Solutions of the Maxwell equations and photon wave functions

Properties of six-component electromagnetic field solutions of a matrix form of the Maxwell equations, analogous to the four-component solutions of the Dirac equation, are described. It is shown that the six-component equation, including sources, is invariant under Lorentz transformations. Complete sets of eigenfunctions of the Hamiltonian for the electromagnetic fields, which may be interpreted as photon wave functions, are given both for plane waves and for angular-momentum eigenstates. Rotationally invariant projection operators are used to identify transverse or longitudinal electric and magnetic fields. For plane waves, the velocity transformed transverse wave functions are also transverse, and the velocity transformed longitudinal wave functions include both longitudinal and transverse components. A suitable sum over these eigenfunctions provides a Green function for the matrix Maxwell equation, which can be expressed in the same covariant form as the Green function for the Dirac equation. Radiation from a dipole source and from a Dirac atomic transition current are calculated to illustrate applications of the Maxwell Green function.     

Rotation effect on near-wall turbulence statistics and flow structures

Turbulent flow in an axially rotating pipe, involving complicated physical mecha- nism of turbulence, is a typical problem for the study of rotating turbulent flow. The pipe rotation induces two effects on the flow. One is the stabilizing effect due to the centrifu- gal and Coriolis forces, which accounts for the relaminarization of the turbulence[1—3] and the reduction of the friction coefficient at the pipe wall. The behavior is also related to the wall streaks inclining to the azimuthal di…     

Classical probability waves

Probability waves in the configuration space are associated with coherent solutions of the classical Liouville or Fokker-Planck equations. Distributions localized in the momentum space provide action waves, described by the probability density and the generating function of the Hamilton-Jacobi theory. It is shown that by introducing a minimum distance in the coordinate space, the action distributions aquire the phase-space dispersion specific to the quantum objects. At finite temperature, probability density waves propagating with the sound velocity can arise as nonstationary solutions of the classical Fokker-Planck equation. The results suggest that in a system of quantum Brownian particles, a transition from complex to real probability waves could be observed.     

用求解概率密度函数输运方程的方法模拟湍流自由射流

用求解概率密度函数输运方程的方法模拟湍流自由射流周向阳，郑楚光，马毓义（华中理工大学煤燃烧国家重点实验室武汉４３００７４）关键词概率密度函数；湍流；自由射流１前言和通常的湍流统计矩模型（如ｋ－ε模型或Ｒｅｙｎｏｌｄｓ应力模型等）相比，用求解速度和标量...     

Scattering of sound waves by a turbulent wake

In this investigation, the Doppler shifted power spectrum of the scattering cross-section is obtained for plane acoustic waves scattered by fluid flow fluctuations appropriate to a turbulent wake. The wake considered in this paper is assumed almost homogeneous and isotropic and of low Reynolds number.It is shown that the evaluation of the Doppler scattering cross-section essentially reduces to the calculation of the wave number converted and frequency shifted energy spectrum function of the turbulent flow fluctuations. In prescribing the low Reynolds number turbulence spectrum, inertial forces are assumed negligible. Convective effects of the macro-eddies, which cause a Doppler shift in the scattered waves, are considered using a Lagrangian-type of space-time velocity correlation.After finding the spectrum of turbulent fluctuations, the Doppler shifted power spectrum of the scattering cross-section, which characterizes the scattered waves, is obtained explicitly for the far field approximation.     

Analysis of the stability and density waves for traffic flow

In this paper, the optimal velocity model of traffic is extended to take into account the relative velocity. The stability and density waves for traffic flow are investigated analytically with the perturbation method. The stability criterion is derived by the linear stability analysis. It is shown that the triangular shock wave, soliton wave and kink wave appear respectively in our model for density waves in the three regions: stable, metastable and unstable regions. These correspond to the solutions of the Burgers equation, Korteweg－de Vries equation and modified Korteweg－de Vries equation. The analytical results are confirmed to be in good agreement with those of numerical simulation. All the results indicate that the interaction of a car with relative velocity can affect the stability of the traffic flow and raise critical density.     

Experimental investigation of the travel-time variance of an acoustic wave propagating through the grid-generated turbulence

An experimental technique for the investigation of the behaviour of acoustic wave propagation through a turbulent medium is discussed. The present study utilizes the ultrasonic travel-time technique to diagnose a grid-generated turbulence. Travel-time variance is studied versus mean flow velocity, travel distance and outer turbulence scale. The effect of thermal fluctuations, which result in fluctuations of sound speed, is studied using a heated-grid experiment. Experimental data obtained using ultrasonic technique confirm numerical and theoretical predictions of nonlinear increase of the travel-time variance with propagation distance, which could be connected to the occurrence of caustics. The effect of turbulent intensity on the travel-time variance and appearance of caustics is studied. It is demonstrated experimentally that the higher turbulence intensity leads to the shorter distance, at which the first caustic occurs. The probability density for caustics appearance is analysed against the measured wave amplitude fluctuations. The analysis reveals that the region of high-amplitude fluctuations corresponds to the region where the probability of formation of random caustics differs from zero. Experimental results are in very good agreement with theoretical and numerical predictions.     

Anfachung und Dämpfung magneto-akustischer Wellen in MHD-Kanälen und ihr Einfluß auf die mittlere Stromdichte und die mittlere Hall-Feldstärke

Magneto-acoustic waves generated by fluctuations in the Hall parameter, the electric conductivity and the stream velocity are theoretically investigated in a weakly ionized plasma streaming across a strong external magnetic field and bearing a current flowing perpendicular to both magnetic field and stream velocity. The investigations hold for seeded rare gas plasmas at any degree of seed ionization but are resticted to waves propagating in parallel or antiparallel direction to the current density vector and in parallel or antiparallel direction to the stream velocity vector and to wave lengths which are small in comparsion to the interaction length which occurs as a characteristic wave length. The influence of these waves on the mean current density and the mean Hall field intensity is calculated in case of small amplitudes and low degree of seed ionization up to second order terms. Omitting Ohmic heating the dispersion equation can be solved exactly. A phase shift exists between the fluctuations in gas density and gas velocity. The phase velocity and the amplification rate depend on the wave length. Typical results are represented in a diagram. For both types of waves the phase velocity slightly rises with increasing wave length, while the amplification rate decreases. Waves propagating in opposite direction to the current density vector are amplified, if the electron velocity exceeds a critical value. They reduce the mean current density and the mean Hall field intensity. Waves propagating in opposite direction to the stream velocity vector are also amplified except for very high degrees of seed ionization. The threshold current density is greater than that for the waves of the first type approximately by the Hall parameter as factor. At extremely high degree of seed ionization the phase velocity is directed opposite to the direction occuring at weakly ionized seed. Waves of the second type decrease the mean current density, but increase the mean Hall field intensity.     

Transverse-longitudinal coherence function of a sound field for line-of-sight propagation in a turbulent atmosphere

Using the narrow-angle and Markov approximations, a formula for the transverse-longitudinal coherence function of a sound field propagating in a turbulent atmosphere with temperature and wind velocity fluctuations is derived. This function, which applies to observation points that are arbitrarily located in space, generalizes the transverse coherence function (coherence when the observation points are in a plane perpendicular to the sound propagation path), which has been studied extensively. The new result is expressed in terms of the transverse coherence function and the extinction coefficient of the mean sound field. The transverse-longitudinal coherence function of a plane sound wave is then calculated and studied in detail for the Gaussian and von Kármán spectra of temperature and wind velocity fluctuations. It is shown, for relatively small propagation distances, that the magnitude of the coherence function decreases in the longitudinal direction but remains almost constant in the transverse direction. On the other hand, for moderate and large propagation distances, the magnitude of the coherence decreases faster in the transverse direction than in the longitudinal. For some parameters of the problem, the coherence function has relatively large local maxima and minima as the transverse and longitudinal coordinates are varied. With small modifications, many results obtained in the paper can be applied to studies of electromagnetic wave propagation in a turbulent atmosphere.     

化学反应体系中涨落的时间空间关联(Ⅰ)——涨落、扩散和波

本文着重分析了如何描述化学反应体系中密度涨落的空间关联,对照反应扩散方程,我们在密度涨落分布函数所满足的Master方程中引入了扩散项或压力项,对无限介质,解Master方程,得到了一系列波,第一支波是与反应扩散方程的解一致,描述了平均密度起伏在空间的传播,在气体中就是声波,其它各支波,则描述了局部密度涨落高阶矩的变化在空间的传播(平均密度不改变),其实就是局部机率分布函数畸变后的传播过程,我们称之为涨落波,文中还讨论了如何求解线性初值问题。 关键词：     

Decay instability of ion-acoustic wave train (or soliton) and formation of the shock profile

The stability of a periodic ion-acoustic wave of a finite amplitude propagating in a nonisothermal plasma is investigated. It is demonstrated that such a wave is unstable with respect to the splitting into a large number of satellite waves with effective wave numbers different from the wave number of the initial wave. The phase velocity of the satellite waves differs therefore from that of the initial pulse. Hence, the satellite waves with bigger phase velocity will “overtake” the initial pulse and turbulize the upstream plasma. The scattering of ions and electrons by the fluctuations of electric field of turbulent oscillations will cause the energy dissipation of the initial ion-acoustic wave translational motion and produce a collisionless shock wave.     

Nonlinear propagation of fast and slow magnetosonic waves in collisional plasmas

Low-frequency fast and slow magnetosonic waves propagating in electron ion plasmas with damping effects through ions and neutral atoms collisions are investigated. Linear wave analysis is performed to obtain dispersion relation. The reductive perturbation method is applied and it is shown that fast and slow modes of nonlinear magnetosonic wave are governed by damped Korteweg-de Vries (DKdV) equation in the presence of ion neutral collisions in plasmas. The analytical solution of DKdV soliton is presented under the assumption of weak collisional effects and numerical solutions of DKdV equation are also obtained using two-level finite difference scheme with the help of Runge–Kutta method at different plasma parameters. The damping of nonlinear fast and slow magnetosonic wave structures at different times are discussed in the context of space plasma situations where ions and neutral atoms collisions exist.     

On the quantum motion of a generalized time-dependent forced harmonic oscillator

In this work, we use linear invariants and the dynamical invariant method to obtain exact solutions of the Schrödinger equation for the generalized time-dependent forced harmonic oscillator in terms of solutions of a second order ordinary differential equation that describes the amplitude of the classical unforced damped oscillator. In addition, we construct Gaussian wave packet solutions and calculate the fluctuations in coordinate and momentum as well as the quantum correlations between coordinate and momentum. It is shown that the width of the Gaussian packet, fluctuations and correlations do not depend on the external force. As a particular case, we consider the forced Caldirola-Kanai oscillator.     

Propagation and Damping of Two-Fluid Magnetohydrodynamic Waves in Stratified Solar Atmosphere

An extreme ultra-violet(EUV) wave is characterized as a bright pulse that has emanated from the solar eruption source and can propagate globally in the solar corona. According to one leading theory, the EUV wave is a fast magnetoacoustic wave, as the coronal counterpart of the Moreton wave in the chromosphere. However, previous observations have shown that the EUV wave differs significantly from the Moreton wave in both velocity and lifetime. To reconcile these differences, here we analyze the wave characteristics of a two-fluid MHD model in the stratified solar atmosphere with a height-dependent ionization rate. It is found that the collision between neutral and ionized fluids is able to attenuate the wave amplitude, while causing a slight change in its propagation velocity. Because the chromosphere has the lower ionization rate and the stronger magnetic fields than the corona,the velocity of the Moreton wave is much higher than that of the EUV wave. In contrast to the Moreton waves damped strongly by the collision between neutral and ionized fluids, the EUV wave in the fully ionized corona is able to propagate globally on a time scale of several hours. Our results support the previous theory that fast magnetoacoustic waves account for both EUV and Moreteon waves in the different layers of the solar atmosphere.     

Acoustic scattering by turbulent fluctuations of pressure and entropy

Detailed analysis is presented of the well-known Tatarskii’s formula, which describes sound wave scattering in a turbulent atmosphere. The adiabaticity of the acoustic fluctuations and incompressibility of the turbulent fluctuations are assumed only. This yields to additional 1 terms in the classical formula (probably, small in the inertial range of turbulence). We show the change of Obukhov’s formula, which describes the connection between turbulent fluctuations of pressure and velocities in a compressible atmosphere, and also demonstrate the effect of the independence of fluctuations of the potential and thermodynamic temperatures. By analogy with the formula for small-scale isotropic temperature fluctuations, which was also obtained by Obukhov, we derive a formula for the fluctuations of entropy and potential density as function of entropy, which describes spatial distribution of the probability density of identical “fluid particles” in the turbulent media.     

Landau damping of longitudinal oscillation in ultra- relativistic plasmas with nonextensive distribution

The generalized dispersion equation for longitudinal oscillation in an unmagnetized, collisionless, isotropic and relativistic plasma is derived in the context of nonextensive q-distribution. An analytical expression for the Landau damping is obtained in an ultra-relativistic regime, which is related to q-parameter. In the limit q → 1, the result based on the relativistic Maxwellian distribution is recovered. It is shown that the interactions between the wave and particles are stronger and the waves are more strongly damped for lower values of q-parameter. The results are explained by the increased number of superthermal particles or low velocity particles contained in the plasma with the nonextensive distribution.     

Experimental study of nonlinear dust acoustic solitary waves in a dusty plasma

The excitation and propagation of finite-amplitude low-frequency solitary waves are investigated in an argon plasma impregnated with kaolin dust particles. A nonlinear longitudinal dust acoustic solitary wave is excited by pulse modulating the discharge voltage with a negative potential. It is found that the velocity of the solitary wave increases and the width decreases with the increase of the modulating voltage, but the product of the solitary wave amplitude and the square of the width remains nearly constant. The experimental findings are compared with analytic soliton solutions of a model Korteveg-de Vries equation.     

湍流两相流动有燃烧颗粒相概率密度函数输运方程理论

由有燃烧的湍流气粒两相流动的瞬态方程和统计力学概率密度函数概念出发,推导了有燃烧颗粒相的质量－动量－能量联合概率密度函数（ＰＤＦ）输运方程,并对方程中条件期望项用梯度模拟概念进行了模拟封闭。封闭后的ＰＤＦ方程可作为建立颗粒拟流体模型方程和封闭二阶矩模型的基础,也可以通过Ｍｏｎｔｅ－Ｃａｒｌｏ 法求解用以直接计算颗粒雷诺应力和湍流动能,以便和二阶 矩模型的结果相对照,改善二阶矩模型。     

Phase Fluctuations of Radio Waves in the Saturated-Scintillation Regime

We consider the problem of phase fluctuations of radio waves behind a strong phase screen and in an optically thick layer. It is shown that the phase-fluctuation distribution of the received radiation at an observation point located in the saturated-scintillation area behind a turbulent phase screen is almost identical to the normal distribution of phase fluctuations of the wave on the screen. Amplitude and phase fluctuations of the received radiation are uncorrelated both for single-point and space-diversity reception if, in the latter case, the distance between the observation points exceeds the spatial scale of the diffraction component of the complex field of the received signal. Expressions for the mean square and the structural function of phase fluctuations of radio waves behind a turbulent phase screen in the saturated-scintillation regime are obtained. It is shown that the structural function of phase fluctuations in the diffraction component of the scattered field, which is exactly the function that forms saturated scintillations of the received radiation, almost coincides with the structural function of phase fluctuations on the screen. It is also shown that the diffraction effects can be neglected and the geometric-optical approximation should be used when calculating statistical characteristics of phase fluctuations of a plane wave in the saturated-scintillation area in an optically thick layer with large-scale refractive-index irregularities. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 4, pp. 275–282, April 2005