Overturning of nonlinear Alfvén waves in a collisionless plasma

An analysis is made of the overturning of nonlinear Alfvén waves in a collisionless plasma. It is shown that overturning is followed by the appearance of a region which broadens with time and consists of two collisionless shock waves which can be joined at the point s²=1. If only one Riemann invariant changes in the region of the collisionless shock waves, the waves are simple. The structures of the collisionless shock waves are constructed for different initial conditions of the nonlinear wave. The Whitham averaging method is used for this purpose. Conditions are obtained which are similar to the Rankine-Hugoniot adiabats for passage through the collisionless shock waves. The effect of overturning one of the collisionless shock waves, involving the zeroing of the density at the soliton peak on its trailing edge, is treated as a bifurcation for which a discontinuity occurs in an analog of the hydrodynamic velocity and phase of the nonlinear Alfvén wave. The width of one of the collisionless shock waves decreases with an increase in the parametera which determines the magnitude of the field discontinuity when overturning occurs.L. N. Tolstoi State University, Checheno-Ingushk. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 62–67, January, 1993.     

运动目标辐射声场干涉结构映射域特征研究

浅海低频声场呈稳定而显著的干涉特征,并蕴含声源状态和波导特性等信息.本文研究运动目标辐射声场干涉结构的简化映射以及映射域能量分布对目标运动状态的指示特征.理论分析了声压场和矢量声场空(时)频干涉谱图的二维傅里叶变换映射特征,推导了匀速运动目标时频干涉谱图映射域能量脊斜率与波导不变量以及距变率、航向角的关系式,证明了映射域脊斜率符号、脊斜率绝对值变化等对目标来袭或远离以及目标威胁程度的指示,并进行了数值仿真和海上试验研究.实测结果与理论、仿真分析有较好的一致性.研究结果表明:二维傅里叶变换可将声压场和矢量场时(空)频谱图干涉结构简化,匀速运动目标辐射声场干涉结构映射域的能谱脊斜率、距变率、航向角与波导不变量有解析关系式,声强谱、动能密度谱、声强流谱等声场干涉结构经映射后更为一致,映射域脊能简明的指示目标运动状态和威胁程度.     

The Asymptotic Behaviors of Solutions to the Perturbed Riemann Problem near the Singular Curve for the Chromatography System

The Riemann problem for a simplified chromatography system is considered and the global Riemann solutions are constructed in all kinds of situations. In particular, the zero rarefaction wave, the zero shock wave and the zero delta shock wave are discovered in the Riemann solutions in some limit situations, which have infinite propagation speeds. Furthermore, these zero waves are analyzed by introducing the so-called double Riemann problem with three pieces of constant states. More precisely, we take the approximations of zero waves and investigate wave interactions in details before the limits are taken.     

An evaluation of the FCT method for high-speed flows on structured overlapping grids

This study considers the development and assessment of a flux-corrected transport (FCT) algorithm for simulating high-speed flows on structured overlapping grids. This class of algorithm shows promise for solving some difficult highly-nonlinear problems where robustness and control of certain features, such as maintaining positive densities, is important. Complex, possibly moving, geometry is treated through the use of structured overlapping grids. Adaptive mesh refinement (AMR) is employed to ensure sharp resolution of discontinuities in an efficient manner. Improvements to the FCT algorithm are proposed for the treatment of strong rarefaction waves as well as rarefaction waves containing a sonic point. Simulation results are obtained for a set of test problems and the convergence characteristics are demonstrated and compared to a high-resolution Godunov method. The problems considered are an isolated shock, an isolated contact, a modified Sod shock tube problem, a two-shock Riemann problem, the Shu–Osher test problem, shock impingement on single cylinder, and irregular Mach reflection of a strong shock striking an inclined plane.     

Investigating shock-wave transient processes in explosives by means of synchrotron radiation

The results from studying the transient processes induced by a shock in porous TATB, obtained using an original and tested method based on employing the soft X-ray component of synchrotron radiation, are presented. The method enables us to determine the parameters of a shock-wave striker, the distribution of velocity and density behind the front of the shock and detonation wave, and the characteristics of flow after a shock wave is reflected from a rigid wall, all in one experiment. Trials with charges 1.8 and 1.9 g/cm³ in density show that modes such as the absence of detonation and initiation in direct and reflected shock waves, are possible depending on the loading conditions.     

光盘光学系统的矢量衍射理论分析

本文以完整的矢量衍射理论分析了光盘光学系统。首先将入射的聚焦光束分解为平面波谱 ,得到每个平面波的振幅矢量 ;然后计算光盘对每个平面波的衍射 ,得到衍射波的振幅矢量 ,从而得到了整个衍射波场的空间频谱 ;最后计算物镜光瞳上的能通量 ,得到光盘系统的读出信号。在衍射计算中 ,光盘被定义为二维金属光栅 ,根据信息符的不同模型 ,选用坐标变换方法、耦合波方法或模态方法。对于典型的 DVD光学系统来说 ,矢量理论的结论与标量理论相差甚远 ,要得到正确的结果就必须采用矢量衍射理论     

Magnetoacoustic waves in magnetizable liquids

Within the framework of the Neuringer-Rosenzweig equations, the solutions describing transverse linearly polarized and longitudinal plane-polarized magnetoacoustic waves are obtained for magnetizable liquids with an arbitrary orientation of the wavevector and the magnetization vector. In the general case, the group velocity vector of magnetoacoustic waves has a component orthogonal to the wavevector. For the solutions obtained here, the velocity of sound decreases from the maximal value for a wave propagating along the magnetization vector to the minimal value corresponding to a wave propagating at right angles to the magnetization vector. Exact solutions of the equations for magnetizable liquids are obtained in the form of the Riemann waves which are transformed into the magnetoacoustic waves under investigation for small perturbations of the parameters of the liquid and magnetic field.     

Behavior of viscous solutions in Lagrangian formulation

In this paper, the behavior of shock-capturing methods in Lagrangian coordinate is investigated. The relation between viscous shock and inviscid one is analyzed quantitatively, and the procedure of a viscous shock formation and propagation with a jump type initial data is described. In general, a viscous shock profile and a discontinuous one include different energy and momentum, and these discrepancies result in the generation of waves in all families when a single wave Riemann problem (shock or rarefaction) is solved. Employing this method, some anomalous behavior, such as, viscous shock interaction, shock passing through ununiform grids, postshock oscillations and lower density phenomenon is explained well. Using some classical schemes to solve the inviscid flow in Lagrangian coordinate may be not adequate enough to correctly describe flow motion in the discretized space. Partial discrepancies between von Neumann artificial viscosity method and Godunov method are exhibited. Some reviews are given to those methods which can ameliorate even eliminate entropy errors. A hybrid scheme based on the understanding to the behavior of viscous solution is proposed to suppress the overheating error.     

激光超声方法研究固-固界面波传播特性

对界面波的传播特性进行了理论及实验研究.首先探讨了界面波的求根问题，基于黎曼面分析，给出了求解界面波特征方程所有根的一般方法.理论上对三种常见的界面波——Stoneley波，Leaky Rayleigh及Leaky Interface波传播机理进行了分析，描述了三种界面波的波矢及位移势在两种介质中的状态.最后基于光弹效应原理, 利用全光学的激光超声手段对界面波进行了实验测量，实测结果与理论符合很好.     

含运动物体流场计算的自适应非结构二维网格生成方法

采用自动插点的Delaunay方法和局部网格重新生成方法,对含运动边界自适应非结构二维网格生成方法进行了系统研究,实现了带有非定常运动物体流场的数值计算,并进行了数值实验.     

基于黎曼解的粒子间接触算法在SPH中的应用

 采用光滑粒子流体动力学（SPH）方法模拟大变形问题具有明显的优点,但传统的SPH方法在模拟冲击波与接触界面的作用时,往往会出现压力的反常跳动。采用黎曼解描述粒子间相互作用的接触算法对传统SPH方法进行修正,计算了激波管和飞片碰撞（包含接触界面）问题中波的传播,并将计算结果与解析解作比较。结果表明,与传统的光滑粒子法相比,该改进的光滑粒子法无需引入人工粘性项和人工热流项,程序结构简洁,且能较好地处理接触界面问题,从而能有效提高计算精度。     

凝聚炸药爆轰波在高声速材料界面上的折射现象分析

凝聚炸药爆轰在边界高声速材料约束下传播时,爆轰波会在约束材料界面上产生复杂的折射现象.本文针对凝聚炸药爆轰波在高声速材料界面上的折射现象展开理论和数值模拟分析.首先通过建立在爆轰ZND模型上的改进爆轰波极曲线理论给出爆轰波折射类型,然后发展一种求解爆轰反应流动方程的基于特征理论的二阶单元中心型Lagrange计算方法来数值模拟典型的爆轰波折射过程.从改进爆轰波极曲线理论和二阶Lagrange方法数值模拟给出的结果看出,凝聚炸药爆轰波在高声速材料界面上的折射类型有四种:反射冲击波的正规折射、带束缚前驱波的非正规折射、带双Mach反射的非正规折射、带λ波结构的非正规折射.     

Scaling Limits of Waves in Convex Scalar Conservation Laws Under Random Initial Perturbations

We study waves in convex scalar conservation laws under noisy initial perturbations. It is known that the building blocks of these waves are shock and rarefaction waves, both are invariant under hyperbolic scaling. Noisy perturbations can generate complicated wave patterns, such as diffusion process of shock locations. However we show that under the hyperbolic scaling, the solutions converge in the sense of distribution to the unperturbed waves. In particular, randomly perturbed shock waves move at the unperturbed velocity in the scaling limit. Analysis makes use of the Hopf formula of the related Hamilton-Jacobi equation and regularity estimates of noisy processes. AMS subject classifications: 35L60, 35B40, 60H15     

On high-order shock-fitting and front-tracking schemes for numerical simulation of shock–disturbance interactions

High-order methods that can resolve interactions of flow-disturbances with shock waves are critical for reliable numerical simulation of shock wave and turbulence interaction. Such problems are not well understood due to the limitations of numerical methods. Most of the popular shock-capturing methods are only first-order accurate at the shock and may incur spurious numerical oscillations near the shock. Shock-fitting algorithms have been proposed as an alternative which can achieve uniform high-order accuracy and can avoid possible spurious oscillations incurred in shock-capturing methods by treating shocks as sharp interfaces. We explore two ways for shock-fitting: conventional moving grid set-up and a new fixed grid set-up with front tracking. In the conventional shock-fitting method, a moving grid is fitted to the shock whereas in the newly developed fixed grid set-up the shock front is tracked using Lagrangian points and is free to move across the underlying fixed grid. Different implementations of shock-fitting methods have been published in the literature. However, uniform high-order accuracy of various shock-fitting methods has not been systematically established. In this paper, we carry out a rigorous grid-convergence analysis on different variations of shock-fitting methods with both moving and fixed grids. These shock-fitting methods consist of different combinations of numerical methods for computing flow away from the shock and those for computing the shock movement. Specifically, we consider fifth-order upwind finite-difference scheme and shock-capturing WENO schemes with conventional shock-fitting and show that a fifth-order convergence is indeed achieved for a canonical one-dimensional shock-entropy wave interaction problem. We also show that the method of finding shock velocity from one characteristic relation and Rankine–Hugoniot jump condition performs better than the other methods of computing shock velocities. A high-order front-tracking implementation of shock-fitting is also presented in this paper and nominal rate of convergence is shown. The front-tracking results are validated by comparing to results from the conventional shock-fitting method and a linear-interaction analysis for a two-dimensional shock disturbance interaction problem.     

Propagation of p-polarized electromagnetic waves obliquely incident on stratified random media: Random phase approximation

We consider the propagation of p-polarized electromagnetic waves obliquely incident on stratified random dielectric media. Using the invariant imbedding method generalized to random media and applying the random phase approximation, we derive a simple analytical expression of the localization length and calculate the disorder-averaged reflectance and transmittance and the fluctuations of the localization length and the reflectance as functions of the incident angle. We also calculate the disorder-averaged intensity profile of the magnetic field inside the random medium. We find that within the random phase approximation, the p wave can be delocalized and transmitted completely at a certain critical incident angle, which is bigger than the Brewster angle in the uniform case.     

Spin reorientation and magnon-phonon hybridization in a ferromagnet

A model is presented for the magnetic excitations and magnon-phonon coupling in a localised moment ferromagnet in which spins can reorientate by application of a magnetic field. The model is suitable for those materials which possess a spin wave gap at zero wave vector and therefore the magnon and acoustic phonon branches can intersect. A magnon-phonon coupling linear in both spin and phonon operators is employed which has proved successful for the ferrous salts. The main effect of the applied field is to modify the spin wave gap, and to introduce a critical value for the coupling constant which enables the system to remain stable as the gap goes to zero. Furthermore the wave vector of the anticrossing point decreases as the spin wave gap increases and therefore the value of the sound velocity determined by high resolution inelastic neutron experiments is dependent on the gap.     

Direct analysis of dispersive wave fields from near-field pressure measurements

Flexural waves play a significant role for the radiation of sound from plates. The analysis of flexural wave fields enables the detection of sources and transmission paths in plate-like structures. The measurement of these wave fields can be carried out indirectly by means of near-field acoustic holography, which determines the vibrational wave field from pressure information measured in a plane close to the plate under investigation. The reconstruction of the plate vibration is usually obtained by inverting the forward radiation problem, i.e., by inversion of an integral operator. In this article, it is shown that a pressure measurement taken in the extreme near-field of a vibrating plate can directly be used for the approximate analysis of the dispersive flexural wave field. The inversion step of near-field acoustic holography is not necessarily required if such an approximate solution is sufficient. The proposed method enables fast and simple analysis of dispersion characteristics. Application of dispersion compensation to the measured field allows for visualizations of propagating wavefronts, such that sources and scatterers in the plate can be detected. The capabilities of the described approach are demonstrated on several measurements.     

Excitation of spin remagnetization waves in systems with spin-orbit coupling

Elementary excitations of a new type in paramagnetic materials with spin-orbit interaction are predicted theoretically within the Rashba model and named the spin remagnetization waves. These normal modes arise from rotation of the spin magnetic moment in a medium where the electric field contains a constant component and a traveling wave component. A method is proposed for exciting these vibrations by illuminating the sample with an oscillating interference pattern. The spin remagnetization waves can be experimentally detected by measuring the dependence of the current through the sample on the oscillation frequency and wave vector of the interference pattern.     

Shock tube exit flow fields through thin membranes

The flow field characteristics that form for a shock wave propagating through a membrane-like termination at the exit of a shock tube are studied. The strength of the shock wave reflected back into the tube, as well as the strength of the shock wave transmitted, is examined. Six different materials are used, ranging from copper and aluminium foils to a variety of elastic and plastic sheets, in a few cases with different initial pressure differentials. High-speed shearing interferometry imaging is done of the external flow. Three principal characteristics are present in the transmitted flow: a diffracted shock wave, an expansion wave and a re-compression shock wave. It is found that the prominence of these features varies depending on the material type. For the later flow development and material rupture, there are a number of principal characteristics: small vortices, secondary shock waves, a vortex ring, oblique waves and a Mach disc.     

Application of the wavenumber jump condition to the normal and oblique interaction of a plane acoustic wave and a plane shock

A kinematic approach is considered whereby the wavenumber jump conditions in conjunction with the appropriate dispersion relations is applied to the investigation of the normal and oblique interaction of a plane acoustic wave with a plane shock wave. For the normal interaction of an acoustic wave with a stationary plane shock a logarithmic shift in the wave spectra is obtained. For the normal interaction with a moving shock front it is shown that for shock Mach numbers above a critical value, the frequency of the transmitted wave becomes negative. This results in the fact that the crests of the transmitted signal arrive at a fixed observer in a reverse order to their generation. Finally, the oblique interaction of an acoustic wave with a stationary shock is considered. The “Snell's Law” for the transmitted wave is derived and two special angles of incidence are identified. The first is a no-refraction angle: i.e., the transmitted wave angle is the same as the incident wave angle. The second is a critical angle such that for incident angles greater than this critical angle there is no transmitted wave. A necessary and sufficient condition for the existence of a transmitted wave is derived in terms of the speed of sound and Mach number of the fluid and the frequency and tangential wavenumber component of the incident wave.The dynamics aspects of the interaction concerning the determination of the frequency independent transmission coefficients and shock displacements are determined for the simple case of the normal interaction with a moving shock as an illustration.