Wave turbulence and intermittency in directional wave fields

The evolution of surface gravity waves is driven by nonlinear interactions that trigger an energy cascade similarly to the one observed in hydrodynamic turbulence. This process, known as wave turbulence, has been found to display anomalous scaling with deviation from classical turbulent predictions due to the emergence of coherent and intermittent structures on the water surface. In the ocean, waves are spread over a wide range of directions, with a consequent attenuation of the nonlinear properties. A laboratory experiment in a large wave facility is presented to discuss the sensitivity of wave turbulence on the directional properties of model wave spectra. Results show that the occurrence of coherent and intermittent structures become less likely with the broadening of the wave directional spreading. There is no evidence, however, that intermittency completely vanishes.     

The character and the wave front set correspondence in the stable range

We relate the distribution characters and the wave front sets of unitary representation for real reductive dual pairs of type I in the stable range.     

Colloidal ZnO nanostructures and functional coatings: A survey

The past research work devoted to ZnO nanocolloidal sol-gel route is reviewed. It highlights the cluster chemistry of alcoholic ZnAc₂ solutions and the results of ZnO colloid growth investigations performed worldwide. Moreover, the role of doping and co-doping in the processing of functional ZnO coatings is discussed. The possibilities of tuning the optical properties are also reported with a particular attention to luminescence. The last part of this paper deals with electrical and photoelectrochemical properties of ZnO nanocrystals and their aggregates. This contribution is dedicated to the 80th birthday of Prof. Arnim Henglein from the Hahn-Meitner-Institut in Berlin and to the memory of Prof. Jacques Mugnier from the Université Claude-Bernard Lyon 1 in France.     

The Markov power moment problem in problems of controllability and frequency extinguishing for the wave equation on a half-axis

In this paper necessary and sufficient conditions of null-controllability and approximate null-controllability are obtained for the wave equation on a half-axis. Controls solving these problems are found explicitly. Moreover, bang-bang controls solving the approximate null-controllability problem are constructed with the aid of solutions of a frequency extinguishing problem in the restricted band (−a,a) for this equation and the Markov power moment problem.     

Simulation of the nonlinear vibration of a string using the Cellular Automata based on the reflection rule

In this study, the nonlinear dynamic responses of a string are simulated using the Cellular Automata method based on the reflection rule. In the case of nonlinear systems, the velocity of wave propagation is not constant and depends on the amplitude. A new treatment of the dynamic time step is proposed for the Cellular Automata method considering the effect of the propagation velocity. As numerical examples, first, the dynamic responses of a string with linear characteristic are simulated using the Cellular Automata method. A typical resonance curve can be obtained. Second, the dynamic responses of a string with nonlinear characteristic are simulated using the proposed method. Some characteristic types of vibration can be obtained. It is concluded that the linear and nonlinear dynamic responses of a string may be obtained by simulation using the Cellular Automata method.     

Universal elementary constituents of potential transformations shifting waves (qualitative theory)

It is shown that the potential perturbation that shifts a chosen standing wave in space is a block of potential barrier and well for every wave bump between neighbouring knots. The algorithms shifting the range of the primary localization of a chosen bound state in a potential well of finite width are as well applicable to the scattering functions if states of the continuous spectrum are considered as bound states normalized to unity but distributed on an infinite interval with vanishing density. The potential perturbations of the same type on the half-axis concentrate the scattering wave at the origin, thus creating a bound state embedded into the continuous spectrum (zero width resonance).     

Two-dimensional numerical calculation of the flow field about a scoop inlet by the piecewise linear method

The piecewise linear method (PLM) based on time operator splitting is used to solve the unsteady compressible Euler equations describing the two-dimensional flow around and through a straight wall inlet placed stationary in a rapidly rotating supersonic flow. The PLM scheme is formulated as a Lagrangian step followed by an Eulerian remap. The inhomogeneous terms in the Euler equations written in cylindrical coordinates are first removed by Sod's method and the resulting set of equations is further reduced to two sets of one-dimensional Lagrangian equations, using time operator splitting. The numerically generated flow fields are presented for different values of the back pressure imposed at the downstream exit of the inlet nozzle. An oblique shock wave is formed in front of the almost whole portion of the inlet entrance, the incoming streamlines being deflected towards the higher pressure side after passing through the oblique shock wave and then bending down to the lower pressure side. A reverse flow appears inside the inlet nozzle owing to the recovery pressure of the incoming streams being lower than the back pressure of the inlet nozzle.     

运动目标声信号的时频特征研究

提高声被动目标定位精度需要研究运动目标在有风条件下目标声信号的特征。本文从声学波动方程出发，对无风和有常速风情况下的波动方程进行了求解，得到了运动目标声信号的延迟关系；分析了解的主要影响项，并得到了其解析信号；用解析信号对运动目标声信号的延迟特性和时频特征进行了仿真计算。     

Total energy decay for the wave equation in exterior domains with a dissipation near infinity

We show that the energy of solutions to the initial boundary value problem for the wave equation in exterior domains with a dissipation which is localized only near infinity tends to zero as the time goes to infinity. We do not make any geometrical condition like star-shapedness on the boundary.