiation and space-charge fields. These equations are readily solved numerically since the amplitude and wavelength vary on a spatial scale which is comparable to a growth length of the output radiation. A number of numerical and analytical illustrations are presented, ranging from the optical to the submillimeter-wavelength regime. Our nonlinear formulation in the linear regime is compared with linear theory, and agreement is found to be excellent. Analytical expressions for the saturated efficiency and radiation amplitude are alsomore » shown to be in very good agreement with our nonlinear numerical solutions. Efficiency curves are obtained for both the optical and submillimeter FEL examples with fixed magnetic-pump parameters. It is shown that these intrinsic efficiencies can be greatly enhanced by appropriately contouring the magnetic-pump period. In the case of the optical FEL, the theoretical single-pass efficiency can be made greater than 20% by appropriately decreasing the pump period and increasing the pump magnetic field.« less
180 citations
Esso1
TL;DR: Reflection cycle patterns include the configuration of reflections (i.e., layered, chaotic, and reflection-free) and the nature of cycle terminations at the depositional unit boundaries as mentioned in this paper.
Abstract: Depositional environments can be predicted from seismic data through an orderly approach to the interpretation of seismic reflections. One keystone to this approach is an understanding of the effects of lithology and bed spacing on reflection parameters. Amplitude, frequency, and continuity are some of the parameters most useful for interpreting environments. Reflection amplitude contains information on the velocity and density contrasts at individual interfaces and on the extent of interbedding. Frequency is primarily a characteristic of the nature of the seismic pulse, but it is also related to such geologic factors as the spacing of reflectors or lateral changes in interval velocity. Continuity of reflections is closely associated with continuity of bedding (e.g., continuous reflections suggest widespread, layered deposits).A second keystone to this interpretive approach is the parallelism of reflection cycles to gross bedding and, therefore, to physical surfaces that separate older from younger sediments. Exceptions to this concept include (1) fluid contact reflections, (2) limitations imposed by seismic resolution, and (3) various non-geologic coherent events. In spite of these exceptions, this concept provides a powerful tool for the analysis of reflection patterns.Reflection cycle patterns include the configuration of reflections (i.e., layered, chaotic, and reflection-free) and the nature of cycle terminations at the depositional unit boundaries. The external form of the depositional unit can be analyzed from a grid of seismic lines and is valuable in interpreting the depositional processes responsible for the unit. Sheet, sheet drape, wedge, lens, fan, and other forms are described. The areal associations of these forms are often critical to environmental interpretation. Examples of facies interpretation from seismic sections are shown for depositional environments ranging from shelf to basin floor.
177 citations
TL;DR: Solutions to Long's equation for a stably stratified incompressible fluid traversing a mountain range are obtained for various terrain shapes and amplitudes when the horizontal scale is large compared to the vertical wavelength as mentioned in this paper.
Abstract: Solutions to Long's equation for a stably stratified incompressible fluid traversing a mountain range are obtained for various terrain shapes and amplitudes when the horizontal scale is large compared to the vertical wavelength. Nonlinear lower and upper (radiative) boundary conditions are utilized and found to have a strong influence on the wave structure at large amplitudes. The results for symmetric and asymmetric mountain profiles reveal that the wave amplitude and wave drag are significantly enhanced for mountains with gentle windward and steep leeward slopes. These results confirm and explain those obtained by Raymond (1972) using a different solution method. Several results obtained by Smith (1977) from perturbation analysis are also confirmed and extended to large amplitudes. The methods are also applied to investigate the nonlinear nature of the singularity predicted by linear theory for flow over a step.
TL;DR: There was a positive correlation between the amplitude of F32 and the M wave, and this relationship was abnormal in 60 percent of the studies of patients with spasticity.
Abstract: The amplitude of 32 averaged F responses (F32) recorded with surface electrodes was 1 percent of the amplitude of the M wave. The largest F response (Fmax) was 4.5 percent of the M wave. In spasticity, Fmax did not increase in amplitude but became more persistent, resulting in a significant increase of F32. There was a positive correlation between the amplitude of F32 and the M wave, and this relationship was abnormal in 60 percent of the studies of patients with spasticity.
TL;DR: In this article, the slowly varying solitary wave is constructed as an asymptotic solution of the variable coefficient Korteweg-de Vries equation, and a multiple scale method is used to determine the amplitude and phase of the wave to the second order in the perturbation parameter.
Abstract: The slowly varying solitary wave is constructed as an asymptotic solution of the variable coefficient Korteweg-de Vries equation. A multiple scale method is used to determine the amplitude and phase of the wave to the second order in the perturbation parameter. The structure ahead and behind the solitary wave is also determined, and the results are interpreted by using conservation laws. Outer expansions are introduced to remove non-uniformities in the expansion. Finally, when the coefficients satisfy a certain constraint, an exact solution is constructed.
TL;DR: In this article, the waveforms of the two polarizations at both frequencies were presented explicitly, and the amplitude of the precession amplitude was derived from observations of gravitational wave signals.
Abstract: An axially symmetric, torque-free rigid body, rotating and precessing, emits gravitational quadrupole radiation at two frequencies, omega and 2 omega, corresponding to the l = 2, m = 1,2 spherical harmonics. The paper presents explicitly the waveforms of the two polarizations at both frequencies. From observations of gravitational waves, one can derive information about the body's orientation and its precession amplitude. Electromagnetic radiation emitted by a spot fixed on the surface of the body arrives in pulses at a mean frequency Omega which is typically different from omega. If the body is not axially symmetric but the amplitude of the precession is small, the gravitational radiation at the lower frequency omega is split into two frequencies on either side of the electromagnetic pulse frequency. Explicit waveforms for the two polarizations in this case are also presented.
TL;DR: In this article, the importance of higher configuration mixing is shown to increase the amplitude of a reducedwidth amplitudes YL in the nuclear surface area, which produces a tremendous enhancement of the α-decay widths of 212Po.
TL;DR: In this article, a general description of internal surfaces is considered which allows for irregularities and partially closed cracks, leading to a Q−1 that increases with strain amplitude and suggests that under in situ (small strain) conditions, frictional attenuation becomes secondary to linear loss mechanisms.
Abstract: Frictional sliding on crack surfaces and grain boundaries is examined as a mechanism of wave attenuation. In contrast to previous work based on idealized elliptic crack models a general description of internal surfaces is considered which allows for irregularities and partially closed cracks. This leads to Q−1 that increases with strain amplitude. Such an amplitude dependence is often observed in large-strain laboratory measurements. This suggests that under in situ (small strain) conditions, frictional attenuation becomes secondary to linear loss mechanisms, either disappearing or becoming masked.
TL;DR: In this paper, the instability of two layers of immiscible inviscid and incompressible fluids in relative motion is studied with allowance for small, but finite, disturbances and for spatial as well as temporal development.
Abstract: The instability of two layers of immiscible inviscid and incompressible fluids in relative motion is studied with allowance for small, but finite, disturbances and for spatial as well as temporal development. By using the method of multiple scaling, a generalized formulation of the amplitude equation is obtained, applicable to both stable and marginally unstable regions of parameter space. Of principal concern is the neighbourhood of the critical point for instability, where weakly nonlinear solutions can be found for arbitrary initial conditions. Among the analytical results, it is shown that (1) the nonlinear effects can be stabilizing or destabilizing depending on the density ratio, (2) the existence of purely spatial instability depends upon the frame of reference, the density ratio, and whether the nonlinear effects are stabilizing, (3) exact nonlinear solutions of the amplitude equation exist representing modulations of permanent form travelling faster than the signal velocity of the linear equation (in particular, a solution is found that represents a solitary wave packet), and (4) the linear solution to the impulsive initial value problem has 9fronts’ which travel with the two (multiple) values of the group velocity (the packet as a whole moves with the mean of the two values). Numerical solutions of the amplitude equation (a nonlinear, unstable Klein-Gordon equation) are also presented for the case of nonlinear stabilization. These show that the development of a localized disturbance, in one or two dimensions, is highly dependent on the precise form of the initial conditions, even when the initial amplitude is very small. The exact solutions mentioned above play an important role in this development. The numerical experiments also show that the familiar uniform solution, an oscillatory function of time only, is unstable to spatial modulation if the amplitude of oscillation is large enough.
TL;DR: In this paper, the linearized water wave theory is used to show that a submerged long circular cylinder suitably constrained by springs and dampers to make small harmonic oscillations, can be extremely efficient in absorbing the energy in an incident regular wave whose crests are parallel to the axis of the cylinder.
TL;DR: In this article, a resistivity structure whose responses are acceptably close to the observations, that is, the measured amplitudes and/or phases, is constructed through an automated algorithm which is characterized by numerical stability and rapid convergence.
Abstract: Natural source magnetotelluric (MT) data are inverted to find a subsurface resistivity which is isotropic and a continuous function of depth. The inversion consists of two parts. In the first, our concern is to construct a resistivity structure whose responses are acceptably close to the observations, that is, the measured amplitudes and/or phases. This construction proceeds iteratively and is realized through an automated algorithm which is characterized by numerical stability and rapid convergence. In the second part, we attempt to investigate the degree of nonuniqueness inherent in the problem. This is accomplished by considering only spatial averages of the resistivity because all models linearly close to the constructed model will have the same average resistivity. The predictions of this statement are examined quantitatively in an example where the averages from five different models which reproduce the observations are compared. In an example using data from a moderately complex layered model, we h...
TL;DR: The shorter the time constant of the recording system, the smaller the amplitude of both the P300 and Slow Wave components, and the ERP waveform was markedly affected.
Abstract: A standard counting task was used to illustrate the effect of the time constant of the recording system on the amplitude and waveform of the P300 component. A random sequence of 1500 Hz (probability = .10) and 1000 Hz (probability = .90) tones was presented to one male subject. The EEG from Cz and Pz was recorded simultaneously at time constants of 0.1, 0.3, 1.0, and 10.0 sec. The ERP waveform was markedly affected by the time constant: the shorter the time constant, the smaller the amplitude of both the P300 and Slow Wave components.
TL;DR: The nonlinear fluid equations which characterize the electrostatic ion cyclotron wave have traveling-wave solutions with sinusoidal, spiky, and sawtooth forms.
Abstract: Electrostatic ion cyclotron waves observed in space at altitudes between 5000 and 8000 km often have a sinusoidal form. Occasionally, however, wave forms having a spiky or sawtooth form indicative of steepening are observed. The nonlinear fluid equations which characterize the electrostatic ion cyclotron wave have traveling-wave solutions with sinusoidal, spiky, and sawtooth forms. The wave form depends on the amplitude and phase velocity of the wave.
TL;DR: In this article, a study of large amplitude, progressive interfacial waves moving between two infinite fluids of different densities was carried out and it was shown that the maximum height of a Boussinesq wave, which has the density almost the same above and below the interface, is 2·5 times higher than a surface wave of the same wavelength.
Abstract: This paper contains a study of large amplitude, progressive interfacial waves moving between two infinite fluids of different densities. The highest wave has been calculated using the criterion that it has zero horizontal fluid velocity at the interface in a frame moving at the phase speed of the waves. For free surface waves this criterion is identical to the criterion due to Stokes, namely that there is a stagnation point at the crest of each wave. I t is found that as the density of the upper fluid increases relative to the density of the lower fluid the maximum height of the wave, for fixed wavelength, increases. The maximum height of a Boussinesq wave, which has the density almost the same above and below the interface, is 2·5 times the maximum height of a surface wave of the same wavelength. A wave with air over the top of it can be about 2% higher than the highest free surface wave. The point at which the limiting criterion is first satisfied moves from the crest for free surface waves to the point half-way between the crest and the trough for Boussinesq waves. The phase speed, momentum, energy and other wave properties are calculated for waves up to the highest using Pade approximants. For free surface waves and waves with air above the interface the maximum value of these properties occurs for waves which are lower than the highest. For Boussinesq waves and waves with the density of the upper fluid onetenth of the density of the lower fluid these properties each increase monotonically with the wave height.
TL;DR: In this article, two classes of fast solar-wind streams are identified: quiet streams and perturbed streams, coming from active regions producing type-IV solar flares, which are accompanied by Forbush decreases whose amplitude and time behaviour are not directly related to speed increase.
Abstract: Two classes of fast solar-wind streams are identified.Quiet streams, coming from near equatorial holes: stream interface in the initial phase followed by low proton density, quiet interplanetary magnetic field with constant polarity and proton temperature following the wind speed time profile.Perturbed streams, coming from active regions producing type-IV solar flares, for which the previous requirements are not satisfied. Superposed epoch analyses applied on solar-wind speed and neutron monitor intensity show that during the high-speed streams presumably coming from coronal holes the cosmic-ray intensity is depressed; the time behaviour of this depression follows the time profile of the wind speed: for neutron monitors at high latitude ΔI/I≈—K·ΔV, whereK=5·10−5 km−1 s. The perturbed streams are accompanied by Forbush decreases whose amplitude and time behaviour are not directly related to the speed increase.
TL;DR: In this article, two integral invariants of Shuto's (1974) generalization of the Korteweg-de Vries equation for a unidirectional wave in a channel of gradually varying breadth b and depth d are derived.
Abstract: Two integral invariants of Shuto's (1974) generalization of the Korteweg—de Vries equation for a unidirectional wave in a channel of gradually varying breadth b and depth d are derived. The second-order (in amplitude) invariant measures energy, as expected, but the first-order invariant measures mass divided by b½d¼; accordingly, mass is conserved only if either the mean free-surface displacement vanishes or bd½ is constant. This difficulty is associated with the reflected wave that is excited by the channel variation but neglected in the KdV approximation. The total mass flux is resolved into a primary (KdV) flux and a residual flux that is proportional to the mean displacement of the primary wave. The reflected wave associated with the residual flux is constructed by neglecting both nonlinearity and dispersion (even though both are significant for the primary wave). The results are applied to a slowly varying cnoidal wave, which is fully determined by conservation of mass and energy and the known results for a uniform channel, and to a slowly varying solitary wave, for which mass is not conserved and both trailing and reflected residuals are excited. The development of the Boussinesq equations for a gradually varying channel and their reduction to Shuto's equation are sketched in an appendix.
TL;DR: In this article, the Calculus of Variations is used to derive a normalized suboptimal slewing profile, F(x), applicable to a 1 1 maneuvers for a dynamically varying spacecraft maneuvering between two quiescent states.
Abstract: Using the Calculus of Variations, optimal slewing profiles minimizing a structural e xcitation criterion are e stablished for a dynamically s imple spacecraft maneuvering between two quiescent states. Two problem types are considered. In the free end point problem, the structural deformation and its time derivative are unconstrained at maneuver's end. For the constrained end point problem, these variables a re r equired to vanish, which necessarily degrades the excitation criterion. Several figures are presented that illustrate both the n ature and the limitations inherent in maneuvering the spacecraft from one attitude state to another. For a given maneuver amplitude, en, the key parameter influencing structural e xcitation is the product of the maneuver time, Ta, and the lowest significant structural frequency, w. It is shown that when wTa 10, however, this penalty is fairly minor, and some reasonable control of terminal conditions is then practical. Thus it is generally d esirable that all maneuver times meet this criterion. When this is the case, it is possible to derive a normalized suboptimal slewing profile, F(x), applicable to a1 1 maneuvers. Given 0" and Ta, the commanded maneuver rate becomes e( t) = eO F(t/Ta)/Ta. Only a minor computational and memory burden is therefore necessary to perform almost optimal re-orientations.
TL;DR: In this article, the authors derived expressions for the distribution in angle and frequency of electromagnetic radiation emitted from fluctuations in the tunneling current between two metals separated by a thin oxide barrier, and provided an explicit description of the decoupling of the surface polariton from the surface by virture of small-amplitude roughness present there.
Abstract: In this paper, we derive expressions for the distribution in angle and frequency of electromagnetic radiation emitted from fluctuations in the tunneling current between two metals separated by a thin oxide barrier. The calculation provides an explicit description of the decoupling of the surface polariton from the surface by virture of small-amplitude roughness present there. In addition, we find radiation from direct coupling of current fluctuations in the junction structure to the transverse radiation field. Numerical calculations are presented which explore the predictions of the theory, when applied to structures similar to those studied experimentally by Lambe and McCarthy. We suggest interpretations of some features of their data, and data reported by Adams, Wyss, and Hansma. The theory indicates that as the amplitude of the roughness is increased, the quantum efficiency of the device should saturate to approach a value independent of the roughness amplitude.
TL;DR: In this article, the authors compared the Noda simulation of a vertically falling and horizontally moving slide by linearized impulsive wave theory and estimation of nonlinear wave properties, and the Raney and Butler modification of vertically averaged nonlinear Wave equations written for two horizontal dimensions to include three landslide forcing functions, solved numerically over a grid for wave amplitude and celerity.
Abstract: Large water waves generated by landslides impacting with a body of water are known from Disenchantment and Lituya Bays, Alaska; Vaiont reservoir, Italy; Yanahuin Lake, Peru; Shimabara Bay, Japan; and many fiords in Norway. The combined death toll from these events most likely exceeds 20,000 people. Such waves may be oscillatory, solitary, or bores and nonlinear mathematical theories or linearizing assumptions are thus needed to describe their wave amplitudes, celerities, and periods. In this paper the following approaches are compared: (1) the Noda simulation of a vertically falling and horizontally moving slide by linearized impulsive wave theory and estimation of nonlinear wave properties; (2) the Raney and Butler modification of vertically averaged nonlinear wave equations written for two horizontal dimensions to include three landslide forcing functions, solved numerically over a grid for wave amplitude and celerity; (3) the empirical equations of Kamphuis and Bowering, based on dimensional analysis and two-dimensional experimental data; and (4) an empirical equation developed in this report from three-dimensional experimental data, i.e., log(η max /d) = a + b log(KE), where a, b = coefficients, η max = predicted wave amplitude, d = water depth, and KE = dimensionless slide kinetic energy. Beyond the slide area changes in waveform depend upon energy losses, water depth and basin geometry and include wave height decrease, refraction, diffraction, reflection, and shoaling. Three-dimensional mathematical and experimental models show wave height decrease to be a simple inverse function of distance if the remaining waveform modifiers are not too severe. Only the Raney and Butler model considers refraction and reflection. Run-up from waves breaking on a shore can be conservatively estimated by the Hall and Watts formula and is a function of initial wave amplitude, water depth, and shore slope. Predicted run-ups are higher than experimental run-ups from three-dimensional models. The 1958 Lituya Bay and 1905 Disenchantment Bay, Alaska events are examined in detail, and wave data are developed from field observations. These data and data based on a Waterways Experiment Station model are compared to wave hindcasts based on various predictive approaches, which yield a large range of predicted wave heights. The most difficult problems are in matching the exact basin geometry and estimating slide dimensions, time history, and mode of emplacement. Nevertheless, the hindcasts show that the mathematical and experimental model approaches do provide useful information upon which to base engineering decisions. In this regard the empirical equation developed in this report is at least as satisfactory as existing methods, and has the advantage of requiring less complicated input data.
TL;DR: In this article, a linearized theory applicable to optically thin waves is used to show that the resulting fluctuation in the absorption-line force can cause the wave amplitude to grow.
Abstract: The velocity perturbation associated with an outwardly propagating sound wave in a radiation-driven stellar wind gives rise to a periodic Doppler shifting of absorption lines formed in the flow. A linearized theory applicable to optically thin waves is used to show that the resulting fluctuation in the absorption-line force can cause the wave amplitude to grow. Detailed calculations of the acceleration due to a large number of lines indicate that significant amplification can occur throughout the high-velocity portion of winds in which the dominant force-producing lines have appreciable optical depths. In the particular case of the wind of Zeta Pup (O4f), it is found that the e-folding distance for wave growth is considerably shorter than the scale lengths over which the physical properties of the flow vary. A qualitative estimate of the rate at which mechanical energy due to nonlinear waves can be dissipated suggests that this mechanism may be important in heating the supersonic portion of winds of early-type stars.
TL;DR: In this paper, the slowly varying solitary wave is constructed as an asymptotic solution of the variable coefficient nonlinear Schrodinger equation, and the results are interpreted by using conservation laws.
Abstract: The slowly varying solitary wave is constructed as an asymptotic solution of the variable coefficient nonlinear Schrodinger equation. A multiple scale method is used to determine the amplitude and phases of the wave to the second order in the perturbation parameter. The method is similar to that used in (I) (R. Grimshaw 1979 Proc. R. Soc. Lond. A 368, 359). The results are interpreted by using conservation laws. Outer expansions are introduced to remove non-uniformities in the expansion. Finally, when the coefficients satisfy a certain constraint, an exact solution is constructed.
01 Aug 1979
TL;DR: In this paper, the authors reviewed the Kelvin-Helmholtz instability as it applies to the dayside magnetopause and showed that the boundary should generally be unstable to waves moving at a large angle to the Earth's field.
Abstract: The Kelvin-Helmholtz instability as it applies to the dayside magnetopause is reviewed. Simple theory suggests the boundary should generally be unstable to waves moving at a large angle to the Earth's field. Nonlinear effects, how amplitudes might be limited, and what dynamic role the instability could have in boundary regions in stimulating mass and momentum transfer are discussed. Examination of data from a particular ISEE spacecraft pass shows relatively small amplitude (750 km) waves present on the boundary. Corresponding wavelength estimates show wave momentum is not significant at the time of the pass.