Traveling Surface Waves Research Articles

Travelling interface waves in a brake-like system under unilateral contact and Coulomb friction

This article considers the frictional interface waves generated by the flutter instability of the sliding steady state for an elastic tube in frictional contact with a rigid and rotating shaft. According to the values of the contact pressure, the rotation velocity and the friction coefficient, several periodic dynamical responses can be found under the form of travelling surface waves. Such a periodic solution may be interesting in the study of a possible dynamic transition from the sliding steady state in the spirit of Andronov–Hopf bifurcation. Examples of stick-slip, stick-slip-separation and stick-slip-separation-reverse-slip waves propagating along the contact surface, obtained by various semi-analytical and numerical approaches, are reported here. Some results on the stability of these travelling waves are also indicated. To cite this article: Q.S. Nguyen et al., C. R. Mecanique 336 (2008).

Dispersion of the Composite-Fermion Cyclotron-Resonance Mode

The dispersion of the composite-fermion cyclotron-resonance mode is measured with an optical detection scheme under the combined excitation of microwave radiation and a surface acoustic wave from an interdigital transducer. The slowly traveling surface wave defines the transferred wave vector. Momenta up to 10;{8} m;{-1} are accessible. The cyclotron-resonance mode exhibits strong negative dispersion, which suggests predominant short range residual interaction among composite fermions. From an extrapolation, the cyclotron mass at k=0 is obtained and investigated as a function of electron density.

Phonon-polariton waves on the surface of SiC crystal

The excitation and propagation of traveling phonon-polariton waves on the surface of silicon carbide (SiC) excited by light at a frequency close to the lattice resonance have been investigated. These waves are excited in the presence of the boundary of a metal mask deposited on the crystal surface. The use of the Green’s function has been shown to provide good qualitative agreement with the observed distribution of the amplitude and phase of the field on the surface under these experimental conditions. It has been shown that only consideration of the mask boundary as an extended source of traveling surface waves, which removes the inhibition of the generation of waves in the noncoincidence of the wave vector, cannot quantitatively describe the phenomenon. The spatial resolution of the used scanning near-field optical microscope is no worse than 150 nm at a wavelength of 10 μm.

Direct Inversion of Spatial Autocorrelation Curves with the Neighborhood Algorithm

Ambient vibration techniques are promising methods for assessing the subsurface structure, in particular the shear-wave velocity profile ( Vs ). They are based on the dispersion property of surface waves in layered media. Therefore, the penetration depth is intrinsically linked to the energy content of the sources. For ambient vibrations, the spectral content extends in general to lower frequency when compared to classical artificial sources. Among available methods for processing recorded signals, we focus here on the spatial autocorrelation method. For stationary wavefields, the spatial autocorrelation is mathematically related to the frequency-dependent wave velocity c ( ω ). This allows the determination of the dispersion curve of traveling surface waves, which, in turn, is linked to the Vs profile. Here, we propose a direct inversion scheme for the observed autocorrelation curves to retrieve, in a single step, the Vs profile. The powerful neighborhood algorithm is used to efficiently search for all solutions in an n -dimensional parameter space. This approach has the advantage of taking into account the existing uncertainty over the measured curves, thus generating all Vs profiles that fit the data within their experimental errors. A preprocessing tool is also developed to estimate the validity of the autocorrelation curves and to reject parts of them if necessary before starting the inversion itself. We present two synthetic cases to test the potential of the method: one with ideal autocorrelation curves and another with autocorrelation curves computed from simulated ambient vibrations. The latter case is more realistic and makes it possible to figure out the problems that may be encountered in real experiments. The Vs profiles are correctly retrieved up to the depth of the first major velocity contrast unless low-velocity zones are accepted. We demonstrate that accepting low-velocity zones in the parameterization has a dramatic influence on the result of the inversion, with a considerable increase in the nonuniqueness of the problem. Finally, a real data set is processed with the same method.

On analyticity of travelling water waves

In this paper we establish the existence and analyticity of periodic solutions of a classical free-boundary model of the evolution of three-dimensional, capillary–gravity waves on the surface of an ideal fluid. The result is achieved through the application of bifurcation theory to a boundary perturbation formulation of the problem, and it yields analyticity jointly with respect to the perturbation parameter and the spatial variables. The travelling waves we find can be interpreted as resulting from the (nonlinear) interaction of two two-dimensional wavetrains, giving rise to a periodic travelling pattern. Our analyticity theorem extends the most sophisticated results known to date in the absence of resonance; ‘short crested waves’, which result from the interaction of two wavetrains with unit amplitude ratio are realized as a special case. Our method of proof also sheds light on the convergence and conditioning properties of classical boundary perturbation methods for the numerical approximation of travelling surface waves. Indeed, we demonstrate that the rather unstable numerical behaviour of these approaches can be attributed to the strong but subtle cancellations in the formulas underlying their classical implementations. These observations motivate the derivation and use of an alternative, stable, formulation which, in addition to providing our method of proof, suggests new stabilized implementations of boundary perturbation algorithms.

Stability of a Rotating Hollow Rotor Partially Filled with Liquid(Effect of Discharging Liquid by Centrifugal Force)

This paper describes experimental study on the stability characteristics of a rotor partially filled with water. Constant amount of water is supplied to the rotor continuously and is discharged radially by centrifugal force. Consequently, the rotor becomes unstable for some rotating speed range. The unstable speed range depends on the water supply rate as well as the amount of water in the rotor. Formardly traveling surface waves are also observed while the rotor undergoes an unstable orbital whirling motion. The wave travels at the same frequency as the rotor vibration frequency. As the water supply rate increases, the rotor becomes more stable.

Molecular dissociation in N2–H2 microwave discharges

A microwave N2–H2 discharge driven by a travelling surface wave is investigated as a source of ground state N(4S) and H(1s) atoms. Experimental investigations have been carried out in a plasma source operating at 2.45 GHz at low-pressure conditions (p = 0.5–2 Torr). By means of optical emission spectroscopy and probe diagnostic techniques, the population densities of ground state atoms have been detected. The dissociation kinetics is discussed in the framework of a theoretical model based on a self-consistent treatment of the main discharge balances, wave electrodynamics and plasma–wall interactions. Electron–ion surface recombination processes involving and ions are the most important sources of N(4S) gas phase atoms for the conditions considered. The relative number of N(4S) atoms in respect to the total neutral density remains approximately constant for percentages of H2 between 10% and 50% at nearly constant electron density. The competitive interplay of two important source channels of H(1s) atoms, namely electron impact dissociation of H2 and H2 dissociation via the quenching of nitrogen and metastables, determines a smooth decrease of hydrogen dissociation when the amount of hydrogen increases up to 50% in the mixture.

Modeling of wave driven molecular (H/sub 2/, N/sub 2/, A/sub 2/-Ar) discharges as atomic sources

Microwave H/sub 2/, N/sub 2/, and N/sub 2/-Ar discharges driven by traveling surface waves are investigated as sources of ground state N(/sup 4/S), H(1s) atoms. The dissociation kinetics is discussed in the framework of theoretical models based on a self-consistent treatment of the main discharge balances, wave electrodynamics and plasma-wall interactions. It is shown that the number density of hydrogen H(1s) atoms depends heavily on the wall conditions at low pressure conditions. The kinetics of N(/sup 4/S) and metastable N(/sup 2/D) and N(/sup 2/P) atoms and of the molecular N/sub 2/(A/sup 3//spl Sigma//sub u//sup +/) metastable state in a pure N/sub 2/ discharge are shown to be strongly coupled. One possible way to control and to enhance nitrogen dissociation is the use of an N/sub 2/-Ar mixture. The increase in dissociation degree of N/sub 2/ molecules at high Ar fractional concentration can be attributed to dissociative recombination between electrons and N/sub 2//sup +/ positive ions. The predicted results for the atomic density are compared with emission spectroscopy data.

Wave driven molecular discharges as sources of active species

Microwave N 2, H 2, N 2–Ar discharges driven by travelling surface waves are investigated as sources of active species [N( 4S), H(1s), N 2(A 3Σ u +),Ar( 3P 2)]. By means of optical emission and absorption spectroscopy, the population density of the species of interest has been detected. The results are discussed in the framework of self-consistent models. The correlation between wall conditions and volume density of H(1s) atoms and H − negative ions in H 2 discharge is pointed out.

Effect of gas heating on the spatial structure of a traveling wave sustained Ar discharge

In this work we report a theoretical and experimental study of the influence of gas heating on the spatial structure of a microwave Ar discharge sustained by a traveling surface wave. The theoretical analysis is based on a discharge model which couples in a self-consistent way electron and heavy particle kinetics, discharge electrodynamics, and gas thermal balance. The set of coupled equations used includes the electron Boltzmann equation, the rate balance equations for the most important excited species and charged particles, the gas thermal balance equation, and the equations describing wave propagation and power dissipation. The principal collisional and radiative processes which determine the populations in the Ar(3p54s) and Ar(3p54p) levels are accounted for. The field strength necessary for steady-state discharge operation is obtained from the balance between total rates of ionization (including direct and step-wise ionization and energy pooling reactions) and of electron loss due to the diffusion to the wall and bulk recombination. The gas thermal balance equation is solved using the experimentally obtained wall temperature as a boundary value. The model determines the axial discharge structure, i.e., the axial variation of the main discharge quantities. An experimental validation of the model predictions is achieved using probe techniques, emission spectroscopy, and radiophysics methods. In particular, spatially resolved measurements of the electron energy distribution function, gas temperature, wave electric field components, and wave attenuation have been carried out. As a result of the nonuniform wave power absorption along the wave path the gas temperature varies along the column. This variation induces axial changes in the neutral density and the reduced electric field which strongly affects the particle kinetics and the discharge electrodynamics, as demonstrated here.

A laser photodetachment technique for the measurement of H− in a high frequency traveling wave discharge

A probe based laser photodetachment system has been developed to measure the H− density in a high frequency hydrogen discharge sustained by a traveling surface wave. Problems associated with application of this technique in high frequency discharges in general are pointed out. The influence of the time varying voltage across the plasma probe sheath on the probe measurement has been minimized by applying a passive method of compensation. An emissive probe, placed inside the launcher, has been used as a reference electrode in order to minimize the discharge disturbance and to reduce the additional resistance in the measuring system. A filtering technique has been incorporated in the detection system to separate the photodetachment signal from the signal at the discharge stimulating frequency. The big heating of the probe, set at electron saturation condition, has been avoided by using a convenient time sequence of the detection system operation. The photodetachment H− density measurements are confirmed by applying a high sensitivity second derivative probe technique as a second reference method. Axial variation of H− density, as measured, correlates with the axial distribution of hydrogen atoms. Experimentally obtained radial H− density profile confirms the well known fact that the negative ions are confined in the existing radial potential well.

Envelope structure of Synechococcus sp. WH8113, a nonflagellated swimming cyanobacterium

BackgroundMany bacteria swim by rotating helical flagellar filaments [1]. Waterbury et al. [15] discovered an exception, strains of the cyanobacterium Synechococcus that swim without flagella or visible changes in shape. Other species of cyanobacteria glide on surfaces [2,7]. The hypothesis that Synechococcus might swim using traveling surface waves [6,13] prompted this investigation.ResultsUsing quick-freeze electron microscopy, we have identified a crystalline surface layer that encloses the outer membrane of the motile strain Synechococcus sp. WH8113, the components of which are arranged in a rhomboid lattice. Spicules emerge in profusion from the layer and extend up to 150 nm into the surrounding fluid. These spicules also send extensions inwards to the inner cell membrane where motility is powered by an ion-motive force [17].ConclusionThe envelope structure of Synechococcus sp. WH8113 provides new constraints on its motile mechanism. The spicules are well positioned to transduce energy at the cell membrane into mechanical work at the cell surface. One model is that an unidentified motor embedded in the cell membrane utilizes the spicules as oars to generate a traveling wave external to the surface layer in the manner of ciliated eukaryotes.

Printing with Ink Mist Ejected by Ultrasonic Waves

A novel ink jet printing technology using ink mist jet has been developed. It enables multilevel printing within a single dot because a density controllable cluster of fine ink droplets is formed by focused ultrasonic waves. The ultrasonic wave radiated into an ink chamber is reflected by the parabolic chamber wall and focused on a nozzle hole. Under the suitable driving condition of the ultrasonic transducer, a traveling surface wave is generated at the ink meniscus and it separates many fine ink droplets at the peak point of the wave. Changing the number of ultrasonic waves within the interval to achieve one dot printing can control the density of the cluster. We have obtained a print sample with reduced graininess using a prototype print head employing a 10 MHz transducer that produces ink droplets with an average diameter of 2.5 μm. We also confirmed a basic performance having a maximum optical density of 2.3, 32 controllable gray levels and a resolution of 300 dpi using glossy paper with a dot frequency of 2 kHz.

Biologically-Inspired Bodies Under Surface Waves—Part 1: Load Measurements

Measurements have been carried out in a tow tank on cylindrical bodies submerged in proximity of traveling surface waves. Two bodies are considered: a reference plain cylinder and another cylinder containing a pair of wings (or hydrofoils) below the cylinder, not above. The latter body owes its origin to certain species of fish which has small wings for maneuverability. The wavelength of the surface waves (λ) is of the order of the cylinder length (L) or higher (1 < λ/L < 10). Temporal measurements of axial and vertical forces and pitching moments, phase matched to the surface elevation of traveling waves, have been carried out. The time periods of the waves and depth of water pertain to deep water and intermediate depth waves. The forces and moments exhibit characteristic phase relationship with water elevation. Towing affects only vertical forces in the speed range of 0 to 1 m/s. The effect of towing and surface waves on vertical forces is roughly additive. Within the low speed range of towing evaluated, the effects of surface waves dominate those of towing. The presence of the hydrofoil and intermediate depth waves bring in some additional effects which are not well understood. In intermediate depth waves, a small plain cylinder may encounter a resonance with traveling waves which can be averted by attaching a pair of small wings to dampen pitching moment and make it speed invariant, although at a cost of increased vertical forces.

Printing with Ink Mist Ejected by Ultrasonic Waves

A novel ink jet printing technology using ink mist jet has been developed. It enables multilevel printing within a single dot because a density controllable cluster of fine ink droplets is formed by focused ultrasonic waves.The ultrasonic wave radiated into an ink chamber is reflected by the parabolic chamber wall and focused on a nozzle hole. Under the suitable driving condition of the ultrasonic transducer, a traveling surface wave is generated at the ink meniscus and it separates many fine ink droplets at the peak point of the wave. The density of the cluster can be controlled by changing the number of ultrasonic waves within the interval to achieve one dot printing.We have obtained a print sample with reduced graininess using a prototype print head employing a 10 MHz transducer, which produces ink droplets with an average diameter of 2.5 μm. We also confirmed a basic performance having a maximum optical density of 2.3, 32 controllable gray levels and a resolution of 300 dpi using glossy paper with a dot frequency of 2 kHz.

Investigating discrepancies among measurements of traveling and standing wave attenuation

In studies of long‐period (150 s to 300 s) seismic wave attenuation, the mean decay reported for surface waves is generally 10 to 15% greater (lower quality factor Q) than that measured from equivalent fundamental modes of oscillation. Towards reconciling this inconsistency, we first establish through forward modeling that observed waveforms are more compatible with the rapid rate of decay inferred from traveling wave analyses. Second, we apply traveling and standing wave measurement techniques to a common set of predicted and observed seismograms and compare the inferred levels of surface wave attenuation. We demonstrate that the discrepancy documented in the literature is a consequence of the measurement techniques applied and not an effect of the individual data sets used in previous studies. Experiments with synthetically generated seismograms illustrate that the presence of noise elevates the mean Q inferred for the standing wave methods considered. This bias is related to the nonrandom influence of noise on the phase spectrum. However, for realistic noise levels, the experiment fails to reproduce the magnitude of the discrepancy present in the literature or observed in this study. The synthetic experiments motivate a new measurement approach based on the decrease of spectral power with time that incorporates the behavior of noise into the parameterization. When this technique is applied to data, the mean observed Q decreases from values consistent with normal mode studies to values consistent with traveling surface wave analysis. We thus conclude that noise is the dominant cause of the discrepancy.

Ambient Gases and Heaping Instability of Granular Materials Under Vertical Vibration

We consider layers of non-cohesive granular materials lying on a vertically vibrating surface. Above a threshold acceleration, Γ = Γc internal convective motion begins, and the free surface of the granular material becomes unstable to the formation of a heap. As Γ increases further, there are several higher order instabilities, traveling surface waves, subharmonic bifurcations, and bubbling. We find that for particles of diameter d ≤ 1 mm, the pressure P of the surrounding gas plays a key role in the instabilities. We propose criteria to determine when gas effects are relevant.

BEM-numerics and KdV-model analysis for solitary wave split-up

Abstract In this paper we consider travelling surface waves on a layer of water of decreasing depth. A numerical scheme based on the boundary element method is used to present calculations for the run-up of a solitary wave. The numerical results are compared with an analytical approximation based on a modified Korteweg-de Vries equation.

Chaotic particle motion under linear surface waves.

We investigate the motion of infinitesimal particles in the flow field inside the fluid under a traveling surface wave. It is shown that, even for two-dimensional waves, a superposition of two or more traveling harmonic waves is enough to generate chaotic particle motion, i.e., Lagrangian chaos. (c) 1996 American Institute of Physics.

Do cyanobacteria swim using traveling surface waves?

Bacteria that swim without the benefit of flagella might do so by generating longitudinal or transverse surface waves. For example, swimming speeds of order 25 microns/s are expected for a spherical cell propagating longitudinal waves of 0.2 micron length, 0.02 micron amplitude, and 160 microns/s speed. This problem was solved earlier by mathematicians who were interested in the locomotion of ciliates and who considered the undulations of the envelope swept out by ciliary tips. A new solution is given for spheres propagating sinusoidal waveforms rather than Legendre polynomials. The earlier work is reviewed and possible experimental tests are suggested.