Generation of free-surface gravity waves by an unsteady Stokeslet

The interaction of unsteady Stokeslets with the free surface of an initially quiescent incompressible fluid of infinite depth is investigated analytically for two- and three-dimensional cases. The disturbed flows are generated by an unsteady singular force moving perpendicularly downwards away from the surface. The analysis is based on the assumption that the motion satisfies the linearized unsteady Navier–Stokes equations with linear kinematic and dynamic boundary conditions. Firstly, the asymptotic representation for the transient free-surface waves due to an instantaneous Stokeslet is derived for a large time with a fixed distance-to-time ratio. As is well known, the corresponding inviscid waves predicted by the potential theory do not decay to zero as the time goes to infinity. In the present study, the transient waves predicted by the viscous theory eventually vanish due to the presence of viscosity, which is consistent with reality from the physical point of view. Secondly, the asymptotic solutions are obtained for the unsteady free-surface waves due to a harmonically oscillating Stokeslet. It is found that the unsteady waves can be decomposed into steady-state and transient responses. The steady state can be attained as time approaches infinity. It is shown that the viscosity of the fluid plays an important role in the evolution of the singularity-induced waves.     

Design and implementation of a novel multi-scroll chaotic system

This paper proposes a novel approach for generating a multi-scroll chaotic system. Together with the theoretical design and numerical simulations, three different types of attractor are available, governed by constructing triangular wave, sawtooth wave and hysteresis sequence. The presented new multi-scroll chaotic system is different from the classical multi-scroll chaotic Chua system in dimensionless state equations, nonlinear functions and maximum Lyapunov exponents. In addition, the basic dynamical behaviours, including equilibrium points, eigenvalues, eigenvectors, eigenplanes, bifurcation diagrams and Lyapunov exponents, are further investigated. The success of the design is illustrated by both numerical simulations and circuit experiments.     

Three-dimensional interfacial wave theory of dendritic growth： （Ⅱ）. non-axi-symmetric global wave modes and selection criterion of pattern formation

This paper is the continuation of part (I), which completes the derivations of the 3D global wave modes solutions, yields the stability criterion and, on the basis of the results obtained, demonstrates the selection criterion of pattern formation.     

Application of higher-order KdV——mKdV model with higher-degree nonlinear terms to gravity waves in atmosphere

Higher-order Korteweg-de Vries (KdV)-modified KdV (mKdV) equations with a higher-degree of nonlinear terms are derived from a simple incompressible non-hydrostatic Boussinesq equation set in atmosphere and are used to investigate gravity waves in atmosphere. By taking advantage of the auxiliary nonlinear ordinary differential equation, periodic wave and solitary wave solutions of the fifth-order KdV--mKdV models with higher-degree nonlinear terms are obtained under some constraint conditions. The analysis shows that the propagation and the periodic structures of gravity waves depend on the properties of the slope of line of constant phase and atmospheric stability. The Jacobi elliptic function wave and solitary wave solutions with slowly varying amplitude are transformed into triangular waves with the abruptly varying amplitude and breaking gravity waves under the effect of atmospheric instability.     

Experimental investigation of secondary steady flows in Faraday surface waves

It is shown that in the two-dimensional Faraday surface waves excited in a vertically oscillating rectangular water-filled vessel there is a system of secondary circulatory flows that occupies the entire fluid volume between the vessel bottom and the free surface. In parallel with the oscillations at the wave frequency, the fluid particles are slowly displaced in accordance with these circulatory flows. The secondary flow velocity field is measured and the trajectories of individual fluid particles in the standing wave are determined. The experimental data are compared with the Longuet-Higgins model. It is shown that the initial stage of formation of regular structures on the surface of a sediment layer on the vessel bottom may be related with the presence of secondary circulatory flows.     

Dependence of the force action of a water wave on the shape of its leading front

The results of experiments in which bore-type waves with various leading front shapes propagated first above an even horizontal bottom, then above a rising bottom, then again above a horizontal bottom segment, and were finally reflected from a vertical wall are presented. It is shown that the impact force is greatest if the leading front breaks directly on approaching the wall. This force is much greater than the impact force of smooth waves or waves that break before they reach the wall.     

Gyroscopic waves in a rotating liquid layer

The dispersion characteristics of gyroscopic waves in an incompressible liquid layer in a cavity of a rapidly rotating cylinder are studied. It is shown that in a viscous incompressible liquid layer, an inertial wave can be represented as the sum of six helical harmonics. The effects of the liquid viscosity and the ratio of the wave frequency to the angular velocity of rotation of the cylinder on the real and imaginary parts of the wavenumber are studied. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 2, pp. 15–20, March–April, 2008.     

毫米波辐射下悬液细胞膜电压变化研究

根据有效介质理论,用Maxwell-Wagner等效公式计算细胞悬液中的平均场．然后基于时变场中单细胞膜电压第二计算模型,用场近似等效方法,建立了毫米场辐射下悬液中细胞膜电压计算模型．模型表明悬液细胞膜电压变化和毫米波的功率、频率、细胞半径、细胞排列及细胞的浓度有关。     

毫米波LFMCW雷达加速运动目标回波检测与加速度-速度估计

在毫米波线性调频连续波（LFMCW）雷达中,目标加速度存在使回波多普勒信号受到二次项调制,造成多普勒频谱畸变,从而导致目标检测性能下降和参数估计精度损失．采用最大似然模型进行加速运动目标检测和加速度-速度估计,提出了适合在一般高斯噪声环境中（包括色噪声）该模型的速度-加速度联合估计快速算法．另外也推导出了一般高斯环境下Chirp信号参数估计的CRB界,为一般高斯环境下Chirp信号参数的方差提供了实际下界．     

Spiral and Antispiral Waves in Reaction-Diffusion Systems

Spiral waves are ubiquitous phenomena in nonlinear chemical, physical, and biological systems. But antispiral waves are infrequent to date. The transition between spiral and antispiral waves has been rarely explored. We have analyzed the extended Brusselator model and the extended Oregonator model by linear stability analysis. We have demonstrated that it is possible and plausible to realize the transition between them by control of diffusion coefficient of inactivator from theoretical analysis and numerical simulations.