Excitation of wake-field waves in plasma by a microtron beam

The experimental study of excitation of wake-field waves in plasma by a sequence of electron bunches of a microtron beam has been carried out. Results of measurement of the spectrum of electrons after their passage through plasma confirm the effect of adding of waves from a sequence of about 100 bunches which leads to the increase in the amplitude from 1 V/cm up to 100 V/cm.     

Transient stationary waves and angular momentum

We report new transient stationary spherical waves generated by the time evolution of wave functions with angular momentum. In the study the 3D problem of the sudden release of a particle which initially was inside a spherical trap, the exact solution for the particle's time evolution is described by expected traveling incoming and outgoing spherical waves. However, unexpected transient stationary spherical waves are also present. The traveling waves have amplitudes describing diffraction in time, in a way similar to the optical diffraction by a single slit. In striking contrast with the similar 1D problem, the angular momentum generates unexpected transient stationary spherical waves which have their main contribution at points inside the sphere but only for very short times.     

Solitons in relativistic laser-plasma interactions

Single or/and multipeak solitons in plasma under relativistic electromagnetic field are reviewed. The incident electromagnetic field is allowed to have a zero or/and nonzero initial constant amplitude. Some interesting numerical results are obtained that include a high-number multipeak laser pulse and single or/and low-number multipeak plasma wake structures. It is also shown that there exists a combination of soliton and oscillation waves for plasma wake field. Also, the electron density exhibits multi-caviton structure or the combination of caviton and oscillation. A complete eigenvalue spectrum of parameters is given wherein some higher peak numbers of multipeak electromagnetic solitons in the plasma are included. Moreover, some interesting scaling laws are presented for field energy via numerical approaches. Some implications of results are discussed.      

On the origin of solar wind. Alfvén waves induced jump of coronal temperature

Absorption of Alfvén waves is considered to be the main mechanism of heating in the solar corona. It is concluded that the sharp increase of the plasma temperature by two orders of magnitude is related to a self-induced opacity with respect to Alfvén waves. The maximal frequency for propagation of Alfvén waves is determined by the strongly temperature dependent kinematic viscosity. In such a way the temperature jump is due to absorption of high frequency Alfvén waves in a narrow layer above the solar surface. It is calculated the power per unit area dissipated in this layer due to damping of Alfvén waves that blows up the plasma and gives birth to the solar wind. A model short wave-length (WKB) evaluation takes into account the 1/f² frequency dependence of the transversal magnetic field and velocity spectral densities. Such spectral densities agree with old magnetometric data taken by Voyager 1 and recent theoretical calculations in the framework of Langevin-Burgers MHD. The presented theory predicts existence of intensive high frequency MHD Alfvén waves in the cold layer beneath the corona. It is briefly discussed how this statement can be checked experimentally. It is demonstrated that the magnitude of the Alfvén waves generating random noise and the solar wind velocity can be expressed only in terms of satellite experimental data. It is advocated that investigation of properties of the solar surface as a random driver by optical methods is an important task for future solar physics.     

Nonlinear instability of charged liquid jets: Effect of interfacial charge relaxation

A linear and nonlinear study has been made of cylindrical interface, carrying a uniform surface charge in the presence of a finite rate of charge relaxation, is investigated by using multiple scales method. The linear stability flow is analyzed by deriving a dispersion relation for the growth waves, and solving it analytically and numerically to find marginal stability curves. We investigate the electric charge relaxation effects on the stability of the flow by considering various limiting cases. We also examine the effects of finite charge relaxation times in axisymmetric and nonaxisymmetric modes. In the nonlinear approach, it is shown that the evolution of the amplitude is governed by a Ginzburg–Landau equation. There is also obtained a nonlinear modified Schrödinger equation describing the evolution of wave packets for small charge relaxation time. Further, the classic Schrödinger equation is obtained when the influence of relaxation time charge is neglected. On the other hand, the complex amplitude of quasi-monochromatic standing waves near the cutoff wavenumber is governed by a similarly type of nonlinear Schrödinger equation in which the roles of time and space are interchanged. This equation makes it possible to estimate the nonlinear effect on the cutoff wavenumber. The nonlinear theory, when used to investigate the stability of charged liquid jet, appears accurately to predict a new unstable regions. The effects of the surface charge and charge relaxation on the stability are identified. The various stability criteria are discussed both analytically and numerically and the stability diagrams are obtained.     

Traveling wave solutions of a reaction-diffusion model for bacterial growth

In this paper, we consider a reaction-diffusion model for the bacterial growth. Mathematical analysis on the traveling wave solutions of the model is performed. This includes traveling wave analysis and numerical simulations of wave front propagation for a special case. Specifically, we show that such solutions exist only for wave speeds greater than some minimum speed giving wave with a sharp front. The minimum speed is estimated and the wave profile is calculated and compared with different numerical methods.     

Dynamic instabilities in scalar neural field equations with space-dependent delays

In this paper we consider a class of scalar integral equations with a form of space-dependent delay. These nonlocal models arise naturally when modelling neural tissue with active axons and passive dendrites. Such systems are known to support a dynamic (oscillatory) Turing instability of the homogeneous steady state. In this paper we develop a weakly nonlinear analysis of the travelling and standing waves that form beyond the point of instability. The appropriate amplitude equations are found to be the coupled mean-field Ginzburg-Landau equations describing a Turing-Hopf bifurcation with modulation group velocity of O(1). Importantly we are able to obtain the coefficients of terms in the amplitude equations in terms of integral transforms of the spatio-temporal kernels defining the neural field equation of interest. Indeed our results cover not only models with axonal or dendritic delays but also those which are described by a more general distribution of delayed spatio-temporal interactions. We illustrate the predictive power of this form of analysis with comparison against direct numerical simulations, paying particular attention to the competition between standing and travelling waves and the onset of Benjamin-Feir instabilities.     

Time-frequency analysis of transient dispersive waves: A comparative study

The goal in this work is to investigate the effectiveness of time-frequency representations for analysing dispersive waves by comparing the performance of three different methods. In particular, the smoothed pseudo-Wigner distribution, the continuous wavelet transform and the Hilbert-Huang transform are compared and evaluated in terms of their ability to analyse dispersive elastic waves. The waves under consideration are transient flexural ones generated by an impact in a beam. In view of the results of the comparative study, the advantages and shortcomings of each method are presented and discussed.     

Searching for gravitational waves with the LIGO and Virgo interferometers

The first generation of ground-based interferometric gravitational wave detectors, LIGO, GEO, and Virgo, have operated and taken data at their design sensitivities over the last few years. The data has been examined for the presence of gravitational wave signals. Presented here is a comprehensive review of the most significant results. The network of detectors is currently being upgraded and extended, providing a large likelihood for observations. These future prospects will also be discussed.     

Internal waves in a two‐layer system using fully nonlinear internal‐wave equations

In order to understand the nonlinear effect in a two‐layer system, fully nonlinear strongly dispersive internal‐wave equations, based on a variational principle, were proposed in this study. A simple iteration method was used to solve the internal‐wave equations in order to solve the equations stably. The applicability of the proposed numerical computation scheme was confirmed to agree with linear dispersion relation theoretically obtained from variational principle. The proposed computational scheme was also shown to reproduce internal waves including higher‐order nonlinear effect from the analysis of internal solitary waves in a two‐layer system. Furthermore, for the second‐order numerical analysis, the balance of nonlinearity and dispersion was found to be similar to the balance assumed in the KdV theory and the Boussinesq‐type equations. Copyright © 2009 John Wiley & Sons, Ltd.