Mean flow properties for equatorially trapped internal water wave–current interactions

The aim of this paper is to provide an analysis of the mean flow velocities, and the related mass transport induced by equatorially trapped internal water waves with a constant underlying current.     

Internal gravity–capillary solitary waves in finite depth

We consider a two‐dimensional inviscid irrotational flow in a two layer fluid under the effects of gravity and interfacial tension. The upper fluid is bounded above by a rigid lid, and the lower fluid is bounded below by a rigid bottom. We use a spatial dynamics approach and formulate the steady Euler equations as a Hamiltonian system, where we consider the unbounded horizontal coordinate x as a time‐like coordinate. The linearization of the Hamiltonian system is studied, and bifurcation curves in the (β,α)‐plane are obtained, where α and β are two parameters. The curves depend on two additional parameters ρ and h, where ρ is the ratio of the densities and h is the ratio of the fluid depths. However, the bifurcation diagram is found to be qualitatively the same as for surface waves. In particular, we find that a Hamiltonian‐Hopf bifurcation, Hamiltonian real 1:1 resonance, and a Hamiltonian 0²‐resonance occur for certain values of (β,α). Of particular interest are solitary wave solutions of the Euler equations. Such solutions correspond to homoclinic solutions of the Hamiltonian system. We investigate the parameter regimes where the Hamiltonian‐Hopf bifurcation and the Hamiltonian real 1:1 resonance occur. In both these cases, we perform a center manifold reduction of the Hamiltonian system and show that homoclinic solutions of the reduced system exist. In contrast to the case of surface waves, we find parameter values ρ and h for which the leading order nonlinear term in the reduced system vanishes. We make a detailed analysis of this phenomenon in the case of the real 1:1 resonance. We also briefly consider the Hamiltonian 0²‐resonance and recover the results found by Kirrmann. Copyright © 2016 John Wiley & Sons, Ltd.     

An approximation to the minimum traveling wave for the delayed diffusive Nicholson's blowflies equation

In this work, we study the approximation of traveling wave solutions propagated at minumum speeds c ₀(h ) of the delayed Nicholson's blowflies equation: In order to do that, we construct a subsolution and a super solution to (?). Also, through that construction, an alternative proof of the existence of traveling waves moving at minimum speed is given. Our basic hypothesis is that p /δ ∈(1,e ] and then, the monostability of the reaction term. Copyright © 2017 John Wiley & Sons, Ltd.     

Monotonicity,uniqueness, and stability of traveling waves in a nonlocal reaction‐diffusion system with delay

The purpose of this paper is to study the traveling wave solutions of a nonlocal reaction‐diffusion system with delay arising from the spread of an epidemic by oral‐faecal transmission. Under monostable and quasimonotone it is well known that the system has a minimal wave speed c* of traveling wave fronts. In this paper, we first prove the monotonicity and uniqueness of traveling waves with speed c ?c _?. Then we show that the traveling wave fronts with speed c >c _? are exponentially asymptotically stable.     

On the Whitham system for the (2+1)-dimensional nonlinear Schrödinger equation

Whitham modulation equations are derived for the nonlinear Schrödinger equation in the plane ((2+1)-dimensional nonlinear Schrödinger [2d NLS]) with small dispersion. The modulation equations are obtained in terms of both physical and Riemann-type variables; the latter yields equations of hydrodynamic type. The complete 2d NLS Whitham system consists of six dynamical equations in evolutionary form and two constraints. As an application, we determine the linear stability of one-dimensional traveling waves. In both the elliptic and hyperbolic cases, the traveling waves are found to be unstable. This result is consistent with previous investigations of stability by other methods and is supported by direct numerical calculations.     

Characteristic Features of Gravitational Wave Lensing as Probe of Lens Mass Model

To recognize gravitational wave lensing events and being able to differentiate between similar lens models will be of crucial importance once one will be observing several lensing events of gravitational waves per year. In this work, the lensing of gravitational waves is studied in the context of LISA sources and wave-optics regime. While different papers before the studied microlensing effects enhanced by simultaneous strong lensing, the focus is on frequency (time) dependent phase effects produced by one lens that will be visible with only one lensed signal. It is shows how, in the interference regime (i.e., when interference patterns are present in the lensed image), one is able to i) distinguish a lensed waveform from an unlensed one, and ii) differentiate between different lens models. In pure wave-optics, on the other hand, the feasibility of the study depends on the signal-to-noise ratio of the signal and/or the amplitude of the lensing effect. To achieve these goals, the phase of the amplification factor of the different lens models and its effect on the unlensed waveform is studied, and the signal-to-noise calculation to provide some quantitative examples is exploited.     

Landau damping of ion-acoustic waves with simultaneous effects of non-extensivity and non-thermality in the presence of hybrid Cairns-Tsallis distributed electrons

The dispersion properties and Landau damping rate of ion-acoustic waves (IAWs) with the hybrid Cairns-Tsallis distributed (CTD) electrons and Maxwellian ions are investigated using the plasma kinetic model based on Vlasov-Poisson's equations. For both super-extensive (q < 1) and sub-extensive (q > 1) plasmas, the dielectric response function, real frequency, and Landau damping rate of IAWs are derived. By taking the effect of θ_{i, e} (ion-to-electron temperature ratio) into account, it is found that with the increase of ion temperature, the real frequency and wave dispersion effects increase as well (for both super-extensive and sub-extensive cases). Exploring the properties of the Landau damping rate of IAWs with the simultaneous presence of non-thermal parameter α and non-extensive parameter q, a comparison of numerical and analytical results is presented. It is found that in different ranges of θ_{e, i} (electron-to-ion temperature ratio), on decreasing the values of the non-extensive parameter and increasing values of the non-thermal parameter, the weak damping rate is observed (vice versa) in super-extensive or super-thermal plasma, although the trend of the damping rate in sub-thermal plasma is similar (as in the case of super-thermal plasma) but is less weak. It is further revealed that the damping rate of IAWs in thermal plasmas (Maxwellian) is stronger than the damping rate of IAWs in the case of non-thermal plasmas (CTD). The current study is applicable to provide deep insight and further allow the exploration of electrostatic plasma modes in different space and laboratory plasma environments where the hybrid CTD plasma exists.     

相位失配弹性平板复合波导中的缺陷态*

为了在弹性波波导中实现缺陷态的调控,该文基于相位失配原理设计了一种周期性平板波导结构。以正弦边界弹性波导为例,通过连接具有不同相位的两段波导结构,形成了弹性板中不同程度的缺陷,并分析了其谱带特性和能量局域化特征。结果表明,禁带中存在两个不同模式的缺陷态,其以透射峰形式出现并随着相位的改变产生频移。与此同时,两个缺陷态在空间上对应的应力场和位移场分布也具有不同的模态特征。该文提出的复合弹性波导缺陷态调控方法,不仅为研究弹性波与结构之间的内在联系提供了关键的理论支持,也为实际弹性波探测器件的设计提供重要参考。     

Fine structure of a stratified flow near a flat-plate surface

The pattern of disturbances arising during the motion of a strip along a horizontal surface in a continuously stratified fluid with identified upstream and attached internal waves, boundary layers, and edge singularities is calculated in the liner approximation. The flow pattern behind a flat plate moving with a constant velocity in a continuously stratified fluid is studied with the use of the optical schlieren technique; transformation of waves and finely structured elements of the flow with increasing plate velocity is analyzed. The calculated and experimentally observed patterns of internal waves at low velocities are demonstrated to be in good agreement. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 6, pp. 77–91, November–December, 2007.     

Interaction of elastic waves with a periodic array of collinear inplane cracks

A boundary integral equation method is applied to the study of the interaction of plane elastic waves with a periodic array of collinear inplane cracks. Numerical results are presented for the dynamic stress intensity factors. The effects of the wave type, wave frequency, wave incidence angle, and crack spacing on the dynamic stress intensity factors are analyzed in detail. The project supported by the Committee of Science and Technology of Shanghai and Tongji University