Effect of excavated trapped electron distributions on ion-acoustic solitary structures in an electron-positron-ion plasma

Fully nonlinear propagation of ion-acoustic solitary waves in an unmagnetized electron-positron-ion plasma is investigated. A more realistic situation is considered in which electrons interact with the wave potential during its evolution and, follow the vortex-like excavated trapped distribution. The basic properties of large amplitude solitary waves are studied by deriving an energy integral equation involving Sagdeev potential. It is shown that effects of such electron behavior and positron concentration change the maximum values of the Mach number and amplitude for which solitary waves can exist. The small amplitude limit is also investigated by expanding the Sagdeev potential to include third-order nonlinearity of electric potential. In this case, exact analytical solution is obtained which is related to the contribution of the resonant electron to the electron density. It is shown from both highly and weakly nonlinear analysis that the plasma system under consideration supports only compressive solitary waves.     

A highly accurate analytical solution for the surface fields of a short vertical wire antenna lying on a multilayer ground

A highly accurate analytical solution is derived to the electromagnetic problem of a short vertical wire antenna located on a stratified ground. The derivation consists of three steps. First, the integration path of the integrals describing the fields of the dipole is deformed and wrapped around the pole singularities and the two vertical branch cuts of the integrands located in the upper half of the complex plane. This allows to decompose the radiated field into its three contributions, namely the above-surface ground wave, the lateral wave, and the trapped surface waves. Next, the square root terms responsible for the branch cuts are extracted from the integrands of the branch-cut integrals. Finally, the extracted square roots are replaced with their rational representations according to Newton’s square root algorithm, and residue theorem is applied to give explicit expressions, in series form, for the fields. The rigorous integration procedure and the convergence of square root algorithm ensure that the obtained formulas converge to the exact solution. Numerical simulations are performed to show the validity and robustness of the developed formulation, as well as its advantages in terms of time cost over standard numerical integration procedures.     

Analytic waves

Physical aspects of wave theory are discussed. Analytic waves (AW) neatly define the amplitude and frequency of real running waves and generalize and justify some points of wave theory. It is shown that the local group delay averaged in frequency defines the velocity of a wave center at each point. An asymptotic solution is developed for running spectra in slowly varying media. Also, Whitham's method is generalized not only for the frequency but also the amplitude of a wave. The theory is applied to quantum mechanics, and the paradox of tunneling is clarified. This paradox is not specifically quantum but occurs and can be explained in a classical area.     

Integral Reduction Arising in Double Transfer and Excitation Amplitude

The purpose of this article is to develop an integral derived from the double transfer and excitation theory. The reduced form of this integral, so obtained, can serve in the computation of the transition amplitude which is from numerical point of view difficult to implement. This amplitude is of great interest in the resonant and non resonant transfer and excitation （RTE and NTE） processes.     

切变基本纬向流中β效应的赤道Rossby孤立波包

从描写赤道Rossby 波的正压大气位涡方程出发,采用多重尺度摄动方法推导出在切变基本纬向流中具有β效应的非线性赤道Rossby波包演变满足非线性Schrdinger方程,并得到单个包络孤立子波解,分析了基本切变流,β效应对非线性赤道Rossby波的影响. 关键词： 赤道Rossby波 β效应 非线性Schrö dinger方程 包络孤立子     

Dynamic vertical interaction of a foundation–soil system generated by seismic waves

Based on Biot's dynamic poroelastic theory, a foundation–soil interaction model is established to investigate the vertical vibrations of a rigid circular foundation on poroelastic soil excited by incident plane waves, including the fast P waves and SV waves. Scattering waves caused by the foundation and fluid–solid coupling due to the pore water in the soil are also considered in the model. The solution of the vertical vibrations of the foundation subjected to seismic waves are obtained by solving two sets of dual integral equations derived from the mixed boundary-value conditions. The different vertical vibrations of foundation rest on elastic and saturated half-space are compared. The influences of incident angle, permeability of soil and foundation mass on the vertical vibrations of the foundation are then discussed. The results show that resonant phenomenon of the foundation is observed at certain excitation frequencies; the effects of the pore water on the foundation vertical vibrations are significant. In addition, significant differences are found when the foundation is excited by P waves and SV waves, respectively.     

Effect of deviations from isothermality of ions on the propagation of localized dust-acoustic waves

The effect of deviations from isothermality of ions on arbitrary amplitude dust-acoustic solitary structures is studied in an unmagnetized dusty plasma which consists of a negative charged dust fluid, free electrons and hot ions obeying a trapped distribution. For the finite deviation from isothermality of ions, the basic properties of large amplitude solitary waves are studied by employing pseudo-potential approach. It is shown that the effect of such ion behavior changes the maximum values of the Mach number and the amplitude for which solitary wave can exist. For the case that the deviation from isothermality due to nonlinear resonant particle effects is small, calculations by reductive perturbation method leads to a generalized Korteweg-de Vries equation with mixed nonlinearity. The latter admits a stationary dust-acoustic solitary solution with similar width and qualitatively different amplitude in comparison to the case that deviations from isothermality are finite. Furthermore, effects of the equilibrium free electron density and such trapped ions on the amplitude of solitary structures imply a non-uniform transition from the Boltzmann ion distribution to the trapped ion one.     

基于Washout滤波器的Rössler系统Hopf分岔控制

针对Rössler系统平衡点的Hopf分岔,以Washout滤波器为控制器,详细讨论了控制器参数对Hopf分岔点位置、分岔类型以及周期解振幅的控制问题.首先根据Routh-Hurwitz判据计算了受控系统的参数空间稳定域,找出了对应的Hopf分岔边界,并由此分析了滤波器时间常数、线性控制增益对分岔点位置的影响.然后,引入Normal Form直接法方便地求出系统Hopf分岔Normal Form系数,由此确定出改变分岔类型和周期解振幅的控制器非线性增益选择原则.最后用数值计算验证了本文的结论. 关键词： Rö ssler系统 Washout滤波器 Hopf分岔 Normal Form     

New ion-wave path in the energy cascade

We present the results of kinetic numerical simulations that demonstrate the existence of a novel branch of electrostatic nonlinear waves driven by particle trapping processes. These waves have an acoustic-type dispersion with phase speed comparable to the ion thermal speed and would thus be heavily Landau damped in the linear regime. At variance with the ion-acoustic waves, this novel electrostatic branch can exist at a small but finite amplitude even for low values of the electron to ion temperature ratio. Our results provide a new interpretation of observations in space plasmas, where a significant level of electrostatic activity is observed in the high frequency region of the solar-wind turbulent spectra.     

The thermoelastic excitation of air-solid interface waves using the pulsed laser

In the 1920s, the solid-solid interface wave, Stoneley wave, was first studied by Stoneley. From the 1930s to 1940s, the fluid-solid interface waves, usually called Scholte wave or Scholte-Stoneley wave, were studied by Cagniard and Scholte respec-tively[1]. The Scholte wave corresponds to the real root of the fluid-solid interface secu-lar equation, which is usually called the Scholte equation, and the velocity of Scholte wave is only slightly lower than the longitudinal velocity of the f…     

Weakly nonlinear analysis of the magnetorotational instability in a model channel flow

We show by means of a perturbative weakly nonlinear analysis that the axisymmetric magnetorotational instability (MRI) of a viscous, resistive, incompressible rotating shear flow subject to a background vertical magnetic field in a thin channel gives rise to a Ginzburg-Landau equation for the disturbance amplitude. For small magnetic Prandtl number (P(m)), the saturation amplitude is proportional square root P(m) and the resulting momentum transport scales as R(-1), where R is the hydrodynamic Reynolds number. Simplifying assumptions, such as linear shear base flow, mathematically expedient boundary conditions, and continuous spectrum of the vertical linear modes, are used to facilitate this analysis. The asymptotic results are shown to comply with numerical calculations using a spectral code. They suggest that the transport due to the nonlinearly developed MRI may be very small in experimental setups with P(m)<1.     

On stochastic stabilization of the Kelvin-Helmholtz instability by three-wave resonant interaction

An analytical investigation of the effect of three-wave resonant interactions with the linearly unstable wave is proposed. We consider the waves in the Kelvin-Helmholtz model, consisting of two fluid layers with different densities and velocities. We suppose that the velocity shear is weakly supercritical, the instability is of the algebraic type, i.e., the amplitude of the unstable wave grows linearly, and the instability occurs within the framework of a single mode. The amplitudes of two other waves taking part in the nonlinear interaction are assumed to be stable. The initial amplitudes of these waves are supposed to be small in comparison with the initial amplitude of the unstable wave. We present an analysis of the system of amplitude equations derived for this case using JWKB-method. As a result, we obtain equations that couple solutions pre- and post-passing the singular point, i.e., the point where the amplitude of the unstable wave has a local minimum. These equations give us the transformation rule of a parameter that characterizes the phase shift between fast and slow waves and defines the behavior of the system. This parameter is constant between two singular points and varies by chance at a singular point. As long as it stays positive, the amplitude of the wave remains limited and performs stochastic oscillations. If this parameter passes over zero, then we leave the region of stabilization and turn out in the region, where the amplitude grows infinitely. Accordingly, the transition to the region of instability happens stochastically. However, if the time interval, when the amplitude remains bounded, is large enough, the proposed scenario can be treated as a partial stabilization of instability.     

Asymptotic analysis of nonlinear nonaxisymmetric waves on the surface of a neutral dielectric jet in a longitudinal electrostatic field

The problem of calculation of finite-amplitude waves on the cylindrical surface of an ideal incompressible dielectric liquid jet in a uniform electrostatic field collinear to the unperturbed jet axis is solved using a second-order asymptotic analytic procedure in ratio of the wave amplitude to the jet radius. Nonlinear corrections to the jet profile, velocity field potential, and electrostatic potentials inside and outside the jet are of resonant nature. The degenerate resonant interaction between the wave determining the initial strain and the waves excited due to nonlinearity of the hydrodynamic equations can take place for waves with different symmetries (different azimuth numbers).     

Exact and Asymptotic Solutions for the Field of a Point Source in a Transversely Isotropic Medium

Exact and asymptotic solutions are obtained for the acoustic field generated by an isotropic pulsed point source in an infinite transversely isotropic elastic medium. The exact solution for the displacement field is obtained in the form of a double integral over the horizontal slowness and the frequency by using the method of integral transforms. The calculation of the integral over the horizontal slowness by the method of stationary phase reduces the exact solution to an asymptotic solution that is convenient for numerical calculations. Formulas are given for calculating the spreading factors and the wave fronts of quasi-longitudinal qP-waves and quasi-transverse qSV-waves. With the formulas obtained, the displacement field of a point source is investigated for a particular transversely isotropic medium.     

Numerical analysis of the Eckhaus instability in travelling-wave convection in binary mixtures

The Eckhaus stability boundaries of travelling periodic roll patterns arising in binary fluid convection is analysed using high-resolution numerical methods. We present results corresponding to three different values of the separation ratio used in experiments. Our results show that the subcritical branches of travelling waves bifurcating at the onset of convection suffer sideband instabilities that are restabilised further away in the branch. If this restabilisation is produced after the turning point of the travelling-wave branch, these waves do not become stable in a saddle node bifurcation as would have been the case in a smaller domain. In the regions of instability of the uniform travelling waves we expect to find either transitions between states of different wave number or modulated travelling waves arising in these bifurcations.     

Point mobility of a cylindrical plate incorporating a tapered hole of power-law profile

The paper describes the results of experimental measurements of point mobility carried out on circular plates containing tapered holes of quadratic power-law profile with attached damping layers. The obtained results are compared to the developed numerical model, as a means of validation. The profiles of the tapered hole in the plates are designed to replicate near zero reflection of quasi-plane waves from a tapered hole in geometrical acoustics approximation, also known as acoustic black hole effect. The driving point mobility measurements are provided, showing a comparison of the results for a constant thickness circular plate, a constant thickness plate with a layer of damping film applied and a plate with a quadratic power-law profile machined into the center, which is tested with a thin layer of elastic damping material attached. The results indicate a substantial suppression of resonant peaks, agreeing with a numerical model, which is based on the analytical solution available for the vibration of a plate with a central quadratic power-law profile. The paper contains results for the case of free boundary conditions on all edges of the plates, with emphasis placed on the predictions of resonant frequencies and the amplitudes of vibration and loss factor.     

Modeling the quasicompressional wave field of a rectangular transducer in a transversely isotropic solid

A fast model for simulating the transient quasicompressional wave field of a rectangular ultrasonic transducer directly coupled to a transversely isotropic elastic half-space of general orientation is developed. The so-called two-tier asymptotic approach and the uniform stationary phase method are used to derive the high-frequency asymptotics of time-harmonic displacements. Then, transient fields are modeled by means of harmonic synthesis. In geometrical regions, the formulas involve elementary and inside boundary layers, well-known special functions (Fresnel integral and generalized Fresnel integral), and are applicable in the radiating near field. The asymptotics elucidate the physics in terms of various arrivals and give explicit dependence of the radiated waves upon model parameters. The asymptotic code is tested against a direct numerical solution. It is at least a thousand times faster but describes accurately both arrival times and amplitudes of various pulses radiated by the transducer.     

Analytical solution based on the wavenumber integration method for the acoustic field in a Pekeris waveguide

An exact solution based on the wavenumber integration method is proposed and implemented in a numerical model for the acoustic field in a Pekeris waveguide excited by either a point source in cylindrical geometry or a line source in plane geometry. Besides, an unconditionally stable numerical solution is also presented, which entirely resolves the stability problem in previous methods. Generally the branch line integral contributes to the total field only at short ranges, and hence is usually ignored in traditional normal mode models. However, for the special case where a mode lies near the branch cut, the branch line integral can contribute to the total field significantly at all ranges. The wavenumber integration method is well-suited for such problems. Numerical results are also provided, which show that the present model can serve as a benchmark for sound propagation in a Pekeris waveguide.