The influence of cell geometry on the Godunov scheme applied to the linear wave equation

By studying the structure of the discrete kernel of the linear acoustic operator discretized with a Godunov scheme, we clearly explain why the behaviour of the Godunov scheme applied to the linear wave equation deeply depends on the space dimension and, especially, on the type of mesh. This approach allows us to explain why, in the periodic case, the Godunov scheme applied to the resolution of the compressible Euler or Navier–Stokes system is accurate at low Mach number when the mesh is triangular or tetrahedral and is not accurate when the mesh is a 2D (or 3D) cartesian mesh. This approach confirms also the fact that a Godunov scheme remains accurate when it is modified by simply centering the discretization of the pressure gradient.     

The combined quasineutral and low Mach number limit of Euler–Poisson equations coupled to a magnetic field

In this paper, we consider the combined quasineutral and low Mach number limit of compressible Euler–Poisson system coupled to a magnetic field. We prove that, as the Debye length and the Mach number tend to zero simultaneously in some way, the solution of compressible Euler–Poisson system coupled to a magnetic field will converge to that of ideal incompressible magnetohydrodynamic equations with a sharp convergence rate.     

Anelastic Approximation as a Singular Limit of the Compressible Navier–Stokes System

Considering compressible Navier–Stokes system in a slab geometry in the regime when both Mach and Froude numbers vanish at the same rate, we study the behavior of corresponding weak solutions, that are known to exist globally-in-time (for large data). We establish their convergence to a solution of the so-called anelastic approximation when the limit flow is stratified, i.e., the limit density depends effectively on the vertical coordinate.     

Low Mach limit to one-dimensional nonisentropic planar compressible magnetohydrodynamic equations

This paper is concerned with a one-dimensional nonisentropic compressible planar magnetohydrodynamic flow with general initial data, whose behaviors at far fields x→±∞ are different. The low Mach limit for the system is rigorously justified. The limit relies on the uniform estimates including weighted time derivatives and an extended convergence lemma.     

BEC Dynamics in a Double‐Well with Interferometric Feedback

The feedback control scheme for a Bose‐Einstein condensate (BEC) in a double‐well trapping potential located in one arm of Mach‐Zehnder interferometer (MZI) is investigated. The off‐resonant light beam performs the phase probing in one of the wells, thus creating information about the number of atoms in this well. The parameters of the trapping potential are controlled via a feedback loop based on the measured output of the MZI. The problem is analyzed in the framework of master equations for hybrid quantum‐classical systems. Significant modifications of the stationary distribution of atoms over the wells are predicted. These distributions can effectively be controlled by the tunable phase shift in the other arm of the MZI.     

Distributed fiber sensing system with wide frequency response and accurate location

A distributed fiber sensing system merging Mach–Zehnder interferometer and phase-sensitive optical time domain reflectometer (Φ-OTDR) is demonstrated for vibration measurement, which requires wide frequency response and accurate location. Two narrow line-width lasers with delicately different wavelengths are used to constitute the interferometer and reflectometer respectively. A narrow band Fiber Bragg Grating is responsible for separating the two wavelengths. In addition, heterodyne detection is applied to maintain the signal to noise rate of the locating signal. Experiment results show that the novel system has a wide frequency from 1 Hz to 50 MHz, limited by the sample frequency of data acquisition card, and a spatial resolution of 20 m, according to 200 ns pulse width, along 2.5 km fiber link.     

金刚石镀膜装置中的等离子体参数测量

利用平行马赫探针和单探针对金刚石镀膜装置中的等离子体漂移速度、,离子密度及电子温度进行了测量,采用ＣｈｕｎｇＫｙｕ－Ｓｕｎ理论对平行马赫探针数据进行分析得到的马赫数为０．２８,电子温度为５ｅＶ,等离子体流速约为９８０ｍ．ｓ＾－１。单探针测行离子密度在１０＾１８～１０＾２０ｍ＾－３的范围内,电子温度在２－８ｅＶ的范围内。     

A finite element analysis of mach reflection by using the Boussinesq equation

The numerical analysis of ‘Mach reflection’, which is the reflection of an obliquely incident solitary wave by a vertical wall, is presented. For the mathematical model of the analysis, the two-dimensional Boussinesq equation is used. In order to solve the equation in space, the finite element method based on the linear triangular element and the conventional Galerkin method is applied. The combination of explicit and semi-implicit schemes is employed for the time integration. Moreover, one of the treatments for the open boundary condition, in which the analytical solution of the linearized Boussinesq equation in the outside domain is linked to the discrete values of velocity and water elevation in the inside domain, is applied for the modeling of the Mach reflection problem. © 1998 John Wiley & Sons, Ltd.