Chemical turbulence and standing waves in a surface reaction model: The influence of global coupling and wave instabilities

Among heterogeneously catalyzed chemical reactions, the CO oxidation on the Pt(110) surface under vacuum conditions offers probably the greatest wealth of spontaneous formation of spatial patterns. Spirals, fronts, and solitary pulses were detected at low surface temperatures (T<500 K), in line with the standard phenomenology of bistable, excitable, and oscillatory reaction-diffusion systems. At high temperatures (T greater, similar 540 K), more surprising features like chemical turbulence and standing waves appeared in the experiments. Herein, we study a realistic reaction-diffusion model of this system, with respect to the latter phenomena. In particular, we deal both with the influence of global coupling through the gas phase on the oscillatory reaction and the possibility of wave instabilities under excitable conditions. Gas-phase coupling is shown to either synchronize the oscillations or to yield turbulence and standing structures. The latter findings are closely related to clustering in networks of coupled oscillators and indicate a dominance of the global gas-phase coupling over local coupling via surface diffusion. In the excitable regime wave instabilities in one and two dimensions have been discovered. In one dimension, pulses become unstable due to a vanishing of the refractory zone. In two dimensions, turbulence can also emerge due to spiral breakup, which results from a violation of the dispersion relation.     

A set of Boussinesq-type equations for interfacial internal waves in two-layer stratified fluid

Many new forms of Boussinesq-type equations have been developed to extend the range of applicability of the classical Boussinesq equations to deeper water in the study of the surface waves. One approach was used by Nwogu (1993. J. Wtrw. Port Coastal and Oc. Eng. 119, 618--638) to improve the linear dispersion characteristics of the classical Boussinesq equations by using the velocity at an arbitrary level as the velocity variable in derived equations and obtain a new form of Boussinesq-type equations, in which the dispersion property can be optimized by choosing the velocity variable at an adequate level. In this paper, a set of Boussinesq-type equations describing the motions of the interfacial waves propagating alone the interface between two homogeneous incompressible and inviscid fluids of different densities with a free surface and a variable water depth were derived using a method similar to that used by Nwogu (1993. J. Wtrw. Port Coastal and Oc. Eng. 119, 618--638) for surface waves. The equations were expressed in terms of the displacements of free surface and density-interface, and the velocity vectors at arbitrary vertical locations in the upper layer and the lower layer (or depth-averaged velocity vector across each layer) of a two-layer fluid. As expected, the equations derived in the present work include as special cases those obtained by Nwogu (1993, J. Wtrw. Port Coastal and Oc. Eng. 119, 618-638) and Peregrine (1967, J. Fluid Mech. 27, 815-827) for surface waves when the density of the upper fluid is taken as zero.     

Generation of alfvén and magnetosonic waves due to HF and parametric instabilities in an ionized gas flow in a plane waveguide

We report on the analysis of the up-conversion and parametric instability of Alfvén and magnetosonic waves in a flow of completely ionized gas propagating in a plane waveguide. A nonlinear boundary-value problem has been solved and equations for slowly varying complex amplitudes of modes have been derived. The high efficiency of the energy up-conversion due to gas flow energy is shown. State Technical University, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 7, pp. 845–850, July, 1997.     

Stabilization of domain walls between traveling waves by nonlinear mode coupling in Taylor-Couette flow

We present a new mechanism that allows the stable existence of domain walls between oppositely traveling waves in pattern-forming systems far from onset. It involves a nonlinear mode coupling that results directly from the nonlinearities in the underlying momentum balance. Our work provides the first observation and explanation of such strongly nonlinearly driven domain walls that separate structured states by a phase generating or annihilating defect. Furthermore, the influence of a symmetry breaking externally imposed flow on the wave domains and the domain walls is studied. The results are obtained for vortex waves in the Taylor-Couette system by combining numerical simulations of the full Navier-Stokes equations and experimental measurements.     

Nonlinear interfacial waves in a constant-vorticity planar flow over variable depth

Exact Lagrangian in compact form is derived for planar internal waves in a two-fluid system with a relatively small density jump (the Boussinesq limit taking place in real oceanic conditions), in the presence of a background shear current of constant vorticity, and over arbitrary bottom profile. Long-wave asymptotic approximations of higher orders are derived from the exact Hamiltonian functional in a remarkably simple way, for two different parametrizations of the interface shape.     

Life time of a phase mode due to interchain coupling in a quasi-one-dimensional CDW system

The vibrational modes are studied in an incommensurate quasi-ome-dimensional system. It is shown that interchain coupling causes the life time of a phason which is proportional to the momentum along the chain.     

Parametric generation of whistler waves due to the interaction of high-frequency wave beams with a magnetoplasma

The parametric generation of low-frequency whistler waves by a pump wave beam formed by high-frequency whistler waves with close frequencies is studied experimentally. The electromagnetic fields excited by the beats of two co- or counterpropagating high-frequency waves, or by an amplitude-modulated pump are studied. It is shown that the nonlinear currents at the beat (modulation) frequency are generated by a transverse ponderomotive force arising due to the finite width of the high-frequency beam. In this case, the nonlinear azimuthal drift currents enclose the pump beam and can radiate low-frequency whistler waves to the surrounding plasma.     

Bond stretching phonon anomalies due to incommensurate charge density wave instabilities in high-Tc cuprates

Phonon anomalies observed in various high T_c cuprates are analyzed theoretically within the Hubbard-Holstein model in the limit of strong local electron correlations and in presence of long-range Coulomb interaction. The phonon self-energy is evaluated by taking into account the charge collective modes that become critical upon doping approaching an instability towards an incommensurate charge density wave (ICDW) driven by electron correlations. The doping dependence of phonon softening features and the highly distinctive phonon self-energy dependence on the wave vector agree with experiments. We discuss relevance of dynamical corrections to the density correlation function to achieve a sizeable bond-stretching phonon softening with a kink-like profile away from the zone boundary.     

3-D PTV measurement on turbulence modification due to an oil droplet in a plane Couette water flow

Three-dimensional particle tracking velocimetry (3-D PTV) measurements with a two-camera system have been conducted for a turbulent water plane Couette flow with an oil droplet in order to understand the modification of shear-dominant turbulence by the droplet. The parameters of the stereogrammetry, which are crucial for calculating the spatial coordinate of tracer particles from 2-D images of two cameras, have been determined with a careful calibration. The experimental results show that the axial and wall-normal turbulence intensities and the turbulent kinetic energy are enhanced locally in the confluence regions where axial main flow over the interface meets the secondary flow along the interface in the wall-normal direction. The secondary flows were observed only around the equator of the droplet. The wall-normal and transverse turbulence intensities are found to increase in the region above the droplet. This is due to the change in the direction of the primary flow over the top of the droplet. The turbulence in the other region is attenuated mainly because of the attenuation of the generation and evolution of the coherent structure in the neighbourhood of the droplet.     

Electrostatic mode excitation in electron holes due to wave bounce resonances

A kinetic theory of resonant interaction between electrostatic waves and the bounce motion of electrostatically trapped electrons is developed. Precise criteria are derived for the stability of electrostatic potential structures which trap electrons in a highly magnetized plasma. The theory explains the energy transfer from electron phase space holes to waves observed in simulations. It may also account for the destabilization of electrostatic waves propagating obliquely to the geomagnetic field and some characteristics of the holes as observed in the auroral ionosphere.     

Reflection of spin waves from a ferromagnetic multilayer with interfacial coupling of finite strength (reflection of spin waves from multilayer)

The reflection coefficient of bulk spin waves from a ferromagnetic multilayer with periodically modulated parameters of the exchange interaction, the uniaxial magnetic anisotropy and the saturation magnetization (a magnonic crystal) is calculated. The dependence of the reflection coefficient upon the spin wave frequency and the values of the bias magnetic field, the parameter of interfacial coupling, and the internal structure of the unit cell are investigated.      

Parametric instabilities of langmuir waves in a non-uniform magnetoplasma

It is shown that an obliquely propagating electron plasma wave in a non-uniform magnetoplasma is unstable with respect to drift wave perturbations. The growth rates for the three-wave decay interaction as well as modulational instabilities are obtained.     

Reflection of radiofrequency waves by a two-layer medium with randomly rough boundaries

Using perturbation theory, we have investigated the electromagnetic field reflected by a two-layer medium with rough boundaries. To first order in perturbation theory with respect to the asperities on the boundaries, we consider the scattering fading effect. To a second approximation, we have obtained analytical expressions for the perturbations of the mean field reflected and transmitted into the medium, and also analytical expressions for the second moment of the field with orthogonal polarization scattered in the plane of incidence. We have investigated the dependences of the second moment of the field on the character of the asperity spectrum, the frequency of the radiation, and the layer thickness.Scientific-Research Institute of Physics at Rostov University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 37, No. 12, pp. 1483–1498, December, 1994.     

Disappearance of laser instabilities in a Gaussian cavity mode

We consider a homogeneously-broadened ring laser with spherical mirrors. We show that if ones assumes a gaussian transverse profile for the electric field, all the instabilities predicted by the plane wave theory vanish. The analysis is performed in the mean field limit, assuming that a suitably defined Fresnel number is much larger than unity and that perfect tuning between atoms and cavity exist.     

Decay and modulation instabilities of beat waves in a plasma

Summary A large-amplitude beat wave excited at the beat frequency of two copropagating laser beams is extremely unstable and suffers strong three- and fourwave parametric instabilities with large growth rates. The relativistic effects are seen to be negligible on both the decay and modulation instabilities. However, the growth rates of these instabilities are sensitive functions of the plasma parameters. The authors of this paper have agreed to not receive the proofs for correction.     

Onset of wave drag due to generation of capillary-gravity waves by a moving object as a critical phenomenon

The onset of the wave resistance, via generation of capillary-gravity waves of a small object moving with velocity V, is investigated experimentally. Because of the existence of a minimum phase velocity V(c) for surface waves, the problem is similar to the generation of rotons in superfluid helium near their minimum. In both cases waves or rotons are produced at V>V(c) due to Cherenkov radiation. We find that the transition to the wave drag state is continuous: in the vicinity of the bifurcation the wave resistance force is proportional to sqrt[V-V(c)] for various fluids.     

Nonphysical noises and instabilities in plasma simulation due to a spatial grid

A series of plasma numerical simulation has been performed in order to understand the enhancement of nonphysical noises and instabilities due to the use of a spatial grid. Several different superparticle models including the Nearest Grid Point (NGP) model, Cloud-in-Cell (CIC) or Particle-in-Cell (PIC) models, Lewis energy conserving code, and the multipole expansion code have been examined for a Maxwellian plasma and a one beam plasma using a one-dimensional, one-specie (electron) plasma. An instability was observed for all of the models when the Debye length was too small compared with the grid size. When the Debye length is comparable to the grid size, no instabilities were observed. However, the enhancement of noises at high frequencies (ω > 3ω_pe may not always be negligible- even for long wavelength modes for the NGP model. For the NGP and CIC, PIC models, the experimental results are in good agreement with Langdon's theory. It is observed that the dipole expansion model, which is the first-order approximation to the multipole expansion scheme, is similar to CIC, PIC models in many respects and appears to be the same order of approximation.