Constant-amplitude Wave Research Articles

Observable and reproducible rogue waves**This paper was an intended contribution to the special issue on optical rogue waves (iopscience.iop.org/2040-8986/15/6).

In physical regimes described by the cubic, focusing, nonlinear Schrödinger (NLS) equation, the N-dimensional homoclinic orbits of a constant amplitude wave with N unstable modes appear to be good candidates for experimentally observable and reproducible rogue waves. These homoclinic solutions include the Akhmediev breathers (N = 1), which are among the most widely adopted spatially periodic models of rogue waves, and their multi-mode generalizations (N > 1), and will be referred to as multi-mode breathers. Numerical simulations and a linear stability analysis indicate that the breathers with a maximal number of modes (maximal breathers) are robust with respect to rather general perturbations of the initial data in a neighborhood of the unstable background.

Travelling waves in boundary-controlled, non-uniform, cascaded lumped systems

A companion paper considers travelling and standing waves in cascaded, lumped, mass-spring systems, controlled by two boundary actuators, one at each end, when the system is uniform. It first proposes definitions of waves in finite lumped systems. It then shows how to control the actuators to establish desired waves from rest, and to maintain them despite disturbances. The present paper extends this work to the more general, non-uniform case, when mass and spring values can be arbitrary. A special “bi-uniform” case is first studied, consisting of two different uniform cascaded systems in series, with an obvious, uncontrolled, impedance mismatch where they meet. The paper shows how boundary actuator control systems can be designed to establish, and robustly maintain, apparently pure travelling waves of constant amplitude in either the first or the second uniform section, in each case with an appropriate, partial, standing wave pattern in the other section. Then a more general non-uniform case is studied. A definition of a “pure travelling wave” in non-uniform systems is proposed. Curiously, it does not imply constant amplitude motion. It does however yield maximum power transfer between boundary actuators. The definition, and its implementation in a control system, involves extending the notions of “pure” travelling waves, of standing waves, and of input and output impedances of sources and loads, when applied to non-uniform lumped systems. Practical, robust control strategies are presented for all cases.

Continuous atom laser with Bose–Einstein condensates involving three-body interactions

We demonstrate, through numerical simulations, the emission of a coherent continuous matter wave of constant amplitude from a Bose–Einstein condensate in a shallow optical dipole trap. The process is achieved by spatial control of the variations of the scattering length along the trapping axis, including elastic three-body interactions due to dipole interactions. In our approach, the outcoupling mechanism is atomic interactions, and thus, the trap remains unaltered. We calculate analytically the parameters for the experimental implementation of this continuous wave atom laser.

The influence of magnetic islands on drift mode stability in magnetized plasma

The impact of a chain of thin magnetic islands on the stability of electrostatic drift modes is studied for plasma confined by a sheared slab magnetic field geometry. Small magnetic islands are considered, with a width comparable to the ion Larmor radius. Gyrokinetic theory is employed to derive self-consistently the equilibrium modifications due to the island chain, as well as the drift mode structure and stability. The island has two effects on the equilibrium: it modifies the density and temperature gradients and, in general, strong sheared plasma flows must exist in its vicinity. A reduced model is developed to illustrate the impact of this new equilibrium on drift modes, focusing on the ion temperature gradient (ITG) mode. It is found that magnetic islands tend to stabilize these modes. The ITG mode structure is also studied. In the absence of magnetic islands, the drift modes are plane waves of constant amplitude in the y-direction (magnetic flux surfaces are defined by the x–y plane, with inhomogeneities in the x-direction and the main component of magnetic field in the z-direction). However, the drift modes become more localized in the y-direction in the presence of magnetic islands. An interesting result is that the position of localization is not where the drive for the instability is strongest. An analytic WKB theory is presented for a simplified model which sheds light on this result.

Designer based Fourier transformed voltammetry: A multi-frequency, variable amplitude, sinusoidal waveform

Fourier transform methods allow custom-designed complex waveforms to be used in ac voltammetry. Commonly a single wave or sum of sine waves of variable angular frequency ( ω ) but constant amplitude ( Δ E ) superimposed onto a dc ramp are employed. In the present case, a custom-designed waveform consisting of a combination of eight sine waves is introduced, with the property that each sine wave within the composite waveform has the property Δ E i ∝ 1 / ω i where i represents the i th sine wave. Frequencies (and amplitudes) employed in a single experiment cover the range from 34.94 Hz (20 mV) to 1970.01 Hz (2.66 mV). Reversibility is readily detected via use of this designer waveform by noting a constant peak height ( I p ( ω t ) ) for all eight frequencies, whereas I p ( ω t ) values decrease in a characteristic manner with increasing frequency for a quasi-reversible process or when uncompensated resistance is present, as demonstrated experimentally and theoretically. Importantly, background charging current contributions do not increase to a level that makes measurement of faradaic current difficult at high frequencies and hence charging current is readily corrected for over the entire frequency range of interest.

Evolution of Higher-Order Gray Hirota Solitary Waves

The defocusing Hirota equation has dark and gray soliton solutions which are stable on a background of periodic waves of constant amplitude. In this paper, gray solitary wave evolution for a higher-order defocusing Hirota equation is examined. A direct analysis is used to identify families of higher-order gray Hirota solitary waves, which are embedded for certain parameter values. Soliton perturbation theory is used to determine the detailed behavior of an evolving higher-order gray Hirota solitary wave. An integral expression for the first-order correction to the wave is found and analytical expressions for the steady-state and transient components of the solitary wave tail are derived. A subtle and complex picture of the development of solitary wave tails emerges. It is found that solitary wave tails develop for two reasons, one is decay of the solitary wave caused by resonance, the second is corrections at first-order to the background wave. Strong agreement is found between the theoretical predictions of the perturbation theory and numerical solutions of the governing equations.

Beam-wave Coupling in a Double-beam Gyrotron Traveling Wave Amplifier

Abstract| A linear theory is used to study the beam-wave coupling in a double-beam gyrotrontraveling wave amplifler (Gyro-TWA). Numerical results show that the beam-wave coupling inthis type of amplifler excites six waves, which include one constant-amplitude backward wave,and flve forward waves consisting of two growing waves, two decaying waves and one constant-amplitude wave. The growing wave, whose growth rate is much larger than that of the other,has a larger operating bandwidth which is approximately the superposition of the interactionbandwidths of the two single-beams in the Gyro-TWA.DOI: 10.2529/PIERS0609062117151. INTRODUCTION High power and broad bandwidth capability of the gyrotron traveling wave amplifler makes it anattractive source of coherent radiation in the millimeter and sub-millimeter wavelength ranges.Gyro-TWAs are applied very broadly, especially in radar and communication systems. Steadyprogress in theory and experiment has been made over an extended period of time. Major advancesin Gyro-TWA performances have been reported in the review papers [1{3].The Gyro-TWA interaction comes from the coupling between the electron beam cyclotron modeand the waveguide mode, which respectively satisfy

Decay instability of a laser pulse propagating in a transverse direction in a magnetized plasma

The decay instability of a lser pulse propagating across an external magnetic field in a subscritical plasma is investigated analytically and numerically. It is shown that, when the relaxation of the pulse is taken into account, the hydrodynamic growth rate of the decay instability is slower than that obtained earlier in the constant-amplitude pump wave approximation. The results of numerical simulations by a particle-in-cell method demonstrate that an increase in the amplitude of the parametrically excited waves is accompanied by a decrease in their group velocity; in this case, up to 85% of the laser energy is converted into the energy of the plasma particles. It is found that, under resonance conditions, the magnetic field acts to increase the energy of the accelerated ions that escape from the plasma slab through its front boundary.

Growth/decay of transverse acceleration waves in nonlinear elastic media

A study of transverse acceleration wave phenomena in the context of nonlinear elasticity is carried out. Using singular surface theory, exact amplitude expressions for acceleration waves arising from a sinusoidal boundary condition (BC) are obtained and their temporal evolution and propagation speeds determined. It is shown that amplitude blow up is possible only if the medium ahead is in motion, otherwise a constant amplitude wave occurs. Analytical results are illustrated numerically using simple computational methods/tools. Lastly, erroneous results that were reported in a recently published related study are noted and/or corrected.

Influence of higher-order dispersion on modulational instability and pulse broadening of partially incoherent light.

The Wigner-Moyal equation for the Wigner distribution of a partially incoherent optical wave field propagating in dispersive and nonlinear media has been generalized to include the effects of both arbitrary order of dispersion and arbitrary nonlinearity. The theory predicts partial incoherence to enhance the pulse broadening during linear wave pulse propagation. Furthermore, an application of the theory to the modulational instability of constant amplitude waves shows how higher-order dispersion affects the instability growth rate.

Landau damping of partially incoherent Langmuir waves

It is shown that partial incoherence, in the form of stochastic phase noise, of a Langmuir wave in an unmagnetized plasma gives rise to a Landau-type damping. Starting from the Zakharov equations, which describe the nonlinear interaction between Langmuir and ion-acoustic waves, a kinetic equation is derived for the plasmons by introducing the Wigner–Moyal transform of the complex Langmuir wave field. This equation is then used to analyze the stability properties of small perturbations on a stationary solution consisting of a constant amplitude wave with stochastic phase noise. The concomitant dispersion relation exhibits the phenomenon of Landau-like damping. However, this damping differs from the classical Landau damping in which a Langmuir wave, interacting with the plasma electrons, loses energy. In the present process, the damping is non-dissipative and is caused by the resonant interaction between an instantaneously-produced disturbance, due to the parametric interactions, and a partially incoherent Langmuir wave, which can be considered as a quasi-particle composed of an ensemble of partially incoherent plasmons.

Breather$ndash$phonon resonances in finite-size lattices: $lquot$phantom breathers$rquot$?

We investigate the resonance mechanisms for discrete breathers in finite-size Klein-Gordon lattices, when some harmonic of the breather frequency enters the linear phonon band. For soft on-site potentials, the second-harmonic resonances typically result in the appearance of solutions with non-zero tails, phonobreathers. However, these tails may be very weak, and for small systems where the phonon frequencies are sparsely distributed, we identify 'phantom breathers' as being practically localized solutions, existing with frequencies in-between the phonon frequencies. For particular parameter values the tails completely vanish, and the phantom breathers decay exponentially over the whole system. We also describe briefly a first-harmonic resonance with a constant-amplitude wave and the generation of phonobreathers for hard potentials.

다방향 극한파 생성의 이론적 연구

파랑집중 이론에 기초하여 모형시험수조에서 다방향 극한파를 생성하는 연구를 수행하였다. 파랑의 집중도에 대한 파향 범위, 주파수 폭, 중심 주파수 등의 영향을 고찰하였다. 등파고와 등기 울기 스펙트럼 모델에 의한 결과를 서로 비교하였으며, Boussinesq 방정식과 유한요소법에 기초한 수치해와 이론해를 또한 서로 비교하였다. 효율적인 파랑집중을 위해서는 파향과 주파수 모두를 효과적으로 제어하는 것이 필수적이다. 파랑집중도는 중심주파수 보다는 주파수 폭에 좌우되며, 동일한 조건하에서 두 스펙트럼 모델은 동등한 정도의 파랑집중 효율을 나타낸다. Theoretical development to generate the directional extreme waves in model basin is established based on wave focusing method. The effects of associated parameters, such as the directional range, frequency width, and center frequency, are investigated in terms of wave focusing efficiency. The two different spectral models of constant wave amplitude and constant wave slope are applied to control the wave characteristics. The wave packets simulated by theory are compared with numerical results based on Boussinesq equation and FEM. Both controls of direction and frequency spectrum are essential to focus directional waves effectively. It is noticed that wave focusing ability depends on the frequency bandwidth of spectrum rather than center frequency, and both spectral models with same parameters result in the equivalent efficiency of wave focusing.

STORMSED1.0: hydrodynamics and sediment transport in a 2-D, steady-state, wind- and wave-driven coastal circulation model

STORMSED1.0 is a MATLAB TM program that solves the steady-state, linearized, horizontal momentum equations in the along-shelf and cross-shelf directions for a linear shoreline given a constant wind stress and waves of constant amplitude and period. The model provides a quantitative link between storms and sedimentation that may assist geologists interpreting the stratigraphic record. It provides a rapid analytical approach to quantify the sedimentation that results from coastal circulation that may be extended to long time scales and linked to other sedimentation models. In the northern hemisphere, shore-parallel wind, where flow is to the right as the viewer faces the ocean, produces downwelling as the Coriolis force rotates bottom flow from shore-parallel to slightly offshore with increasing water depth. In the shallow and intermediate zones, cross-shelf flow velocities and sediment flux increase offshore and erosion occurs. Seaward, in the deep zone, velocities are constant, wave-effect declines with depth, cross-shelf sediment flux decreases offshore, and deposition results. Shore-parallel winds oriented in the opposite direction produce upwelling and the sedimentation pattern is reversed. The model solves for the current distribution, the sediment concentration profile, the bedload and suspended load, and the sedimentation rate at any node along a continental shelf. The circulation model is based on a wind-driven circulation model derived by Jeffries (1923). Waves are included using Airy wave theory, and the wave–current interaction is quantified using the bottom boundary layer model of Grant and Madsen (1979).

The multiple source feedback of supersonic jet screech. IV. Space–time diagrams and the fast/slow waves of transitory wave theory

In Part II [J. Acoust. Soc. Am. 108, 2588 (2000)] the space–time wave diagrams of multiple (point) source screech were elucidated, showing the condition for perfect, or nearly so, reinforcement of the feedback sound at the nozzle. In the transitory wave theory [J. Acoust. Soc. Am. 106, 2194 (1999)] the velocity modulation of a transitory instability wave as it traverses the periodic cell structure results in a continuous phased array which was resolved into fast (approx. sonic) upstream and slow downstream source waves (of constant sinuous amplitude, apart from the envelope factor), only the former radiating strongly, in the upstream direction. The two points of view are reconciled by constructing fast and slow waves in the space–time diagrams by: (a) introducing intermediate negative sources: (b) taking the sources at half strength and adding virtual sources at the zero positions on the fast wave traces, of the same sign as adjacent sources: (c) taking the other half-strength sources and adding virtual sources of opposite sign, the sources then being of the same sign along the slow wave traces. The implications of the need to introduce negative sources in the point source array are discussed.

K-0824 地震荷重を受けるき裂付き配管の破面解析(S11-6 構造健全性評価(6))(S11 構造健全性評価)

In order to clarify the behavior of cracked pipes under seismic events, cyclic four-point bending tests were conducted on the straight pipes with an electric discharge machining notch. The specimens were subjected to the constant amplitude wave or random amplitude wave, and resulted in low-cycle fatigue failure. Fracture surfaces were observed using scanning electron microscope after the tests and crack propagation characteristic were obtained. From the results of fractography of the specimens, it seems that loading cycles to cause crack penetration were mainly consumed in crack propagation, not in crack initiation. And relation between crack propagation rate and the stress intensity factor range obtained from fractography showed good agreement with that of high-cycle fatigue test results.

Description of arbitrary deformation of deep water waves with fractional derivatives

A single equation governing weakly nonlinear gravity waves traveling on deep water has been derived. This equation, which includes fractional derivatives, can describe any wave motion under the influence of second-order nonlinearity. Deriving dynamic wave behavior is much easier from this equation than using the original set of equations. To obtain a better understanding of wave–wave interaction, several solutions were examined under a periodic boundary condition. The initial value problem for one monochromatic wave and its harmonic shows that the monochromatic wave generates the second harmonic in a certain period which travels with nearly constant velocity. A Stokes-like wavetrain then appears periodically, though not asymptotically, as a result of the periodic generation of the harmonic. A new type of three-wave interaction was seen to exist where two waves of larger wave number interact with each other through a long wave of constant amplitude and constant velocity.

Local transit-time dissipation and Landau damping

A generalization of local transit-time dissipation theory to coherent electrostatic wave packets with nonzero mean wave number is presented. The connection between Landau damping and transit time damping is derived in a concise, mathematically rigorous manner, settling a longstanding controversy. It is shown that transit time dissipation involves both Landau-type resonant damping and nonresonant damping. For small wave packets with nonzero mean wave number or asymmetric incident particle distributions, the nonresonant damping can dominate over Landaudamping. In the opposite extreme of infinitely large, constant-amplitude wave packets, the nonresonant part of transit time dissipation vanishes, and only Landau damping remains. All the analytical results presented are verified independently by numerical test-particle calculations.

Heating of Jupiter's Thermosphere by Dissipation of Gravity Waves Due to Molecular Viscosity and Heat Conduction

Heating Jupiter's thermosphere by viscous dissipation of upward propagating gravity waves is evaluated with correct formulations of total energy conservation and the total wave induced vertical energy flux. In contrast to the results of L. A. Young et al. (1997, Science276, 108–111), our calculations, with their wave amplitudes and parameters, yield a maximum thermospheric temperature of T=380 K at 552 km above the 1-bar level in comparison to the Galileo probe inferred temperature of T=900 K and therefore gravity waves may not be solely responsible for the observed steep temperature gradient just above the homopause. The large sensible heat flux associated with dissipating gravity waves generates net heating of the lower regions and net cooling of the upper regions of wave dissipation due to energy redistribution. The transition from net heating to net cooling occurs at the level of constant wave amplitude. In regions of substantial wave dissipation the local cooling rate due to sensible heat flux divergence can exceed the local heating due to convergence of the Eliassen–Palm flux to produce (1) net cooling of and (2) a distinct temperature decrease (≈65 K) in the topside thermosphere. To simulate Jupiter's thermospheric temperature profile inferred from the Galileo probe data with (1) gravity wave heating only, (2) 100% conversion of wave energy to internal energy, and (3) radiative cooling by H+3 near-IR emission ∼0.1 erg cm−2 s−1, gravity waves must deposit their energy high in the thermosphere with peak heating occurring near ∼500 and ∼1000 km with near saturation amplitudes at very high altitudes (>1100 km).

Propagation of linear and nonlinear spin wave excitations in YIG and Lu2.04Bi0.96Fe5O12 films studied by space resolved Brillouin light scattering (abstract)

We have investigated the propagation of surface and backward volume spin waves (BVSW) with the in-plane wavevector k∥=10–900 cm−1 excited by microwaves in YIG and Lu2.04Bi0.96Fe5O12 (LBIG) films with the film thicknesses 5 and 1.5 μm, respectively. In all cases the magnetization and k∥ were in the film plane. The frequencies of the spin wave excitations as well as the spatial distribution of their intensities in the linear and in the nonlinear excitation regime were measured by means of a fully automated, high-stabilization, small-angle Brillouin light scattering (BLS) setup with a spatial resolution of 30 μm. It is well known1 that in the case of BVSW modes, the Lighthill criterion2 for modulational instability is fulfilled for both the longitudinal and the transverse perturbations of the initially constant-amplitude wave beam. Therefore, this mode is very much suitable for the investigation of the evolution of a plane-front, constant-amplitude initial beam, and for a direct experimental study of two-dimensional nonlinear diffraction effects of the beam leading to self-focusing. The garnet films with in-plane dimensions of 2×10 mm2 were grown by liquid phase epitaxy onto a single crystalline (111)-oriented gallium gadolinium garnet substrate. Two strip antennas, 35 μm wide and situated at the ends of the films, were used for the excitation of the spin waves and for monitoring. The working frequency was 8.10 GHz. Special efforts were taken to minimize the beam divergence due to the finite length of the input antenna. For all nonlinear studies the initial angular beam divergence was not larger than Θmax=0.05 rad. In the linear regime the attenuation factor was measured, and the reflection of the spin waves from the sample boundaries was studied. We also observed the interference between the two lowest order lateral modes having different initial spatial distributions of the magnetization. The BLS technique was shown to provide a signal to noise ratio exceeding 60 dB. In the nonlinear regime the propagation of the BVSW mode was thoroughly investigated. We have found clear evidence for the self-focusing effect, which exists in a narrow interval of input powers. In these studies overheating of the sample by the microwave power was carefully avoided by using an intermittent source of maximum average power of 100 mW working at a frequency of 4 kHz. That allowed us to claim that the observed focusing of the spin waves was not an artifact caused by sample heating. The distance between the focusing maximum and the antenna was 1.5 mm for LBIG sample and 6 mm for YIG sample. These values are in a good agreement with our theoretical calculations, if one takes into account the thicknesses of the films. For a comparison of the observed values of the width and the length of the focusing spot and their dependence on the microwave power with the theory, more numerical calculations are needed. Our results demonstrate the wide applicability of an advanced combined microwave-BLS technique for a two-dimensional mapping of the spin wave amplitudes in the media.